Linear augmented Slater-type orbital method for free standing clusters

We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schr?dinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yields the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium.     

Theoretical study on the adsorption of aromatic compounds on platinum clusters

B3 LYP hybrid functional with LACVP* pseudopotential was applied for the optimization of geometries of complexes resulting from interaction of benzene, pyridine, naphthalene, and quinoline with Pt_n (n = 4, 7) clusters. For benzene‐containing complexes, the most stable form corresponds to a bridge adsorption, with benzene undergoing considerable geometric distortions, assuming a boat‐like conformation. C? H bonds are bended upward from the plane of the cluster. C? C bonds stretch, especially when they form π‐complexes with low coordinated Pt atoms. Some arrangements for pyridine complexes involving the N atom of the organic moiety undergo further distortions, apparently preserving a formal C? N π bond. Except for that distortion, the behavior of any heteroaromatic complex is similar to that of benzene in the same arrangement. The quinoline–Pt₇ complex can suitably be used for simulation of the cinchonidine (CD) anchorage over Pt. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Small binary iron-carbon clusters with persistent high magnetic moments. A theoretical characterization

Characterization of the structural and electronic properties of binary iron-carbon clusters composed by six iron atoms and with up to nine carbon atoms was carried out with density functional theory calculations. Neutral, cations (q = +1), and anions (q = −1), some of them experimentally detected, were studied. The formation of dimers and trimers of carbon atoms over the iron surface were preferred. Moreover, some large carbon chains, with up to five atoms, were determined. High spin states emerged for the ground states, with multiplicities above 16, for all clusters independently of the number of carbon atoms attached to the iron core. All neutral clusters were stable because fragmentation (into carbon chains), dissociation (of a single carbon atom), and detachment of all carbons need high amounts of energy. Reactive species were defined by small HOMO-LUMO gaps. Charge transfer, to the carbon atoms, increased as the carbon content increased, producing, for some cases, an even-odd behavior for the magnetic moment of the Fe₆C_n particles.     

Electronic structure and stability of AlnPn (n = 2-4) clusters

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of aluminum phosphide clusters have been investigated using the density functional theory. For dimers and trimers, the lowest energy structures are cyclic (IIs, IIIs) with D(nh) symmetry. The caged structure with Td symmetry (Xs) lie lowest in energy among the tetramers. The Al--P bond dominates the structures for many isomers so that one preferred dissociation channel is loss of the AlP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with silicon and boron nitride clusters, the ground state structures of Al(n)P(n) clusters are analogous to those of their corresponding Si(2n) counterparts. This similarity follows the isoelectronic principle.     

Density functional study of AgnPd and AgnPdH clusters

Small Ag_nPd (n = 5) clusters and their hydrides Ag_nPdH (n = 5) have been studied by density functional theory calculations. For bare clusters, the structures in which the Pd atom has a maximum number of neighboring Ag atoms tend to be energetically favorable. Hydrogen prefers binding to Ag? Pd bridge site of Ag_nPd clusters except for Ag₅Pd. The binding energy has a strong odd–even oscillation. The electron transfers are from Ag atoms to Pd in bare clusters and are from metal clusters to H in cluster hydrides. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study of aromaticity in inorganic tetramer clusters

Ground state geometry and electronic structure of M ₄ ^2- cluster (M = B, Al, Ga) have been investigated to evaluate their aromatic properties. The calculations are performed by employing the Density Functional Theory (DFT) method. It is found that all these three clusters adopt square planar configuration. Results reveal that square planar M ₄ ^2- dianion exhibits characteristics of multifold aromaticity with two delocalised π-electrons. In spite of the unstable nature of these dianionic clusters in the gas phase, their interaction with the sodium atoms forms very stable dipyramidal M₄Na₂ complexes while maintaining their square planar structure and aromaticity.     

Magic number silicon dioxide-based clusters: laser ablation-mass spectrometric and density functional theory studies

The magic number silica clusters [(SiO(2))(n)O(2)H(3)](-) with n = 4 and 8 have been observed in the XeCl excimer laser (308 nm) ablation of various porous siliceous materials. The structural origin of the magic number clusters has been studied by the density functional theoretical calculation at the B3LYP/6-31G** level, with a genetic algorithm as a supplementary tool for global structure searching. The DFT results of the first magic number cluster are parallel to the corresponding Hartree-Fock results previously reported with only small differences in the structural parameters. Theoretical calculation predicts that the first magic number cluster (SiO(2))(4)O(2)H(4) and its anion [(SiO(2))(4)O(2)H(3)](-) will most probably take pseudotetrahedral cage-like structures. To study the structural properties of the second magic number cluster, geometries of the bare cluster (SiO(2))(8), the neutral complex cluster (SiO(2))(8)O(2)H(4), and the anionic cluster [(SiO(2))(8)O(2)H(3)](-) are fully optimized at the B3LYP/6-31G** level, and the corresponding vibrational frequencies are calculated. The DFT calculations predict that the ground state of the bare silica octamer (SiO(2))(8) has a linear chain structure, whereas the second magic number complex cluster (SiO(2))(8)O(2)H(4) and its anion [(SiO(2))(8)O(2)H(3)](-) are most probably a mixture of cubic cage-like structural isomers with an O atom inside the cage and several quasi-bicage isomers with high intercage interactions. The stabilization of these structures can also be attributed to the active participation of the group of atoms 2O and 4H (3H for the anion) in chemical bonding during cluster formation. Our theoretical calculation gives preliminary structural interpretation of the presence of the first and second magic number clusters and the absence of higher magic numbers.     

Nickel and copper doped palladium clusters from a first-principles perspective

A complete study on the evolution of structures and the variation of the energy properties of MPd_n−1 (M = Ni and Cu; n = 2-13) clusters is presented. The study was performed employing auxiliary density functional theory. The obtained results were compared with the results of Pd_n clusters studied with the same methodology. For each cluster size, several structures were studied to determine the lowest energy structures. The initial structures for the geometry optimization were taken along ab initio Born-Oppenheimer molecular dynamics trajectories. Different potentials energy surfaces were studied. All cluster structures were fully optimized without any symmetry restriction. Stable structures, frequencies, spin multiplicities, averaged bond lengths, spin density plots, different energy properties, dipole and magnetic moments as well as charge transfers are reported. This investigation indicates that the palladium clusters doped with a Ni atom are the most stable and potentially the most chemical active ones.     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Glucose interaction with Au,Ag, and Cu clusters: Theoretical investigation

Interactions of α‐D ‐glucose with gold, silver, and copper metal clusters are studied theoretically at the density functional theory (CAM‐B3LYP) and MP2 levels of theory, using trimer clusters as simple catalytic models for metal particles as well as investigating the effect of cluster charge by studying the interactions of cationic and anionic gold clusters with glucose. The bonding between α‐D ‐glucose and metal clusters occurs by two major bonding factors; the anchoring of M atoms (M = Cu, Ag, and Au) to the O atoms, and the unconventional M…H? O hydrogen bond. Depending on the charge of metal clusters, each of these bonds contributes significantly to the complexation. Binding energy calculations indicate that the silver cluster has the lowest and gold cluster has the highest affinity to interact with glucose. Natural bond orbital analysis is performed to calculate natural population analysis and charge transfers in the complexes. Quantum theory of atoms in molecules was also applied to interpret the nature of bonds. © 2012 Wiley Periodicals, Inc.     

Quantum mechanical study on plasmon resonances in small ring clusters

The collectivity of the electronic motion in small sodium clusters with ring structure is studied by time‐dependent density functional theory. The formation and development of collective resonances in the absorption spectra were obtained as a function of the ring radius. In small ring clusters, besides the lower‐energy mode and the higher‐energy mode, there is another plasmon resonance mode, that is, the reverse two‐dipole mode. For the reverse two‐dipole mode, the formations of these two dipoles are due to the external field inducement and the shielding effect, although the resonant excitation is mainly due to the coupling effect of the electrons of these two dipoles. © 2012 Wiley Periodicals, Inc.     

Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.     

Density functional theory study of geometry and stability of small Zrn (n = 2–10) clusters

Geometric structures, electronic properties, and stabilities of small Zr_n and Zr (n = 2–10) clusters have been investigated using density functional theory with effective core potential LanL2DZ basis set. For both neutral and charged systems, several isomers and different multiplicities were studied to determine the lowest energy structures. Many most stable states with high symmetry were found for small Zr_n clusters. The most stable structures and symmetries of Zr clusters are the same as the neutral ones except n = 4 and 7. We found that the clusters with n > 3 possess highly compact structures. The clusters are inclined to form the caged‐liked geometry containing pentagonal structures for n > 8, which is in favor of energy. From the formation energy and second‐order energy difference, we obtained that 2‐, 5‐, 7‐atoms of neutral and 4‐, 7‐atoms cationic clusters are the magic numbers. Furthermore, the highest occupied molecular orbital‐lowest unoccupied molecular orbital gaps display that the Zr₃, Zr₆, Zr, and Zr are more stable in chemical stability. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structure and stability of (AlN)n clusters

AIN and Al2N2 have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)n (n = 1-15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists AI-N bond in the ground state structures of (AIN)n clusters; and the "magical number" regularity of (AIN)n is those whose atom number Is 4, 8, 12,16, 20, etc, all of which are times of four.     

Structure and stability of B+13 clusters

The structures and energies of B⁺₁₃, observed experimentally to be an unusually abundant species among cationic boron clusters, have been studied systematically with B3LYP/6–31G* density functional theory. The most thermodynamically stable B⁺₁₂ and B⁺₁₃ clusters are confirmed to have planar or quasiplanar rather than globular structures. However, the computed dissociation energies of the 3-dimensional B⁺₁₃ clusters are much closer to the experimental values than those of the planar or quasiplanar structures. Hence, planar and 3-dimensional B⁺₁₃ may both exist. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 203–214, 1998     

Theoretical evidence of d‐orbital aromaticity in anionic metal X (X = Sc,Y, La) clusters

The equilibrium geometries, total electronic energies, and vibrational frequencies for singlet, triplet, and quinted states of three all‐metal X (X = Sc, Y, and La) anions and nine relevant neutral singlet MX₃ (M = Li, Na, K, X = Sc, Y, La) clusters are investigated with four density functional theory (DFT) and correlated ab initio methods B3LYP, B3PW91, MP2, and CCSD(T). To our knowledge, the theoretical study on these clusters composed of the transition metal Sc, Y, La is first reported here. The calculated results show that for the X clusters the singlet states with trigonal D_3h structures are the lowest energetically, while the neutral singlet MX₃ clusters each have two stable isomers: one trigonal pyramidal C_3v and one bidentate C_2v structures with the pyramidal C_3v isomer being ground state. In addition, we calculate the resonance energies (RE) and nucleus‐independent chemical shift (NICS) for the singlet trigonal X rings and show that these singlet trigonal X rings exhibit higher degree of aromaticity. The detailed molecular orbital (MO) analyses reveal that the singlet trigonal X anions have one delocalized σ‐type and one delocalized π‐type MOs, which follow the 4n + 2 electron counting rule, respectively and play an important role in rendering these species two‐fold aromaticity. Here, an explicit theoretical evidence is given to prove that the contribution to the two‐fold aromaticity of the singlet trigonal X (X = Sc, Y, and La) rings originates primarily from the d‐orbital bonding interactions of these component transition metal X atoms. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

PDECO: Parallel differential evolution for clusters optimization

The optimization of the atomic and molecular clusters with a large number of atoms is a very challenging topic. This article proposes a parallel differential evolution (DE) optimization scheme for large‐scale clusters. It combines a modified DE algorithm with improved genetic operators and a parallel strategy with a migration operator to address the problems of numerous local optima and large computational demanding. Results of Lennard–Jones (LJ) clusters and Gupta‐potential Co clusters show the performance of the algorithm surpasses those in previous researches in terms of successful rate, convergent speed, and global searching ability. The overall performance for large or challenging LJ clusters is enhanced significantly. The average number of local minimizations per hit of the global minima for Co clusters is only about 3–4% of that in previous methods. Some global optima for Co are also updated. We then apply the algorithm to optimize the Pt clusters with Gupta potential from the size 3 to 130 and analyze their electronic properties by density functional theory calculation. The clusters with 13, 38, 54, 75, 108, and 125 atoms are extremely stable and can be taken as the magic numbers for Pt systems. It is interesting that the more stable structures, especially magic‐number ones, tend to have a larger energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. It is also found that the clusters are gradually close to the metal bulk from the size N > 80 and Pt₃₈ is expected to be more active than Pt₇₅ in catalytic reaction. © 2013 Wiley Periodicals, Inc.     

Charge-transfer processes in the assembly of Si(n)O(m) neutral clusters

The chemical bond formation in oxygen-rich Si(n)O(m) clusters was investigated by sampling the potential energy surface of the model systems SiO + SiO(2) → Si(2)O(3) and (SiO)(2) + SiO(2) → Si(3)O(4) along a two-dimensional reaction coordinate, by density functional theory calculations. Evidence for crossing between the weakly bound neutral-neutral (SiO)(n) + SiO(2) and the highly attractive ion-pair (SiO)(n)(+) + SiO(2)(-) surfaces was found. Analysis of frontier molecular orbitals and charge distribution showed that surface crossing involves transfer of valence electron charge from (SiO)(2) to SiO(2). The sum of the natural atomic charges over the (SiO)(n) and (SiO(2)) groups of the Si(n)O(m) cluster products, gave a net positive charge on the (SiO)(n) "core" and a net negative charge on the (SiO(2)) groups. This is interpreted as the "ion-pair memory" left on the Si(n)O(m) products by the charge-transfer mechanism and may provide a way to assess the role of charge-transfer processes in the assembly of larger Si(n)O(m) neutral clusters.     

Structural evolution of small gold clusters doped by one and two boron atoms

The potential energy surfaces (PES) of a series of gold–boron clusters with formula Au_nB (n = 1–8) and Au_mB₂ (m = 1–7) have been explored using a modified stochastic search algorithm. Despite the complexity of the PES of these clusters, there are well‐defined growth patterns. The bonding of these clusters is analyzed using the adaptive natural density partitioning and the natural bonding orbital analyses. Reactivity is studied in terms of the molecular electrostatic potential. © 2014 Wiley Periodicals, Inc.     

Ab initio studies on the polarizability of lithium clusters: Some unusual results

The polarizability of lithium clusters was studied using ab initio as well as Density Functional Theory (DFT)‐based methods. The electron correlation was found not to play any major role in the evaluation of polarizability of the lithium clusters, contrary to the case of sodium and other types of clusters. The theoretical methods used in the present study are not able to reproduce the unusual features in the size evolution of the polarizability observed experimentally. An interesting feature is that the polarizability of lithium clusters calculated by various methods at 0K temperature is found to be higher than the experimental results measured at higher temperature, which is quite unusual. The significance of these issues is highlighted and the need of highly accurate DFT exchange‐correlation functionals and ab initio methods in the study of the electronic properties of lithium clusters is emphasized. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005