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El espectro vibracional del cúmulo tetraédrico Au20 fue calculado mediante la teoría del funcional de la densidad (DFT) dentro de dos aproximaciones diferentes: la híbrida B3LYP y la GGA-BP86. Los modos normales de vibración obtenidos fueron clasificados de acuerdo a las representaciones irreducibles del grupo Td. Las frecuencias vibracionales calc...
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Citations
... Tetrahedral structure of Au20 showing its three non-equivalent sites: Au a , Au f and Au e corresponding to apexes, face centres and edges respectively (the last ones corresponding to the empty spheres infigure). Reproduced with permission from Ref.[25]. Copyright Sociedad Mexicana de Física (2008). ...
This review provides an insight into the simulation of gold nanoparticles supported on oxide surfaces, with particular emphasis on the applications in heterogeneous catalysis. Some important methodological issues are firstly addressed: the polymorphism of small gold clusters, the difficulty in determining the actual charge state of adsorbed gold atoms, the relevance of long‐range dispersion and relativistic effects and the size‐effects in modelling Au nanoparticles. Then, the adsorption of Au species on oxides is addressed by comparing bulk oxides to ultrathin oxide films supported on metals. The role of defects as nucleation centres is also discussed. Finally, this review addresses the contribution from computational studies on the mechanisms involving Au‐based heterogeneous catalysts in important reactions such as the CO oxidation, the water‐gas shift reaction and the CO2 hydrogenation to methanol.
... Likewise, the Au 20 cluster with T d symmetry is one of the most widely investigated clusters because of its high symmetry and wide gap of 1.77 eV between its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), which provides increased structural stability compared to other small Au clusters. 47 Because both the Au 8 and Au 20 clusters have been synthesized experimentally, 15,48 we used these two cluster in our study with the objectives of interpreting how small gold clusters interact with amino acids and/or biological molecules and how the interactions of such clusters differ from those of larger clusters. ...
The stability and electronic properties of gold (Au) clusters interacting with Alanine (Ala) and Tryptophan (Trp) amino acids in their canonical and zwitterionic (zw.) configurations are investigated using first-principles density functional theory (DFT). The structures of the Au clusters along with the polarity of the amino acids determine the nature of the interactions in the gas and solvent phases. In the gas phase, the Au8 (D4h) and Au20 (Td) clusters prefer single-site interactions through the amine group for the canonical amino acids, while in the solvent phase, the carboxylic site is preferred for the zw. amino acids. A limited screening of intermolecular interactions introduced by the solvent medium for the canonical forms of Ala and Trp conjugated with the Aun complexes, suggests the bonding to be primarily covalent in nature. The screening is significantly more pronounced for the zw. complexes where the electrostatic interactions dominate. The cluster-size along with the configurations defines the extent of the interactions and overall stability of the complexes. The structures of Aun clusters govern the charge distribution and electrostatic potential directing the selectivity towards the preferential binding sites with the amino acids.
... The intensity of the enhancement of the specific heat and experimental results calculated by Bishea and Morse [64], Gruene et al., [65] Mancera [66], Molina et al. [67], and with Nose [68], for the vibrational spectrum of Au N = 3,4,5,6,7,19,20 clusters. Interestingly, our results were in excellent agreement with their results. ...
... Our calculated Au 20 (C 1 ) cluster's vibrational modes are comparable and in excellent agreement with the Au20 Tetrahedron (Td) symmetry calculated using density functional theory (DFT) with two different approximations: the hybrid-B3LYP and GGA-BP86 by Molina et al. [67]. Their ranges for BLYP and BP86 are 26.42-162.22 ...
The vibrational heat capacity Cvib of a re-optimized neutral gold cluster was investigated at temperatures 0.5-300 K. The vibrational frequency of an optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system Eigen frequencies (3N-6) was obtained by diagonalization of the symmetric positive semi definite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size, and structure and bond-order dependency. The effect of the range of interatomic forces is studied; especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. In addition to that, we have exactly predicted the vibrational frequencies (ωi) which occur between 0.55 to 370.72 cm-1 , depending on the nanoparticle morphology at T=0 for small neutral gold clusters AuN=3-20. This result has been proved and confirmed by the size effect values. It was found that beside the particle size, geometric shape, defect structure and an increase in asymmetry of nanoparticles effects on heat capacity. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters have been studied for the first time.
... Molina et al. detected the presence of RBM in a cluster Au 20 by DFT. They predict the location of a RBM in 89 and 97 cm −1 for the approximation levels B3LYP and BP86, respectively [53]. This manuscript confirms that the RBM in bimetallic clusters Au 20-n Ag n does not show a big shift in the vibrational spectrum and it is located at low wave numbers. ...
The synthesis of nanometric alloys, or nanoalloys, is gaining interest in nanoscience due to their new and attractive physical properties. Furthermore, they improve the efficiency and performance of the diverse nanotechnological applications in comparison with the nanostructures composed of only one material. This study presents a novel synthesis method that facilitates the production of Au-Ag random bimetallic nanoalloys with uniform shape at room temperature, using the reducing and stabilizing properties of low-toxicity molecules, such as sucrose, ascorbic acid, and rongalite. The images taken with a transmission electron microscope (TEM) showed spherical bimetallic nanoparticles between 7 and 12 nm. The presence of Au and Ag in the nanostructures was confirmed by EDS. The optical absorption analysis showed a band centered at 480 nm, associated with surface plasmon resonance in Au-Ag nanoalloys. A Raman band was observed around 98 cm−1 after the nanoparticles were synthesized. Additionally, the behavior of the radial breathing modes (RBM) of mixed bimetallic nanoalloys of Au20-nAgn (con n = 0–20) clusters was analyzed. The analysis was performed with the density functional theory (DFT) at Becke level, three-parameter, Lee-Yang-Parr (B3LYP) in combination with basis set Los Alamos Laboratory 2 double ζ (LANL2DZ). The predicted vibrational modes associated with RBM are located around 90–100 cm−1 approximately. This shows a good tendency and correlation with the Raman band detected experimentally at low wave numbers.
... The intensity of the enhancement of the specific heat and experimental results calculated by Bishea and Morse [64], Gruene et al., [65] Mancera [66], Molina et al. [67], and with Nose [68], for the vibrational spectrum of Au N = 3,4,5,6,7,19,20 clusters. Interestingly, our results were in excellent agreement with their results. ...
... Our calculated Au 20 (C 1 ) cluster's vibrational modes are comparable and in excellent agreement with the Au20 Tetrahedron (Td) symmetry calculated using density functional theory (DFT) with two different approximations: the hybrid-B3LYP and GGA-BP86 by Molina et al. [67]. Their ranges for BLYP and BP86 are 26.42-162.22 ...
The vibrational heat capacity Cvib of a re-optimized neutral gold cluster was investigated at temperatures 0.5-300 K. The vibrational frequency of an optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system Eigen frequencies (3N -6) was obtained by diagonalization of the symmetric positive semi definite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size, and structure and bond-order dependency. The effect of the range of interatomic forces is studied; especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. In addition to that, we have exactly predicted the vibrational frequencies (ωi) which occur between 0.55 to 370.72 cm-1, depending on the nanoparticle morphology at T=0 for small neutral gold clusters AuN=3-20. This result has been proved and confirmed by the size effect values. It was found that beside the particle size, geometric shape, defect structure and an increase in asymmetry of nanoparticles effects on heat capacity. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters have been studied for the first time.
... The HOMO-LUMO (HL) gaps obtained for the rst six methods are larger than Au 20 (1.77 eV), 62 being the B3LYP HL gaps considerably overestimated, as it has been reported for other gold clusters. 63 The ZORA-SR HL gaps for all methods, except M06L, are in the range between 1.8 and 1.89 eV, and are in good agreement with the corresponding BP86, PBE/LANL2DZ and PBE/STUTTGART calculations; whereas the ZORA-SO is the smallest, due to the extra splitting of the electronic structure produced by the spin-orbit (SO) effect. As can be seen in Table 1, the inclusion of dispersion corrections shows no effect on the bond length or in the HL gap, for the two tested methods. ...
Determining the structure for gold nanoclusters at which the 2D–3D transition occurs has been a challenging problem for both theoretical and experimental studies. For gold cation clusters, quantum chemistry calculations have produced controversial results concerning the last most stable planar structure, some indicating that corresponds to n 1⁄4 7, whereas others conclude that at this value, the structure is already 3D. Experimentally, ion mobility spectroscopy measurements, assisted by DFT calculations, have been interpreted as a planar structure for Au7+. Here, we show that the usually assumed 2D non-degenerate ground state cluster structure for Au7+ with D6h symmetry is unstable against a puckering distortion, ending in a 3D stable structure with D3d symmetry. The analysis is based on the pseudo Jahn–Teller effect through vibronic coupling between the ground state and two excited states. This structure presents, in average, the same surface area than the 2D, being therefore compatible with experimental results. We discuss the effects the vibronic coupling would have on Raman, IR and UV-vis spectra. The study is based on a scalar and spin orbit relativistic DFT calculation in the Zero Order Regular Approximation (ZORA).
... On the other hand, calculations performed on the Au 20 gold cluster were reviewed in a paper by Kryachko [4]. In those previous reports, the BP86 functional was established as the best functional with which to estimate a HL gap closely related to the experimental value [5], and the Perdew-Burke-Ernzerhof (PBE) functional with a double basis set including d polarization functions (DSPP) gave the best value of the IR maximum [6]. The high stability of the Au 20 cluster is due to both its large HL gap and its lack of fluxionality at 300 K (interconversion between minima) as determined by Born-Oppenheimer molecular dynamics simulations [7]. ...
The study reported herein addressed the structure, adsorption energy and normal modes of zwitterion L-cysteine (Z-cys) adsorbed on the Au(20) cluster by using density functional theory (DFT). It was found that four Z-cys are bound to the Au(20) apexes preferentially through S atoms. Regarding normal modes, after adsorption of four Z-cys molecules, a more intense infrared (IR) peak is maintained around 1,631.4 cm(-1) corresponding with a C=O stretching mode, but its intensity is enhanced approximately six times. The enhancement in the intensity of modes between 0 to 300 cm(-1) is around 4.5 to 5.0 times for normal modes that involve O-C=O and C-S bending modes. Other two normal modes in the range from 300 to 3,500 cm(-1) show enhancements of 6.0 and 7.4 times. In general, four peaks show major intensities and they are related with normal modes of carboxyl and NH(3) groups of Z-cys.
... This agrees also with the values obtained using the LANL2DZ basis set, where the maximum ∆E HL values can be seen for clusters with n=2, 6, 8, 20 (Fig 2A). Actually, by comparing with previous results it can be concluded that B3LYP functional overestimates orbital interactions [48]. As an example, one can consider the reported ∆E HL values for 20-atom tetrahedral cluster computed by B3LYP approach. ...
... The Au 20 stands out as particularly stable among all other small clusters (together with Au 2 , Au 6 and Au 8 ). It also has an extremely large band gap between the HOMO and LUMO of about 2.93 eV, this value is similar to previously published data [48,49]. The experimentally determined value of ∆E HL for Au 20 is 1.8 eV [41]. ...
A fundamental understanding of the physical and chemical properties of gold clusters, namely, the size dependence of these properties, is necessary for developing wide range of gold clusters' applications. Having this purpose in mind, the structural and energetic properties, such as binding energies, relative stability and band gaps ∆E HL (HOMO-LUMO gaps) are evaluated. The gold clusters in a wide range of sizes, Au n (n=2 -2016), were constructed and studied by Density Functional Theory and Extended Hückel Theory approaches. It was shown that the high values of ∆E HL for the clusters with n= 2, 6, 8, 20 correlate with the highest stability. This finding explains the existence of magic numbers for gold clusters. The 20 atom tetrahedral cluster stands out as particularly stable, comparing to the other small clusters. The binding energy E B is found to increase with the cluster size. The second difference in energy -∆ 2 E(n) value is used as the criterion of stability, in addition to ∆E HL and also shows a tendency to increase with the cluster size. This behavior suggests a transition of larger clusters towards bulk metallic properties. Both curves -∆ 2 E(n) and ∆E HL show sharp transformation from high values to close to 0 eV at n=252-504 cluster sizes (it relates to ca 2 nm cluster size).
Nanoparticle properties are strongly correlated with their morphologies, such as shape and size. By combining density functional theory calculations with ab initio molecular dynamics simulations, we investigated the CO adsorption behavior on Au13 nanoparticles of Ih, Oh, and planar symmetries. Our results revealed a shape-specific adsorption response of the nanoparticles. Contrary to the behavior in bulk, we observe a symmetry-dependent d-band center shift on the nanoparticles with CO coverage, which affects the overall electronic stability of the nanoparticles. As a result, we observe 2D to 3D (planar to Ih) transition at high CO coverage. Because of the interactions with the adsorbed CO molecules, the 3D nanoparticles can accommodate more charge in their core than the 2D. All of these effects result in observing an unconventional, stronger CO adsorption on Ih Au13 nanoparticles that expose higher surface coordination number (CN = 6) than the peripheral atoms of the planar Au13 (peripheral CN = 3.4). This work highlights the shape effect on the adsorption behavior of small-sized Au nanoparticles (∼1 nm diameter).
In this work we explored the competition between spin-orbit and Jahn-Teller effects as decisive influences in the ground states of the Td Au20 ±gamma (gamma=1,2,3). All our electronic calculations were based in the relativistic density functional theory in the zeroth-order regular approximation (ZORA) to the Dirac equation. Calculations were done in both versions of ZORA: scalar relativistic and full-relativistic including the spin-orbit interaction. We concluded that for the Au20 -3 ion is necessary to use a full-relativistic theory in order to predict a symmetry-lowering from tetrahedral. We predict a trigonal C3v isomeric form for this trianion due to a Jahn-Teller distortion of its parent Td. For the rest of ions we found a tendency to conserve their pristine tetrahedral configurations. In these cases we found one of both possibilities: a quenching of the vibronic interaction by spin-orbit coupling or simply a weak Jahn-Teller effect which is not enough to distort appreciably the cluster.
