Chiral Inorganic Nanostructures - Chemical Reviews (ACS Publications)

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Chiral Inorganic Nanostructures Wei Ma,†,‡,∇ Liguang Xu,†,‡,∇ André F. de Moura,§ Xiaoling Wu,†,‡ Hua Kuang,*,†,‡ Chuanlai Xu,†,‡ and Nicholas A. Kotov*,∥,⊥,# †

State Key Lab of Food Science and Technology and ‡International Joint Research Laboratory for Biointerface and Biodetection, Jiangnan University, Wuxi, Jiangsu 214122, P. R. China § Department of Chemistry, Federal University of São Carlos, CP 676, CEP 13.565-905, São Carlos, SP, Brazil ∥ Department of Chemical Engineering, ⊥Department of Biomedical Engineering, and #Biointerface Institute, University of Michigan, Ann Arbor, Michigan 48109, United States ABSTRACT: The field of chiral inorganic nanostructures is rapidly expanding. It started from the observation of strong circular dichroism during the synthesis of individual nanoparticles (NPs) and their assemblies and expanded to sophisticated synthetic protocols involving nanostructures from metals, semiconductors, ceramics, and nanocarbons. Besides the well-established chirality transfer from bioorganic molecules, other methods to impart handedness to nanoscale matter specific to inorganic materials were discovered, including three-dimentional lithography, multiphoton chirality transfer, polarization effects in nanoscale assemblies, and others. Multiple chiral geometries were observed with characteristic scales from ångströms to microns. Uniquely high values of chiral anisotropy factors that spurred the development of the field and differentiate it from chiral structures studied before, are now well understood; they originate from strong resonances of incident electromagnetic waves with plasmonic and excitonic states typical for metals and semiconductors. At the same time, distinct similarities with chiral supramolecular and biological systems also emerged. They can be seen in the synthesis and separation methods, chemical properties of individual NPs, geometries of the nanoparticle assemblies, and interactions with biological membranes. Their analysis can help us understand in greater depth the role of chiral asymmetry in nature inclusive of both earth and space. Consideration of both differences and similarities between chiral inorganic, organic, and biological nanostructures will also accelerate the development of technologies based on chiroplasmonic and chiroexcitonic effects. This review will cover both experiment and theory of chiral nanostructures starting with the origin and multiple components of mirror asymmetry of individual NPs and their assemblies. We shall consider four different types of chirality in nanostructures and related physical, chemical, and biological effects. Synthetic methods for chiral inorganic nanostructures are systematized according to chirality types, materials, and scales. We also assess technological prospects of chiral inorganic materials with current front runners being biosensing, chiral catalysis, and chiral photonics. Prospective venues for future fundamental research are discussed in the conclusion of this review.

CONTENTS 1. Introduction 1.1. Common Grounds 2. Different Venues of Classification of Chiral Nanomaterials 2.1. Synthetic Methods for Chiral Nanomaterials 2.1.1. Chiral Metal Nanoparticles 2.1.2. Chiral Semiconductor Nanoparticles 2.2. Chemical and Physical Origins of Chirality of Nanoscale Inorganic Matter 2.2.1. Chiral Geometries of Nanoparticles 2.2.2. Experiments and Simulations Establishing Structural Origins of Chirality in Individual Nanoparticles 2.3. Relation with Known Chiral Materials 2.3.1. Similarity with Chiral Inorganic and Organic Molecular and Supramolecular Compounds © 2017 American Chemical Society

2.3.2. Similarity with Biological Nano- and Mesoscale Compounds 2.3.3. Hierarchical Chirality 2.4. Optical Activity of Chiral Nanostructures 2.5. Computational Studies of Chiral Nanoparticles 2.5.1. Methodological Aspects 2.5.2. Selected Computer-Modeling Studies 2.6. Chirality and Optical Activity of Individual Nanoparticles 2.6.1. Metal Nanoparticles and Nanorods 2.6.2. Semiconductor Nanoparticles 2.6.3. Magnetic Nanoparticles 2.6.4. Polymeric Nanoparticles 2.7. Chiral Nanowires

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Received: November 17, 2016 Published: April 20, 2017

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Chemical Reviews 2.7.1. Metal Nanowires 2.7.2. Semiconductor Helicoids 2.7.3. Ceramic Nanohelices 2.8. Carbon Nanostructures 2.8.1. Fullerenes 2.8.2. Carbon Nanotubes 2.8.3. Coiled Carbon Nanotubes 3. Chiral Nanoscale Assemblies 3.1. Twisted Nanorod Pairs 3.2. Nanoparticle Dimers 3.3. Pyramidal Assemblies of Nanoparticles 3.4. Nanoparticle Helices 3.5. Scalable Chiral Nanoassemblies: Nanoparticle Chains, Lithographic Oligomers, and Microfabricated Chiral Nanostructures 3.5.1. Nanoparticle Chains 3.5.2. Lithographic Nanoparticle Oligomers 3.5.3. Microfabricated Chiral Nanostructures 4. Potential Applications of Chiral Nanostructures 4.1. Chiral Catalysis 4.2. Enantiospecific Separation 4.3. Sensing 4.3.1. Biomolecular Analytes 4.3.2. Enantiomer Analysis 4.4. Biology and Medicine 4.5. Optical Metamaterials 5. Concluding Remarks and Perspectives 5.1. Homochiral Synthesis of Chiral Inorganic Nanostructures 5.2. Chiroptical Properties 5.3. Reconfigurable Chirality 5.4. Origin of Homochirality 5.5. Applications Associated Content Special Issue Paper Author Information Corresponding Authors ORCID Author Contributions Notes Biographies Acknowledgments References Note Added after ASAP Publication

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Figure 1. Publications for the last 10 years (2005−2016).

Although the likelihood of this review becoming obsolete in a few years considering trend in Figure 1 is high, the ongoing and future studies in the area of chiral inorganic nanostructures will likely benefit from a different, perhaps more comprehensive, assessment of the theoretical, experimental, computational, and translational aspects of this field. The chirality of NPs was empirically observed in many studies by rotatory optical activity, i.e., the ability of a medium to rotate the polarization axis of the incident light, manifesting among other chiroptical effects as circular dichroism (CD) spectra.17,18 Polarization rotation is the principal property of chiral molecular and nanoscale structures. Sometimes we can obtain a three-dimensional (3D) image of the nanostructures by electron microscopy and identify chiral geometrical elements responsible for the chiroptical activity. However, in many cases the geometry of the nanoscale objects and, therefore, the origin of their optical activity are still poorly understood. In large part, this can be associated with numerous possibilities of chiral geometries for NPs. In addition to traditional chiral centers known from organic chemistry based on the tetradedral geometry of sp3 hybridized atoms,19 chirality of nanostructures could be found at atomic, nanoscale, submicron scale (also known as mesoscale), and sometimes at micron scale, when for instance thin nanoscale ribbons have micron-scale length.20 Rotatory optical activity and other properties are the derivative of chirality of nanostructures at several scales. Similarly to organic supramolecular assemblies,21 the level of their understanding suitable for their predictive engineering across the several orders of physical dimensions is, however, lacking and is likely to be a source of upcoming discoveries. Unlike the well-established theory of chirality for simple organic molecules, the notion of chirality for metal, semiconductor, and other inorganic nanostructures is still evolving. When one makes a step from the familiar relations between mirror reflections of tetrasubstituted sp3 carbons, the chirality of inorganic nanostructures may be confusing even for the simplest NPs because there are multiple symmetric and asymmetric relations in the geometry of their atoms. Some of them are specific to inorganic nanomaterials and are not observed or not as pronounced in organic/biological nanoscale materials. The assignment of chiral stereoisomers in nanostructures may utilize some of the notations borrowed from classical chiral chemistry but, by and large, are inadequate to capture

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1. INTRODUCTION The subject of chirality in inorganic nanomaterials represents one of the most dynamic areas of nanoscale materials today and has emerged recently as a new “growth point” of nanoscience.1 The number of publications addressing both experimental and theoretical aspects of chiral nanostructures has rapidly increased in the past several years (Figure 1). Many interesting properties of chiral NPs and their assemblies have been studied,2−4 and some of them demonstrated realistic technological prospects.5−7 It is important to review the current developments in this field with these achieved milestones in mind and discuss future research venues. Subsets of chiral nanostructures have been previously reviewed by several authors with the focus placed on (sub)nanoscale clusters,8,9 synthesis of chiral nanostructures,10,11 helical nanostructures,12 and plasmonic and similar effects in chiral nanoscale metals and semiconductors.13−16 8042

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organization.20 Note that several of them are specific to inorganic materials; there are also ones that are more suitable to inorganic materials than to organic ones. These methods to impart handedness to nanoscale matter can be exemplified by three-dimentional lithography, multiphoton chirality transfer, polarization effects in nanoscale assemblies, and others. Synthesis of chiral nanostructures furthers our understanding of the origin of homochirality on earth, which is often associated with the cosmic circularly polarized light.37 Since inorganic NPs were and are a part of the stellar and earth environments and display high optical and chemical activity, it is conceivable that they played a role in the appearance of enantiomeric excess of amino acids or other early chiral molecules.38 The importance of computational tools in the interpretation of spectroscopic data and identification of the chiral geometries at different scales is difficult to overestimate. They have been greatly improved over the past few years and their survey is integrated in this review with a survey of experimental advances in the field. One can observe the transition from the specialized codes to commercial software packages for academic research with great capabilities, powerful algorithms, and user-friendly interfaces. For instance, simulations of the dynamics of light interacting with the chiral systems became possible. Visualization of the chirality transfer from molecular level to mesoscale during different assembly processes is now also feasible. The power of computational techniques is further enhanced by advanced optical methods, such as single particle spectroscopy.39,40 In fact, we can now precisely match the geometry of some NP assemblies from TEM or STM images, their CD spectra, and computations. At the same time, one can also see the limitations of the current techniques, especially at the atomistic level.41 It is also a right time to assess practical applications of chiral nanostructures in different areas of technology.42−48 Many of them are just beginning to emerge.13,14 Besides negative refractive index materials that served as an impetus to many studies of optical properties of chiroplasmonic nanostructures,49−51 there are several other promising application areas. To name a few, chiral nanomaterials enable new polarization modulation tools52 and polarization-based photonics and optoelectronics.26,53−56 Recent studies32,57,58 indicate that hierarchical chirality enables spectral tuning of polarization rotation in inorganic nanostructures. Chiral inorganic materials also offer a new potent platform for bioanalysis,59,60 featuring ultrasensitive detection of DNA segments of different lengths,6,61 cancer antigens,62 small chiral molecules,63 and most recently micro-ribonucleic acids (miRNA).64 We shall offer our considerations for future research directions.

both similarities and differences of the chiral relations of inorganic and, for instance, biological nanostructures. Therefore, in this review, we assess the current status of research on chiral nanostructures encompassing most if not all types of nanomaterials, paying specific attention to the fundamentals. One of the central topics is the chirality of individual NPs. The types of chirality associated with chirality of surface ligands, the shape of the inorganic core,22 chiral reconstruction of the NP surface,23,24 and tetrahedral geometry of atomic packing in many nanoscale crystals19 will be discussed among others. The intrinsic chirality of NPs due to symmetrybreaking geometry and the mechanical strain in crystal lattices will also be evaluated.20 A better understanding of the structural determinants for chirality will make it possible to chart the course for future research and to set immediate and long-term research goals in this direction. The latter might include significant enhancement of the volume-specific polarization rotation intensity, fast temporal modulation, and spectral tuning of the polarization rotation peak from far infrared (IR) to far ultraviolet (UV) regions. NP assemblies with different chiral geometries constitute the second part of the review. Their classification simpler than that of individual NPs. At the same time, additional degrees of freedom for chiral geometries become possible in constructs made from two or more individual NPs. For example, chiral NP assemblies may be formed from NPs that may or may not be chiral. The NP positions in space are the source of mirror asymmetry at different scales for these nanomaterials. Furthermore, while the dimension of chiral NPs encompass the scales from 10−10 to 10−8 m, NP assemblies made by either solution-based synthesis or lithography20,25,26 can traverse the scales from 10−9 to 10−1 m, engendering previously unknown physical and chemical manifestations of chirality. Increased dimensions simplify the use of different forms of microscopy, e.g., transmission/scanning electron microscopy (SEM) and super-resolution optical microscopy, that enable identification of chiral geometries. Organization of the NPs into two- and three-dimensional constructs with chiral geometry at nano- and mesoscale increase polarization rotation27 and has been studied both experimentally28 and theoretically.14,29 NP assemblies also reveal hierarchical chirality when the chiral organization at smaller, say atomic, scale produces chiral geometry at a much bigger scale, say at micron scale. There is a wealth of examples for such structures in the realm of biomacromolecules and organic supramolecules. For instance, α-helices within proteins are made from chiral amino acids and present a CD response reflecting the superstructure arrangement instead of the chirality of the individual amino acids.30 Similar effects of hierarchical organization within inorganic nanostructures will also be discussed. The challenges in making NPs and their assemblies of selected chirality (left- or right-rotating) are central to this area of research. Analysis of experimental methods for preparation of chiral individual NPs and chiral NP assemblies is included in this review. These techniques evolve very rapidly, with new methods appearing annually, and enable new applications of chiral nanomaterials. These sections of the review are meant to serve the reader as a guide for the multiple necessary synthetic tools available. They will include chirality transfer from molecular to nanoscale structures, utilization of chiral templates, represented most often by biomolecules (DNA, peptides, fibers, etc.),31−36 as well as a spontaneous self-

1.1. Common Grounds

Before we can properly discuss chiral inorganic nanomaterials as a part of nanotechnology, the common grounds with other fields of chemistry, physics, and materials science with a long history of research in chiral structures need to be established. Terminology is a large part of it. Chirality is defined as a geometrical property describing the fact that the mirror image of an object is not superimposable with the original.65,66 Note that this property has no reference to scale or the state of matter and can be present, therefore, in any object−real or imaginary. In fact, the word chirality refers to a distinct geometry of atoms, molecules, particles, etc., rather than the optical or chemical effects that emerge as a result. One also has to admit 8043

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2. DIFFERENT VENUES OF CLASSIFICATION OF CHIRAL NANOMATERIALS In the past decade, the spectrum of chiral inorganic nanomaterials has been tremendously expanded. To start, let us assess the different types of chirality of individual NPs and their assemblies, which will help us to systematize the large variety of inorganic materials based on their geometrical elements. This approach to classification is based on the physical origin of chiral geometries in nanostructures. The subject of classification seems to be tedious and, perhaps, unnecessary, but it is fundamental to the field of chiral inorganic nanostructures and will help with its logical organization (see Section 2.2). Furthermore, it is suprisingly difficult even given the long history of chiral studies before. Even for NP dispersions with distinct chiroptical activity, establishing the relation between the chirality of the model structure on paper (or on the computer screen) and the chiroptical or other secondary properties is challenging and often uncertain.8,10 In fact, most inorganic nanostructures have chiral symmetry for several geometrical elements and scales simultaneously. The latter gives one, however, a compelling reason to identify and formulate with some degree of rigor the types of chirality that are being discussed in conjunction with an empirical secondary effect. Chiral assemblies constituted from a few thousand NPs can be subject to additional classifiers. NP assemblies can be manipulated using a multitude of noncovalent interparticle interactions and may have large variety of geometrical shapes and forms.20,39 They can be classified using the chiral geometries and materials of the nanoscale components. A description based on the characteristic geometry of the nanostructures and symmetry elements in this case is easier in NP assemblies than in the individual NPs, because of the larger scale, since experimental methods for imaging of inorganic nanostructures on the scale of 100−1000 nm are routine. Note also that different methods of classification are possible and valid. One classification that was used in the past is based on the inorganic materials from which they are made. For instance, one can classify inorganic nanostructures as those based on metal NPs,10,73,74 semiconductor NPs,48,75,76 magnetic NPs,77 metal oxide NPs and silica structures,76,78−80 carbon nanomaterials,81−84 and others.85−90 Such classification of chiral inorganic nanostructures utilizing de facto the band structure of solids is simple and makes sense because it affords the direct transition to optical, chemical, and other properties. The methods of classification based on chiral geometries or on base materials do not contradict each other and could be used complementarily.

that identification of the actual objects and their geometric features responsible for these effects is not entirely straightforward for individual NPs as will be discussed below. In the realm of chemistry, the two nonsuperimposable objects related by the mirror symmetry are referred to as enantiomers. Simple physical properties, such as melting temperature, evaporation temperature, and color of pure enantiomeric solids of organic materials are the same. The chiral molecules with identical chemical composition that are not related by mirror symmetry are typically called diastereomers. The physical properties of diastereomers are not the same. Due to multiple options for geometrical placement of atoms in NPs, diastereomers are most prevalent for NPs, although the difference in their, for instance, phase transition temperatures or color becomes miniscule. The frequent reference to physical properties reflects the fact that we deal here with small chemical and physical objects, the geometry of which cannot be visualized directly most of the time. However, it can be inferred from the secondary propertiesoptical, chemical, biological, etc.obtained from an ensemble of chiral structures. We use here the word “secondary” because these properties are derivatives of the object geometry of the particular chemical object at one or all the scales mentioned above. These properties, of course, can be and most of the time are the primary reason why chiral molecular and nanoscale structures are made and determine the functionality and practicality of chiral materials. Reading the latest literature on chiral nanostructures, I notice that the distinction between chirality and, for instance, the optical activity of NPs is often blurred. The tendency to equate these two different attributes of nanostructures can lead to mistaken conclusions, and by making this semantic differentiation we want to help some readers to avoid these mistakes. Furthermore, the difference between individual objects being chiral and a collection of a large number of these objects (that we normally deal with in the case of solutions of chiral molecules or dispersions of individual chiral NPs) exhibiting these secondary effects of chiral structures needs to be made, too. The possibility to observe the secondary properties of chiral chemical structures depends on the relative amount of the respective enantiomers. The individual objectsmolecules, NPs, or higher order structurescan be chiral, but spectroscopic examination of such dispersion or solutions may reveal, for instance, no rotatory optical activity because the positive and negative polarization rotation from different enantiomers cancel each other. Ensembles of chiral molecules, NPs, and their superstructures may and most often do have equal amounts of the enantiomers. These chemical systems may exhibit a few but not some of the other secondary properties. Such ensembles are typically referred to as racemic mixtures. Concomitantly, ensembles in which the amount of one enantiomer is greater than the other one will be referred to as nonracemic. The molar preference of one enantiomer over another is typically expressed as enantiomeric excess measured in percent (%) and is often abbreviated as ee. When the solution or dispersion consists of a single enantiomer, that is ee = 100%, it is called homochiral. Homochiral compounds are common among bioorganic substances, as was noted by Kelvin,67 Pasteur,68 and Piutti,69 but, as we shall see later in the text, not for many inorganic nanostructures. Nearly homochiral chemical systems from inorganic nanostructures were obtained only recently using chiral separation,70 e-beam lithography,25,71 and NP self-organization.72

2.1. Synthetic Methods for Chiral Nanomaterials

To understand the geometry of NPs at atomic, molecular, and nanometer scales, we need to start with the methods of chiral NP synthesis. Despite the fact that NPs coated with chiral surface ligands have been reported for a considerable period of time,8,10,91 the solution-based synthesis of individual colloidal NPs with a priori defined chiral shapes92 of the inorganic core remains elusive.70 Note that the problem here is not whether it is possible or not to synthesize chiral NPs but rather whether it is possible or not to carry out such synthesis enantioselectively and whether it is possible or not to separate the enantiomers and numerous diastereomers. 8044

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The general approach for the synthesis of chiral NPs is based on the nucleation and arrested growth in liquid media in the presence of chiral surface ligands, which act as stabilizers. These molecules coat the NP surface, impart colloidal and thermodynamic stability to nanoscale colloids, and are the foundation for understanding various aspects of chemical, physical, and biological behavior of NPs.93 This method of synthesis is de facto the well-established chirality transfer reactions from biological components to the products. In order to obtain chiral NPs, homochiral biomolecules, such as amino acids, nucleotides, peptides, sugars, lipids, etc., are used as surface ligands. The chiral molecules become either chemically bonded or physically adsorbed on the NP surface.17,94 Even if the chiral molecules remain free in solution and do not form a coating on the NPs, some degree of chirality may be still be imparted to them via the chiral environment generated around growing NPs, especially when the chiral solute and solvent interact strongly.95 The optical activity of the NP dispersions often displays CD bands in the part of the spectrum characteristic for light absorption by the inorganic NP core. The rotatory optical activity of dispersions of NPs typically changes to the opposite one when, for example, the L-form of the amino acid cysteine is replaced by its D-form.19,96 The sign of the CD peaks associated with the inter- or intraband transitions of the inorganic material is determined by the enantiomer of the stabilizer used in the arrested precipitation process,17,96 illustrating the point about chirality transfer from the surface ligands to the NPs cores. It can follow and be followed by a plethora of chemical and physical effects that can generate a variety of geometrical objects with different scales and measures of chirality. In fact, little is known about the actual geometrical arrangements of atoms that give rise to the optical activity of the resulting NPs. Nevertheless, when the individual NPs are assembled into larger structures, the molecular scale chirality of the surface ligand may propagate through the geometry of the higher-level structures72 via collective effects known for NP assemblies.93 2.1.1. Chiral Metal Nanoparticles. Classification by the type of inorganic material is both logical and characteristic of inorganic chiral nanostructures. A greater amount of structural information is available about the chiral metal NPs than about chiral semiconductor NPs. Therefore, let us start the discussion with the current knowledge on chiral gold and silver NPs. NPs from metals are known for the strongest rotatory optical activity among all nanostructures of similar size. They also attract special interest due to potential applications in metaoptics56,97,98 and enantioselective catalysis.73 There are several general methods for the preparation of metal NPs with organic surface ligands that differ by the nature of chemical reactions leading to the formation of metal:10,16,99,100 (a) chemical reduction of salts; (b) displacement from organometallic complexes; (c) electrochemical reduction; (d) thermal, photochemical, or sonochemical decomposition of organometallic precursors; and (e) laser ablation. In most studies, metallic NPs with chiroptical activity have been prepared by the chemical reduction method.8,10,16 Tetrachloroauric(III) acid and silver nitrate are the commonly used precursors, while the most typical reduction reagents are sodium borohydride (NaBH4) and sodium citrate.101,102 Amino acids, peptides, and DNA oligomers are frequently employed as surface ligands for the synthesis of chiral metal NPs. The use of ligand-exchange reactions for postsynthetic modification of metal NPs with chiral molecules or clusters is rare.103−105

Bonding of stabilizers to NPs cores containing heavy metals can be very strong compared to other nanoscale materials. Hence, the growth of the metallic particles is often arrested at a relatively early stage, giving gold and silver clusters with a size of 1−2 nm. Such NPs are denoted sometimes as nanoclusters. For the purpose of this review, we shall not differentiate between NPs and nanoclusters. Optically active gold NPs was first synthesized by Schaaff et al. in 1998.17 Since then, numerous examples of chiral metal NPs have been reported.10,70 Using the chemical reduction method, gold NPs exhibiting some degree of polarization rotation activity were prepared with many chiral ligands. The latter included glutathione,17 N-isobutyryl-L-cysteine,22 1,1′binaphthyl-2,2′-dithiol,106,107 D-/L-penicillamine,108 captopril,109 and DNA oligomers.110 Importantly, achiral molecules including 2-phenylethanethiolate (2-PET),111 p-mercaptobenzoic acid,112 and others,113 can also yield chiral metal NPs should they form chiral arrangements on metal surface. This fact highlights the complexity of the chiral geometry identification responsible for optical and other secondary properties of individual NPs. Chiral separation techniques, such as chromatography, electrophoresis, and selective precipitation with chiral biomolecules,114,115 may help to improve the yield of specific sizes as well as our understanding about the structure of the chiral particles.17,116,117 Importantly, they can afford separation of an initially racemic mixture of the NPs to dispersions with rotatory optical activity.70 2.1.2. Chiral Semiconductor Nanoparticles. The typical synthesis of chiral semiconductor NPs (aka quantum dots, QDs) follows the same idea of arrested particle growth in solution. The first publication on chiral semiconductor NPs was the preparation of chiral CdS NPs using penicillamine as a surface ligand by Moloney et al.18 These particles were obtained by mixing cadmium perchlorate and a basic solution of D-, L-, or rac-penicillamine. Subsequent addition of thioacetamide creates weakly luminescent CdS nanoclusters, which are then annealed to form highly luminescent chiral CdS NPs.18,75 A similar method118 has been used for the synthesis of chiral CdTe NPs functionalized by (D,L)-cysteine (Cys)19 or (D,L)-glutathione (GSH).119,120 Later a similar technique was also used to make chiral graphene quantum dots (GQDs) that are also semiconducting and luminescent.96 In this case, the chiral surface ligands were attached via conjugation through covalent bonds. While the nature of chirality transfer from ligands to the semiconductor core is quite clear for graphene particles and can be associated with 3D twisting of the flexible graphene sheet, the same is still under investigation for II−VI semiconductor NPs. On the basis of the recent data on crystal lattice dislocations,121 the induction of overall chiral shapes of the NPs can be associated with the chirality of the inorganic core.122 2.2. Chemical and Physical Origins of Chirality of Nanoscale Inorganic Matter

The observation of the polarization rotation of photons in dispersions of metal and semiconductor NPs behooves us to understand better the structural mechanisms of chirality in individual NPs. In other words, here we shall attempt to give an answer to the question, “What part of the NP does have chiral geometry?” 2.2.1. Chiral Geometries of Nanoparticles. The common pictorial representation of NPs as perfect spheres, 8045

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A hypothetical case of an inorganic material with a chiral crystal lattice made by the top-to-bottom method, for instance, by lithography, as a mirror-symmetric cube is realistic. If, however, we are interested in the manifestations of chirality in such a material, one will need to obtain a nonracemic ensemble of such NPs, which will require a chiral bias at atomic scale during the growth. Importantly, surface ligands are not considered in Type 1 chirality. Certainly, the surface ligands strongly influence the organization of the inorganic core from the synthetic point of view and, in practice, it is problematic to distinguish whether the chiral packing of atoms in the small cores (0.5−1.5 nm) is the cause of the surface layer chirality or vice versa. From this perspective one might think that making the distinction between the chirality of the ligand shell and that of the core is a moot point, but this is not the case. It is actually possible to de-couple the chirality of the NP cores and the organic shells. Chiral geometries of inorganic cores with characteristic dimensions of several nanometers, as exemplified by twisted rods and helices,6,38,61,122 are retained when the composition of the surface layer changed. Additionally, the presence of organic ligands is not needed for appearance of chirality in the NP cores because geometrically distorted structure can be thermodynamically more stable than the perfectly packed symmetric crystal lattice. For instance, the transition from the symmetric cubic to the twisted lattice occurs due to the energy preferences to distorted rather than a symmetric structure as was observeved in gold clusters.128 As a point demonstrating significance of understanding the chirality of ligand-free NPs, I can point to the fact that chiral inorganic NPs that have a limited amount of stabilizers may be characteristic of interstellar matter. The driving force to chiral configurations of NP cores is distinct from that for surface ligands and involves, among other factors, thermodynamically favorable distortions of the crystal lattice for nanoscale inorganic matter. As one example of thermodynamic preference for chiral core, a perfect tetrahedron can be achieved by only one atomic packing, whereas a tetrahedron with four different apexes has 4! (factorial) degenerate ways to arrange these apexes. This degeneracy contributes with ca. 8 kJ/mol of entropic stabilization favoring the defects in comparison with the achiral perfect tetrahedron. So depending on the enthalpic contributions arising from each defect, a noticeable population of chiral NPs might be observed. Obviously, this purely geometrical reasoning cannot account for all the NPs; it is necessary to investigate for each case how much entropy and enthalpy are produced by the defects leading to chirality. Type 2 chirality in NPs is associated with the asymmetries of the NP core surface. It may be called a chiral footprint when such asymmetries are the result of chiral surface ligands.129 In a more general case, this is the chirality of the inorganic surface; it manifests as distortions and displacements of the atoms of the NP core in response to the presence of the stabilizers or other factors, for instance erosion of atoms, addition of atoms, or atomic reconstruction in response to chiral media (Figure 2B). Unlike Type 1 chirality, the shape of the inorganic core in this case can be achiral. In most practical cases, Type 2 chirality is associated with surface ligands. Note that the latter can be chiral, racemic or achiral. The secondary manifestations of the second type of chirality are very different than Type 1 and, as we shall see later, Type 3 because only the specific surface states of inorganic

cubes, ellipsoids, etc., may not be the best to keep in mind when it comes to understanding their chirality. Asymmetric NP cores, ridges, apexes, adatoms, vacancies, dislocations, etc., all contribute to the appearance of chiral geometry of these chemical species.121 Furthermore, edges, apexes, and faces of the inorganic material may not be coated with surface ligands uniformly or in a widely accepted radial fashion. The surface layer, thereby, contains asymmetry (in addition to the imperfections of the core) and thus can lead to the appearance of chiral geometrical elements. The latter can occur, for instance, via epitaxial lattice-to-lattice coalescence of NPs, also known as oriented attachment.123−125 Even when the overall shape of the NP is spherical, the crystallinity of the inorganic core is perfect, and the stabilizers coat it uniformly, the NP may still be chiral. Given an external bias by electrical or magnetic field, the chirality may originate from an asymmetry of electron density of the inorganic core because of its high polarizability. So there could be multiple sources of chirality in NPs, and understanding which of them is/are responsible for specific secondary effect can be both difficult and fascinating. Let us now consider atomic, molecular, and nanoscale chiral geometries that have been identified in different NPs. Type 1 chirality is associated with the asymmetry of the inorganic core of the NP. The object that we consider here is the continuous piece of the inorganic matter that defines the inorganic properties of this nanostructure (Figure 2A), for example, NPs

Figure 2. (A) Type 1 chirality: the inorganic core has chiral shape. (B) Type 2 chirality: the chiral surface of the inorganic core. (C) Type 3 chirality: the chiral pattern of the surface ligands. (D) Type 4 chirality: polarization effects in the inorganic core.

with the shapes of tetrahedrons with variable truncations,41 fused twisted nanorods (NRs),122 and twisted gold clusters.10,24,94,113,126,127 Besides NPs, nanohelices,98 twisted ribbons,20 and assymmetric objects with less traditional shapes such as nanopillar caps56 can also be assigned to this group. In most cases and, in particular, for nanocolloids made by bottom-up techniques, it is sufficient to consider the geometry of NP core as a whole rather than as the collection of atoms packed in a specific crystal lattice. This is because a material with chiral crystal lattice should give the overall shape of the NPs that is also chiral (as with the classical example of macroscale crystals of tartaric acid separated by Pasteur). 8046

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The fourth type of chirality in individual NPs may be depicted as the chiral f ield ef fect (Figure 2D).8,140 This type of chirality is specific to NPs and is associated with the high polarizability of some inorganic materials. As in the third type of chirality, the distribution of atoms in the NP core is essentially achiral, but the distribution of electrons is affected by the electrical field from the surface ligands or other source. The asymmetric polarization patterns will be generated in response to achiral ligands with chiral adsorption patterns, chiral ligands with achiral adsorption patterns, and, of course, chiral ligands with chiral adsorption patterns. The high polarizability of the inorganic core typical for plasmonic NPs almost inevitably results in such chirality in the vicinity of enantiomers. The chiral ligands with achiral adsorption patterns is normal for Type 4 chirality, and when modified, plasmonic NPs usually have chiral bands in the UV region (200−400 nm). The CD bands in the UV region could exhibit alterations compared to the original chiral ligand due to the polarizability of NPs. The high polarizability can also generate CD bands at the plasmon resonance frequency (∼405 nm for Ag NPs, 520 nm for Au NPs, etc.). Such NP systems may involve proteins,141 peptide nanotubes,142 or peptides36,143 that are physi- or chemisorbed on their surfaces. High polarizability of metal NPs also results in localized areas high electrical field around them under incident electromagnetic radiation, known as “hot spots”. The latter result in a strong enhancement of electronic transitions of organic ligands present there. Besides enhancement of Raman scattering, the hot spots are known to enhance chiroptical activity.5 Since this effect originates in polarization of electron density in NPs and reflects the chirality of the organic matter present in the hot-spot, we classify it as Type 4. Note that the hot-spot-induced chiroptical activity is enhanced in assemblies of NPs due to the resonance between the polarization oscillations in adjacent plasmons. It may be tempting to assign chiroptical activity in NP assemblies to plasmon enhancements effects due to their popularity in academic literature. In reality, multiple contributions to chiroptical activity needs to be assessed.6 The distinction between Types 1, 2, 3, and 4 chirality for NPs requires the knowledge of their atomic and molecular structure. In practice, the de-coupling the chiroptical effects from all these asymmetric geometries, based only on CD or ORD data is fairly hard. However, it is possible when multiscale computational methods described in Section 2.5 involving both molecular dynamics of NPs and their interactions with incident photons are applied. In the case of plasmonic NPs carrying a chiral surface layer, one can safely assume that the fourth type of chirality is present. 2.2.2. Experiments and Simulations Establishing Structural Origins of Chirality in Individual Nanoparticles. Type 1 chirality in NPs was identified in experiments144,145 and simulations for gold clusters.24,146 Among the computational tools used for the latter, the Density Functional Theory (DFT) calculations taking advantage of genetic algorithms and many-body potentials represent a powerful tool for simulations of chiral nanostructures. Although they can be carried out at present only for fairly small atomic systems that were described above as chiral clusters, DFT studies demonstrated that the interaction of methyl thiol ligands on a truncated cuboctahedron with face-centered cubic structure, i.e., a Au38 cluster coated with 24 HSCH3 molecules, leads to chiral distortions on the Au38(SCH3)24 cluster and, hence, to chiral atomic packing of the inorganic core.147,148 The value of

matter are affected, while the electronic states associate with the inorganic core (excitonic, plasmonic, etc.) are not. Considering a common case when Type 2 chirality originates from the organic shell, the surface ligands that have strong interactions with the inorganic material of the core often carry two anchoring groups (two oxygen atoms from two carboxylates, or carboxylate groups and thiolates); such surface ligands cause inorganic lattice distortions more easily than the ligands with a single point of attachment. The N-isobutyrylcysteine, L-cysteine methyl ester, and D/L-penicillamine ligands have carboxylates and thiol groups that could induce the chiral distortions.22,48,130 To further accentuate the significance and generality of Type 2 chirality in individual NPs, it can be discussed in context of the classical studies of surface chirality, such as inorganic surfaces131 related to origins of life.132 Among many cases, this type of chirality can be exemplified by the surface reconstruction taking place, for instance, after adsorption of tartaric acid on Cu133,134 or Ni surfaces129 that leads to the shift of the surface atoms in unusual configurations when all local mirror symmetry planes are destroyed (Figure 2B). The double or higher coordination of the ligands seems to be mandatory, because otherwise the ligands would easily undergo free rotation around their only bond with the NP, and this thermal agitation would lead to full racemization (ee = 0%). Type 3 chirality in individual NPs is associated with the chirality of the stabilizer shell. The examples of such structures are the cases in which the molecules in the organic shell are chiral but the core and its surface are not.70,135 Importantly, achiral surface ligands can also give rise to chirality. The symmetry breaking here is associated with the packing of stabilizer molecules on their surface (Figure 2C). By other words, the object whose geometry we consider here is the collection of the surface-bound organic moieties. The third type of chirality has distinct manifestations for biological and chemical properties of chiral NPs because it will be the primary factor determining, for instance NP-protein interactions, assembly of NP into superlattices, and chiral separations. The bonding pattern of stabilizer molecules may not follow the symmetry of the underlying inorganic crystal lattice and lack essential symmetry elements. Such chirality could arise through the chiral arrangement of gold−thiolate ligand (staples), e.g., arranged in a staggered fashion. For example, the Au38(SCH2CH2Ph)24 NP has a prolate shape and contains a face-fused biicosahedral Au23 core that is protected by three short Au(SR)2 and six long Au2(SR)3 staples, in which the Au23 core is idealized as D3h symmetric.70 The long staples are arranged in a chiral staggered configuration (two triblade fans composed of three staples) that either rotate clockwise or anticlockwise, while the short staples are slightly tilted, following the handedness of the long staples. A similar Type 3 chirality is observed for Au38(2-PET)24, Au40(2-PET)24, and Au38(SCH3)24 clusters with a chiral arrangement of the gold− thiolate ligand shell around the achiral metal core.136−138 The organic shell can also be patchy, which will almost inevitably lead to a nonsuperimposable mirror image, especially considering the three-dimensionality of the surface layer.139 Note that the mobility of the organic molecules on the surface of NPs15 can result in conversion of one NP enantiomer into another when the temperature reaches the activation energy threshold for translation of the molecules of, for instance, thiols along the underlying inorganic surface. 8047

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Figure 3. (A) Calculated conformers of deprotonated N-isobutyryl-L-cysteine on Au8 cluster. (B) Comparison between calculated and experimental vibrational circular dichroism spectra of N-isobutyryl-L-cysteine on a gold cluster.22 (C) Chiral D3 arrangement of the Au−S atoms (left) and the optimal SCH3 distribution on the structure (right). (D) Calculated rotatory strength and CD spectrum of structures.137 (E) Au28(R-methylthiirane)6 (a) and Au28(glutathione)6 (b) using partial charges for the molecules and their image charges. (F) The computed CD spectra.140 Panels A, B and C, D were reproduced with permission from refs 22 and 137, respectively. Copyright 2006 and 2010, respectively, American Chemical Society. Panels E and F were reproduced with permission from ref 140. Copyright 2006 Royal Society of Chemistry.

The chiral memory of the surface is also found for NPs with Type 2 chirality exemplified by CdTe NPs.48 The surface of thiol-capped CdTe NPs is distorted in the presence of a chiral ligand. After the ligand exchange reaction with the achiral thiol, the achiral thiol-capped CdTe still displayed the symmetrical mirror CD spectra that was similar to that of the original chiral L-cysteine methyl ester hydrochloride-capped CdTe. This effect was associated with the fact that chirality is “stored” on the surface of NPs rather than in the NP core. Type 3 chirality was identified for NPs with a symmetric Au core.135,155 As mentioned above, the stabilizers are attached following the so-called “staples” motif producing chiral patterns on the NP surface.137,138 For Au38(SR)24 protected by three RSAuSR and six RS(AuSR)2 units (Figure 3C), both the crystallographic structure and the computationally optimized structure showed an achiral gold core of 23 atoms.137 The geometrical arrangements of the nine gold−thiolate units reveal, however, chiral D3 symmetry (Figure 3C). This cluster reveals strong CD bands associated with metal−metal or ligand−metal charge transfer (Figure 3D). Similarly, Au40(2PET)24 produced enantiomers with opposite chiroptical

the Hausdorff chirality measure (HCM), which gives a quantitative measure of asymmetry for any kind of geometrical figure,149 increases with the number of thiol molecules. For methyl thiol-stabilized Au 28(SCH 3 ) 16 and Au 38 (SCH 3 ) 24 clusters,150,151 the HCM was equal to 0.160 and 0.121, respectively.8 Similarly, several theoretical studies showed that the many topologically interesting structures with null symmetry or asymmetry had an energy near or below the lowest energy ordered isomer for bare gold clusters with a size range of 10−75 atoms.152−154 The Type 1 chirality was identified in NPs stabilized by Nisobutyrylcysteine.22,130 These molecules attach to the Au surface in two points and distort the underlying inorganic core, leading eventually to strong chiroptical activity130 (Figure 3A,B).22 Another study involved Au102(p-MBA)44 clusters. Due to hydrogen bonding between carboxylic acids resulting in a chiral stabilizer shell, the achiral p-MBA generated a chiral displacement of atoms on the gold surface.112 Postsynthetic ligand-exchange experiments have provided evidence for the chiral memory of NPs and therefore likely thermodynamic or kinetic stability of these chiral core shapes. 8048

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Figure 4. (A) CD spectra of gold NPs with or without E5 peptide. (B) The calculated CD spectra for a dipole of a chiral molecule and for a dipole− nanoparticle complex with two separations (R = 5.3 and 6 nm).36 (C) Salt-dependent CD spectra evolution of ssDNA-functionalized Ag NPs with the ionic strength increasing from 0 (deionized water) to 0.06 (10 mM phosphate buffer), 0.07, 0.08, 0.11, and 0.16 M (0.1 M phosphate-buffered saline) in the order indicated by a black arrow. (D) The design of an “individual plasmonic chiral nanoparticle” using a gold/silver (Au/Ag) core− shell nanocube (left) and the UV−vis absorption and CD spectra of ssDNA-functionalized Ag nanocube (right).164 Panels A, B, and C, D were reproduced with permission from refs 36 and 164, respectively. Copyright 2011 and 2013 American Chemical Society.

NPs carrying chiral 1,3-disubstituted diaminocalix[4]arene ligands,163 peptide-functionalized gold NPs (Figure 4A,B),36 and photosynthetic proteins.141 Great enhancement of the rotatory optical activity due to the field effects must be noted (Figure 4C,D),164 as it has substantial practical value. Far-field electromagnetic coupling between a localized plasmon of an achiral nanostructure and the surrounding chiral molecular layer(s) can also induce chiroptical activity. This effect is believe to induce chiral distortions of the electron gas more effectively than one could expect, as was demonstrated by comparing experimental results with a simple electromagnetic model that incorporates a plasmonic object coupled with a chiral medium.162 By now, it is already clear that even single chiral NPs should be considered as complex chiral systems with several types of chiral geometries present at the same time.114,128 Moreover, it is often difficult to point to the true (thermodynamic) origin of chirality in NPs because the chiral arrangements of the stabilizer shell often begets the others. Also note that this does not relief us from the need to understand the different contributions to chirality in NPs, because the secondary properties of interestoptical, chemical, biological, etc.may originate from one and not from the other. To this end, determining the origin of secondary effects of chirality in many nanoscale materials still remains challenging. As such, ligand exchange (e.g., thiolate to phosphine) on the particle surface with chiral ligands often leads to the modification of chiroptical peaks, but how the structure of the NPs changes during this process and whether the metal core structure remains chiral or achiral is intriguing.22,108,130,165 Normally, the atomic structure of the NPs remains unchanged, though the chiral ligand (Nisobutyrylcysteine) was exchanged to induce the chiral inversion due to the stabilizers.130 For the multiply anchored

responses after separation on a chiral cellulose-based HPLC column, although the molecule of the thiolate stabilizer was achiral. The 2-PET staples on the surface of the Au40 cluster are believed to give rise to the enantiomeric preference in NP adsorption to cellulose.136 Note however that other types of chirality are present in these and many other NPs discussed above. Perhaps, it would be worth reiterating the earlier point that rarely NP possess only one type of chirality. The secondary effects of all types are distinct because of the different scales and different matterorganic or inorganicare involved. The Type 4 chirality in NPs is applicable for an achiral metal core placed in a chiral environment.140 Charge-perturbed particle-in-a-box calculations demonstrated that chiral stabilizers placed in achiral adsorption patterns on a surface of metal NPs induced chiral image charges in the inorganic crystal lattice.140 The electrostatic perturbation influenced by both the asymmetry of the adsorption pattern and the ligands was found to be effective in inducing chirality in a symmetric polarizable core (Figure 3E,F).140 Several studies attributed experimentally observed optical and chemical effects to this type of chirality.74,156 Most typically, their dispersions display optical activity in spectral windows characteristic for stabilizers, for instance, L-glutathione,17,94 and for inorganic core, for instance, gold. This observation implies that the chirality of the surface ligands is transferred 157−159 via a number of possible mechanisms140,160 to the structure of the plasmon oscillations in the case of metal cores. Near-field effects are often involved in description of various plasmonic particles and have been extensively treated theoretically91,161 and experimentally.36,162 In fact, an explanation of the chiroptical activity of the plasmonic NPs typically involves the influence of the NP field on chiral stabilizers and/ or the field of stabilizers on the NP core, as exemplified by gold 8049

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of individual NPs. There are, however, others that manifest in both the chirality of individual NPs and their assemblies. Furthermore, the dimensions of NPs are similar to those observed for biomacromolecules. With the characteristic size of amino acids and nucleotides being just below 10−9 m, many proteins have a diameter of a few nanometers. Numerous proteins are even larger and have dimensions of tens of nanometers. Some of the larger and highly anisotropic protein molecules approach mesoscale dimensions in one geometrical measure. As such, the triple helix of a 300 nm long collagen molecule assembles in fibrils of over 20 μm in length.190 Nearly all soluble globular proteins, their oligomers, and complexes display intricate molecular shapes. Such nanoscale shapes have distinct chirality and belong to a number of chiral point groups.191 The analogy to NPs with the first type of chirality is quite obvious in this case. Extending this line of thought further, the surface chemistry of water-soluble NPs has distinct similarities with the chemistry at the interface of protein molecules and aqueous media, because it is determined by the same chemical groups: −OH, −COOH, −NH2, etc. Therefore, the chirality of the stabilizer shell discussed in the Type 3 of chiral NPs can be compared to the atomic scale packing of the similar chemical groups and chain segments at the outer surface of protein or DNA globules. A similar parallel can be made between the “staples” of the surface ligands on NP surface and packing of peptide segments, for instance, in chaperonin molecular units.192,193 2.3.3. Hierarchical Chirality. The similarity of chiral geometries of inorganic and biological nanostructures is apparent. The juxtaposition of biological and inorganic nanostructures may lead to new insights into NPs and other nanoscale structures. One of them is hierarchical chirality. In the case of proteins, the cooperative behavior of hydrogen bonds and other intermolecular interactions results in the translation of the atomic scale chirality of amino acids to nanoscale chirality of the secondary structural motifs, such as αhelices and β-sheets, which, in turn, produce the tertiary and quaternary structure of proteins.191 Self-assembly and aggregation of proteins194 produce helicoids that are very well-known from protein complexes and rodlike viruses.195 The atomic scale chirality of the NP stabilizers and NP cores should lead to a similar hierarchy of chiral structures made from inorganic NPs because the cooperativity of the interactions and complementarity of the chiral patterns remains. The evidence of the cooperativity of the interactions can be found in the arrangements of stabilizers on the NP surface,196−198 while the evidence for the hierarchical chirality can be found in NP assemblies, exemplified by the chiral supraparticles from gold rods in a twisted rod arrangement stemming from the shell from CdTe NPs with amino acid surface ligands.199 Even more complex hierarchical assemblies can be made. The resemblance of the assemblies of chiral NPs to those of tobacco mosaic virus can be noted.200 Relations between the chirality of individual NPs and biomacromolecules can also inspire other research venues related to chiral NPs. They can be based on the distinction of biological activities of different NP enantiomers. An indication of such distinction can be seen in the interactions of chiral graphene quantum dots with the membranes of mammalian cells that was observed both experimentally and computationally.96 As an extension of this line of logic, different enantiomers of NPs may present different environmental and health hazards, because they may interact selectively with chiral biomolecules,

ligand (e.g., carboxylate groups and thiolates ligand), an induced surface chiral distortion can be retained though the ligand is exchanged with achiral ligand.48 Ligand exchange may result not only in the change of the stabilizer shell but also in alterations of the metal core, including the average size.105 The ligand exchange can lead to larger or smaller size of clusters, for example, when Au55 cluster ligand exchanged with hexanethiol, Au75 clusters were obtained,166 while Au25 formed Au13 icosahedron through core etching.167 The chirality of ligand exchange induced metal core alterations remains for future investigations. 2.3. Relation with Known Chiral Materials

2.3.1. Similarity with Chiral Inorganic and Organic Molecular and Supramolecular Compounds. Considering the multiplicity of structural origins of chirality in NPs, the fact that some of these geometries can be found in many other chiral materials based on traditional chemistries and compounds must be highlighted. The lessons of structural design at different scales and the usage of “building blocks” with multiple functions can be extended from the different branches of classical chemistry to nanomaterials ‘nano’ chemistry.169 For instance, the assemblies of the NPs have well-known counterparts in supramolecular assemblies of organic molecules.21,170 Notably, the 2016 Nobel Prize winning molecular motors contain intrinsic chirality both in the structure and the motional paths of the complex molecular structures and approach the scale of inorganic nanostructures being discussed in this review.171−173 The similarity of scales and geometries of NPs and some of the liquid crystals (LC) phases can be noted as well,174−178 which leads to the hybrid NP−LC materials, a promising direction in the mature field.179 The cholesteric LCs are likely to be the systems of choice for future investigations. Achiral LCs in nematic phase prone to chiral induction can also be an exciting system to work on. The twisted nanorod pairs from gold39,180 or tellurium122 show clear analogies with the celebrated binaphtyl compound (BINAP) with the similar open scissors geometry.181 Extensive similarities also can be found with chiral compounds assembled via coordination bonds around metal centers, although their scale is typically smaller than those for individual NPs or their assemblies.182,183 An example of similar geometries can be given by the helical metal-coordinated nanotubes and fibers182 that can be compared to the NP helicoids from gold55 or CdTe.20 Propeller-like coordination complexes that were some of the first chiral inorganic compounds184 were recently replicated in DNA-bridged nanorod assemblies around a NP.185 Large coordination compounds, exemplified by polyoxometalates (POMs)186 and metal organic frameworks (MOFs),187 can approach the nanometer scale. The chiral geometries and chirality transfer mechanisms in optically active POMs can be particularly similar to those in individual NPs.188 The similarity in scale offers a convenient route for constructing POM−NP hybrid chiral superstructures.189 2.3.2. Similarity with Biological Nano- and Mesoscale Compounds. The vast majority of the biological molecular and supramolecular compounds in biology are, of course, chiral due to the homochirality of life on Earth. The parallels between the chirality of NPs and biomacromolecules originate from several considerations. One of them is the simple fact that chiral biological molecules are often used as ligands at the NPs surfaces and they are, at least, partly responsible for the chirality 8050

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radiation, resulting in a change in the ellipticity of the radiation beam as it crosses the sample. Chiroptical CD bands appear at the same spectral windows where standard absorption bands are obtained for nonpolarized light. CD bands may be either positive or negative, depending on the relative absorption of each circularly polarized component of the incoming radiation. Since it is a differential method, CD spectra may become complex. Rationalizing the sign and intensity of multiple CD “waves” and identifying the chiral geometrical elements responsible for them requires clear understanding of lightmatter interactions in asymmetric nanoscale structures. It may appear to be too complex and convoluted, but, in reality, it is fairly uncomplicated given commercial software packages (e.g. COMSOL, Lumerical, Gaussian and others) once the type of chirality of individual NPs (Types 1, 2, 3, 4 or combination thereof) is identified. The same refers to NP assemblies. The complexity of CD or ORD spectra calculations most often lies in chemical characterization and separation of the mixture nanoscale enantiomers. We expect that with ever increasing computational power it is becoming standard component of the NP studies. From the computational point of view, both ORD and CD spectra can be simulated by semiclassical electrodynamic models based on augmented by quantum mechanical perturbation theory to derive the equations describing the polarized light scattering arising from the oscillating electric dipole moment (linear oscillation) and magnetic dipole moment (circular oscillation), both induced by the incoming electromagnetic radiation. With regard to CD, the electric dipole transition moment interferes with the magnetic dipole transition moment and results in the rotatory strength Rj for the jth transition according to eq 2.205

including enzymes, membranes, and even DNA. These aspects of chiral NPs are not yet experimentally observed and are to be addressed in the future. 2.4. Optical Activity of Chiral Nanostructures

Optical properties represent the central secondary properties of chiral molecular and nanoscale structures in the realm of physical phenomena. For this reason, it might be helpful to go through the origin, relation to the geometry of the chiral NPs, and informational content of different types of chiroptical spectra that can be obtained for NPs. Most of the optical properties of individual NPs are related to two quantum mechanical phenomena typical for nanoscale: plasmons in metallic NPs and excitons in semiconducting NPs. These electronic states characterize the charge carrier delocalization over the NP and are, therefore, primarily dependent on the crystal lattice of the NP core. Additionally, metal-to-ligand charge transfer (MLCT) transitions can be excited at the interface of the metal core and the stabilizers.201,202 All these excited states are affected by the NP size, shape, surface ligand, and the surrounding dielectric environment.203 Once the shape of a nanostructure is chiral, plasmonic and excitonic properties also become chiral, as well as any other optoelectronic property relying on the symmetry of the inorganic core and overall electronic structure involving the NP core excited states. MLCT transitions are certainly dependent on the chirality of the ligands, but due to the second type of chirality in the NPs with some contributions from the others, they are dependent on the symmetry of the NP core as well. CD and optical rotation dispersion (OR or ORD) spectra are the most common spectroscopic tools used in this field and are typically acquired for the visible (vis) to the near-UV photons describing electronic transitions of the chiral NPs including but not limited to electronic and plasmonic transitions. Their vibrational components can also depend on circular polarization of incident photons and can be assessed by means of the vibrational circular dichroism (VCD) and the Raman optical activity (ROA).204 CD and ORD spectroscopy are most commonly used now for inorganic nanostructures, but other spectroscopies should be applicable as well.22 The ORD spectrum describes the rotation of the polarization plane of a linearly polarized light beam when passing through a material. The rotation of the plane per unit length is given by eq 1, which is a statement of the circular birefringence of chiral media. The difference between the refractive indices nL and nR for the propagation of the left and right circularly polarized components of the linearly polarized light through the chiral medium may be either positive or negative, corresponding to the usual chemical nomenclature of dextrorotatory and levorotatory media, respectively. α=

π L (n − n R ) λ

R j = Im(⟨ψ0|d|̂ ψj⟩·⟨ψj|m̂ |ψ0⟩)

(2)

Essential physical insights about the quantum mechanical origins of CD activity can be gathered from this equation. One could notice that only symmetry considerations are necessary to predict the intensity and algebraic sign of any transition. The two integrals involving the ground state wave function ψ0, the jth excited state wave function ψj, the electric dipole moment operator d̂, and the magnetic dipole moment operator m̂ must be simultaneously nonvanishing if the transition is to be observed. In other words, the transition must be simultaneously allowed by the electric dipole moment and by the magnetic dipole moment. This stringent selection rule limits the point groups for which both transition moments are simultaneously nonvanishing, and the only groups for which CD spectra are possible are Cn, Dn, O, T, and I. As a matter of fact, these are the point groups for which chirality in general, and not just the CD spectra of chiral media, is possible. Note that many chiral organic, biological, and nanoscale systems with Cn and Dn point groups exist, whereas chiral point groups O, T, and I are observed less often, but once they are observed, then chirality is necessarily observed. One can also see in eq 2 that the transition moments are vectors and they are combined in a dot product to yield the scalar rotatory strength for each jth state. The fact that the rotatory strength is defined as a dot product also implies that its magnitude may be null if the two transition moments are perpendicular to each other and the larger contributions should come from either parallel transition moments (positive rotatory strength) or antiparallel transition moments (negative rotatory

(1)

ORD spectra could provide a reliable experimental signature for a chiral NP, and they can also be calculated. Nonetheless, these spectra are less convenient when asking the fundamental question about the chiroptical activity of electronic states in NPs because they are strongly affected by scattering. At the same time, ORD spectra can directly address the practicality of the chiral nanomaterials for polarization-based optoelectronics and other applications. The CD spectroscopy measures the difference between the absorption of left and right circularly polarized electromagnetic 8051

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vibrations. The X-ray diffraction (XRD) can reveal the pattern of the lowest energy conformers137 that can be used as candidate methods for characterization of the geometrical placement of ligand on NP surface. Going the solely computational route, one should ideally start with a high-level, ab initio quantum chemistry model of the NPs that includes inorganic core, organic shell, and solvent around it, but the computational cost would not be affordable in most NPs of interest at the present moment; these restrictions are most likely to ease in the next two−five years. In practice, the choice of the level of theory depends strongly on the size of the NPs, ranging from classical molecular modeling and even coarse-grained models to treat large nanostructures comprising tens or hundreds of NPs to stateof-the-art quantum chemical modeling for small clusters with tens of atoms. Before presenting the methods, we would like to point out the tendency to employ DFT-based methods instead of wave-function-based methods due to the better compromise that the former offer between accuracy and efficiency for systems containing transition-metal atoms as compared to the latter.209 DFT-based models (as well as wave-function-based methods) require the choice of basis sets to describe the electronic density. In principle, the larger the number of mathematical functions comprising these basis sets, the better would be the description of the electronic densities and all other properties depending on them. In practice, however, individual NPs and their assemblies are too large for a full description of all electrons. In order to overcome this intrinsic computational limitation, most DFT calculations rely on the so-called effective core potential (ECP), which is a simplified empirical expression for the average electrostatic potential generated by the closedshell, core electrons of the heavier atoms (typically beginning at the third row of the periodic table). So, instead of actually computing the electrostatic screening generated by the inner electrons around the nucleus of an atom, which would require the full quantum chemical treatment of all electrons, we just add an empirical function that has been properly parametrized for that element and get nearly the same screening effect. This approximation usually works because most of the molecular structure, bonding patterns, and electronic properties depend exclusively on the valence electrons, not on the core electrons. Finally, the description of the valence electrons may need some approximation as well. The most used basis sets describe oneelectron atomic orbitals as an empirical sum of Gaussian functions, each one with an exponent ζ defining the decay rate of that function with the distance from the atomic nucleus. Typically, the larger the number of Gaussian functions describing a valence electron, the better the results, but performance degrades quickly as we move from a single-ζ basis (one Gaussian function per valence electron) to a double-ζ one (two Gaussian functions) and so on. In practice, the most recent DFT calculations rely on a double-ζ basis with ECP as a compromise between efficiency and accuracy. Obviously, as computer power increases, larger and better basis sets may become feasible. The quantum chemical computation of excited states is a demanding task, even if the methodological trade-offs just described are used. Most computational implementations use some form of linear response theory to treat the TD-DFT problem and obtain the excitation energies and the description of the excited state orbitals,210 which we assume to be equivalent to the excited state wave functions in eq 2. The TD-

strength). It is interesting to note that the ground state wave function ψ0 is the same for any CD transition (eq 2), meaning that the differences in magnitude and the algebraic sign for different transitions arise predominantly from changes in the excited state wave functions ψj. From eq 2 it is also easy to see the reason behind the unusually high intensity of CD spectra and high values of anisotropy g-factor typically registered for inorganic chiral nanostructures. Electrical polarizability and magnetic susceptibility of metals and semiconductorsthe typical representatives of inorganic materialsis higher than that of organic matter. Hence, the magnitudes of the transient dipole moments representing the interaction of incident photons with the nanoscale inorganic object and the constituent integrals of the dot product are larger than those of similarly sized organic objects. The calculation of CD spectra may rely on several different methodologies to calculate wave functions of excited states in eq 2. In general, time-dependent density functional theory (TD-DFT) is the method of choice for CD spectra calculations of individual NPs. 2.5. Computational Studies of Chiral Nanoparticles

2.5.1. Methodological Aspects. Evaluation of chiroptical properties for the individual NPs and their higher order structures can be accomplished by computer simulations. The calculation of CD spectra may rely on several different methodologies to obtain wave functions of ground and excited states in eq 2 (see Section 2.4). Alternatively, classical models using the polarizability of the individual atoms as input information may compute the CD spectrum from the local dipole moment polarization as a static response to the electric field arising from the other dipole vectors comprising the system and from the incoming electromagnetic radiation. Considering the increasing availability of high-performance computing facilities and efficient computer codes developed during the last two decades, DFT methods can now tackle small NPs at atomistic scale, whereas classical electrodynamic calculations (finite element integration, finite difference time domain, etc.) will most likely continue to be used in the near future for larger assemblies comprising several coarse-grained NPs.14 Computer simulation of chiroptical properties of the individual NPs and their assemblies requires an accurate knowledge of their shape. In principle, high-resolution imaging techniques can provide an atomistic level of detail for individual NPs.206−208 This capability is essential for confirming the intrinsic asymmetry of the inorganic cores (Type 1 chirality). However, the electron tomography can be descriptive at the atomistic level only for NPs with sufficiently high stability and a high-temperature phase transition. Furthermore, the chiroptical properties of NPs are determined by the average geometry in the large ensemble, and the implementation of tomographic geometries in simulations should be done with careful consideration of the variability of their geometries. Organic molecules at the NP surface are transparent to the electron beam and their geometrical placement needs to be established using different techniques, such as first being purified through electrophoresis or solvent extraction and characterized by a combination of NMR, IR, and VCD spectra and computational calculations of chiroptical properties (VCD, CD) based on the geometrically placed ligand on the NP surface.22,107 The ligand orientation on the NP surface could be determined from the orientation of the transition dipole moment for different 8052

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Figure 5. (A) TD-DFT CD spectrum for D-CdS. The charge carriers for six selected states are depicted by red surfaces for the holes and blue surfaces for the electrons.211 (B) UV−vis and corresponding CD spectra of CdS-D (black) and CdS-L (red) NPs from experimental results.211 (C, D) Theoretically simulated CD spectra upon intraband transitions (1, ±2) → (1, ±3) in ZnS nanowires with (a) right-hand (solid curves) and left-hand (dashed curves) screw dislocations.121 (E) The right-hand screw dislocation and the general calculated CD spectra.121 (F) The intrinsic CD (solid lines) of the L- and D-CdSe/ZnS semiconductor nanorods.212 (G) The SEM images for D-Cys CdTe NPs assembly (left), L-Cys CdTe NPs assembly (middle), DL-Cys CdTe NP assembly (right). (H) Experimental and simulated CD spectra of left- and right-helices.72 Panels A and B were reproduced with permission from ref 211. Copyright 2016 Royal Society of Chemistry. Panels C−F were reproduced with permission from refs 121 and 212. Copyright 2015 American Chemical Society. Panels G and H were reproduced with permission from ref 72. Copyright 2017 American Association for the Advancement of Science.

experimental data. Another source of inaccuracy is the need to narrow the range of orbitals around the band gap that will be included in the TD-DFT modeling of the electronic transitions.

DFT formalism is in principle exact, but the approximate form of the exchange−correlation functionals may introduce errors, and in practice, the calculations need to be validated against 8053

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calculations were based on 16 representative transitions in the window of electromagnetic frequencies characteristic of the NPs. Interestingly, the TD-DFT model indicates that the chiroptical band at about 390 nm is likely to originate not only from the band gap transition but also the p → s type excitation of sulfur atoms. The chiral semiconductor nanowires or nanorods model was also calculated on the basis of the quantum states of semiconductor nanowire with a screw dislocation. The two- or three-dimensional periodic lattices can create optically active quantum supercrystals the activity of which can be varied in many ways owing to the size quantization of the nanowires’ energy spectra. The model demonstrates that optical chirality is induced by a screw dislocation in a cylindrical nanowire of length much larger than the diameter (Figure 5C−E).121 The model proposed that the intrinsic chirality of CdSe/ZnS nanocrystals is caused by the presence of naturally occurring chiral distortion (Figure 5F).212 For large semiconductor nanomaterials, mesoscale semiconductor helices can be calculated by the finite-difference time domain (FDTD) Maxwell solver based on the interaction of circularly polarized photons with model structures.72 The calculated CD spectra displayed a nearly perfect match with experimental CD spectra, regarding the spectral shape and positions and the peak-to-valley intensity ratio (Figure 5G,H). DFT calculations employing the B3PW91 hybrid functional were performed by Gautier and Bürgi for a Au8 cluster22 representing very small NPs (double-ζ quality LANL2DZ basis set with ECP) and the 6-31G(d,p) basis set for the Nisobutyryl-L-cysteine ligand. The 6-31G(d,p) basis is also of double-ζ quality but includes extra polarization functions of types p and d, which usually improve the overall quality of the model at the expense of extra computational effort. The ligand was bonded to the Au cluster by the sulfur atom, but a second coordination involving one of the oxygen atoms from the carboxylate was observed as well (Figure 3A,B).22 This double coordination formed a ring between the ligand and the metal cluster and this ring included the stereogenic center, the αcarbon atom. Here, for a cluster comprising only eight atoms, two types of chirality (Types 1 and 2) are effectively the same: the ligand induced distortions in the cluster structure (Type 2), but the cluster is too small and then the effect changes the structure of the whole cluster, not just its surface atoms (Type 1). The degree of chirality was found to depend on the degree of dissymmetry of the stereogenic centers and thus on the local conformation around them. The authors calculated the VCD of six different conformations, and indeed, the intensity, position, and algebraic sign of the vibrational bands were found to depend on the conformation around the chiral carbon atom, without any appreciable contribution arising from the conformation of the side chain. One word of caution is necessary regarding the sampling of the conformational space of the ligand, because flexible chains always have a large number of local minima associated with dihedral rotation and these degrees of freedom are not properly sampled by standard geometry optimization techniques, which are usually based on energy gradients and inadequate to take the molecule from one local minimum to another, since energy gradient approaches zero at the minima. This was an issue for this small model with only one ligand and may become a serious drawback for larger, more realistic systems, with tens of ligands attached to a large NP surface. A genetic−symbiotic algorithm was used to sample the conformations of gold NPs ranging from Au28 to Au75.150,151

In the exact theory, all the Kohn−Sham one-electron orbitals enter into the iterative procedure that mixes them to produce the many-electron orbitals for the hole and charge associated with each transition. In practice, a NP with a few hundred atoms will produce a few thousand orbitals, even if small ECP basis sets are employed to decrease the number of electrons of the model, and this is a prohibitively large number of oneelectron Kohn−Sham orbitals. The choice of the number of occupied and virtual/unoccupied orbitals to be mixed in the description of the hole and the charge pairs for the electronic transitions is a matter of trial and error, seeking a compromise between the computational cost and the accuracy of the results. The number of roots of the iterative procedure also impacts the performance of the calculation and the quality of the results. Each root corresponds to one electronic transition, beginning with the band gap transition and going to higher-energy transitions. There is no rule of thumb defining a priori how many roots need to be computed to describe an energy range in the UV−vis spectra of an NP, so usually the best practice is to incrementally increase the number of roots until the calculated spectra matches the energy range of interest. During this incremental search, there are two issues that need to be addressed if reliable results are to be obtained. First, as the number of excited states increases, it is necessary to reevaluate the range of orbitals entering into the iterative mixing, since low-lying occupied orbitals and high-lying unoccupied orbitals might become important (meaning that their weight in the average describing the excited state orbital pair are not negligible any more). Second, the model calculation needs to be pushed farther into the high-energy region of the spectrum than the last band of actual interest, because the last band is usually ill defined, and this extra number of excited states obviously increases the computational cost of the modeling. These and other trade-offs between accuracy and cost are discussed at length in the tutorial-like review by Autschbach.205 2.5.2. Selected Computer-Modeling Studies. Small CdS NPs stabilized with penicillamine were studied using DFT calculations with the BP86 functional and a double-ζ ECP basis set for the Cd atoms.75 Although the optimized structure was analyzed by means of a detailed description of the distances and angles between atoms in order to assess the distortion of the structure, we must regard their approach as qualitative, since these raw data cannot provide a measure of NP chirality, which would require the calculation of either some chirality index or their CD spectrum. The electronic structure is also discussed qualitatively by means of Kohn−Sham orbitals (which they defined as molecular orbitals), but these orbitals are single electron representations, whereas CD and other electronic excitation phenomena are intrinsically multielectronic processes, which require the actual calculation of the excited states orbitals, as discussed below. One very interesting qualitative finding from their modeling was the observation of multiple bonding of the ligand molecules to the NP, an important finding since a singly coordinated ligand might have free rotation at the surface and this degree of freedom would cause the thermal breakdown of a chiral arrangement of ligands. The quantitative match between the CD spectra in dispersions and TD-DFT calculations (Figure 5A,B) was found for CdS NPs stabilized by L- and D-cysteine.211 Although the NP in simulations was considerably smaller than those in experimental nanocolloids to afford the computations, all the main spectral features as well as the sign of polarization rotation coincided with the experimental spectra nearly perfectly. The 8054

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One important issue is the solvation effects on the chirality of the NPs. Most calculations have been carried out for a single NP in a vacuum, whereas most experimental data deal with NPs in suspensions. Although we do not have specific literature for the solvent effects on the chiroptical properties of individual NPs, there is general literature devoted to the subject and we may point out the two major contributions that are expected to play important roles in the assessment of chiroptical properties in general. First, the geometry optimization step should include solvent effects from the outset because the relative population of different minimum energy conformers may change appreciably under different solvation conditions. Second, the transitions are also affected by the solvation. Both effects are observed even if simplified continuum solvent models are employed.214 Our survey of theoretical investigations of chiroptical properties of NPs presented both quantum chemical and electrodynamic calculations as the natural choices to understand the origins of chiroptical activity of inorganic nanostructures and computational methods appropriate for different types of chirality. Note that the quantum mechanical methods have greater relevance for single NPs whereas the electrodynamic calculations are more applicable to larger NPs superstructures. There is still room for improvement in both kinds of methodologies, and the widespread availability of highperformance computing facilities and software should favor the increase of computer investigations of chiroptical properties in the next few years. Prospectively, we expect that the accumulation of joint experimental and computational studies should provide the basis for the design and fine-tuning of materials based on chiral NPs.

This optimization technique is not based on potential energy gradients and thus it can in principle sample efficiently the local minima in the conformation space. For efficiency reasons, this preliminary optimization was carried out using a classical potential, and only the representative local minima were subject to further optimization at the quantum chemical level, using both the local density approximation (LDA) and the gradientcorrected approximation (GGA) using pseudopotentials (a form of ECP) and a double-ζ basis function. This approach should be considered as an acceptable choice if good-quality classical parameters are available for the conformational search, because a large number of independent structures need to be considered and quantum chemical potentials would be too demanding for a thorough sampling. The authors have found two populations for the Au28 NP, one formed by nearly degenerate amorphous clusters and the other by ordered NPs belonging to the T point group, with the T isomer lying ca. 60 kJ/mol above the disordered structure. The degree of chirality of each population was evaluated using the Hausdorff chirality measure, and both the disordered and the T isomer presented values larger than zero, with a slightly larger value for the T isomer. They also evaluated the effect of adding SCH3 thiol groups to the NP surface, and the general trend was either the induction of chirality in the achiral NPs or the increase of the chirality degree of the chiral NPs. The analyses of the optimized structures provided an indication that the thiol passivation tends to induce a disordered structure in the NP core, resulting in the elimination of planes of symmetry that would otherwise render the NP achiral. The Au28 NPs was later used to test a semianalytical model to compute CD spectra using a dipole moment approximation24 first proposed by DeVoe and Applequist.213 Unfortunately, the authors did not calculate the NPs CD spectra using quantum chemical methods nor compared their calculated spectra with experimental results; thus, we cannot assess the quality of the results. TD-DFT calculations for gold NPs protected with methyl thiol ligands148 enabled optimization of NPs geometry using the GGA exchange−correlation functional PBE and the LANL2DZ basis set with ECP for the gold atoms along with the 6-31G(d,p) basis for the ligands. The same level of theory was used in the TD-DFT calculations, which sampled the first 70 excited states of each NP. Having fixed the number of excited states, the authors obtained different energy ranges for the calculated UV−vis and CD spectra, depending on the size of the NP, from 1.5−3.5 eV for the smallest NP to 2.2−3.3 eV for the largest NP. The spectra included a Gaussian broadening of 0.1 eV to produce the line shapes from the TD-DFT calculated rotatory strengths and resulted in more complex spectra as compared to the UV−vis line shapes with the same broadening for most of the systems under investigation. The most important and general observation regarding these calculated CD spectra for the capped NPs is the presence of individual transitions with either negative or positive rotatory strength for any broadened band, since the overall sign of any CD band arises from the summation of many individual transitions. This is an important point for the analysis of experimental data dealing with changes in either the intensity or the algebraic sign of CD bands, which cannot be assigned to a single transition but must be regarded instead as the collective result of many changes in individual transitions, which might be shifted, damped, or even suppressed. In any case, multiple transitions must be evaluated to characterize a single band.

2.6. Chirality and Optical Activity of Individual Nanoparticles

Using the previous chapters as the foundation, let us review chiral NPs from the perspective of their materials composition. Besides shape, the latter represents the most important determinant of their chiroptical properties. 2.6.1. Metal Nanoparticles and Nanorods. Gold and other metallic NPs represent the best theoretically and experimentally studied chiral nanoscale system (see refs 17, 24, 70, 73, 74, 94, 103, 104, 106−108, 111, 112, 137, 144, 146, 151, 160, and 215−222). A good deal of information about them is given in Sections 2.2 and 3.5.2, where they are used as examples. In general, Au NPs grown in contact with chiral organic molecules, such as D- and L-isomers of diphenylalanine, are chiral.142 The bisignate CD spectra at the plasmonic band of Au NPs typically display opposite polarity for each enantiomer employed as surface ligands. Gold nanorods (NRs) modified with chiral molecules also exhibited a strong rotatory optical activity. Compared to Au NPs, the Au NRs displayed chiroptical bands which are, in general, stronger than those for NPs due to the greater strength of the transition moment. Having said that, we strongly recommend that researchers would perform their own calculations using a variety available software packages for specific NR (and their assemblies) because the the different types of chirality for individual NPs discussed in Sections 2.2.1 and Sections 2.2.2 will have different spectral band shapes for plasmonic and other parts of the spectrum. As described in eq 2, either the magnitude of the transition moments or their relative orientation will change depending on the subtle changes in the atomic and nanoscale geometries. Similarly to 8055

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Figure 6. (A) Circular dichroism spectra of chiral Ag NPs protected with three different enantiomeric thiol ligands: 1, captopril; 2, glutathione; 3, cysteine.227 (B) CD spectra of the poly(dA)−poly(dT) complexed with Ag+ (dotted traces) and with Ag NPs (red traces) and the DNA complexed with Ag NPs treated with DNase before (blue traces) and after (green traces) centrifugation.228 (C) CD spectra of each numbered silver nanocluster compound. Mirror image relationship in the CD signals between each numbered L-Pen-capped (green curve) and D-Pen-capped (red curve) silver nanoclusters.225 (D) CD spectra of Au25 (a) stabilized with R/S-BINAS.105 (E) CD spectra of lower-energy bridgeface isomers with different γ values. (F) SCH4 shows one σ plane and the Ag55 NP. (G) Lower-energy bridgeface isomers obtained from different bridge face and hollowface initial configurations.229 Panels A, B, C, D, and E, F were reproduced with permission from refs 227, 228, 225, 105, and 229, respectively. Copyright 2009, 2010, 2007, 2009, and 2013 American Chemical Society, respectively.

Type 2, is often difficult to make based on available experimental and computational data, although the Type 4 is most certainly present based on the high polarizability of gold. As a matter of fact, we consider this a rich field of research for the quantum chemical modeling of chiral nanostructures, which may provide a detailed picture of the regions within the metal core and the ligands layer that contribute to each band in the spectra, both in terms of spatial localization within the system and the kind of atomic orbitals involved. In another study, thiol-monolayer-protected gold NRs covered with two opposite enantiomers demonstrated chiroptical bands with a mirror image relationship in complete accord with eq 2.135 However, these Au NRs did not display a CD band at the plasmonic wavelengths but rather an enhanced CD band for the adsorbate. Au NRs carrying a layer of chiral mesoporous silica223 exhibited CD signals when D/L-cysteine were loaded onto the porous shells. The silica shell enabled the storage of chiral

amino acids comprising proteins, the CD bands in the UV part of the spectrum can be used to quantify the collective configurations of surface ligands around NPs and NRs that could be likened to α-helical components folded peptides.30 As a matter of fact, the α-helix is one of the best examples of the quantum physics ‘encapsulated’ in eq 2: every complete pitch around the helical axes simultaneously increases the overall electric dipole moment (arising from the 1−4 hydrogen bonds along the helix) and the charge rotation (which is the chiral fingerprint of any helical structure). An increased overall dipole is related to the transition electric dipole moment, whereas the increased number of rotating dipoles is related to the magnetic transition dipole moment (eq 2). CD bands observed in the spectral window characteristic for the stabilizer135 indicate Type 3 chirality, while chiroptical activity in NR plasmon bands is indicative of potentially other types.223 The distinction between the latter, namely Type 1 and 8056

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Figure 7. (A) CD spectra of silver NPs coated with chiral molecular ligand.234 (B) CD spectra of various solution samples. The small- and largeparticle samples were separated from the Ag−L-GS-bimane by centrifugation, and their concentration was estimated as half of that of the original (0.05 mM).231 (C) The CD spectra of Ag NPs grown directly on the DNA (black), Ag NPs grown without DNA (red), and Ag particles adsorbed to the DNA (blue).230 (D) CD spectra of peptide-coated silver nanoparticles (bold line) and Ag/peptide@SiO2 nanoparticles after 48 h of reaction (thin line).233 (E) Calculated CD signals for the complexes with the perpendicular (μ⃗ ⊥R⃗ ) and parallel (μ⃗ ∥R⃗ ) configurations. μ⃗ : The electric dipole of molecule. R⃗ : The vector connecting the NP and molecule centers. Curve 1 is the CD spectrum of the isolated molecule. (F) Calculated CD signals for the R-helix (black line) and for the NP−molecule complex (blue line).91 Panels A, C, D, and E, F were reproduced with permission from refs 234, 230, 233, and 91, respectively. Copyright 2012, 2006, 2011, and 2010 American Chemical Society, respectively. Panel B was reproduced with permission from ref 231. Copyright 2008 Wiley-VCH.

molecules for enhancement of the chiroptical activity of amino acid in the vis and near-IR regions. The metal-silica composites not only had strong plasmonic CD activity but also showed a clear chiral discrimination using the SERS stretching band at 730 cm−1. It was calculated using electromagnetic theory by Fan and Govorov that individual chiral NPs can exhibit a chiroptical activity when they have a shape of twisters, antitwisters, asymmetric pyramids, and chiral tetrahedron-like structures.92 Experimentally, metal helices with similar dimensions were prepared by stepwise glancing angle deposition; they revealed chiroptical bands in the part of the spectrum corresponding to plasmons that partially coincides with theoretical predictions made by Hou et al.224 and Mark et al.98224,98

Silver NPs stabilized by enantiomeric ligands also showed high chiroptical activity.221,225,226 The surface ligands included captopril, glutathione, and mixtures of captopril and glutathione (Figure 6A).227 Both positive and negative CD bands in the plasmonic part of the spectrum were observed that changed signs for stabilizer of opposite handedness (Figure 6B),228 but one should be cautious to attribute this to concrete electronic transitions at the moment. CD bands in silver NPs coated with D/L-penicillamine were rationalized as metal-based electronic transitions (Figure 6C),225 which is similar to the rationale for chiroptical activity identified for Au25 clusters attributed to the metal-based electronic transitions.105 Contemplating different types of chirality, highly degenerated molecule-like electronic states of Ag55SCH3 and Au55SCH3 may 8057

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example, Markovich and co-workers reported larger Cotton effects at the plasmon frequency from silver NPs (g ∼ 0.001) than for other methods.228,230 It was assumed that the atomic structure of the chiral metal core is influenced by DNA characteristic of Type 1 chirality. Silver NPs were also grown on closed supercoiled dsDNA and produced alterations in the plasmid conformation235 and chiral NP cores. When Ag NPs are grown in contact with chiral templates exemplified by insulin helical fibrils with outer diameters of 4−6 nm, lengths of several microns, and a helical pitch of 65 nm,236 the CD displayed a distinct chiroptical band in the plasmonic region. Enantiomeric silver-coordinated compound after mild reduction formed chiral fibers with a diameter of 50−60 nm and lengths of several micrometers.237 Organogel from NPs with a diameter of 10−20 nm showed intense circular dichroism with an anisotropy factor (g-factor) ∼0.02. Overall, further experimental evidence is necessary to determine the molecular geometry of these particles, which will be helpful to set up accurate geometrical models. In particular, it will be vital to elucidate whether chirality is localized on the surface, ligand shell, or the metallic core. The chiral memory effect indicative of surface distortions are less likely in metal clusters and chirality of metal cores followed by the evaluation of CD or ORD spectra at plasmon frequencies, are helpful in establishing Type 1 and Type 2 of chirality in metal clusters. 2.6.2. Semiconductor Nanoparticles. The chirality of semiconductor NPs can be attributed to the same structural effects as those in metallic clusters, namely, (i) chiral distortion of surface atoms (Type 2) (Figure 8A),75 (ii) chirality of organic shell and inorganic core surface (Types 2 and 3) (Figure 8B),19 and (iii) intrinsic chirality from atom packing (type 1) (Figure 8C).168 The first demonstration of the chiroptical activity in

or may not be chiral depending on the adsorption site and orientation of the molecule, as indicated by time-perturbed DFT calculations (Figure 6E−G).229 It was found that optical activity is stronger when the thiol is adsorbed between two atoms of different coordination number. The single ligand is more effective in turning the NP chiral for Au as compared to Ag, which may become chiral or not depending on the orientation of the thiol molecule. As a matter of fact, these NPs became chiral due to two different mechanisms: the metallic core of the Au NPs actually became chiral, whereas the chirality of Ag NPs arose from the misalignment between the atomic planes within the metallic core and the plane formed by the ligand. According to our classification, Au NPs belong to Type 1 chirality, which is not surprising if we consider that even bare Au NPs may belong to this type.126,127 Ag NPs should be classified as Type 3, since the structural feature responsible for the overall chirality of the systems is the relative orientation of the single ligand molecule. One word of caution is necessary here: singly coordinated ligands have a large degree of rotational freedom and then they are expected to become randomized by the thermal agitation even at room temperature. Besides, a single ligand per NP would results in dispersion that would be easy to aggregate/assemble, and therefore would exhibit primarily the chiroptical properties of higher order systems. Larger silver NPs has been coated with different chiral molecules, including DNA,230 L-GS-bimane,231 cysteine and its derivatives,155,232 glutathione and penicillamine,155 and peptides.233 CD spectra varied tremendously between particles with different stabilizer shells, which indicates some contributions of several different types of chirality including Types 2 and 3 chirality being responsible for optical properties, which could be due to the collective chiral packing. As such, glutathione and penicillamine displayed CD bands, while NP stabilized by lysine or glutamine did not.155 Markovich and co-workers reported that larger silver NPs coated with chiral molecules exhibited chiroptical activity that consisted of a molecular CD band and a plasmon CD band (Figure 7A).234 Similarly, it was also demonstrated that the attachment of L-GS-bimane to the surfaces of Ag NPs resulted in enhancement of the CD spectra, which was explained by the plasmon-induced resonant absorption enhancement arising from the larger particles (Figure 7B).231 The chirality of the silver NPs modified with cysteine and its derivatives at various concentrations and pH values was also shown to generate characteristic CD bands. Glutamine and cysteine failed to produce plasmonic CD in other studies that only showed chiroptical activity in the spectral range of the adsorbate that can be viewed as indication that Type 3 chirality does not necessarily begets Types 1 and 2 chirality.155,232 NP synthesis in the presence of Ag NP poly(dG)−poly(dC) double-stranded (ds) DNA resulted in NPs with chiroptical CD bands at plasmon frequency (Figure 7C).230 Peptide-stabilized NPs can be coated with a silica shell that protects the NPs and renders them more biocompatible (Figure 7D).233 The mechanism of chiroptical activity through a dipolar interaction between the plasmon and the molecular dipole of a chiral chromophore on the NP surface was also discussed.91 The dipolar theory predicts a substantial chiroptical activity at the plasmon wavelength of silver NPs (Figure 7E,F). The synthesis of NPs using DNA,228,230,235 peptides,236 and biomolecular fibrils237 was investigated by several groups. For

Figure 8. (A) Top and side views of the (1010) face of the optimized cluster model of CdS. The stick representation with a PenH−Pen− Pen bonding pattern along one face highlighted in the side view. The side views of the proposed bonding of D-Pento on the (1010) surface of wurtzite (Cd, brown; S, yellow; C, gray; O, red; N, blue; H, white, topmost atoms).75 (B) Ideal tetrahedron of CdTe NPs used in calculations (left) and model of the chiral tetrahedral apex (right): Cd, green; Te, brown; O, red; S, cyan.19 (C) Schematic illustration of the opposite spirals of atoms with a fraction of one spiral reconstructed inside the frame of the hexagonal unit cell.168 Panels A and B were reproduced with permission from refs 75 and 19, respectively. Copyright 2008 and 2010 American Chemical Society. Panel C was reproduced with permission from ref 168. Copyright 2013 WileyVCH. 8058

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Figure 9. (A) CD spectra of penicillamine-stabilized CdS NPs and the corresponding TEM image.238 (B) CD spectra of D- (blue), L- (red), and racPen (green)-stabilized CdSe NPs and the corresponding TEM image.239 (C) (left) Schematic presentation of the D-penicillamine-stabilized CdS NP as presented in the original publication18 and (right) CD spectra of the D- (blue), L- (green), and rac-Pen (red)-stabilized CdS NPs.18 (D) LCysteine-stabilized CdTe NPs (red) and D-cystine-stabilized CdTe NPs (black) after 16 h of synthesis.19 Inset: Model of stable chiral pairs of cysteine and CdTe (D-Cys, R-CdTe). Panels A, B, and C were reproduced with permission from refs 238, 239, and, 18, respectively. Copyright 2010, 2010, and 2007 The Royal Society of Chemistry. Panel D was reproduced with permission from ref 19. Copyright 2010 American Chemical Society.

Figure 10. (A) Ligand exchange procedure of FePd NP from oleic acid/oleylamine to chiral BINAP. The dense core is Fe-rich and the pale shell is Pt-rich. (B) TEM image, size distribution diagram, and electron diffraction pattern of FePd NPs stabilized by (S)-BINAP. (C) Circular dichroism (CD) spectra of FePd NPs stabilized by (a) (R)-BINAP and (b) (S)-BINAP in CHCl3.242 Reproduced with permission from ref 242. Copyright 2009 The Royal Society of Chemistry.

semiconductor NPs and subsequently tetrapods was reported by Gun’ko and co-workers (Figure 9A).18,238 In all of these studies, CD bands were observed in the excitonic spectral region; a shift to the red wavelengths was observed when the CdS core was replaced with CdSe (Figure 9B).239 Considering the emissive properties of these NPs, the fluorescence of the NPs primarily originated from defect states rather than the NP excitonic states. The authors concluded that the optical activity

resulted from a chiral distortion of surface atoms; this conclusion was later strengthened by ab initio calculations of the surface structure of the NPs (Figure 9C).18 In the study by Kotov and co-workers, the CD bands of chiral CdTe NPs were significantly blue-shifted compared to band-edge transitions and were attributed to the surface states (Figure 9D).19 Tang and co-workers observed that broad CD absorption in the visible-light region of chiral NPs stabilized by chiral GSH 8059

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Table 1. Geometrical Parameters for Chiral Nanowires nanowires types metal nanowires

semiconductor nanowires

ceramic nanohelixes

nanowires compositions

length

witdth (nm)

pitch (nm)

(AuAg)@Pd double helices245 suspended Au nanowires246 AuAg nanowires216 Au nanohelices98 lead sulfide nanowires resembling pine trees256 cadmium sulfide (CdS)257 ZnO helixes78 ZnO nanohelices79 SnO2 spirals silica helix258 BaCO3 helical fibers254 ZnGa2O4 nanowires259

several micrometers 6 nm 50−150 nm 100 nm several hundreds of micrometers 2000 nm several hundreds of micrometers 100 μm several hundreds of micrometers several hundreds of nanometers several millimeters several micrometers

3.5 0.6 2−5 50 40−350 35−100 500−800 100−500 10 000−50 000 18−64 200−500 80

47 helical angle 60° 4−5 34 16 000−220 000 40−50 150−350 500−2500 20 000 13−27 nonconstant helix pitch 150−200

thought it would be benefitial to briefly address relevant polymeric nanostructures with close relation to the NPs and NRs. Most current studies on chiral organic NPs involve organic polymers and biological macromolecules. A type of organic NP was synthesized by the complexation of divalent metals (i.e., Ca2+, Ba2+) and poly(phenylacetylene) polymers bearing α-methoxyphenylacetic acid (MPA) pendants with cisisomer.243 The resulting helical polymer−metal complex NPs had two interesting properties: (1) their diameter was tunable by changing the polymer/metal ion ratio, and (2) the handedness of the helix both on the surface and in the interior was switchable. The solvent, the metal ion, and the helicity of the polymer in the aggregation were cofactors during the synthesis that tailored the optical activity response. The capability of these chiral NPs to encapsulate various materials opens the door to interesting hybrid supramolecular assemblies, especially in the case of composites formed by the inclusion of chiral NPs. The diameter of the polymeric NPs is larger than 100 nm, and this size is not amenable to quantum chemical modeling, even if semiempirical, parametrized models are employed. Nonetheless, classical coarse-grained models might be able to simulate the helical structures and provide insights into the solvent and metal ions effects.

and Cys can be manipulated through modulation of their size.120 The dependence of CD spectrum intensities for different materials and differently sized NPs was also studied.240 Nakashima et al. have demonstrated related chiral effects, such as preservation of chiroptical activity in CdTe NPs, even when the chiral ligand was replaced by an achiral ligand (Type 2),48 and CdS NPs synthesized with a ferritin template gave rise to circularly polarized emission.241 Theoretical calculations based on the model of chiral ligand protected NPs predicted that broad CD absorption peaks resulted from Coulomb dipole− dipole interactions between chiral molecules and NPs.91 Additionally, α-HgS, selenium, and tellurium were reported to have an intrinsically chiral crystal lattice that can be affected by chiral molecules.122,168 The synthesis of α-HgS NPs with a large enantiomeric excess using chiral surfactant molecules (penicillamine) direct the formation of a chiral crystal phase.168 Similarly, colloidal tellurium and selenium nanostructures with lattice and shape chirality were also explored using thiolated chiral biomolecules (glutathione, penicillamine, and cysteine).122 The chiral molecules can induce enantioselective nucleation and growth, and finally, the NPs crystallized with a chiral lattice conformation (Type 1). Overall, different models of chirality were suggested for semiconductor NPs but they are based on limited experimental results and need to be verified by further experiments and calculations followinf the methods described in Section 2.5. The relations between the type of the surface coating or stabiliziers and CD bands are informative and intriguing; however, the intensity of chiroptical bands for them is typically smaller than for metal nanostructures. 2.6.3. Magnetic Nanoparticles. Studies on chiral magnetic NPs are rare; however, their magnetic properties might provide new insight into the chiral origin of NPs and can be useful in homogeneous catalysis. The magnetic field should interact with magnetic moments of NP. The magnetic state can affect the chiral state of molecules, which may give rise to interesting phenomena. Chiral magnetic FePd NPs have been made using the ligand exchange reaction starting from iron decomposition of carbonyl iron [Fe(CO)5 ] and then subsequent reduction of palladium acetylacetonate [Pd(acac)2] in oleic acid and oleylamine to finally form a FexOy-rich core and Pd-rich shell (Figure 10A,B).242 The resulting NPs were modified with chiral 2,20-bis(diphenylphosphino)-1,10-binaphthene (BINAP) and showed optical activity with a typical Cotton effect (Figure 10C).242 2.6.4. Polymeric Nanoparticles. Although going slightly beyond the boundaries of inorganic nanostructures, would

2.7. Chiral Nanowires

Inorganic nanowires (NWs) represent a special case among chiral nanostructures because their chirality can manifest in a distinct helical geometry that cannot develop in NPs. Some optical, electrical, mechanical, and biological properties arising from helical geometries are different than those for NPs and, therefore, are discussed separately. Helical NWs were obtained for a surprisingly broad range of materials (Table 1). Examples of such nanostructures include semiconductors (e.g., CdS, PbSe),244 metals (e.g., Au, Ag, Pd),245,246 ceramics (e.g., ZnO, SnO2),247,248 mesoporous ceramics (e.g., silica), 249 −252 and carbonates (e.g., BaCO3).253,254 The dimensions of NWs range from hundreds of nanometers to several micrometers.255 2.7.1. Metal Nanowires. Generally, top-down methods, such as lithography, have been well-developed for the preparation of chiral structures,25,71 in which the enantioselective preparation is achievable for many structures. Preparation of chiral metal NWs using bottom-up methods is difficult but possible.245,246 The exact control of the morphology (length, width, pitch, etc.) is difficult for the ligand regulated seed growth process. Furthermore, realization of the same process with enantioselectivity adds another degree of difficulty. Hence, most of the helical NWs were produced as racemic 8060

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Figure 11. (A) The glancing-angle physical vapor deposition processes that combines with nanoseeds. (B) Model two-turn gold nanohelix showing the significant dimensions. (C) Normalized CD spectra of left-handed and right-handed helices. (D) Simulated CD spectra for a model based on dimensions taken from TEM images. (E) CD spectra of nanohelices of different metal compositions in suspension.98 (F) Schematics illustrating the formation of a double helix by growing a metal layer on AuAg alloy NW. (G) TEM image of the as synthesized AuAg NWs.245 SEM images of (AuAg)@Pd double helices of different chirality: (H) right-handed and (I) left-handed. Panels A−E were reproduced with permission from ref 98. Copyright 2013 Macmillan Publishers Ltd. Panels F−I were reproduced with permission from ref 245. Copyright 2011 American Chemical Society.

mixtures. Thanks to the wet chemistry synthesis216,245 and electron beam techniques,246 the fabrications of several types of chiral metal NWs have been achieved. The gold NWs made by Kondo and co-workers in an ultrahigh vacuum246 consisted of coaxial tubes. Each gold tube consisted of rows of atoms organized in a helical pattern. The difference between the number of helical atom rows in the outer and inner shells was seven, resulting in magic shell-closing numbers that facilitated the preparation. Jose-Yacaman and co-workers subsequently demonstrated the formation of helical NWs by the packing of interpenetrating icosahedral and decahedral units.216 These NWs, formed by the reaction of a mixture of metal salts (Au and Ag) in the presence of oleylamine, were obtained when

Ag/Au was 3:1. The experimental results showed that the icosahedral NWs have a high similarity to simulated electron micrographs of structures formed by two or three Boerdijk− Coxeter−Bernal (BCB) helices roped on a single structure. For the decahedral wires, simulations using a model of adjacent decahedrons matched the experimental structures.216 More recently, low-temperature shadow deposition with nanoscale patterning has resulted in the preparation of nanocolloids with helices, sized down to 20 nm, and a wide choice of materials, including Au, Au:Cu, and Cu (Figure 11A, B).98 As a top-down method, it gave helices enantioselectively with controlled handedness and pitch. The computed CD for gold helices agreed well with experimental results (Figure 11C, 8061

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Figure 12. (A) Chemical structure of the Dendron rodcoil (DRC) molecules and a molecular graphic model of a twisted ribbon in ethyl methacrylate. Nucleation and growth on one side of the twisted ribbons (blue) lead to single helices of CdS (yellow), while nucleation and growth on both sides of the ribbon lead to double helices. (B) A mature CdS single helix. (C) TEM micrograph of CdS double helices.80 (D) Scheme of a twisted nanoribbon composed of parallel, longitudinal stripes and the top view and cross-sectional view of the molecular model. (E−G) TEM and SEM images of ZnS semiconductor helical nanotubes.260 Panels A−C were reproduced with permission from ref 80. Copyright 2005 Wiley-VCH. Panels D−G were reproduced with permission from ref 260. Copyright 2009 American Chemical Society.

both right-handed and left-handed helices that had been used for growth of CdS helices (Figure 12A).80,257 The inorganic helices had a pitch of 40−60 nm (Figure 12B,C); however, this process is not enantioselective. Another route to form welldefined right-handed helical nanoribbons in metal−cholate was used for ZnS (Figure 12D−G).260 This process is enantioselective (right-handed) due to the presence of the chiral molecule of cholate. The incorporation of metal ions can endow versatile functionalities and merits to other nanohelices such as SiO2. Metal oxide helices, nanobelts, and rings are also known but it is not easy to achieve enantioselective fabrication.78,79,248,261 The growth of ZnO nanobelts was obtained through vapor− solid growth with polarized ±(0001) facets. Due to the positive and negative ionic charges on the zinc- and oxygen-terminated ±(0001) surfaces, a spontaneous polarization is induced across the nanobelt thickness. Right-handed helical nanostructures and nanorings are presumed to form by rolling up single-crystal nanobelts, which are attributed to minimizing the total energy contributed by spontaneous polarization and elasticity.78 However, enantioselective preparation of these ZnO structures was difficult. The formation of uniform nanohelices due to rigid lattice rotation or twisting was also reported.79 The latter were made of two types of alternating and periodically distributed long crystal strips, which were oriented with their axes perpendicular to each other. The nanohelix was terminated by transforming into a single-crystal nanobelt dominated by nonpolar (0110) surfaces. A similar polar-surface-induced folding mechanism was suggested to be responsible for the formation of rutile-structured SnO2 spirals.247 Oriented helical

D). The CD spectra of the left- and right-handed nanohelices showed the distinct Cotton effect corresponding to plasmonic chiral NPs. Changes in material composition allowed tuning of the chiroptical response of nanohelices across the visible spectrum. The Ag:Cu (65:25), Au, and Cu nanohelices had the same CD shape and stepwise shift to the red part of the spectrum. The CD response for different compositions showed tunable chiroptical properties (Figure 11E). This technology has potential for the preparation of anisotropic nanocolloids with magnetic, semiconducting, metallic, and insulating materials within the same structure. Upon growth of a thin metal (Pd, Pt, or Au) layer, the Au− Ag alloy NW winds around itself to give a metallic double helix (Figure 11F).245 It was found that the rate of metal deposition was critical to induce the winding of NWs. The helical shape probably originated from the chirality within the Au−Ag alloy NWs, which possibly have a BCB-type twisted lattice. A lefthanded and right-handed double helix was observed (Figure 11G−I). 2.7.2. Semiconductor Helicoids. Many synthesis methods for helical or twisted semiconductor materials were performed by a racemic process. For example, PbS “pine trees” with helically rotating epitaxial branch nanowires were synthesized by chemical vapor deposition, in which right- or left-handed rotating trees have roughly equal probability of occurrence, with an experimental ee ratio of 107:126.256 Biomolecular templates are often used to shape nanostructures from inorganic materials, and this method was used to overcome the difficulties of enantioselectivity, while assembled templates of polymers for synthesis of helical nanostructures displayed 8062

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Figure 13. (A) Schematic drawing illustrating the formation of helical mesostructured rods from hexagonally arrayed, straight, rodlike micelles of equal length to a helical rod with two rounded ends and also the hexagonal cross section viewed parallel to the length direction. (B) TEM image of helical silica.266 (C) Schematic drawing of a structural model of the chiral mesoporous material, its cross section, and one of the chiral channels in the material. (D) SEM image of chiral mesoporous silica.267 (E) Transformation from a straight hexagonal fiber to a dual-axis fiber through two twist operations, which is accompanied by a degradation of symmetry. (F) SEM image and simulated 3D model, TEM image, and simulated TEM image of a dual-axis nanofiber.250 (G) Scanning electron micrographs of the Si microtubes prepared by heating the zintl compound NaSi showing a long view of its left-handed double-helical structure.273 Panels A and B were reproduced with permission from ref 266. Copyright 2006 American Chemical Society. Panels C and D were reproduced with permission from ref 267. Copyright 2004 Macmillan Publishers Ltd. Panels E, F and G were reproduced with permission from ref 250 and 273, respectively. Copyright 2006 and 2010 Wiley-VCH.

ZnO columns are also possible.261 Metal oxide helical structures have not been realized by enantioselective synthesis so far but still are of great interest. The semiconductor helical nanostructures provide target materials for understanding piezoelectricity and polarization-induced ferroelectricity at the nanoscale. 2.7.3. Ceramic Nanohelices. The formation mechanisms of ceramic nanohelices can be traced to the general advantages of the helical geometries for fristrated systems.262−264 However, the fabrication of ceramic helices was mostly not an enantioselective process, though single nanowires were chiral.258 Helical NWs can be made in confined environments with different morphologies.258 Confined growth of silica mesostructures within cylindrical nanochannels with varying diameters can lead to chirality,258 in which the fabrication

process is also not enantioselective. The double-helical geometries of silica spontaneously formed inside individual alumina nanochannels. The transition from a coiled cylindrical to a spherical cagelike geometry was observed in the mesopore morphology as confinement tightens. The confined syntheses produced mesostructures that can be used as a template for fabricating highly ordered NWs.258 The free-standing mesoporous materials with chiral cavities could potentially be used for enantioselective separation. Many enantioselective processes have been explored for fabrication of helical NWs. BaCO3 nanofibers with doublestranded and cylindrical helical geometry can be formed spontaneously on an organosilane-coated substrate via crystallization and controlled by a phosphonated block copolymer.253 This was an alternative method previously developed by Antonietti and co-workers, in which helices of 8063

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Figure 14. (A) The absolute configurations of the fullerene spheroids (fC and fA; f = fullerene, C = clockwise, A = anticlockwise) and the corresponding CD spectra of fullerene enantiomers.278 (B) Atomic models of the four possible isomers of the fullerene C84 with D2 symmetry, the calculated CD spectrum of isomer 22 of D2-C84 using DFT (left bottom), and the calculated CD spectrum of a mixture composed with 50% of isomer 22 and 50% of isomers 5 and 21 in equal parts.276 (C) The C60-fullerene bisadduct (R,R,f,sA)-[CD(+)280] and the corresponding calculated and experimental CD spectra.280 Panels A and B were reproduced with permission from refs 278 and 276, respectively. Copyright 1999 and 2010 Wiley-VCH. Panel C was reproduced with permission from ref 280. Copyright 2011 American Chemical Society.

processes could help to probe the formation mechanism of inorganic helices to reveal the chiral law of natural construction. Porous silica nanostructures with helical pore channels or helical shape are becoming more common.265 Chiral channels can form in the presence of achiral surfactants due to interfacial interactions, in which the reduction in surface free energy is the driving force for the spontaneous formation of the spiral morphology (Figure 13A,B).266 However, the ratio of righthanded and left-handed helices is 1.1, which means that ee is quite small if any. Chiral surfactants can also be used as templates (Figure 13C,D), and the formation of the chiral structure consisted of chiral anionic surfactants and silicates.267−270 However, the helical mesostructured silica could be obtained using achiral cationic surfactants, indicating that the chiral template molecule

achiral BaCO3 nanocrystals were synthesized with double hydrophilic block copolymers (DHBC), suggesting that a helical alignment can be induced by racemic polymers through selective adsorption on the (110) face of nanocrystals.254 The synthesis of other helical nanostructures has remained limited to ZnO, Si, and SiC materials. Ahn and co-workers synthesized ZnGa2O4/ZnSe nanovines and ZnGa2O4 nanosprings by thermal evaporation using ZnSe NWs. Both the nanovines and nanosprings had a common structure, in which the growth direction of the helical ZnGa2O4NW zig-zagged with the same angle.259 A single crystalline CrSi2 hexagonal nanoweb has been successfully synthesized on silicon substrates in a horizontal tube furnace via the vapor transport method.186 Through investigation of different helical NWs, various fabrication 8064

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Figure 15. (A, B) Schematic representation of two SWNTs with nearly identical diameters but different chiral indices.281 (C) Simulated CD of Pand M-(6,4) (a) and experimental data of M-(6,4) (b) for comparison.283 (D) A DNA barrel on an (8,4) nanotube formed by rolling up a 2D DNA sheet composed of two hydrogenbonded antiparallel ATTTATTTATTT strands. Color coding: orange, thymine; green, adenine; yellow ribbons, backbones.282 (E) Scheme of the helical cage forms of carbon that have the lowest cohesive energy per atom (only two pitch lengths are shown): (a) helix C360, (b) helix C1080, and (c) helix C540. The C5 and C7 rings (shaded) appear in the outer and inner ridgelines, respectively, amid a background of the C6 rings. (F) TEM image of multiwalled helically coiled carbon nanotubes.287 (G) Levorotatory and (H) dextrorotatory CNTarray double helices.288 Panels B and D were reproduced with permission from refs 281 and 282, respectively. Copyright 2008 and 2009 Macmillan Publishers Ltd. Panels C and E, F were reproduced with permission from refs 283 and 287, respectively. Copyright 2010 and 2003 American Chemical Society. Panels G and H were reproduced with permission from ref 288.Copyright 2010 Wiley-VCH.

might not be the sole driving force.251 For example, nanofibers possess ropelike twisted hexagonal morphology, and a helical mesoporous channel was prepared using the achiral cationic surfactant cetyltrimethylammonium bromide (CTAB). These twisted hexagonal nanofibers could further curve spirally to form a second-level helical morphology.271 The silica nanofibers may have two twist axes: one lies outside the nanofiber, and the other one lies in the center of the nanofiber (Figure 13E,F).250 Such dual-axis silica nanofibers do not wind regularly around their primary twist axes. More importantly, the simple and purely interfacial interaction mechanism was suggested to explain the spontaneous formation of helical mesostructures. It was found that the synthesis of helical mesoporous silica by achiral cationic surfactants was aided by small molecular additives.250,271,272 Double helices of silicon tubes can also be prepared using the zintl compound NaSi as the starting material (Figure 13G).273 In general, preparation of helical structures with relatively rigid inorganic materials may require different design criteria, synthesis technology, and stabilizing mechanisms. The inorganic helix can be important and highly desired for many reasons: (1) the synthesis of various inorganic helices has been achieved; however, the formation mechanism for each material is uncertain. An understanding of the formation mechanism of inorganic helices may provide new opportunities to unravel the rule of natural construction. (2) The micrometer scale of inorganic helices is also expected to endow strong physical and

optical properties that will be fascinating but are rarely reported now. 2.8. Carbon Nanostructures

The list of carbon nanostructures is extensive. Many of these carbon nanostructures are intrinsically chiral with mostly Type 1 chirality originating from the special arrangements of carbon atoms in the inorganic core. 2.8.1. Fullerenes. After the discovery of fullerene C60,274 a search for new allotropic forms of carbon was conducted for the synthesis and isolation of other fullerenes:275 C76, C84, C90, and C94. The separation of the two constitutional isomers of C76 was possible,275 which indicated that one of these isomers was chiral with D2 symmetry. Subsequently, C76 and C78 were separated and their optical activity was observed by measuring CD as well as by semiempirical calculations, confirming the existence of chirality for these carbon nanostructures.276 Another interesting fullerene is C84, which has 24 theoretical possible isomers, and 10 of them are chiral.277 Among the chiral constitutional isomers of C84, those with D2 symmetry are the most stable. The reported CD spectra region was located at 300−750 nm, while the CD band exhibited multiple bands, most of which showed broad peak properties (Figure 14A).278 The separation and measurement of the optical activity of D2C 84 fullerenes were obtained independently by two groups.278,279 After that, the theoretical modeling was performed and found that the calculated CD spectrum of one of several possible isomers fitted the best with the experimental 8065

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Figure 16. (A) Schematics of Au NRs dimers made with SCA, SCI, and DNA. TEM images for dimers made by SCA (B), SCI (C), and DNA (D). (E) The dark-field scattering colored image for a single dimer. (F) The measured CD spectra for a single dimer. (G, H) TEM tomography images of NR dimer by SCA. The CD spectra of NR assemblies and their temporal/concentration profiles triggered by (I) DNA, (J) SCI, (K) SCA.39 (L) Schematics of Au NR dimer with an interparticle separation f·d taken from center-to-center and the relative orientation specified by φ = 10° (dihedral angle), α1 = 10°, and α2 = 20°. Coupled dipole calculations of the CD (M) spectrum for the dimer represented extinction, absorption, and scattering (N) in panel L.180 Reconfigurable 3D plasmonic metamolecules between the left-handed, relaxed, and right-handed states (O) and the corresponding CD spectra measured in the first cycle (P).7 Panels A−K and O, P were reproduced with permission from refs 39 and 7, respectively. Copyright 2013 and 2014 Macmillan Publishers Ltd. Panels L−N were reproduced with permission from ref 180. Copyright 2011 American Chemical Society.

CD of D2-C84 fullerenes (Figure 14B).276 TD-DFT and DFT are powerful tools in the calculation of fullerene chirality. TDDFT calculations have been used to investigate UV−vis and CD spectra of the C60-fullerene bis-adduct (R,R,f,sA)-[CD(+)280]; a good agreement between the experimental and the simulated CD spectra was achieved (Figure 14C).280 The CD spectra of fullerene generally displayed multiple bands in the full region of 300−750 nm, while the CD spectra of chiral semiconductor also have multiple bands but in the region of

200−550 nm due to their absorption properties.240 At the same time, the CD peak can be sharper than that of fullerene. The CD spectra for chiral metal NPs were quite different those of fullerene and semiconductors. The CD spectra for chiral metal NPs generally only exhibited plasmonic bands and UV region bands without other additional bands.223,231 2.8.2. Carbon Nanotubes. Tremendous progress has been made toward the synthesis of carbon single-wall nanotubes (SWNTs).281 However, most of the methods used for synthesis 8066

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excess, synthesis can be difficult. The HCNTs structure is formed on the basis of C7 and C5 carbon ring defects in the C6 carbon. The enantioselective synthesis of helical carbon nanostructures can stimulate the development of highfrequency electronics devices, chiral field sensors, and chiral templates for metamaterials.

result in SWNTs mixtures that have a broad range of diameters and chirality. SWNTs with the desired properties can be achieved through separation and selection; however, these procedures for enantioselective synthesis can be challenging.282 SWNTs are chiral objects that resemble the wrapping of a graphene sheet to form a cylinder, which can be rolled up in different ways, and the lattice along the nanotube axis forms a helical twist (Figure 15A,B).281 The two mirror-related forms of chiral SWNTs, right-handed (P-SWNTs) and left-handed (MSWNTs), depend on which way the graphene sheet is rolled up; however, they are usually mixtures. Recently, CD spectra of different nanotubes have been calculated and compared with experimental findings, and good agreement was seen with M(6,4) from experiments (Figure 15C), which displayed multibanded optical activity in the UV−vis spectra region (250−800 nm).283 These results provide theoretical support for the interpretation of optical activity in SWNTs, which is useful for their characterization and configurational assignment and is fundamental for the functionalization of these nanostructures.276 To sort mirror-related forms of chiral carbon nanotubes several strategies have been devised.82,284 Perhaps the most successful approach that gives high enantiomeric excess, involves the wrapping of SWNTs with chiral molecules.285 The SWNTs are wrapped with chiral surfactants, such as DNA,282,284 flavin mononucleotide,83 porphyrins,286 or sodium cholate,285 resulting in stable dispersed solutions. The flavin mononucleotide wraps around single-walled carbon nanotubes in a helical pattern due to the cooperative hydrogen bonding between adjacent flavin moieties, which imparts efficient chirality selection.83 The high affinity of the flavin mononucleotide for (8,6)-SWNTs resulted in enantiomer-enriched nanotubes with an ee of 85%. A more efficient purification method was proposed, based on short DNA sequences, which recognizes and enables chromatographic purification of a particular nanotube species from the synthetic mixture.282 The DNA recognition method wrapped a nanotube with a periodic purine−pyrimidine pattern that can selectively fold on it to form a well-ordered three-dimensional barrel (Figure 15D). A potential application of chiral SWNTs could be chiral separation of biomolecules. 2.8.3. Coiled Carbon Nanotubes. The presence of energetically and thermodynamically stable helically coiled CNTs (HCNTs) was predicted by physicists on the basis of molecular-dynamics simulations.289 Later, for the first time, Amelinckx et al. reported the experimental observation of HCNTs obtained with cobalt distributed on a silica support (catalyst) and acetylene as the carbon source.290 The helically coiled CNTs are usually synthesized using catalyst, such as Co, Fe, or Ni;290 Fe2(SO4)3/SnCl2 or FeCl3/SnCl2;228 or Co−silica or Fe−silica.287 After confirmation of the presence of HCNTs, researchers then tried to identify effective ways of improving the synthesis yield. Hou et al. obtained HCNTs as the main products in large quantities by copyrolysis of Fe(CO)5 as the floating catalyst precursor and pyridine or toluene as the carbon source (Figure 15E,F).287 Since then, significant effort has recently been made to synthesize single-helical carbon nanofibers (CNFs)291−293 and nanotubes.290,294,295 For example, Zhang et al. reported interesting carbon nanotube array double helices on layered double hydroxide (LDH) plates as a node which served as 2D lamellar substrates (Figure 15G,H).288 However, enantioselective synthesis of helical CNTs still remains challenging; even for one enantiomer

3. CHIRAL NANOSCALE ASSEMBLIES Ability of NPs to spontaneously assembly into superstructures of complex geometries is well-known and is being already technologically utilized although not yet taking advantage of their asymmetries. There are distinct fundamental incentives for chiroplasmonic, chiroexcitonic and other “chiral” technologies based on the nanoscale assemlies.296,297 One of them is that even if individual building blocks do not reveal chirality and chiroptical activity, the higher order superstructures can.1,9,298−300 A variety of methods were devised to construct them via the self-assembly from a variety of building blocks.301 The self-assembly process may take place in colloidal dispersions or on the interfaces. According to the Nicolis−Prigogine theory, the only restriction to the system to undergo the self-organization process is that the structural units are mobile.255,302,303 Chirality at the level of NP assemblies originates from chiral geometries of NPs assembled into particular patterns. Therefore, the types of chirality for nanoscale assemblies differ from those for individual NPs. The geometry of these patterns provides the convenient classification protocol and serves as method to organize these chiral systems into subgroups. When nanoscale assemblies are made from spherical and identical (in the first order of approximation) individual NPs, the classification into chiral symmetry groups applicable to chiral molecules are also valid with exception that the symmetric relations between atoms are replaced to those for individual NPs. 3.1. Twisted Nanorod Pairs

Arguably the simplest chiral system of NPs is formed by a scissor-like dimer of NRs separated by a certain distance, d. The absence of a symmetry plane is ensured by a dihedral angle φ different from 0° and 90° (Figure 16L−N).180 Nanoscale assemblies with such geometry were made and computationally described for twisted metal NRs. Simplicity of such geometries enables better understanding of chiral plasmonic effects, facilitate theoretical description/simulation of their optical properties, and stimulate the practical applications of chiroplasmonics.9,12,235,304,305 Gold NRs self-assembled sideby-side as twisted pairs and “ladders” exhibited strong chiroptical activity even when the dihedral angle between the NRs is relatively small, i.e. between 9 and 13 degrees (Figure 16A−D).39 Twisting of NRs with respect to each other, forming a scissor-like structure, is thermodynamically favorable and originates from the balance of attractive and repulsive forces. Similarly to many biological assemblies from charged rod-like units, twisting originates from the minimization of electrostatic repulsion that decreases as the dihedral angle increases from 0 to 90 degrees. Two possible enantiomeric conformations with positive and negative dihedral angles were obtained with different assembly triggers, sodium citrate (SCI) or sodium carbonate (SCA), and DNA. The scissor-like geometry of NR pairs was confirmed by single-particle spectroscopy and TEM tomography (Figure 16E−H). Furthermore, the twisted NR pairs can switch the sign of their dihedral angle from positive to negative after the assembly 8067

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Figure 17. Chiral dimers from Au NPs:319 (A) schematics of a model incorporating Au NP dimer and a chiral molecule; (B) extinctions of single molecule and single noble metal NPs (top), extinction of Au NP dimer for various separations d (middle), and enhancement factor A versus the wavelength of incident light in the center of a gold dimer in the absence of molecule (bottom); (C) CD spectrum of Ag NP dimer for d = 1 nm, where the inset shows the CD spectra for the separation d = 0.5 nm (top), and CD spectrum of Ag NP dimer averaged over the molecular orientation. (D) Schematics of the synthetic method for chiral NP heterodimers. Typical TEM images of heterodimers assembled via hybridization of DNA strands (E) and screening of ionic repulsion (F). The UV−vis and CD spectra of NP heterodimers triggered by DNA (G) and NaCl (H). The calculated spectra of NP heterodimers assembled via screening of ionic repulsion triggered by NaCl (I).324 Panels A−C were reproduced with permission from ref 319. Copyright 2013 American Physical Society. Panels D−I were reproduced with permission from ref 324. Copyright 2013 American Chemical Society.

with corresponding reversal of the polarity of the CD peaks (Figure 16I−K). This observation is essential because it (a) pinpoints the origin of the chiroptical activity in 3D geometry of the nanoscale assemblies and (b) provides the distinct example of dynamic chiroplasmonic assemblies with chemical modulation.180 A twisted NR dimer mimics the geometry of a chiral molecule with two isolated chromophores well known from organic chemistry exemplified by BINAP. The relative rotation between the NRs opens the possibility to observe charge transfer electronic transitions between different NRs, in the same fashion as those transitions observed between aromatic chromophores tilted with respect to each other.308 Using the more recent terminology of plasmon hybridization, the qualitative explanation of the origin of the CD in this structure is reasonable.180

Among DNA-bridged nanoscale assemblies, DNA origami attracted attention as assembly templates pioneered by the groups of T. Liedl and L. Liu Na because they offer a certain precision in engineering of the chiral NP superstructures.7,55,180,309 Furthermore, reconfigurable 3D plasmonic metamolecules made from Au NRs can be made. They execute DNA-regulated conformational changes of NRs and display tunable left-handed, relaxed, and right-handed states (Figure 16O,P).7 These and other studies (see Section 3.4 on Helical assemblies) demonstrated the origami is a powrful approach for fabrication of 3D nanostructures with tailored optical chirality; the known disadvantages of and concerns about DNA origami still remain. 8068

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Figure 18. Au NP chiral pyramids. (A−L) TEM images of PCR products observed after a number of PCR cycles. (M) CD spectra of PCR products for an increasing number of cycles.57 (N) Chiral pyramids of Au NPs using DNA scaffolds.32 (O) Models of chiral NP pyramids. (P) Calculated CD spectra of pyramidal complexes with asymmetric frames.27 Panels A−M, N, and O, P were reproduced with permission from refs 57, 32, and 27, respectively. Copyright 2009, 2009, and 2010 American Chemical Society, respectively.

3.2. Nanoparticle Dimers

(Figure 17A). The calculated enhancement factors for CD spectra were found to be 12 and 150 for the Au and Ag NPs, respectively (Figure 17B). For randomly oriented chiral molecules, the enhancements were smaller, 4- and 12-fold (Figure 17C).319,320 These results are in agreement with experiments on dense disorganized NP aggregates and narrow gaps (ca 0.5−2 nm) necessary for high field enhancement.161 The transfer of molecular chirality to the plasmon resonances was found for assemblies of Au NPs and proteins.321 It is important to point out that hot-spot amplification of the chiroptical activity of the organic molecules (e.g. DNA) is a local effect. The chirality of the assembly as a whole must also be considered. Since the physical dimensions of the NP assemblies are comparable to the wavelengths of visible photons, the polarization rotation caused by the geometry of the assemblies as a whole can be a lot greater. Simple electrodynamic simulations (Section 2.5) can demonstrated that the polarization rotation originating from the asymmetry of the dimer geometry as a whole can be 10x greater than from the hot-spot enhancement. The restrictions of small gaps necessary to generate the strong electrical fields in the single nanometer scale are also removed.6 Note however, that the chiroptical activity as whole would require the NP in the dimers to be non-

Self-assembly offers a scalable and versatile way to organize individual inorganic NPs into sophisticated nanostructures, allowing rational structural design that leads to nanostructures with novel collective properties and functions depending on the size, morphology, and spatial configuration of the constituent units.23,42,142,238,310−315 The level of electromagnetic theory and computer simulations generally afford a fairly accurate prediction of their optical properties including the chiroptical bands (see Section 2.4). Note that these calculations require as an input the knowledge of the NP shapes and the 3D geometries of the assembled structures. The studies on chiroptical properties of the NP dimers represent a great example how influential the slight deviations of the NP shapes from idealized spherical geometries can be and how important is to verify some of the starting seemingly obvious assumptions. Dimers assembled from NPs can be selectively prepared through DNA hybridization,316,317,318 or can be separated from other assemblies by different means of purification.316 For the symmetric configuration of idealized NPs, theoretical calculations showed that the chiroptical activity of a molecule can be enhanced by a plasmonic hot spots in NP dimers 8069

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Figure 19. (A) Scheme of a chiral NP pyramid. (B) TEM images and (C) CD spectra of self-assembled pyramids made from four Au1 (type 1) and three Au2 + Au3 (type 2) (top); two Au2 + two NPs (type 3 and Au2 + Au3 + two NPs (type 4) (middle) (inset: CD spectrum in 300−450 nm region); and Au2 + Au3 + Ag + QD as S- (type 5) and R-enantiomers (type 6) (bottom).318 Types of assembly in this figure refer to the special arrangements of the NPs rather than the types of chirality discussed in Section 2.2 as indicated by the different font. Reproduced with permission from ref 318. Copyright 2012 American Chemical Society.

nature of two uniform spheres, which was confirmed by simulations.323,324 The strong chiroptical activity of the NP dimers and similar assemblies can be used to monitor the assembly of DNA origami and similar DNA-based superstructures in academic research322,323,316 and it was also utilized for sensing.325

superimposable with their mirror image. This is difficult to imagine under the assumption of NP being perfect metallic spheres. Indeed, they are not and were found to have a small asymmetry between long and short axes with aspect ratio about 1:1.1.62,324 It turned out that even fairly small non-spherisity of individual NPs is sufficient for generation of large chiroptical activity for highly polarizable assemblies. The geometry of such assemblies de facto replicates the geometry of twisted rod assemblies.323 The dimers made from these slightly oblong NPs with small dihedral angles between them in the range of 10 degrees were fabricated by DNA bridges and ionic assembly (Figure 17D−F). The CD band had a magnitude of (−) 20 or (+) 10 mdeg at the plasmonic frequency of Au NPs for DNAand NaCl-triggered heterodimers (Figure 17 G−I).324 As we mentioned in Sections 1.1 and 2.1, the nanoscale inorganic structures must display have a certain ee in order to observe secondary effects of chirality in CD or ORD. In case of NP dimers bridged by DNA, one source of ee is the helicity of the oligonucleitides that makes, say, positive dihedral angles preferred over the negative ones. Other sources of ee are certainly also possible. Importantly, these experiments provided new insight into the origins of chirality in chiroplasmonic assemblies. For example, the strong polarization rotation observed in the first publications on assemblies from NPs with chiral assemblies and strong chiroptical activity should partially be attributed to contribution of the constituent dimers.57,318 The relationship between chiral geometries of NP assemblies with scissor-like orientation of the long axes on NP ellipses break the symmetric

3.3. Pyramidal Assemblies of Nanoparticles

DNA sequences on the surface of NPs enable nanoscale superstructures, which resembles stereochemical control in organic chemistry. Thus, DNA has been used to build NP assemblies with different linear, triangular, pyramidal, and octahedral configurations.326 Among this family of methods, polymerase chain reaction (PCR) allows one to produce various NPs assemblies in automatic fashion,327 including complex superstructures from Au NRs,39 Au NPs,57,313,328 semiconductor NPs,329 and magnetic NPs.330 The automated steps of PCR enable programming assemblies controlled by temperature regimes and cycles to reach a predetermined complexity of NPs. PCR was realized on the surface of plasmonic gold nanospheres as a tool for chiral selforganization with single-stranded DNA (ssDNA).57 The geometry of the products (ranging from dimers, trimers, and tetramers to complex agglomerates) was controlled through the density of DNA primers on the NP surface and the number of reaction cycles (Figure 18A−L).57 Purification by gel electrophoresis was required to achieve optically active chiral assemblies (Figure 18M). Note that multiple components of chiroptical activity need to be considered for these structures with tetrahedral assemblies being only one of many 8070

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Figure 20. Chiral nanotubes from NPs. (A) The different DNA-tube-assembled NP conformations were observed in a single TEM image. (B) One view of the tomogram of a single-spiral tube of 5 nm Au NPs (top). Tomogram of a double-spiral tube of 5 nm AuNPs with a single spiral of 5 nm NPs inside each coded with a different color (bottom).33 (C) Tuning the structural parameters of double helices of Au NPs relies on peptide conjugate molecules.34 From left to right, the used NPs were created by citrate-modified synthesis, typical synthesis, and ATP-modified synthesis. 8071

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Figure 20. continued (D) Illustration of the Au NPs is automatically arranged into a 3D helix based on DNA origami.338 Assembly of DNA origami gold NP helices (E) and the corresponding TEM image (F). (G) The measured CD for NPs helices.55 (H) Calculated CD spectra of helixes (number of NPs = 4, 5, 6, and 7) with the parameters given in the text.27 (I) Optical rotatory dispersion of self-assembled gold nanohelices.55 Panels A and B were reproduced with permission from ref 33. Copyright 2009 American Association for the Advancement of Science. Panels C, D, and H were reproduced with permission from refs 34, 338, and 27, respectively. Copyright 2010, 2012, and 2010 American Chemical Society. Panels E−G and I were reproduced with permission from ref 55. Copyright 2012 Macmillan Publishers Ltd.

vivid in comparison of, for instance, CD spectra from organic and inorganic helicoids. Let us, as consider first, the synthesis of helical assemblies from NPs, NR, and other nanocolloids. Biomacromolecules as templates or linkages have been explored in different types of assemblies.28,31,33,55 One of the representative example is dsDNA used to direct the formation of NWs from poly-Llysine-capped gold NPs and 2-pyrrolidinone-capped magnetic NPs.335 The arrangement of both metallic and magnetic NPs on DNA was the result of attractive electrostatic interactions between positively charged NPs aligned along both negatively charged strands. The 1:1 DNA:NP mass ratio exhibited a similar CD signal to B-form DNA for both metallic and magnetic NPs. The use of a 3D chiral templates for producing geometrical chiral geometries plays an important role in assemblies of NPs.336,337 The DNA and original molecular templates themselves have chiral dimensions in the nanometer range which limit the assembly to small NPs (few nanometers). DNA origami,55,338 peptides,31,34 and fibers28 have emerged as promising platforms for NP assemblies in 3D space where the parameters of diameter, length, and pitch can be controlled from several nanometers to microns. NP helices were successfully assembled on DNA nanotubes, forming assemblies with geometries of stacked rings, single spirals, double spirals, and nested spirals (Figure 20A,B).33 Electron tomography revealed a left-handed chirality in the spiral tubes and doublehelical wall tube features. The double helix has a better ordered pattern of a double helix of NPs made by the peptide (Figure 20C).34 Subsequently, a left-handed helix of DNA-origamiorganized NPs was synthesized with a CD peak at the plasmonic band (Figure 20D).338 More complex geometries with 24-helix bundles that offered nine helically arranged attachment sites for plasmonic particles coated with ssDNA, were later achieved using the same toolbox (Figure 20E,F).55 The CD spectra measured from both NP helices exhibited the anticipated spectral signatures in 500−600 nm window (Figure 20G). The helical NP assemblies produced a strong chiroptical activity with a characteristic bisignate peak located at the plasmon resonance frequency in accordance with the handedness of the helices (Figure 20H).27 The droplets with gold helices rotated the polarization angle of the linearly polarized light as demonstrated in polarization-resolved transmission images (Figure 20I). More recently, the assembly of NPs on an inorganic helical templates from silica was also reported.339 Prasad and co-workers prepared chiral superstructures from anisotropic NPs.58 The control of the size and shape of the anisotropic NPs was achieved by annealing at 100−175 °C, and nonspherical nanocrystals with sizes between 20 and 40 nm were synthesized. The helix of NPs organized in supramolecular polymeric chains resulted in a g-factor as high as 0.02. Au NRs assembled on a fiber template were also reported (Figure 21A− D).28 The Au NRs self-assembled on supramolecular fibers exhibited chiral geometry (Figure 21A,B). Dispersion of the

possibilities. Polarization rotation related to the constituent NP pairs with twisted dimer configuration contributes considerably to their chriroptical activity. Mastroianni et al. created discrete pyramids of dsDNA with gold NPs treated as nanospheres at the pyramid tips in solution. No chiroptical activity was observed; singular two dimensional TEM images were used to identify assemblies made from four different NPs.32 Later, full optical and structural characterization of the pyramidal constructs was reported by Yan et al.;318 multiple constructs with pyramidal geometry were produced with systematic variation of the NP in the apexes.64 Each strand had a unique sequence that allows positioning of specific NPs at the apexes (Figure 18N).32 The enantiomeric nanostructure was obtained by switching the position of two of these particles through conjugation with the opposite strand. They were comprised of small Au NPs (10 nm, Au1), medium Au NPs (15 nm, Au2), large Au NPs (25 nm, Au3), CdSe@ ZnS NPs (5 nm), and silver NPs (10 nm) (Figure 19A−C).318 The synthetic yield of these pyramids approached 80%, which led to further research and their possible utilization in optical devices.9,12,306 Besides the observation of optical activity of systematically synthesized NP pyramids and constructs from a combination of metal and semiconductor NPs,318 the significance of this study arises from their (1) geometrical simplicity of the structure that is amenable to in silico spectroscopy; (2) tunable optical activity; and (3) scalability synthesis by self-organization, especially compared to electron beam lithography.330−334 Furthermore, this study established the firm connection with the previous studies of chiral compounds at the molecular scale (see Section 2.3) assemblies. Note, however, that it also revealed incompleteness of our understanding of chiral geometries of the NP assemblies because it also revealed that components of the pyramids, i.e. DNA-bridged NP pairs also have strong chiroptical activity. Systematic evaluation of this discrepancy eventually led to the discovery of importance of the NP non-sphericity for chiroptical activity of NP dimers.62 The computer simulations of several types of pyramidal assemblies reported indicated a close match with experimental data (Figure 18O,P).27,57,331 3.4. Nanoparticle Helices

Helical assemblies of NPs give another example of nanoscale structures when the asymmetry of the individual NPs (e.g. Types 1, 2, and 3 chirality, Section 2.2), the field-effects specific to inorganic materials (e.g. Type 4 chirality), and 3D organization of nanoscale structural units are synergistically combined to give fascinating set of chemical and physical phenomena. Similarly to tetrahedrons, helical geometries are also essential for making fundamental parallels with supramolecular assemblies from organic building blocks that have the same geometry (Section 2.3). Novelty and utility of the chiroptical effect associated with inorganic matter also becomes 8072

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Figure 21. (A) TEM image of the M nanocomposite showing twisted fibers with adsorbed NRs. (B) Scheme of the system. NRs are randomly positioned onto the surface of a cylinder of radius R = 100 nm (top). Same as in panel L, but with only two particles (bottom). (C) Experimental CD spectra of a helix of Au NRs. CD spectra are shown for both P (red) and M (blue) nanocomposites. (D) Modeled CD spectra using the coupleddipole model. The calculations are presented for monodisperse (red) and polydisperse (black) particle size distributions.28 (E) SEM images of bundles of twisted ribbons (TRs). (F) HRTEM images for CdTe TRs taken in the “twist region”. Individual straight Te nanowires (G) and CdTe/ CdS TRs (H). SEM (J) and AFM (K) images of individual TRs with pitch lengths of 380 nm (J) and 400 nm (K). (I) A truncated tetrahedron particle simulations.20 Tapping-mode atomic force microscopy (AFM) topographic (left) and phase (right) images of a left-handed (LH) nanoribbon (L) and a right-handed (RH) nanoribbon (M). (N) Distributions of LH, RH, and nontwisted nanoribbons obtained after 50 h illumination with right circularly polarized (RCP), left circularly polarized (LCP), unpolarized (UnP), linearly polarized (LinP) light and in the dark. (O) Ensemble CD spectra (solid line) and g-factor (dotted line) of dispersions of LH and RH nanoribbons obtained after 50 h of circularly polarized light illumination.68 Panels A−D were reproduced with permission from ref 28. Copyright 2011 Wiley-VCH. Panels E−K were reproduced with permission from ref 20. Copyright 2010 American Association for the Advancement of Science. Panels L−O were reproduced with permission from ref 68. Copyright 2015 Macmillan Publishers Ltd.

obtained right- and left-handed assemblies showed intense

The helical assemblies of NPs made by DNA and similar templates, e.g., DNA origami33,55,338 and peptides,31,34 typically have a pitch length of a few nanometers (