First-Principles Investigations of Chirality in Trimetallic Alloy Clusters

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First-Principles Investigations of Chirality in Trimetallic Alloy Clusters: AlMnAu (n=1-7) n

Meng Zhang, Jianfei Zhang, Teng Gu, Hongyu Zhang, Youhua Luo, and Wei Cao J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp511575y • Publication Date (Web): 18 Mar 2015 Downloaded from http://pubs.acs.org on March 24, 2015

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The Journal of Physical Chemistry

First-Principles Investigations of Chirality in Trimetallic Alloy Clusters: AlMnAun (n=1-7)

Meng Zhang1, Jianfei Zhang1, Teng Gu2, Hongyu Zhang1, Youhua Luo1*, and Wei Cao3* 1

Department of Physics, East China University of Science and Technology, Shanghai 200237,

China 2

Department of Physics, State Key Laboratory of Surface Physics and Advanced Materials

Laboratory, Fudan University, Shanghai 200433, China 3

Department of Physics, University of Oulu, P.O. Box 3000, FIN-90014, Finland

* To whom correspondence should be addressed. E-mail: [email protected] (Y.L.); [email protected] (W.C.)

ABSTRACT: Chirality, also called handedness, plays a crucial role ranging from biological self-assembly schemes, organic polymer functionalities, to optical material designs. In this article, we demonstrated a first-principles investigation of chirality in magnetic AlMnAun0/+1/−1 (n=1-7) clusters. Optimized structures of the AlMnAun clusters exhibit configurational combinations between AlAu n+1 and MnAun+1 clusters, indicating a subtle but equal competition between Au-Al and Au-Mn interactions in the alloy clusters. High magnetic moments are equal or bigger than 4 µB in AlMnAun clusters due to the presence of the Mn dopant. Chirality turns up with the forms of right-handed and left-handed in stable AlMnAu5, AlMnAu6, and AlMnAu7 clusters. As a result, reflection symmetries 1 ACS Paragon Plus Environment


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are found in vibrational Raman and circular dichroism spectra of these chiral pairs. Present study shows that chiral magnetic clusters can be composed by doping two heteroatoms with one intrinsic magnetic dopant into small gold clusters. KEYWORDS: Density functional theory; Gold clusters; Chiral clusters; Magnetic properties;

1. INTRODUCTION The past few decades have witnessed a rapid development of cluster science. One of the major goals within this domain has been dedicated to discovering highly stable clusters with unique properties for the purpose of building blocks in novel nanomaterials. Clusters often show different physical and chemical features from their bulk counterparts, yet drawing tremendous attentions due to their inimitable optical and magnetic properties, as well as catalytic reactivities.1-5 Uniqueness is mostly originated from combinations of different metallic pieces, size effects, as well as steric configurations6,7. In three-dimensional space, clusters and molecules are considered chiral if their corresponding mirror images are not able to superpose on themselves by any rotations and translations. Coined by Lord Kelvin, the chirality subsequently refers to incapability of coinciding clusters and molecules with their mirrored counterparts.8 It is of great importance in physics, chemistry, and biology. For example, chiral phases of organic molecules are the main cornerstones in light display devices.9 In life science, chirality ensures orders of the repair mechanism in the DNAs.10 2 ACS Paragon Plus Environment

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While studies towards chirality have been proposed through knot theory in organic chemistry, 11, 12 theoretical investigations of chirality in metallic clusters are scarce and quantifications of handedness in many cases remain challenging13. In monometallic clusters, chirality has been discovered in pure gold clusters but with relatively larger number of gold atoms at 32, 34, 55, and 72.14-21 Later, structures of a thiolate-protected gold clusters were predicted chiral via density functional theory calculations.22-28 Potential applications of the chiral gold clusters in enantioselective and catalytic reactivity were also discussed therein. A recent study by Elgavi et al. demonstrated that chirality could exist in copper nanoalloy clusters.29 Chirality was further predicted in bimetallic clusters by doping hetero metal atom to lower cluster symmetries.30 A combined study utilizing anion photoelectron spectroscopy and density functional theory was conducted to search for chiral structures in a system of four-atom metal clusters.31 Moreover, recent experiments showed that when chirality meets magnetism in metallic clusters, cross effects from chiral dichroism and magnetic dichroism lead to magnetic-chiral dichroism (MChD). Such a second-order effect can selectively enhance or filter out light harvesting efficiencies.32, 33 Deeping in insights of the previous works, chirality in small-sized clusters can be triggered by adding more dopant species. But searching for magnetic chiral clusters, though demanded, requires elaborated efforts. In this article, we investigated chirality in MN-doped (M=Mn, N=Al) magnetic gold cluster hosts. The gold clusters were chosen as matrices due to their distinctive catalytic, electronic, optical, magnetic 3 ACS Paragon Plus Environment


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properties, and possible applications in the nanoscale devices34-75. The Mn dopant was selected to breed magnetism and the Mn-doped Au clusters have been well studied76-82. Pal et al. reported a joint experimental and theoretical study on the structures of a series of gold clusters doped with a group-14 atom.83 Similar to the group 14 dopants, the electronically non-spherical p-block Al atom has also show its distinct role when doped into the small Aun clusters in our previous works

84-86

. It was also employed as the

dopant to break symmetries of the Aun clusters. 87-90 Thus, introducing the Al dopant will lower the system symmetries which may prompt the appearances of chirality in the dually doped Aun clusters. To make a clear illustration of the present study, the content in the article is arranged as follows. Firstly we performed the low-energy isomers identification and studied structural evolution of the neutral, anionic, and cationic MN-doped gold clusters. Chirality was found in three cluster groups. Then, magnetic and electronic properties of the trimetallic AlMnAun clusters were discussed. Following discoveries of chiral clusters, optical spectra of the chiral pairs were calculated to show their responses to light. It is hoped that the present research will stimulate experimental realization and verifications of the ternary magnetic and chiral metal clusters.

2. COMPUTATIONAL METHODS To search for local minima structures systemically in the present work, possible initial structures of AlMnAun clusters were generated through four ways as follows. (1) A basin-hopping global optimization method using Gupta potential with 3 species was 4 ACS Paragon Plus Environment

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employed to produce a large number of isomers for further DFT optimization.91, 92 Each run consisted of 10000 basin-hopping steps at a reduced temperature of 0.8 K. The initial linear and angular step parameters were 0.36 and 0.4. (2) Our cluster structure search was also based on the CALYPSO method, which has been proved as an efficient structure prediction method93,94. A local version of particle swarm optimization (PSO) algorithm was implemented to utilize a fine exploration of potential energy surface for a given non-periodic system.95 The Gaussian code with PBEPBE/ LANL2DZ was used for local structure optimization during the structure prediction in CALYPSO calculations. (3) Recurrence was employed as the third way where a previous result of M or N- doped Au clusters was employed as a guideline to generate the structures of AlMnAun.79,89,96 In particular we added one extra Au atom to the configurations available from the previous optimized geometries of the doped clusters MnAun+1 and AlAun+1. (4) Some initial structures were obtained by randomly replacing the Au atoms by Mn and Al atoms in the host Au clusters. When more than 500 distinct isomer structures were collected, they were reoptimized at a higher level of convergence by using density functional theory (DFT) implemented in the DMOL3 program.97 Relativistic calculations were carried out with scalar relativistic corrections to valence orbitals relevant to atomic bonding properties via a local pseudopotential (VPSR). All-electron spin-unrestricted calculations with double-numerical basis sets including d polarization functions (DNP) were employed. Generalized gradient approximation in the Perdue-Burke-Ernzerhof (PBE) functional 5 ACS Paragon Plus Environment


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form was chosen.98 The quality of self-consistent field (SCF) convergence tolerance was set as ‘fine’ with a convergence criterion of 1×10-5 Hartree on total energy and electron density, 2×10-3 Hartree/Å on the gradient, and 5×10-3Å on the displacement in our calculations. Harmonic vibrational frequency analysis was also carried out at the same level of theory to confirm that the low-energy isomers were true minima. No imaginary frequencies for structures were found here. In addition, we carried out a detailed calculation for each possible spin multiplicity (SM) ranging from 1 to 12 of this system. The local minima structures at the higher level (PBE/ VPSR in DMOL3) arrived at the same set of the results of CALYPSO method. To justify the results of the isomers obtained in present work, we repeated the structure optimizations independently with other two functional forms for several starting geometries. They are the Perdew and Wang’s 1991 exchange and correlation functional (PW91), and Becke’s 1988 exchange functional and the correlation functional of Perdew (BP86).99,100 The final lowestenergy structures were found the same as the results given by the present PBE methods. The validity of PBE/VPSR method in first-principles prediction of gold clusters was also investigated. Physical parameters of Au2, Au2-, AlAu, Au7, and Au7- clusters were calculated with this method. The results are listed in Table 1. It can be seen from the Table 1 that the properties of these clusters computed using PBE functional, DNP basis and VPSR pseudopotential are in excellent agreements with available experiment data. Thus, the PBE/VPSR method is valid in calculating the present Au cluster system. 6 ACS Paragon Plus Environment

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The vibrational spectra of the chiral clusters were calculated and simulated at PBE/LANL2DZ level in the Gaussian09 package (G09). 101

3. RESULTS AND DISCUSSIONS 3.1. Geometric structures and relative stabilities. Isomers of the bimetallic MN-doped Aun clusters (n=1-7) are more abundant than these gold clusters doping with single metal atom. In order to investigate chirality in the present system, we considered extensive two-dimensional (2D) and threedimensional (3D) structures to determine the lowest-energy geometry for each trimetallic cluster. Many stable isomers were obtained and top low-lying isomers were collected and shown in Figure 1. The x,y,z coordinates of the proposed structures of the AlMnAun (n=1-7) clusters are given in the Supporting Information. The symmetries, spin multiplicities and differences of the total binding energies between an isomer and the lowest-energy structure were also listed below each isomer in Figure 1. Contributions of the vibrational zero-point energy corrections were added when making comparisons of the relative energies for the low-lying structures. The optimized geometries reveal that neutral AlMnAun clusters prefer 3D structures. The dominant growth pattern is in the form of single Au atom capping the structure of AlMnAun-1. The lowest-energy structures are all compact with the shortest Au-Al bond length ranging from 2.353 to 2.508 Å, Au-Mn bond length from 2.524 to 2.573 Å, and Al-Mn bond length from 2.737 to 3.070 Å. The bond lengths are listed in Table 2. It should be noted that geometries of these mixed clusters AlMnAun are very different from their 7 ACS Paragon Plus Environment


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corresponding pure Aun+2 clusters and the M- or N- single metal atom doped Aun+1 clusters as Figure 2 shows. When a 3d transition-metal (TM) atom Mn and a 3p atom Al are doped into Aun clusters together, both the 3d and 3p orbitals of the heteroatoms can evidently influence structures of the gold clusters. By comparing the structures of these clusters, the lowest-energy structures of AlMnAun (n=1-7) are found as the combinations of the configurations of AlAun+1 and MnAun+1 clusters. In AlMnAun clusters both Mn and Al atoms tend to be centrally (less peripheral) doped to maximize its coordination number. The coordination number of Mn atom and Al atom in each AlMnAun cluster are almost the same as tabulated in Table 2. The Au-Al and Au-Mn interactions play an equivalently crucial role in determining the structures of AlMnAun clusters. This also denotes strong competitions between tendencies of forming the planar structures around the Mn atom and three-dimensional structures around the Al atom. The lowest-energy structure of the trimer AlMnAu is a triangle with the Cs symmetry. The linear configurations in which the Al atom or Au atom takes the central position are much higher in energy. For AlMnAu2 cluster, a 3D structure adding one Au atom to the triangle AlMnAu is found to be the most stable structure. Three 2D rhombic forms are all much higher in energy. The trigonal bipyramidal shape structure with C3v symmetry is the lowest-energy isomer for AlMnAu3. A distorted isomer of 3D pyramidal structure and two lower-symmetry 2D arrangements are all much higher in energy. The most stable structure for AlMnAu4 is the bicapped square structure with 8 ACS Paragon Plus Environment

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high C4v symmetry. However, the energy of metastable 3D isomer is very close to that of the most stable geometry, within 0.01eV. As pointed out by Bonačić-Kouteckýand coworkers

75

, the DFT methods afford very different surfaces for gold clusters when

compared to traditional wavefunction methods. The structures and properties of the global minimum in gold clusters seem to depend on the level of theory used to calculate the potential energy surfaces.44 In this way the DFT computations could not clearly establish their ground states. This may indicate that these two isomers can coexist in a certain environment, especially at room temperature. Within all the clusters studied in the present work, it is noticed that chirality debuts in lowest-energy structures when n=5, and also exists in AlMnAu6 and AlMnAu7. The evidences of handedness are obvious in Figure 1e), 1f), and 1g). Moreover, a large number of chiral clusters were found when n=7. The top five low-lying isomers of AlMnAu7 clusters are all chiral structures as shown in Figure 1g). Current chiral clusters have the disordered structures with the C1 point symmetry, but pure chiral gold clusters have high symmetries. For instance, anionic Au34- is a chiral structure with C3 symmetry and Au72 is a cage with icosahedral symmetry.14,19 In this work, we also systematically optimized the charged AlMnAun+1/−1 clusters to investigate the possible existence of chirality in these charged clusters. It is found that chirality also exists in the cationic and anionic system. For anionic clusters, chiral structures appear on the stage in the size of n=5, and the lowest-energy chiral structures are all similar to the case of neutral system as Figure 1 shows. For cationic clusters, chiral structures appear 9 ACS Paragon Plus Environment


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in AlMnAu4+ in the fifth lowest-energy isomer for the first time. However, the lowestenergy structures of AlMnAu5+, AlMnAu6+, and AlMnAu7+ clusters are all achiral. Although adding one Au atom based on the lowest-energy structures of the prior AlMnAun-1 is a dominant growth pattern in the neutral and anionic AlMnAun clusters, the border edge of transform is obvious in the size of n=5, namely, the occurring of chiral structure in n=5 breaks the normal procedure of cluster growth. Before the chiral AlMnAu5 cluster, the AlMnAun prefers the structure with high symmetry, while the symmetries of the clusters change to the lowest C1 point group after the size of n=5. Figure 1 shows that doping with two different types of metal impurities is likely to lower symmetries of the clusters. This is due to the existence of different bond arrangements around the heteroatom in such structures, and will result in chiral structure emerging. Consequently, we conclude that, in the neutral, anionic and cationic states, the chirality is likely to appear in small gold clusters by introducing two different metallic dopants. A number of other new isomers are also worthy of mentioning. For example, the planar 6-fold ring for n=5 with symmetry broken by the Al atom at the edge evolves from the structure of Au6 ring with the transition metal Mn atom sitting in the center, finalizing in a perfect D6h symmetry. As shown in Figure 2 the structure is in accordance to previous studies.80,81 The distorted cube geometry of the metastable isomer for n=6 with a subtle energy difference 0.06eV in Figure 1e) is noteworthy for its possible functions of precursors in a bulk alloy. The stabilities of the lowest-energy structures of neutral AlMnAun were further 10 ACS Paragon Plus Environment

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proved by comparing average bonding energies per atom (Eb) of the binary atoms doped Aun, M- or N- single atom doped Aun+1, and pure Aun+2 clusters. The calculated results were shown in Figure 3. From this figure, it can be seen that the Ebs of AlMnAun clusters are significantly higher than those of the corresponding pure Aun+2. In addition, the

average

binding

energies

commonly

exhibit

in

a

sequence

of

AlMnAun>AlAun+1>MnAun+1>Aun+2 for each size n, especially when 3 ≤ n ≤ 7. The larger values of Eb indicate that doping with two different types of metal atoms (Al and Mn) can effectively enhance the stabilities of the Aun clusters. The thermodynamic stabilities of the ground-state structures of three neutral AlMnAun (n=5-7) clusters were also confirmed through Born-Oppenheimer molecular dynamics simulation implemented in the DMOL3 code at room temperature (T=300 K). Each molecular dynamics simulation lasted for 4 ps and the structure was monitored during this time. The time interval in molecular dynamics simulations was set to 0.4 fs. As shown in Figure 4, the relative potential energy remains unchanged within the time of dynamic simulations. Thus, the chiral structures are stable at room temperature.

3.2. Electronic and magnetic properties In the following, we will discuss the electronic and magnetic properties of the AlMnAun clusters. The energy gaps (Egap) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of these clusters were calculated herein and listed along with isomers in Figure 1. It can be seen that the electronic properties are not only dependent on the size of the cluster but also on the 11 ACS Paragon Plus Environment


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structures of the isomers. The size dependent magnetism of AlMnAun (n=1-7) clusters were depicted in Figure 5. Magnetic moments of 4 μB, 5 μB, and 6 μB are clearly seen in the AlMnAun clusters. The moments are much larger than those of bare Aun+2 and AlAun+1 clusters which are in the form of odd-even alternations (0 μB and 1 μB, respectively). This tells that the 3d TM atom Mn decisively dominates the magnetic moment of doped gold clusters. The total magnetic moments of the clusters are mainly located on Mn atoms, and the 3p Al atoms almost have no contributions to magnetic properties of the clusters as shown in Figure 5. A case study to illustrate electron charge density and spin density distributions was carried out for the lowest-energy structures of chiral MnAlAu6 clusters. Their charge and spin distributions were graphed in Fig 6a) and 6b). It can be seen that although the total charge density is extended over the whole clusters, the spin density is almost entirely located on the manganese sites. To investigate geometry impacts on cluster magnetism, we also calculated the magnetic moments of other low-lying isomers. The results were listed in the very left column in Figure 1 and found the same in clusters of the same size. To find origins of the magnetic and electronic properties, we further investigated orbital hybridizations of the most stable AlMnAun clusters. For transition metal impurities in a nonmagnetic host, the hybridization of the impurity d states with the host metal plays a crucial role in determining the local magnetic moments. However, the hybridization is sensitive to both the local structure and the electronic nature of the host. The partial density of states (PDOS) of the AlMnAu6 case in Figure 6c) clarifies 12 ACS Paragon Plus Environment

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the hybridization between the atomic orbitals of the guest Mn (d orbital) and Al (p orbital) atoms and host atom Au (s orbital). Shapes of total density of states for α electron (spin-up) and β electron (spin-down) are quite different in forming the magnetism in AlMnAu6. Similar situations also exist in PDOS of other clusters. To facilitate comparison with future experiments, we simulated photoelectron spectra (PES) of the anionic AlMnAun– clusters (n=5-7) for the lowest-energy structures. As shown in Figure 7, the PES results were drawn by adding the occupied orbital energy relative to the HOMO to the vertical detachment energies with Gaussian profiles of 0.01 eV width. The distinct PES spectra can be used by experimentalists to identify the cluster structures.

3.3. Optical properties of the chiral AlMnAun clusters Following the discovery of chirality in stable AlMnAun (n=5-7) clusters, we further examined unique optical properties of these chiral clusters. The vibrational spectroscopy as a result of the chirality-induced physical characteristics in natural optical activity was investigated.102,103 On the basis of theoretical calculations at PBE/LANL2DZ level in G09, various spectral characteristics including infrared (IR) vibrational spectra, Raman scattering activity (RSA) spectra, vibrational Raman optical activity (VROA) spectra, and vibrational circular dichroism (VCD) spectra for the lowest energy AlMnAu5, AlMnAu6, and AlMnAu7 clusters are collected from the calculated vibrational frequencies. All simulated spectra in Figure 8 are convoluted with Lorentzian functions with a full width at half maximum (FWHM) of 4 cm−1 as a 13 ACS Paragon Plus Environment


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common number for many experimental resolutions. The IR and RSA spectra of the enantiomer I and enantiomer II are the same. However, the VROA and VCD spectra show scatterings and attenuations of polarized light by the chiral clusters are totally different. The VROA and VCD spectra display mirror image symmetries for different handed enantiomers. Beside identifications of absolute conﬁgurations of chiral pairs, the VROA and VCD spectra also indicate possibilities of using these chiral magnetic clusters in magnetic drive light filtering or harvesting systems.

4. CONCLUSIONS The equilibrium structures, growth behavior, stabilities, electronic, magnetic, and spectroscopic properties of binary metal impurities (3p Al and 3d Mn) doped small Aun clusters have been systematically studied using density functional theory with generalized gradient approximation in DMOL3 and PBE/LANL2DZ level in G09. For each cluster, an extensive search of the most stable structure was conducted by considering a large number of structural isomers and spin multiplicity. To the best of our knowledge, systematic investigation of trimetallic MNAun clusters has not been reported in literature. Though small metal clusters usually exhibit extraordinary sizedependence, in the case of dual dopant doped gold clusters system, structures and properties depend not only on cluster size but also on the competition or synergy between the heteroatoms in bonding with the host atoms. Combinations of the configurations of AlAun+1 and MnAun+1 clusters dominate the cluster growth. Such a growth pattern demonstrates strong competitions between Au-Al interactions and Au14 ACS Paragon Plus Environment

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Mn interactions. Relative larger magnetic moments were found in stable AlMnAun clusters, as a result of introducing the Mn dopants. Chiral structures exist in thermostable AlMnAun (n=5-7) clusters. This denotes chirality is able to be induced by doping two different heteroatoms into the small gold clusters. These enantiotopic clusters have identical electronic and magnetic properties in this work. The optical properties were also presented to identify the presence of enantiomers of the chiral clusters. Although the IR and RSA spectra of the two enantiomers are identical, the VROA and VCD spectra show clear mirror image relationship. It is hoped that the present work of small AlMnAun clusters combining magnetism and chiral features will be served as a starting point for further systematic search of such nanoalloy clusters. The detailed structural information on neutral gold AlMnAun cluster can be experimentally verified by using vibrational spectroscopies. Taking the relative large magnetic moments and light dichroic properties into consideration, the chiral AlMnAun clusters may have great potentials in magnetic field driving light filtering devices.

ACKNOWLEDGEMENTS This work is financially supported by the National Natural Science Foundation of China (Grant no. 11204079, 11304096 and 51205001), the Natural Science Foundation of Shanghai (Grant no. 12ZR1407000), the University Student Innovation Program of Shanghai (Grant no. S12084) and the Strategic Grant of Oulu University. M.Z. acknowledges financial support from Oulu University during his stay in Finland. 15 ACS Paragon Plus Environment


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Authors thank X. Y. Shi for his help of language improvements.

Supporting Information Available: Full description of the x,y,z coordinates of the calculated structures presented in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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The TOC graphic



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TABLE 1. Calculated Bond Distance d (Å), Vibrational Frequency ωe (cm−1), Average Binding Energies Per Atom Eb (eV), Ionization Potential IP (eV), Vertical Electron Detachment Energies VDE (eV), and Adiabatic Electron Detachment Energies ADE (eV) of the Au2, Au2-, AlAu, Au7, and Au7- Clusters Optimized with PBE/VPSR (DMOL3).

System Au2

Au2AlAu

Au7

Au7-

Property d ωe Eb IP d VDE d ωe Eb ωe1 ωe2 ωe3 VDE ADE

This work 2.51 173 1.15 9.44 2.63 1.98 2.39 313 1.66 153 172 185 3.39 3.35

Experimental 37-40,50,56 2.47 191 1.15,1.18 9.50, 9.22 2.58 2.01 2.34 333 1.67 165 185 203 3.46 3.40


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TABLE 2. Symmetry Type, Shortest Au-Al, Au-Mn, and Al-Mn Bond Lengths RAu-Al (Å), RAu-Mn (Å), and RAl-Mn (Å), Average Binding Energy Per Atom Eb (eV), Coordination Number (CN) of the Mn and Al Atoms of Neutral AlMnAun (n=17) Clusters for the Lowest-Energy Structures Optimized with PBE/VPSR (DMOL3). I and II in Brackets Represent the Enantiomer I and Enantiomer II of the Chiral Structures, Respectively. System Symmetry Eb RAu-Al RAu-Mn RAl-Mn CNMn CNAl AlMnAu1 Cs 1.89 2.435 2.534 2.737 1 1 AlMnAu2 Cs 2.22 2.454 2.524 3.050 2 2 AlMnAu3 C3v 2.44 2.460 2.530 2.932 3 3 AlMnAu4 C4v 2.49 2.508 2.573 3.064 4 4 AlMnAu5 (I) C1 2.54 2.354 2.531 2.918 4 4 AlMnAu5 (II) C1 2.54 2.357 2.531 2.912 4 4 AlMnAu6 (I) C1 2.56 2.388 2.544 2.998 5 4 AlMnAu6 (II) C1 2.56 2.383 2.540 2.985 5 4 AlMnAu7 (I) C1 2.71 2.353 2.524 3.070 6 4 AlMnAu7 (II) C1 2.71 2.359 2.530 3.068 6 4



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Figure 1. Lowest-energy structures and low-lying isomers of the neutral, anionic, and cationic AlMnAun clusters with n=1−7 in Figures a)-u), respectively. Red, purple and yellow circles represent aluminum, manganese and gold atoms, respectively. Relative energies (in eV), the spin multiplicity (SM) and HOMO-LUMO energy gap (Egap) are listed under each isomer. The symmetry type is given at 0.01 Å tolerances. Neutral clusters a) n=1

C∞v

SM=6

Cs SM=6

C∞v

Egap=0.82 eV

Egap=0.43 eV

Egap=0.41 eV

ΔE=0 eV

ΔE=0.93 eV

ΔE=1.18 eV

Cs SM=7

Cs SM=7

C2v

Egap=0.51 eV

Egap=0.61 eV

ΔE=0 eV

ΔE=0.12 eV

SM=6

b) n=2

SM=7

Cs SM=7

Cs SM=7

Egap=1.51 eV

Egap=0.52 eV

Egap=1.03 eV

ΔE=0.15 eV

ΔE=0.65 eV

ΔE=0.72 eV

c) n=3

C3v

SM=6

Cs SM=6

C2v SM=6

Cs SM=6

Cs SM=6

Egap=1.64 eV

Egap=1.35 eV

Egap=1.65 eV

Egap=0.96 eV

Egap=0.84 eV

ΔE=0 eV

ΔE=0.56 eV

ΔE=0.57 eV

ΔE=0.69 eV

ΔE=0.78 eV

d) n=4

C4v

SM=5

Cs SM=5

Cs SM=5

C1

Egap=0.60 eV

Egap=0.55 eV

Egap=0.60 eV

Egap=0.52 eV

Egap=0.60 eV

ΔE=0 eV

ΔE=0.01 eV

ΔE=0.15 eV

ΔE=0.17 eV

ΔE=0.22 eV

ACS Paragon Plus Environment

SM=5

C3v SM=5

34

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e) n=5

C1 SM=6

Cs SM=6

Cs SM=6

Cs SM=6

C1

Egap=1.37 eV

Egap=1.54 eV

Egap=1.20 eV

Egap=1.45 eV

Egap=0.36 eV

ΔE=0 eV

ΔE=0.02 eV

ΔE=0.03 eV

ΔE=0.04 eV

ΔE=0.07 eV

SM=6

f) n=6

Cs SM=5

C1

Egap=0.45 eV

Egap=0.46 eV

Egap=0.45 eV

Egap=0.39 eV

Egap=0.53 eV

ΔE=0 eV

ΔE=0.06 eV

ΔE=0.07 eV

ΔE=0.08 eV

ΔE=0.14 eV

C1

SM=5

SM=5

C1

SM=5

Cs SM=5

g) n=7

C1

SM=6

C1

SM=6

C1 SM=6

C1

SM=6

C1

SM=6

Egap=0.86 eV

Egap=1.14 eV

Egap=0.86 eV

Egap=0.81 eV

Egap=1.28 eV

ΔE=0 eV

ΔE=0.02 eV

ΔE=0.08 eV

ΔE=0.14 eV

ΔE=0.17 eV

SM=6

C1

SM=6

Cs SM=6

Cs SM=6

C1

Egap=0.70 eV

Egap=0. 92 eV

Egap=0.87 eV

Egap=0.69 eV

Egap=0.79 eV

Egap=1.05 eV

ΔE=0.19 eV

ΔE=0.20 eV

ΔE=0.22 eV

ΔE=0.23 eV

ΔE=0.27 eV

ΔE=0.33 eV

C1

SM=6

Cs SM=6



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Page 36 of 46

Anionic clusters h) n=1

SM=5

C∞v

SM=5

Cs SM=5

C∞v

Egap=0.70 eV

Egap=0.49 eV

Egap=0.30 eV

ΔE=0 eV

ΔE=0.82 eV

ΔE=0.91 eV

i) n=2

Cs SM=6

C1

SM=6

Egap=1.10 eV

Egap=0.55 eV

ΔE=0 eV

ΔE=0.65 eV

C2v

SM=4

C1 SM=6

C1

SM=4

Egap=0.18 eV

Egap=0.68 eV

Egap=0.54 eV

ΔE=0.71eV

ΔE=0.92 eV

ΔE=1.18 eV

j) n=3

C3v

SM=5

Cs SM=5

C1 SM=5

C1 SM=5

Cs SM=5

Egap=0.39 eV

Egap=0.42 eV

Egap=0.35 eV

Egap=0.50 eV

Egap=0.57 eV

ΔE=0 eV

ΔE=0.20eV

ΔE=0.46 eV

ΔE=0.49 eV

ΔE=0.57 eV

k) n=4

C3v

SM=6

C3v

SM=6

Cs SM=6

Cs SM=6

Cs SM=6

Egap=1.70 eV

Egap=1.02 eV

Egap=1.76 eV

Egap=0.79 eV

Egap=0.83 eV

ΔE=0 eV

ΔE=0.27 eV

ΔE=0.28 eV

ΔE=0.46 eV

ΔE=0.52 eV


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l) n=5

C1 SM=5

Cs SM=5

C1 SM=5

Cs SM=5

C3v SM=5

Egap=0.55 eV

Egap=0.32 eV

Egap=0.50 eV

Egap=0.28 eV

Egap=0.47 eV

ΔE=0 eV

ΔE=0.06 eV

ΔE=0.09 eV

ΔE=0.10 eV

ΔE=0.11 eV

m) n=6

Cs SM=6

Cs SM=6

C1 SM=6

C1

Egap=1.22 eV

Egap=1.21 eV

Egap=1.04 eV

Egap=1.17 eV

ΔE=0.02 eV

Egap=1.10 eV

ΔE=0 eV

ΔE=0.21 eV

ΔE=0.33 eV

ΔE=0.35 eV

C1

SM=6

SM=6

n) n=7

C1 SM=5

C1

Egap=0.49 eV

Egap=0.49 eV

ΔE=0 eV

ΔE=0.17 eV

C1

SM=5

SM=5

C1

SM=5

Cs SM=5

Cs SM=5

Egap=0.44 eV

Egap=0.45 eV

Egap=0.47 eV

ΔE=0.18 eV

ΔE=0.24 eV

ΔE=0.27 eV

C1

C1

SM=5

SM=5

Cs SM=5

C1

SM=5

Egap=0.29 eV

Egap=0.31 eV

Egap=0.42 eV

Egap=0.57 eV

Egap=0.42 eV

ΔE=0.29 eV

ΔE=0.31 eV

ΔE=0.35 eV

ΔE=0.35 eV

ΔE=0.37 eV



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Page 38 of 46

Cationic clusters o) n=1

SM=5

C∞v

SM=7

Cs SM=7

C∞v

Egap=0.71 eV

Egap=0.55 eV

Egap=1.08 eV

ΔE=0 eV

ΔE=058 eV

ΔE=0.99 eV

p) n=2

C2v SM=6

C∞v

Egap=1.54 eV ΔE=0 eV

SM=6

Cs SM=6

C1

SM=6

C1

SM=6

Egap=1.41 eV

Egap=1.30 eV

Egap=1.68 eV

Egap=1.00 eV

ΔE=0.54 eV

ΔE=0.81eV

ΔE=0.99eV

ΔE=1.00 eV

q) n=3

C1

SM=5


C1

SM=5

C3v SM=5

Cs SM=5

Cs SM=5

Egap=0.56 eV

Egap=0.34 eV

Egap=0.52 eV

Egap=0.36 eV

ΔE=0.06eV

ΔE=0.08 eV

ΔE=0.11 eV

ΔE=0.17 eV

r) n=4

C4v

SM=6

C1

SM=6

Cs SM=6

C2v SM=6

C1 SM=6

Egap=1.37 eV

Egap=0.90 eV

Egap=1.36 eV

Egap=1.08 eV

Egap=1.24 eV

ΔE=0 eV

ΔE=0.12 eV

ΔE=0.21 eV

ΔE=0.34 eV

ΔE=0.36 eV


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s) n=5

Cs SM=5

C1


C1 SM=5

C1 SM=5

C1

Egap=0.50 eV

Egap=0.45 eV

Egap=0.32 eV

Egap=0.56 eV

ΔE=0.02 eV

ΔE=0.03eV

ΔE=0.04 eV

ΔE=0.19 eV

Cs SM=6

C1

Egap=1.47 eV

Egap=1.27 eV

Egap=1.60 eV

Egap=1.30 eV

ΔE=0.02 eV

ΔE=0.08 eV

ΔE=0.15 eV

ΔE=0.20 eV

SM=5

SM=5

t) n=6

Cs SM=6

C1


SM=6

SM=6

C1 SM=6

u) n=7

C1

SM=5

C1

SM=5

C1

SM=5

C1 SM=5

C1 SM=5

Egap=0.43 eV

Egap=0.50 eV

Egap=0.47 eV

Egap=0.57 eV

Egap=0.39 eV

ΔE=0 eV

ΔE=0.07 eV

ΔE=0.10 eV

ΔE=0.11 eV

ΔE=0.12 eV

C1

SM=5

C1 SM=5

C1

Egap=0.28 eV

Egap=0.31 eV

Egap=0.38 eV

ΔE=0.30 eV

ΔE=0.31 eV

ΔE=0.59 eV

Cs SM=5

C1

Egap=0.53 eV

Egap=0.76 eV

ΔE=0.14 eV

ΔE=0.15 eV

SM=5

SM=5



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Page 40 of 46

Figure 2. Lowest-energy geometries of pure Aun+2, bimetallic MnAun+1 and AlAun+1, and neutral trimetallic AlMnAun (n=1-7) clusters. Red, purple and yellow circles represent aluminum, manganese and gold atoms, respectively. n=1

Au3, C2v

MnAu2, D∞h

AlAu2, C2v

AlMnAu1, Cs

n=2

Au4, D2h

MnAu3, C2v

AlAu3, D3h

AlMnAu2, Cs

Au5, Cs

MnAu4, C2v

AlAu4, Cs

AlMnAu3, C3v

n=3

n=4

Au6, C3v

MnAu5, C2v

AlAu5, C4v

AlMnAu4, C4v

n=5

Au7, Cs

MnAu6, D6h

AlAu6, C4v

AlMnAu5, C1

Au8, D4h

MnAu7, C2v

AlAu7, Cs

AlMnAu6, C1

n=6

n=7

40 Au9, C2v

MnAu8, C2v

AlAu8, Cs

ACS Paragon Plus Environment

AlMnAu7, C1

Page 41 of 46

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Figure 3. Comparison of the average binding energies per atom (Eb) of the neutral AlMnAun, MnAun+1, AlAun+1, and bare Aun+2 clusters (n=1-7) for the lowestenergy structures.



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Page 42 of 46

Figure 4. Relative potential energy (eV) of the chiral clusters AlMnAun (n=5-7) for the lowest-energy structures during 4 ps of molecular dynamics simulation.


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Figure 5. The local magnetic moment on Mn and Al atoms and total magnetic moment of the neutral AlMnAun clusters (n=1-7) for the lowest-energy structures.



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Page 44 of 46

Figure 6. The total electron density (a), net spin electron density (b), and electronic density of states (DOS) (c) of two enantiomers of neutral AlMnAu6 cluster. The surface isovalue for molecular orbital plotting is 0.3 e/Å3. The DOS is obtained by Gaussian extension applied to the eigenvalues and the broadening width parameter is chosen to be 0.1 eV. Spin-up (positive) and spin-down (negative) of the DOS are given and the dashed lines indicate the location of the HOMO level.

a

b c


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Figure 7. Simulated photoelectron spectra of the anionic AlMnAun- clusters (n=5-7) for the lowest-energy structures.



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Page 46 of 46

Figure 8. Infrared (IR) vibrational spectra, Raman scattering activity (RSA) spectra, vibrational Raman optical activity (VROA) spectra, and vibrational circular dichroism (VCD) spectra for the lowest-energy structures of the chiral clusters: (a) AlMnAu5; (b) AlMnAu6; (c) AlMnAu7. All simulated spectra have been broadened with the Lorentzian functions having a full width at half maximum (FWHM) of 4 cm−1.


First-Principles Investigations of Chirality in Trimetallic Alloy Clusters

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