Optical Properties of Gold Nanoclusters Functionalized with a Small

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Optical Properties of Gold Nano-Clusters Functionalized with a Small Organic Compound: Modelling by an Integrated Quantum-Classical Approach Xin Li, Vincenzo Carravetta, Cui Li, Susanna Monti, Zilvinas Rinkevicius, and Hans Ågren J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b00283 • Publication Date (Web): 25 May 2016 Downloaded from http://pubs.acs.org on May 27, 2016

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Journal of Chemical Theory and Computation

Optical Properties of Gold Nano-Clusters Functionalized with a Small Organic Compound: Modelling by an Integrated Quantum-Classical Approach Xin Li,∗,† Vincenzo Carravetta,‡ Cui Li,¶,‡ Susanna Monti,∗,§,† Zilvinas Rinkevicius,† and Hans Ågren† Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology, SE-10691 Stockholm, Sweden, CNR-IPCF , Institute of Chemical and Physical Processes, via G. Moruzzi 1, I-56124 Pisa, Italy, Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden, and CNR-ICCOM , Institute of Chemistry of Organometallic Compounds, via G. Moruzzi 1, I-56124 Pisa, Italy E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology, SE10691 Stockholm, Sweden ‡ CNR-IPCF , Institute of Chemical and Physical Processes, via G. Moruzzi 1, I-56124 Pisa, Italy ¶ Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology, SE10044 Stockholm, Sweden § CNR-ICCOM , Institute of Chemistry of Organometallic Compounds, via G. Moruzzi 1, I-56124 Pisa, Italy †

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Abstract Motivated by the growing importance of organometallic nanostructured materials and nanoparticles as microscopic devices for diagnostic and sensing applications, and by the recent considerable development in the simulation of such materials, we here choose a prototype system – para-nitro-aniline (pNA) on gold nanoparticles – to demonstrate effective strategies for designing metal nanoparticles with organic conjugates from fundamental principles. We investigated the motion, adsorption mode and physical chemistry properties of gold–pNA particles, increasing in size, through classical molecular dynamics (MD) simulations in connection with quantum chemistry (QC) calculations. The QM/CMM calculations of the properties use the time dependent density functional theory for the QM part and a capacitance–polarizability parameterization of the MM part, where induced dipoles and charges by metallic charge transfer are considered. Dispersion and short-range repulsion forces are included as well. The scheme is applied to one- and two photon absorption of gold–pNA clusters increasing in size towards the nanometer scale. Charge imaging of the surface introduces red-shifts both because of altered excitation energy dependence and variation of the relative intensity of the inherent states making up for the total band profile. For the smaller nanoparticles the difference in the crystal facets are important for the spectral outcome which is also influenced by the surrounding MM environment. Keywords: para–nitro–aniline, gold nanoparticles, hybrid quantum chemistry/molecular mechanics method, reactive molecular dynamics, linear and non–linear optical properties.

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Introduction Nanostructured metal-organic materials have received considerable interest not only for their diverse potential technological importance in communication, data storage, sensing and imaging, but also for the understanding of the fundamental principles which regulate the interaction of nanostructured matter with light. Nanoparticles can act as agents that immobilize organic species but at the same time as direct enhancers of the sensitization and molecular response to an external perturbation. This can in turn be a plasmonic process, i.e. generated by collective oscillations resonantly excited by a perturbing time-dependent laser field, or a physicochemical mechanism where the metallic surfaces directly modify the molecular response at non-resonant frequencies of the perturber. The efforts towards a rational design of these kinds of nanostructured materials with tailored functionality in terms of enhanced optical and magnetic properties call for basic understanding and derivation of possible relationships between structure and function. Such rational–based design requires the control and utilization of electronic structure, structural conformation and dynamics as well as of the interaction with the perturbing fields, which could be generated inside the material or due to the external environment and different electro-magnetic sources. As far as gold nanoparticles (AuNPs) are concerned, this tendency is testified by the increasing use of relatively small, accurately shaped and appropriately functionalized AuNPs in a wide variety of sectors due to their improved unique electronic, magnetic, optical and catalytic properties, and to their low toxicity and biocompatibility. 1–8 Indeed, controlling AuNPs morphology and surface characteristics is by all means fundamental for obtaining specific actions, especially when the AuNPs are employed as delivering systems or detecting agents. AuNPs size and shape rule self-interactions, molecular organization, sintering and, last but not least, their dynamics in different environments. The organization of the nanoparticles crystallographic surfaces is generally determined by competitive growth mechanisms (relative growth rates)

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which can be altered by a proper control of the experimental parameters. 9–13 The modulation of the nucleation and reaction conditions, such as reagents and stabilizers concentrations, temperature, time, pH, etc. together with the addition of specific functionalities to their surfaces, can be effective to tune shape and behavior of the AuNPs and to obtain stable and reliable multifunctional vehicles. However, the exact role played by each of the aforementioned parameters in the regulation of the morphology and optoelectronic properties of the AuNPs is not yet fully understood, but it is believed that the outcomes are mainly due to cooperative actions. 14 The process of AuNP functionalization can be accomplished through physisorption, where the interaction between the adsorbate and the nanoparticle is presumably weak because of regulation by van der Waals and electrostatic forces, or by means of chemisorption, where proper chemical bonds between the ligand and the nanoparticle are formed. Both techniques confer colloidal stabilization to the AuNPs and prevent their aggregation, 15–19 but, especially in the case of chemisorption, they could affect the properties of the nanoparticles remarkably through the modification of their electronic distribution. 20 The radiative properties (i.e. absorbance and scattering) of AuNPs, which are plasmonic nanostructures, depend on the size, shape, and refractive index near the AuNPs surface. Indeed, it has been observed that the extinction cross-section increases as the AuNPs increase in size, being dominated by absorption for small nanospheres and by scattering for larger systems. The peaks in the spectra broaden significantly and shift towards longer wavelengths. Such a shift can be also caused by an increase in the refractive index near the nanoparticle surface, meaning that the AuNP extinction peak will be red-shifted if the AuNPs are transferred from lower to higher refractive index media. Other phenomena, such as particle aggregation and sintering, are another possible cause of the red-shift of the absorption and scattering peaks. 21–25 In order to test some of these aspects and theoretically characterize the perturbation effects 4


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on the spectroscopic properties of AuNPs caused by their functionalization with a small molecule, namely para-nitro-aniline (pNA), reactive molecular dynamics (MD) simulations (using the ReaxFF paradigm) in connection with quantum chemistry (QC) calculations have been performed. The reliable behavior of the MD-ReaxFF approach to describe the dynamic of AuNPs and their interactions with various types of systems was tested in a number of past investigations 26,27,27,28 and revealed to be a very efficient strategy and a sound methodology. Even though, in principle, pNA should not react with the metal support, the reactive force field was used for this molecule as well because of the specific characteristics of the program which include the incorporation of charge flow, a coherent energy representation (during all chemical reactions), changes of bond orders, and shielding of nonbonding interactions. As a matter of fact, all these features enable to delineate the properties of complex, hierarchical materials as accurately as quantum methods. This is because during the parameterization procedure QC-optimized models are also included in the training set and contribute with their weight to the final balanced data. Moving to the framework representing computationally complex metal-based materials, it has been demonstrated that even relatively small models and quantum methods 29 can be effective both to parameterize a classical force field and to verify its performance, that is the reliability of the data produced by the simulations. In the present investigation, both quantum and classical reactive techniques have been applied to study the adsorption of pNA on the various facets, namely the (111), (100) and (110) surfaces, of four different AuNPs. The main goals of the present work are: • to develop a reactive force field, trained with QC data, for disclosing the dynamics of specific noble metal-adsorbate complexes; • to use the produced data for calculating the spectroscopic properties of the resulted hybrid materials made of an adsorbate on an infinite gold slab or on spherically shaped gold nanoparticles;

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• to combine the MD sampling with property simulations using the so-called integrated approach. 30 These are carried out in a multi-scale mode by combining classical force field molecular mechanics (MM) with quantum mechanics (QM), where the former contributes with the intermolecular perturbations caused by the surrounding environment and the latter define light-matter interactions. The quantum part is rendered through the time-dependent density functional theory implemented for linear and non-linear light matter response, while the environment is addressed by means of an improved heterogenous force field, where the metallic part is described with capacitance–polarizability parameters and the organic part with polarizable charges contributions. The capacitance–polarizability force field regulates the induced dipole and charges, which in turn are used in the coupled response equations to determine the property. With this scheme the charge transfer within the metallic environment is taken into account and mirror-image charges are created in response to the charge flow in the QM part. On the contrary, the charge transfer between the QM and MM parts is not considered. This methodology describes the direct effects of the metal surface, though polarization and charge relocation, on the optical properties of physisorbed chromophores and the indirect effects on their geometries. The scheme, which recently has been employed to compute linear and non-linear absorption, circular dichroism and X-ray spectra of organic molecules physisorbed on metal clusters, oneand two-photon absorption spectra of molecules adsorbed on gold surfaces and other optical properties of model chromophores on silver and gold, 31–34 has been dubbed hybrid quantum mechanics/capacitance molecular mechanics methodology for heterogenous systems (or integrated approach). 30 This method is an established leading technique to study environmental effects on linear and non-linear properties of solvated molecules in contact with metals that uses precisely defined and tuned parameters to describe heterogeneous metallic/non-metallic 6


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environments. 31,32 To a large extent its success can be linked to the usage of accurate hybrid quantum mechanics/molecular mechanics (QM/MM) methods for calculations of molecular properties as such methods allow to describe solvent environments with the level of details inaccessible for conventional continuum methods. 35–39 In this work the application of the QM/MM paradigm is extended towards the nanometer range by examining the properties and behavior of groups of molecules physisorbed on AuNPs of various sizes. The QM/CMM methodology, which significantly differs from conventional QM/MM methods, is built on the basis of three conditions: 31 a) the interaction between the QM and MM regions is dominated by electrostatic and van der Waals interactions; b) the heterogeneous MM region is separable into metallic and non-metallic parts; c) charge transfer between the metallic part and the non-metallic parts of the MM region is negligible. Adopting these requirements the MM region is partitioned into a non-metallic part, which is described by a non-polarizable force field, and a metallic part which is represented through the capacitance–polarizability model. 40 As a consequence, the Hamiltonian of the interaction between the QM and MM regions consists of five terms

ˆ qm/mm = H ˆq ˆ vdW ˆq ˆp ˆ vdW H qm/non−met + Hqm/non−met + Hqm/met + Hqm/met + Hqm/met

(1)

where the first two terms describe the interaction between the QM region and the nonmetallic part of the MM region and the remaining three terms describe the interaction beˆq tween the QM region and the metallic part of the MM region. More specifically, H qm/non−met describes the interaction of permanent charges in the non-metallic part of the MM region 7



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ˆ vdW with electrons and nuclei in the QM region, H qm/non−met describes the van der Waals interˆq action between the non-metallic part of the MM region and the QM region, H qm/met and ˆp H qm/met describe the interaction of the induced charges and induced dipoles in the metallic ˆ vdW describes the part of the MM region with electrons and nuclei in the QM region, and H qm/met van der Waals interaction between the metallic part of the MM region and the QM region. The van der Waals interaction between the QM and MM regions is parameterized using empirical potentials independent on the electron density of the QM region, and does therefore not contribute directly to the Kohn-Sham operator of any order in the QM/CMM method. 31 Thus, the contributions from the MM region to the zero order Kohn-Sham operator arise ˆ qm/mm and can be written as from the first, third and fourth terms in H

hφp |

X

pq

n

X

hφp |

X

Fˆqm/mm =

X

−

pq

qnperm Tˆn (r)|φq iEpq +

X X ind ˆ q qm Tm (r)|φq iEpq hφp | pq

ˆp pind m Tm (r)|φq iEpq

m

(2)

m

ind } where {qnperm } are the permanent charges in the non-metallic part of the MM region, {qm

and {pind m } are the induced charges and induced dipoles in the metallic part of the MM region, ˆ p (r) are the electrostatic interaction operators (a detailed description Tˆn (r), Tˆmq (r) and T m of these operators can be found in the appendix of Ref. 31 ), and Epq is the conventional one-particle excitation operator in second quantization. The permanent charges {qnperm } in the non-metallic part of the MM region are trivially defined by the force field selected to ind describe this part of the system, while the induced charges {qm } and induced dipoles {pind m }

in the metallic part of the MM region are defined within the framework of the capacitance– polarizability model. Thus, induced charges and induced dipoles are fluctuating between selfconsistent field iterations and are defined by the instantaneous eletrostatic environment of the metallic part of the MM region in each iteration. These charges and dipoles are determined in

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the capacitance–polarizability model 40 by solving the following charge equalization equation 



ind







−M 0 p   E   A      −MT −C 0 qind  =  V            0 0 1 λ q tot

(3)

Here, the column vectors E and V describe the electric field and potential created by the non-metallic part of the MM region and by the QM region at the position of each atom in metallic part of the MM region, q tot is the total charge of the metallic part of the MM region, λ is a Lagrangian multiplier ensuring a charge conservation condition, submatrices A, M and C represent electrostatic interactions of different orders in the capacitance–polarizability model, their exact definition can be found in our previous work. 31 The QM/CMM zero order Kohn-Sham operator, used in the optimization of the electron density of the QM region, is explicitly dependent on the permanent and induced charges as well as the induced dipoles in MM region. The higher order Kohn-Sham operators, used in linear and quadratic response theory, include only induced charges and induced dipoles contributions from the MM region, as in this case the contribution from the permanent charges vanishes due its one-electron nature. To illustrate this point, let us consider the first order Kohn-Sham operator Fˆ ω , which appears in the linear response equations and is explicitly dependent on the first order perturbed electron density. According to our previous work, 31 we can write Fˆ ω as

ω Fˆqm/mm =

X pq

hφp |

X

ind,ω ˆ q Tm (r)|φq iEpq − qm

m

X X ˆ p (r)|φq iEpq hφp | pind,ω T m m pq

(4)

m

ind,ω where the first order induced charges {qm } and first order induced dipoles {pind,ω } are m

obtained by solving Eq.(3), in which the electric field and potential column vectors are replaced by the corresponding column vectors generated by the perturbed first order electron 9



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density. The MM region contributions to higher order Kohn-Sham operators can be obtained following the same principle (see Ref. 32 ). Therefore, in the QM/CMM method the zero order Kohn-Sham operator contains explicit contributions from both the metallic and non-metallic part of the MM environment, and higher order Kohn-Sham operators contain only explicit contributions from the metallic part of the MM environment. Thus, for the electron density optimization in the QM region region both parts of the MM region play a significant role, while in the calculations of the linear and non-linear response properties the importance of the metallic part of the MM region can be more significant and in some cases dominates the environmental effects. 31–34 This difference in importance of the metallic and non-metallic parts of the MM region in molecular properties calculations is an inherited property of the QM/CMM method and should be considered in any analysis of the effects caused by heterogeneous environments.

Computational details 0.1

Quantum Chemical Data used in the Parameterization Process

Quantum mechanics and dynamics data, from simulations carried out in the gas phase by means of the plane wave density functional theory approach (PW-DFT), reported in an earlier work (see Ref. 41 ), were used as part of the training set to parameterize the force field. Briefly, the selected structures were not only minimum energy conformations, but also higher energy configurations, extracted from quantum molecular dynamics simulations at T=300 K. The systems consisted of a periodic gold slab (three layers of twenty gold atoms), representing an Au(111) surface, and a pNA molecule on top of it that were inserted in a simulation box with dimension of 14.42, 9.99 and 43 Å in x, y and z directions. The most stable arrangements of the molecule on the surface were essentially two, namely molecular plane parallel (flat) and perpendicular to the top layer of the slab. In the latter case the 10


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molecule could adopt three main orientations: both nitrogens equidistant from the interface (perp), oxygens (no2) or nitrogen (nh2) of the NH2 group coordinated to the gold atoms (see Figure 1). The other data used for training the force field were non-periodic complexes made of a small gold cluster and molecular fragments useful for parameterizing the interaction of the different atoms with the gold support (see next section and Supporting Information).

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Reactive force field parameterization and validation

The parameterization process consisted in identifying a good set of parameters which could represent not only the internal geometry of the molecule but also appropriate descriptors to depict realistically the interaction of the molecule with the metal support. As far as the intramolecular features are concerned, the initial force field data were extracted from an earlier work by Rom et al. 42 where the authors used quantum calculations, in combination with reactive molecular dynamics simulations, to describe the liquid structure of trinitrotoluene (TNT), its thermal decomposition and the products in the gas phase. Even though TNT and pNA are quite different from each other, they contain a common fragment, namely a benzene ring with an NO2 substituent, whose parameters can be considered a favorable starting point for pNA parameterization and modified effectively to obtain the desired description (corresponding to the quantum chemistry data). Essentially, it was necessary to accurately tune the CN bond term in order to represent correctly both pNA para groups and to modify the NH2 representation in line with its new properties. A suitable force field was identified by means of the single-parameter search optimization method 43 included in the serial version of the ReaxFF program, which was distributed by the author upon request. The training set included constrained energy-minimized geometries of pNA at the B3LYP/6311+G(d) level in the gas phase (Gaussian 09 code 44 ) where the lengths of the selected bonds (N-C and N-O) were frozen at different values while the rest of the molecule was 11



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optimized without any constraint. During the parameterization process, all the structures in the training set were relaxed with the ReaxFF force field, while the selected parameters were restrained to the specified values. In order to reproduce the behavior of pNA on gold, the initial force field parameters were taken from previous studies by van Duin and co-workers. 26–28 The intramolecular description of pNA was kept fixed, whereas the X/Au (where X is equal to N, C, O, H) parameters were re-optimized against the quantum mechanics and dynamics results reported in an earlier investigation 41 and in this manuscript. These include gas-phase energy-minimized complexes where small fragments, containing the selected atoms, were placed at different distances from a small gold cluster (representing a surface) and optimized by fixing Au-X separations and cluster geometry, and the periodic models described above. To improve the quantum representation, the basis set superposition errors were removed from the cluster calculations through the Boys and Bernardi counterpoise correction (CP), 45 whereas the dispersion corrections terms were included in the periodic systems by means of the vdW-DF method by Dion et al. 46 (PW-DFT). In this approach the vdW interactions are directly inserted in the DFT functional as a nonlocal correlation term. 47,48 In view of the fact that no significant difference in the calculations was observed after the dispersion correction, only the data obtained without it were included in the training set. 41 The first validation of the parameters was based on the comparison between the QM and ReaxFF optimized models, that is on structures belonging to the training set (see Supporting Information). As expected, both the bond lengths and the angles of the molecule were well reproduced by the force field with root mean square deviations (RMSDs) lower than 0.01 Å. Beside the satisfactory reproduction of intramolecular parameters, also the intermolecular interactions between the adsorbed molecules and the gold clusters were appropriately described (see the Supporting Information and Figure 1). Considering that intermolecular interactions are dominant factors for the calculation of different kinds of properties of the 12


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adsorbed molecules, the real crucial steps were the evaluation of self-interactions and binding energies of the molecules to the periodic substrates and the reproduction of the real dynamics of these adsorbates on the surface. The final validation of the force field consisted in checking the coherence of the classical data with the results obtained by means of periodic quantum dynamics simulations.

0.3

Molecular dynamics runs of pNA on AuNPs: model building and simulation details

Taking into account that a sphere is the most stable shape 49 and that nanoclusters with the octahedral morphology have been produced experimentally 50–53 a truncated octahedron was adopted for all the nanoparticle models simulated in this work (Figure 2). This was an appropriate choice because it allowed to explore and analyze the behavior of the adsorbate when the different low-index single crystal surface planes (111), (100) and (110) were available for binding. It is well known that on the basis of density and coordination number of the surface atoms the stability of these motifs decreases in the order (111) > (100) > (110) 54,55 whereas their reactivity seems to follow the opposite classification. Indeed, the (111) facet, which is hexagonally close-packed, has the highest surface density (about 74%) and the lowest surface reactivity. In contrast, the (110) surface, where the atom density is about 37%, is the most reactive because of the spaced arrangement of its atoms which leave exposed the second layer sites. Its structure is similar to the one adopted by the (100) surface in one direction, but in the perpendicular direction the atomic rows are separated by open spaces. Differently from the other two morphologies, the (100) surface, which has an atomic density of about 52%, is organized in a cubic close-packed lattice. The AuNPs models built for the present simulations are displayed in Figure 2. The modeled truncated octahedron structures (in some cases slightly modified to obtain specific atom

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numbers) are composed of 887, 1505, 1985 and 3007 Au atoms and have maximum diameters of about 30, 35, 40, 45 Å, respectively. All AuNP models have eight (111), six (100) and twelve (110) faces, with different surface areas (Figure 2 and Table 1S of the Supporting Information) which are arranged symmetrically on the surface of the nanoparticles. As it can be noticed, the (111) facet is the dominant surface plane, followed by the (100) topology, whereas the joining regions (arranged as (110) facets) are much less extended. This variety could be useful to identify preferential regions of pNA-AuNP attachment. In order to simulate the adsorption process each AuNP was surrounded by two shells of pNA molecules (which were located farther than 5 Å from the AuNP surface) and molecular dynamics simulations in the NVT ensemble were carried out to induce adsorption. The temperature was increased slowly to 300 K and the potential energy of each system was constantly checked in order to establish an approximate duration of this first equilibration phase. As a matter of fact, during this stage, which was 50 ps on average, the pNA molecules migrated towards the AuNP surface but did not cover the whole interface because of self-interactions and clustering, which prevented homogeneous distributions of the ligands. Indeed, some molecules remained in the outer layers, and only in the largest AuNP model (AuNP3007) 72% of the pNAs were deposited on the surface. In the other cases the adsorption percentages were lower, namely 44%, 63% and 48% for AuNP887, AuNP1505 and AuNP1985, respectively. MD simulations were carried out by means of the ReaxFF version incorporated into the Amsterdam Density Functional (ADF) 56 program and with the LAMMPs code. 57 All the molecular systems were inserted in cubic simulation boxes where the size was 400×400×400 Å and simulated in the N V T ensemble at T=300 K and ambient pressure. Temperature was controlled through the Berendsen thermostat 58 (with a relaxation constant of 0.1 ps). The total equilibration phase was extended to 75 ps, then followed the production stage which was 500 ps long in each case. The time step was set to 0.25 fs 59 and the equations of motion were 14


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solved with the Verlet leapfrog algorithm. 60 System configurations were saved every 0.025 ps. Four separate simulations were performed without the adsorbates to check the stability/dynamics of the NPs and to disclose, by comparison, the effects caused by the adsorbed molecules on the characteristic features of the nanoparticles. The trajectories were analyzed to estimate pNA preferential binding modes and sites, which were identified on the basis of radial distribution functions (RDFs), spatial distribution functions (SDFs) and minimum distances to the gold atoms. Instead, pNA self-assembling was deduced by the examination of atom(pNA)atom(pNA) RDFs and visual inspection of the saved snapshots. Moreover, the effects of the adsorbate on the shape and size of the gold nanoparticle was disclosed considering Au-Au RDF, radius of gyration, Rgyr, ratio of the maximum and minimum principal moment of inertia, Imax/Imin, and eccentricity. The latter parameters can give an estimate of the deviation of the AuNP shape from a spherical object where the ratio Imax/Imin is one and the eccentricity zero. Representative snapshots of all the molecular complexes, where all the adsorbed molecules had stably settled on the AuNP surfaces, were extracted from the last picoseconds of the trajectories and used for the calculation of the spectroscopic properties and the simulations of the spectra.

0.4

QM/CMM calculations

For each of the AuNPs consisting of 887, 1505, 1985 and 3007 gold atoms, one representative snapshot was extracted from the MD simulation trajectories. With representative snapshots we mean stable configurations (i.e. structures where the molecules on top of the gold supports have settled down and do not change sensibly their arrangements) extracted randomly from the last ps of the production runs. In the subsequent QM/CMM calculations the AuNPs were included as metallic MM region with the charge flow within the AuNP described by the capacitance-polarization model. 40 15



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As such, each gold atom is modeled by superpositioned fluctuating charge and dipole, both Gaussian-broadened, and the charge–charge, charge–dipole and dipole–dipole interactions are taken into account within the capacitance–polarizability interaction model. This socalled QM/CMM method has been proven useful in multiscale simulations of physisorbed chromophores on metallic surfaces. 31–34 Here, we emphasize that the QM/CMM method can by design only describe the interaction between molecule and the metallic part of the heterogeneous environment that is directly induced by the electron density of the molecule, and that plasmonic enhancement effects induced by interaction between the metallic part of the heterogeneous environment and the electromagnetic radiation are not included in the model as presently implemented. This limitation of the QM/CMM method is of little consequence for our study of one-photon absorption spectra of pNA physisorbed on AuNPs, but may affect our study of two-photon absorption as the pNA two-photon absorption band will overlap with the plasmonic band of the AuNPs. Thus the results of the two-photon absorption calculations should be viewed more as a demonstration of QM/CMM method capabilities, rather than as a direct prediction of a coming measurement of the actual two-photon absorption in the pNA-AuNPs.

The most interesting pNA molecules are those in close contact with the AuNPs, namely the pNA molecules directly adsorbed onto the gold surfaces. To account for the different orientation of the pNA molecules, QM/CMM input structures were generated for each of the pNA molecules that are within 3 Å of the gold NPs. This results in 81, 106, 142 and 160 pNA molecules for the four AuNPs models. Averaging over the calculated one- and two-photon spectra offer statistical averages of the pNA molecules with different orientation and adsorption sites. For calculations of each pNA molecule adsorbed on gold NP, we employed the range-separated CAM-B3LYP exchange–correlation functional 61 combined with the triplezeta TZVP basis set, 62 the capacitance–polarizability parameters for gold are taken from the 16


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work of Jensen and Jensen. 40 The one- and two-photon absorption spectra are calculated by linear and quadratic response theory as implemented in the DALTON code. 63

1

Results and discussion

2

Optimized geometries of the pNA-Au complexes

The final arrangements of pNA on the gold slab after energy optimization are shown in Figure 1 and the relative energy of each configuration is reported in Table 1. From the examination of the energy differences reported in Table 1 and the optimized Table 1: Energy difference in kcal/mol of the four optimized complexes of pNA on the Au(111) slab (pNA+Au(111)) with respect to the minimum energy structure.

Model flat perp no2 nh2

PNA+Au(111) (QM) 0.00 1.52 2.67 3.43

PNA+Au(111) (ReaxFF) 0.00 1.67 2.17 3.18

geometries displayed in Figure 1 it is evident that all the complexes are well reproduced by the classical description and that the parallel arrangement is the most stable complex with the highest binding energy (see data in Ref. 41 ) because of the cooperative interactions of the nitrogen and oxygen atoms and the π orbitals of the benzene ring with the gold atoms of the top layer of the slab. Indeed, in the force field optimized flat configuration the molecule is perfectly parallel to the gold slab at a distance of about 3.6 Å and both of its nitrogens, together with the center of the benzene ring, are almost on top of the gold atoms of the surface. This arrangement somewhat differs from the structure obtained with the QC calculations which is, instead, not exactly flat (i.e. the nitrogen adopts a pyramidal configuration with the hydrogens slightly 17



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bent towards the interface) but inclined by a few degrees in order to favor the interaction of one of its oxygens with the atoms of the support. As far as the perpendicular arrangements are concerned, the strongest binding is obtained through the adsorption of the NO2 group (no2) where the oxygens are in contact with gold atoms at a distance of about 3.1 Å, in line with the QC data and characteristic features of the gold-oxygen binding mode.

3

Molecular dynamics simulations of pNA on the Au(111) infinite slab

In order to check if the classical parameterization could reproduce the adsorption and dynamics of PNA on the Au(111) surface, a larger model (in relation to the one simulated at the QMD level - see Ref. 41 ), different from those contained in the training set, was defined and used to explore the evolution of two of the complex configurations analyzed by the QMD technique. The slab size was extended to ten layers containing ninety Au atoms each and the dimensions of the simulation box were fixed at 26×25×80 Å3 . During the dynamics, the positions of the atoms belonging to the bottom layer were frozen at their starting locations, while all the other atoms of the slab were allowed to move and readjust their coordinates. The two different orientations of the molecule on the surface chosen as starting configurations of the classical simulations at 300 K were the ones identified by the QC investigation as weaker (nh2) and stronger (flat) adsorption modes. The effects related to the sampling intervals and the total simulation time were scrutinized in detail. Indeed, in the first case the total simulation time was set to 10 ps and structures were saved every 0.025 ps, whereas in the second case the duration was protracted to 200 ps and the sampling interval fixed to 0.05 ps. To establish proper comparisons between the results of these runs and the QMD series the same descriptors were analyzed accurately and the data concentrated in Figures 3 and 4. 18


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The first salient feature visible in the plots of the center of mass motion, shown in Figure 4, is that 200 ps were not sufficient to identify the supposed weaker binding modes of pNA (i.e. perp, no2, nh2) with their correct populations. This is because during the relatively long run the molecule remained substantially flat on the surface adopting an average inclination of 170±21 degrees and an average distance of 3.8±0.3 Å from the atoms of the top layer. This fact suggests that a complete characterization of the dynamics of a molecule, even small like this, needs sampling times of nanoseconds or several dynamics simulations starting from different initial conditions. Moreover, an accurate choice of the sampling interval is mandatory to maintain important geometrical features which could be reflected in the QC simulated spectra. The second important result is that the short classical simulation (10 ps) was able to reproduce exactly the behavior of the system when the molecule was adsorbed through the NH2 contact (nh2 case) even though in the QMD investigation the center of mass moved very far from the slab at about 6.6±0.4 Å (reaching sometimes 7.3 Å) and maintained an inclination of 95±10 degrees. In the classical description its motion was more contained, the average distance traveled was 4.9±0.5 Å (maximum = 5.7 Å) and the average inclination slightly closer to a perpendicular alignment (91±9 degrees).

4

Molecular dynamics simulations of the adsorption of pNA on AuNPs

Before characterizing the adsorption of pNA onto each AuNP it is advisable to analyze in detail the evolution of the substrate topology when it is isolate in the gas phase and compare this data with those of the functionalized geometries. This should give an idea of the AuNP stability and of the amount of structural changes induced by the action of the adsorbate. As it is shown in the Supporting Information (Table 2S), all AuNP size and shape descrip19



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tors change only slightly, suggesting that the supports preserved their spherical structure and were not affected by the interaction with pNA molecules. However, closer inspection of the individual distributions (Figure 3S) reveals that the substrates expanded slightly and only in the case of the smaller particles the influence of the adsorbate could produce shape mutations (minor surface reconstructions and adatoms). It could be speculated that in those cases the non-homogeneous deposition of pNA on the AuNP surface (Figure 5), and the reduced extension of the various low index faces could cause asymmetrical shape mutations in the contact regions distributed all around the supports. In order to estimate the entity of the effect of pNA adsorption on the AuNP structure, Au-Au RDFs were calculated and compared (Figure 6). The trends displayed in Figure 6, which have been complemented with the RDFs of the lattice (cyan peaks) and data found in the literature regarding crystalline (black curve) and amorphous (green curve) nanoclusters 64 (about 10000-atom theoretical models of pure gold), confirm that the structures were not substantially affected by the interaction with the adsorbate and maintained their crystallinity for the whole simulation time. Indeed, the positions of the peaks of the eight simulations coincide with the locations exhibited by a perfect gold lattice (cyan peaks) where the interatomic distance, which can be deduced from the position of the first maximum, is about 2.88 Å. The almost perfect alignment of all the peaks displayed for the eight simulations suggests that the perturbation did not involve the AuNP core (internal portion) but only the outer atom layer (atom reordering). As far as pNA adsorption mode is concerned, all the simulations showed that pNA could bind to the interface through the four different arrangements identified by the previous QC calculations, namely flat (that was rarer due to pNA-pNA packing and self-interaction which did not leave space enough to accommodate a parallel orientation), no2 (which was one of the most frequently observed orientation, highly stable and populated due to its dual advantage, namely stacked pNA-pNA packing and stronger Au-O binding contacts), nh2 (which 20


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was the second orientation more frequently observed, due to the energetically convenient coordination of the nitrogen atom to the gold substrate and, also in this case, to the formation of stacked pNA-pNA packed complexes) and finally perp (which was moderately populated because in competition with the other stronger binding modes). Intermediate configurations were also identified but these were essentially the result of the trapping action operated by the neighboring units. An idea of the binding mode can be obtained by the examination of the evolution and distributions of the minimum distances of the nitrogen, oxygen and NH2 hydrogen atoms from the Au sites (Figure 7) derived from the simulations. These distances oscillate around average values which are the same in all cases and the distributions are characterized by just a sharp peak with a full width at half maximum (FWHM) in the range 0.05-0.10 Å. The farthest atom from gold is the nitrogen of the NO2 group, which is located at about 2.55 Å, followed by the other nitrogen, where the distance is 2.33 Å on average. This is not surprising because the strongest binders seem to be the oxygens, which are closer than the nitrogens to the surface, having an average minimum distance of about 2.19 Å. However, their interaction is sometime reinforced by the coordination of the NO2 nitrogen, which renders this complex the most persistent adsorption. As far as the amine hydrogens are concerned, they can be found at the shortest distance from the surface (about 1.72 Å) and the distribution of their minimum distances is broader with a FWHM of about 0.1 Å. These findings suggest that amine hydrogens could be found in direct contact with the AuNP atoms or with the neighboring pNA oxygens, and, as expected they are more mobile than the other species. Inspection of the O-H RDFs (Figure 8) confirms the propensities of the hydrogens to be involved in intermolecular interactions with the nearest adsorbates (first peak of the OH RDF at 1.1 Å). However, these complexes are insufficiently populated to be considered preferential aggregation routes, which are instead realized through stacking interactions of the perpendicularly arranged units. The maximum population of intermolecular hydrogen 21



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bonds was found in the largest model (AuNP3007) and it was only 20% of the total possible connections. In contrast, pNA structures belonging to the second shell displayed a greater number of hydrogen bonds essentially because their organization and mutual orientation were more disparate and not influenced directly by the topology of the metal substrate. The packing of the adsorbates, was driven, instead, by a balanced compromise between favorable self-accommodation and optimal atom-surface interactions. A selection of binding modes identified during the simulation of the smallest AuNP (AuNP887) is shown in Figure 9. As already observed in Figure 5, where the final binding arrangements of pNA on each AuNP are displayed, the tendency of the adsorbate is to adopt a perpendicular orientation, which could be no2, nh2, perp but also an intermediate configuration. This is because the small extension of the flat crystalline facets (i.e. (111) and (100)), which are made of 13 atoms at most and thus more prone to reconstruction, prevents them to host the entire molecule in a flat conformation. This is instead more probably realized on the steps (classified as (110) facets), connecting the (111) and (100) patches (Figure 9a,b), where the interaction of pNA with the substrate is maximized by the involvement of the neighboring atoms (i.e. the edges of the boundary faces). Furthermore, deeper inspection of the stably adsorbed molecules reveals two main characteristics: 1) the nh2 binding could be achieved by interaction of both the NH2 hydrogens with two Au atoms (see Ref. 65 for similar events – i.e. hydrogen bonds between H and molecular forms of Au, not with metal Au in the surfaces or nanoparticles) or by direct coordination of the nitrogen (which is thus in pyramidal configuration) lone pair with one Au atom of the support (covalent binding) (Figure 9c); 2) once the molecules are adsorbed, close to each other, a network of intermolecular hydrogen bonds between them, which further stabilize their position on the surface, can be formed, improved and maintained till the end of the simulations. All these findings are in agreement with experimental SERS measurements 66 which suggest the co-existence of all the adsorption modes predicted by the simulations. Moreover, the authors speculated that the 22


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variability of the connections could be due to concurrent adsorption of many molecules and competition to reach specific surface sites. The compromise, that is a relative stabilization, determines the different orientations of the adsorbates. Taking into consideration that beside the adsorption geometry also the alignment of the adsorbates in relation to the three different facets could be important to design specific supports, a tentative classification was made considering the number of contacts of pNA oxygens and hydrogens relatively to the atoms belonging to the three (111), (100) and (110) regions (when the distance is lower than 3 Å), for each AuNP model. The distributions are shown in Figure 4S of the Supporting Information. From that analysis it is evident that pNA binding is mainly realized through the single adsorption of NO2 or the NH2 groups and that for all the models the Au(111) surface was preferred, probably due to its larger extension. However, inspection of the final configurations suggested that most of the molecules were located on the steps connecting the facets, which in principle should be the most reactive zones.

5

One- and Two-Photon Spectra pNA-AuNP Complexes

The averaged one-photon absorption spectra from QM/CMM linear response calculations on the selected snapshots are shown in Figure 10. The spectra in the gas phase (black lines) show a dominant peak at around 325 nm and a shoulder at around 300 nm. The profile of the spectra for AuNP887, AuNP1985 and AuNP3007 are similar to each other in that the intensity of the dominant peak is around 2.3 times of the shoulder. In contrast, the absorption spectra of pNA on AuNP1505 exhibits a smaller difference between the dominant peak and the shoulder with a ratio of about 1.3. This might be attributed to the different composition of gold facets in the AuNP1505 as compared with the other two gold NPs (Table S1 in the Supporting Information). Inclusion of the gold NPs in the QM/CMM calculations results in

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a notable red-shift in the absorption bands (red lines in Figure 10). In addition, the intensity of the dominant absorption bands are enhanced, while the shoulder is reduced. Therefore, AuNPs show opposite effects on these two excitation modes. Moreover, the presence of the nanoparticle may lead to reversal of the excited states; for instance the S1 state, which is weaker than the strong S2 state (in terms of oscillator strength) in vacuo, may become more intense when the AuNP is present. As a consequence, the order of the excited states may change or the oscillator strengths can be notably influenced by Coulomb induction effects arising from the induced dipole and charges at the surface of AuNP. We show in Figure S5 of the Supporting Information how the distribution of the oscillator strengths of the two lowest excited states are altered by the metal surface and surrounding environment. While in vacuum the lowest excited state (S1 ) is often dark (very weak oscillator strength), in the presence of metallic and nonmetallic MM layers the S1 state becomes much more bright. The enhancement in the dominant absorption peak suggests that the connection with the AuNP tends to assist the lowest excited state to become stronger in oscillator strength, owing to the local enhancement effects on the electromagnetic field. Further inclusion of surrounding pNA molecules as point charges in the MM region leads to further red-shift of the absorption spectra, and the statistically averaged absorption becomes diminished due to the broad distribution of the excitation energies (Figure S6 of Supporting Information). As shown in Figure 10, the maximum absorption wavelength increases to around 400 nm, accompanied by a notable decrease in the absorption intensity. To further demonstrate the effects of the metal nanoparticle and surrounding environment, we decomposed the frontier molecular orbitals of pNA into three contributions, namely the NH2 group, the phenyl group, and the NO2 group (Table S7 of Supporting Information). The HOMO-2, HOMO-1, HOMO and LUMO orbitals are analyzed as they contribute dominantly to the low-lying excited states. In general HOMO-2 has its major contribution from NO2 and a minor contribution from the phenyl group, while the opposite holds for HOMO-1. The 24


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HOMO mainly consists of contributions from the phenyl group and NH2 , while the LUMO is composed by almost equal contributions from the phenyl group and NO2 . The presence of a metal nanoparticle puts a small perturbation on the frontier MOs, diminishing the NO2 contribution to HOMO-1 while slightly increasing its contribution to LUMO. The MM environment, however, shows a much greater effect which makes the distribution of HOMO and LUMO more evenly on the donor and acceptor groups, due to the strong electrostatic field generated by the MM point charges. The low-lying excitations are also analyzed in terms of transition among frontier molecular orbitals (Table S8 of Supporting Information). In vacuum the S1 state is usually composed of two transitions, HOMO-1 → LUMO and HOMO-2 → LUMO, which are all dark. The S2 state consists of mainly HOMO → LUMO transition which is bright. When the gold nanoparticle is present, a small portion of HOMO → LUMO transition also enters the S1 state. Meanwhile, the proportion of HOMO → LUMO transition in the S2 state is also slightly enhanced. The surrounding MM environment puts stronger effects on the transitions, leading to an even higher proportion of the HOMO → LUMO transition (40–50%) in the S1 state, and little to none contribution of HOMO → LUMO in the S2 state. This explains the reversal of the two low-lying excited states. The averaged two-photon absorption spectra, obtained by Lorentzian convolution of the calculated data, of pNA adsorbed on the different AuNP models are shown in Figure 11. The in vacuo spectra show broad absorption in the range 550-700 nm. Among the five lowest excited states only one shows significant amplitude (around 1 order of magnitude greater than other states), and the broad absorption results from averaging over many individual adsorbates. It is intriguing to notice that pNAs on the AuNP1505 show greater two-photon absorption than AuNP887, AuNP1985 and AuNP3007, which again may be related to the different ratio of the Au(111), Au(100) facets and Au(110) steps in the AuNP1505 model. In order to clarify this aspect, the absorption of pNA was decomposed into contributions 25



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from the different facets, as shown in Figure S10 of the Supporting Information. It was found that both the Au(111) and the Au(100) facets of AuNP1505 have a distinct effect in enhancing the two-photon absorption cross-section. Upon inclusion of the AuNPs in QM/CMM calculations, the averaged two-photon spectra become red-shifted and slightly diminished. The red-shift effect arises from the preference of AuNPs of assisting the lowest excited states, and the slight decrease in the two-photon absorption cross-section can be ascribed to the fact that the intensity of two-photon absorption is quadratically dependent on the excitation energy. Further inclusion of surrounding pNA molecules as point charges in the QM/CMM calculations leads to greater effects in the red-shift and a diminished two-photon absorption cross section. In the presence of surrounding pNA molecules the calculated spectra can be extended to over 800 nm with a cross section of around 1 GM. The convergence of the computed one- and two-photon absorption of physisorbed pNA with respect to the size of gold NPs was also examined. As shown in Figure 12, the maximum absorption wavelengths are plotted with respect to the sizes of the different AuNPs. The overall trend shows sign of convergence as the size of the AuNP increases. The general trend is that the polarization effects from the gold surface enhance one-photon absorption, whereas the surrounding MM pNA molecules notably diminish the molar extinction coefficient. In the case of two-photon absorption, the trend of cross section with respect to the size of the gold nanoparticle is shown in Figure 13. In Figures 12 and 13, the slopes of the straight lines connecting the points are getting smaller with respect to the size of AuNP, which is an indication that the convergence of the one- and two-photon absorption could be reached at a larger size of AuNP. It is interesting to observe that the calculated two-photon absorption showed rather small change with respect to the size of the gold nanoparticle when surrounding MM pNA molecules are present, indicating that the MM region has a dominant effect over that from the gold surface. Both the gold surface and the surrounding MM pNA molecules diminish the magnitude of the two-photon absorption. Such effects show some oscillation for 26


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smaller AuNPs due to different ratios among Au(111) surface, Au(100) surface and Au(110) steps, but are expected to converge better as the size of the gold NP grows.

Conclusions The purpose of the present work was to generalize the application of the multiscale methodology, developed during the last few years for hybrid metallo-organic species, by extending the representation of the metal part from surface slabs or clusters to realistic metal nanoparticles. As in the earlier studies, the presence of a metal in a heterogeneous environment calls for a specific parameterization. The integrated approach, namely the combination of dynamical sampling with calculations of the properties or spectra from selected configurations extracted from the dynamics sampling, could be a promising choice. Molecular dynamics simulations based on an accurately parametrized reactive force field are carried out without any constraints to identify reliable configurations of the hybrid material, whereas QM/CMM calculations are applied for simulating one- and two-photon absorption spectra of representative models. In this multilevel approach, quantum chemistry plays a fundamental role because it is used on one hand to parameterize the force field and on the other hand as the core electronic structure representation for the light-matter interaction in the molecular adsorbents. The multiscale QM/CMM technique is effectively applied to study the adsorption behavior of pNA on spherical gold nanoparticles differing in size. The models adopted here can be seen as the inner portion of real systems where the covering molecular layers prevent the solvent from reaching the metal supports. The surrounding environment and its effects might be seen as a perturbation to the orientation and position of the adsorbates, which have been exhaustively sampled during the dynamics runs. We note that the dielectric screening due to the surrounding environment is neglected. The simulations have revealed, in agreement

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with the experimental results of Ma and Fang, 66 that various binding modes co-exist on the gold substrates because of the competitive adsorption of the molecules induced by selfinteractions and nanoparticle morphology. In line with the experimental finding, the NO2 binding is highly favored but as probable as the NH2 connection. Other configurations are less populated but also observed. The molecules are further stabilized on the surface by a network of intermolecular hydrogen bonds which is denser when the various facets are more extended because more molecules can adopt a parallel orientation on the substrate. Indeed, this is the case of the larger nanoparticle. Multiscale QM/CMM calculations suggest that the one-photon absorption is red-shifted and enhanced, while the two-photon absorption becomes red-shifted and slightly diminished, owing to the non-linear dependence of two-photon absorption on the excitation energy. AuNPs seem to assist the lowest excited state of pNA molecules through Coulomb interaction arising from the induced dipoles and charges on gold surfaces. The results reveal both general convergence patterns and details of the spectral dependence with respect to the size of the gold nanoparticles, and also difference in those patterns between the one- and two-photon absorption modes, which even can origin in reordering of states by the gold particle presence. Charge imaging of the surface introduces red-shifts both because of altered excitation energy dependence and variation of the relative intensity of the inherent states making up for the total band profile. For the smaller nanoparticles the difference in the crystal facets are important for the spectral outcome. The results of these studies indicate that the QM/CMM model, integrated with dynamics sampling, is a viable approach to extend the analysis of properties of hybrid metal-organic clusters to more realistic hybrid metal nanoparticles-organic composites. Detailed structural, dynamical and spectroscopic characterization of complex materials can be accomplished, paving the way for the establishment of property size-structure relationships of such aggregates. The results of this study indicate that spectral convergence can be obtained for 28


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relatively small size clusters but these are just prototype systems and the extension of the calculations to the ten-nanometer scale is underway. Even though the excitation frequencies considered here seem not to be completely outside the experimental plasmonic resonances, which in the case of spherical NPs are found in the 500-550 nm range, they can be associated with the most useful application aspect of metal nanoparticles, namely the generation of plasmon-polaritons of extreme field strengths for single molecular sensing. However, the new QMCMM model will accommodate the plasmonic regime through special parameterization of the metallic part of the environment in order to study the full coverage of the frequency spectrum, including plasmonic resonances. The new developments will be effective to analyze the properties of hybrid metallo-organic nanoparticle devices.

Supporting Information QM calcualtions used for parametrizing pNA–Au interactions; ReaxFF parameters; geometrical description of the AuNPs models; distributions of Imax/Imin, Eccentricity and Radius of Gyration calculated for each simulation; Distributions of the number of Au-O and Au-N contacts; Calculated oscillator strengths of the two lowest singlet excited states; Frontier molecular orbital composition from the NH2 , phenyl and NO2 groups of pNA; analysis of low-lying excitations in terms of transitions among frontier molecular orbitals of pNA; individual contributions of one-photon peak absorption from three different gold facets; individual contributions of two-photon peak absorption from three different gold facets. This information is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments S.M. is grateful to Adri C. T. van Duin for the serial version of the reactive dynamics program (ReaxFF) and acknowledges partial support from CNR Short Term Mobility program 2016. The Knut and Alice Wallennberg foundation (Grant No. KAW-2013.0020) is acknowl29



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edged for financial support. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC, through the project "Multiphysics Modeling of Molecular Materials", SNIC 2014/11-31.

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Figure 1: Comparison of QC and ReaxFF energy optimized configurations of four different arrangements of pNA on the Au(111) slab. The carbon atoms of the geometries optimized at the QC level are gray, whereas in the ReaxFF optimized structures they are cyan. ACS Paragon Plus Environment

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Figure 2: AuNP models built for the simulations. Blue regions represent the (111) surfaces, red regions the (100) surfaces, whereas the green regions identify the (110) faces. Pink atoms belong to the second layer.



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Figure 3: Center of mass motion on the surface and inclination of the pNA molecule relatively to the xy plane (Au(111) interface). ACS Paragon Plus Environment

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Figure 4: Atom-surface distances as a function of the simulation time and their distributions



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Figure 5: Final structures of the four simulations. Only pNA molecules directly adsorbed on the surface are displayed. ACS Paragon Plus Environment

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Figure 6: Au-Au Radial distribution functions of the 8 MD simulations (functionalized and not functionalized AuNPs). Comparison with the RDFs of the lattice (cyan peaks) and extracted from the literature: crystalline (black curve) and amorphous (green curve) nanoclusters. 64 In the Inset Au-Au minimum distances.



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Figure 7: Minimum distance of nitrogen, oxygen and hydrogen (of the NH2 group) atoms from the Au atoms of the AuNPs. Evolution and distribution.


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Figure 8: pNA atom-atom radial distribution functions to identify intermolecular contacts.



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Figure 9: Typical binding modes identified in the final sampled structure of the AuNP887+pNA dynamics. ACS Paragon Plus Environment

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Figure 10: Calculated one-photon absorption spectra of pNA on AuNPs. Error bars indicate the standard error of mean.



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Figure 11: Calculated two-photon absorption spectra of pNA on AuNPs. Error bars indicate the standard error of mean.


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Figure 12: Size-dependence of one-photon absorption from three different computational models.



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Figure 13: Size-dependence of two-photon absorption cross-section from three different computational models.


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Figure 14: TOC. Typical pNA adsorption modes on AuNPs. Blue spheres belong to Au(111) facets, red spheres to Au(100) facets, whereas green spheres identify the connections between the previous regions. The second layer Au atoms are pink.


Optical Properties of Gold Nanoclusters Functionalized with a Small

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