Structural and electronic properties of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13): Theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13) have been investigated using the ab initio molecular orbital theory formalism. The hybrid exchange-correlation energy functional (B3LYP) and a standard split-valence basis set with polarization functions (6-31+G(d)) were employed to optimize geometrical configurations. The total energies of the lowest energy isomers thus obtained were recalculated at the MP2/aug-cc-pVTZ level of theory. Unlike positively charged clusters, which showed similar structural behavior as that of neutral clusters [Nigam et al., J. Chem. Phys. 121, 7756 (2004)], significant geometrical changes were observed between Si(n) and Si(n)- clusters for n = 6, 8, 11, and 13. However, the geometries of P substituted silicon clusters show similar growth as that of negatively charged Si(n) clusters with small local distortions. The relative stability as a function of cluster size has been verified based on their binding energies, second difference in energy (Delta2 E), and fragmentation behavior. In general, the average binding energy of Si(n)- clusters is found to be higher than that of Si(n) clusters. For isoelectronic PSi(n-1) clusters, it is found that although for small clusters (n < 4) substitution of P atom improves the binding energy of Si(n) clusters, for larger clusters (n > or = 4) the effect is opposite. The fragmentation behavior of these clusters reveals that while small clusters prefer to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size. The adiabatic electron affinities of Si(n) clusters and vertical detachment energies of Si(n)- clusters were calculated and compared with available experimental results. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.     

Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

The TaSi(n) (n=1-13) clusters with doublet, quartet, and sextet spin configurations have been systematically investigated by a relativistic density functional theory with the generalized gradient approximation available in Amsterdam density functional program. The total bonding energies, equilibrium geometries, Mulliken populations as well as Hirshfeld charges of TaSi(n) (n=1-13) clusters are calculated and presented. The emphasis on the stabilities and electronic properties is discussed. The most stable structures of the small TaSi(n) (n=1-6) clusters and the evolutional rule of low-lying geometries of the larger TaSi(n) (n=7-13) clusters are obtained. Theoretical results indicate that the most stable structure of TaSi(n) (n=1-6) clusters keeps the similar framework as the most stable structure of Si(n+1) clusters except for TaSi(3) cluster. The Ta atom in the lowest-energy TaSi(n) (n=1-13) isomers occupies a gradual sinking site, and the site moves from convex, to flatness, and to concave with the number of Si atom varying from 1 to 13. When n=12, the Ta atom in TaSi(12) cluster completely falls into the center of the Si frame, and a cagelike TaSi(12) geometry is formed. Meanwhile, the net Mulliken and Hirsheld populations of the Ta atom in the TaSi(n) (n=1-13) clusters vary from positive to negative, manifesting that the charges in TaSi(n) (n>/=12) clusters transfer from Si atoms to Ta atom. Additionally, the contribution of Si-Si and Si-Ta interactions to the stability of TaSi(n) clusters is briefly discussed. Furthermore, the investigations on atomic averaged binding energies and fragmentation energies show that the TaSi(n) (n=2,3,5,7,10,11,12) clusters have enhanced stabilities. Compared with pure silicon clusters, a universal narrowing of highest occupied molecular orbital-lowest unoccupied molecular orbital gap in TaSi(n) clusters is found.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Photoionization and ab initio study of Ba(H2O)n (n = 1-4) clusters

An experimental and theoretical study of the photoionization energies (IE's) of Ba(H(2)O)(n) clusters containing up to n = 4 water molecules has been performed. The clusters were generated by a pick-up source combining laser vaporization with pulsed supersonic expansion, and then photoionized by radiation of 272.5-340 nm. The experimentally determined IE(e)'s for n = 1 to 4 are 4.56 ± 0.05, 4.26 ± 0.05, 3.90 ± 0.05 and 3.71 ± 0.05 eV. This cluster size dependence of IE is reproduced within ±0.06 eV employing the mPW1PW91 density-functional and CCSD(T, Full) quantum-chemical methods combined with the 6-311++G(d,p) basis set for the H and O atoms and three different relativistic effective core potentials for Ba atoms. The calculations indicate that the lowest energy hydration structures represent the most relevant contributions to both the vertical and adiabatic ionization energies. Experimental and theoretical evidence correlates with the progressive surface-delocalization of the electron from the hydration cavity around the Ba atom and suggests that the intra-cluster electron transfer is possible even for small aggregates.     

Comparative ab initio study of CO adsorption on Sc(n) and Sc(n)O (n = 2-13) clusters

Using a cluster model, we investigated the similarities and differences in chemical activity and the magnetic properties of Sc(n) clusters (n = 2-13) and their oxides, Sc(n)O, toward CO molecule adsorption via a spin-polarized density functional theory approach. The Sc(n) and Sc(n)O clusters have similar chemical activity at small sizes of n = 2-10, whereas remarkable differences are observed at large sizes of n = 11-13. More interestingly, different magnetic responses are found in the Sc(n) and Sc(n)O clusters with the presence of CO molecule: The magnetic moment is attenuated significantly for Sc(n) with n = 2, 4, 12, and 13, whereas for Sc(n)O, it is enhanced at n = 4 and 13 and is reduced for n = 7, 8, 10, and 11. In particular, the magnetic moment remarkably increases from 7 μ(B) of Sc(13)O to 13 μ(B) of Sc(13)OCO, whereas it reduces from 19 μ(B) of Sc(13) to 5 μ(B) of Sc(13)CO.     

Fluxional and aromatic behavior in small magic silicon clusters: a full ab initio study of Si(n), Si(n) (1-), Si(n) (2-), and Si(n) (1+), n=6, 10 clusters

The structural, electronic, vibrational, optical, magnetic, and aromatic characteristics of Si(n), Si(n) (1-), Si(n) (2-), and Si(n) (1+), clusters have been calculated very accurately with a variety of high level ab initio techniques. These calculations have been performed with the aim to clarify existing ambiguities in the literature and to bring up the fluxional and aromatic characteristics of these species. The fluxional behavior, according to earlier conjecture of the present author, could be connected to the magic property. In addition such behavior could also explain the existence of conflicting results. The ab initio techniques include quadratic configuration interaction, coupled cluster, and multireference second order perturbation theory, together with density functional theory ("static" and time dependent) with the hybrid B3LYP functional. Various high quality correlation-consistent basis sets, ranging from 2Z up to 5Z quality, were employed. It is demonstrated that Si(6) is fluxional, fluctuating around a symmetric D(4h) structure. Si(10) is also fluxional but to a lesser degree, in contrast to Si(10) (1-) anion which is highly fluxional. For both clusters, in full agreement with Wade's and Lipscomb's rules for deltahedral boranes, the corresponding dianions have higher symmetry (O(h) and D(4d), respectively) and lower energy than the neutral clusters. The aromatic behavior of Si(6) fits better to a mixed conflicting aromaticity picture. This type of aromatic and fluxional behavior has also been observed in stable "magic" carbon clusters as C(6) and carbon fullerenes such as C(20). The present results, which support possible connection of fluxional and magic properties, are in excellent agreement with experimental measurements of ionization energies, electron affinities, and vibrationally resolved photoelectron spectra.     

Density-functional study of structural and electronic properties of Si(n)C(n) (n=1-10) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic structure of Si(n)C(n) (n=1-10) clusters. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster size n equals 4. Cagelike structures are favored as the cluster size increases. A distinct segregation between the silicon and carbon atoms is observed for these clusters. It is found that the C atoms favor to form five-membered rings as the cluster size n increases. However, the growth motif for Si atoms is not observed. The Si(n)C(n) clusters at n=2, 6, and 9 are found to possess relatively higher stability. On the basis of the lowest-energy geometries obtained, the size dependence of cluster properties such as binding energy, HOMO-LUMO gap, Mulliken charge, vibrational spectrum, and ionization potential has been computed and analyzed. The bonding characteristics of the clusters are discussed.     

Relativistic computational investigation: the geometries and electronic properties of TaSi(n)+ (n = 1-13, 16) clusters

The equilibrium geometries, stabilities, and electronic properties of the TaSi(n)+ (n = 1-13, 16) clusters are investigated systematically by using the relativistic density functional method with generalized gradient approximation. The small-sized TaSi(n)+ clusters with slight geometrical adjustments basically keep the frameworks that are analogous to the neutrals while the medium-sized charged clusters significantly deform the neutral geometries, which are confirmed by the calculated AIP and VIP values. Furthermore, the optimized geometries of the charged clusters agree with the experimental results of Hiura and co-workers (Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of the charged clusters are generally increased as the cluster size goes from n = 1 to 13; and the large HOMO-LUMO gaps of charged clusters resulting from the positive charge indicate that their chemical stabilities are stronger than their neutral counterparts, especially for n = 4, 6, and 7 clusters. Additionally, the contributions of the d orbitals of the Ta atom to the HOMO and LUMO reveal that the chemical activity of the d orbitals of the Ta atom decreases gradually as the number of silicon atoms increases. This interesting finding is in good agreement with the recent experimental results on the reactive activities of the H2O and transition-metal silicon clusters (Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. J. Am. Chem. Soc. 2005, 127, 4998). Generally, the positive charge significantly influences the electronic and geometric structures of the charged clusters. Finally, the most stable neutral and charged TaSi16 clusters are found to be fullerene-like structures and the HOMO-LUMO gap in charged form is detectable experimentally.     

Atomic and electronic structures of neutral and charged Pbn clusters (n=2-15): theoretical investigation based on density functional theory

The geometric and electronic structures of the Pbn+ clusters (n=2-15) have been investigated and compared with neutral clusters. The search for several low-lying isomers was carried out under the framework of the density functional theory formalism using the generalized gradient approximation for the exchange correlation energy. The wave functions were expanded using a plane wave basis set and the electron-ion interactions have been described by the projector augmented wave method. The ground state geometries of the singly positively charged Pbn+ clusters showed compact growth pattern as those observed for neutrals with small local distortions. Based on the total energy of the lowest energy isomers, a systematic analysis was carried out to obtain the physicochemical properties, viz., binding energy, second order difference in energy, and fragmentation behavior. It is found that n=4, 7, 10, and 13 clusters are more stable than their neighbors, reflecting good agreement with experimental observation. The chemical stability of these clusters was analyzed by evaluating their energy gap between the highest occupied and lowest unoccupied molecular orbitals and adiabatic ionization potentials. The results revealed that, although Pb13 showed higher stability from the total energy analysis, its energy gap and ionization potential do not follow the trend. Albeit of higher stability in terms of binding energy, the lower ionization potential of Pb13 is interesting which has been explained based on its electronic structure through the density of states and electron shell filling model of spherical clusters.     

The structural and electronic properties of Ag-adsorbed (SiO2)n (n=1-7) clusters

Equilibrium geometries, charge distributions, stabilities, and electronic properties of the Ag-adsorbed (SiO(2))(n) (n=1-7) clusters have been investigated using density functional theory with generalized gradient approximation for exchange-correlation functional. The results show that the Ag atom preferably binds to silicon atom with dangling bond in nearly a fixed direction, and the incoming Ag atoms tend to cluster on the existing Ag cluster leading to the formation of Ag islands. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of the silica clusters is minor, attributing to the tendency of stability order of Ag(SiO(2))(n) (n=1-7) clusters in consistent with silica clusters. In addition, the energy gaps between the highest occupied and lowest unoccupied molecular orbitals remarkably decrease compared with the pure (SiO(2))(n) (n=1-7) clusters, eventually approaching the near infrared radiation region. This suggests that these small clusters may be an alternative material which has a similar functionality in treating cancer to the large gold-coated silica nanoshells and the small Au(3)(SiO(2))(3) cluster.     

An ab initio study of the formation and structure of NO+-(N2)n (n = 1 and 2) clusters

The geometries and clustering energies of the NO⁺ (N₂)_n (n = 1 and 2) clusters have been determined by ab initio calculations at different levels. At the MP4SDQ/6-31G^* level, plus zero-point vibrational corrections making use of the HF/4-31G-optimized geometries, the energy differences between clusters and their relative fragments have been calculated to be −5.3 and −4.1 kcal/mol for n = 1 and n = 2, respectively. These values can be compared to the experimental enthalpies of clustering of −4.4 and −3.9 kcal/mol. The interaction between NO⁺ and N₂ and the structures of two stable cluster ions have also been examined.     

Doping-enhanced hyperpolarizabilities of silicon clusters: a global ab initio and density functional theory study of Si10 (Li, Na, K)n (n=1, 2) clusters

A global theoretical study of the (hyper)polarizabilities of alkali doped Si(10) is presented and discussed. First, a detailed picture about the low lying isomers of Si(10)Li, Si(10)Na, Si(10)K, Si(10)Li(2), Si(10)Na(2), and Si(10)K(2) has been obtained in a global manner. Then, the microscopic first (hyper)polarizabilities of the most stable configurations have been determined by means of ab initio methods of high predictive capability such as those based on the M?ller-Plesset perturbation and coupled cluster theory, paying extra attention to the (hyper)polarizabilities of the open shell mono-doped systems Si(10)Li, Si(10)Na, Si(10)K, and the influence of spin contamination. These results were used to assess the performance of methods of low computational cost based on density functional theory (DFT) in the reliable computation of these properties in order to proceed with an in-depth study of their evolution as a function of the alkali metal, the cluster composition, and the cluster structure. The most interesting outcomes of the performed (hyper)polarizability study indicate that while alkali doping leaves the per atom polarizability practically unaffected, influences dramatically the hyperpolarizabilities of Si(10). The lowest energy structures of the mono-doped clusters are characterized by significantly enhanced hyperpolarizabilities as compared to the analogue neutral or charged bare silicon clusters Si(10) and Si(11), while, certain patterns governed by the type and the number of the doping agents are followed. The observed hyperpolarizability increase is found to be in close connection with specific cluster to alkali metal charge transfer excited states and to the cluster structures. Moreover, an interesting correlation between the anisotropy of the electron density, and the hyperpolarizabilities of these systems has been observed. Finally, it is important to note that the presented method assessment points out that among the various DFT functionals used in this work, (B3LYP, B3PW91, BhandHLYP, PBE0, CAM-B3LYP, LC-BLYP, LC-BPW91) only B3PW91 and PBE0 out of the seven provided a consistent quantitative performance for both polarizabilities and hyperpolarizabilities with respect to the ab initio methods utilized here. On the other hand, the long range corrected functionals LC-(U)BLYP and LC-(U)BPW91 (μ = 0.47) failed to supply quantitatively accurate hyperpolarizability results in all the studied clusters while the CAM-(U)B3LYP functional performs satisfactory only in the case of the Na and K doped systems.     

Infrared spectra and ab initio calculations for the F- -(CH4)n (n = 1-8) anion clusters

Infrared spectra of mass-selected F- -(CH4)n (n = 1-8) clusters are recorded in the CH stretching region (2500-3100 cm-1). Spectra for the n = 1-3 clusters are interpreted with the aid of ab initio calculations at the MP2/6-311++G(2df 2p) level, which suggest that the CH4 ligands bind to F- by equivalent, linear hydrogen bonds. Anharmonic frequencies for CH4 and F--CH4 are determined using the vibrational self-consistent field method with second-order perturbation theory correction. The n = 1 complex is predicted to have a C3v structure with a single CH group hydrogen bonded to F-. Its spectrum exhibits a parallel band associated with a stretching vibration of the hydrogen-bonded CH group that is red-shifted by 380 cm-1 from the nu1 band of free CH4 and a perpendicular band associated with the asymmetric stretching motion of the nonbonded CH groups, slightly red-shifted from the nu3 band of free CH4. As n increases, additional vibrational bands appear as a result of Fermi resonances between the hydrogen-bonded CH stretching vibrational mode and the 2nu4 overtone and nu2+nu4 combination levels of the methane solvent molecules. For clusters with n < or = 8, it appears that the CH4 molecules are accommodated in the first solvation shell, each being attached to the F- anion by equivalent hydrogen bonds.     

Structures and electronic properties of small FeB n (n=1-10) clusters

The geometries, stabilities, electronic properties, and magnetism of FeB(n) clusters up to n=10 are systematically studied with density functional theory. We find that our optimized structures of FeB(2), FeB(3), FeB(4), and FeB(5) clusters are more stable than those proposed in previous literature. The results show that it is favorable for the Fe atom to locate at the surface, not at the center of the cluster, and that FeB(4) and FeB(9) clusters exhibit high stability. For all the FeB(n) clusters studied, we find the charge transfer from Fe to B site and the coexistence of ionic and covalent bonding characteristics. The computed total magnetic moments of the lowest-energy structures oscillate with the cluster size and are quenched at n=4, 6, 8, and 10.     

Infrared spectra and ab initio calculations for the Cl--(CH4)n (n = 1-10) anion clusters

In an effort to elucidate their structures, mass-selected Cl--(CH4)n (n = 1-10) clusters are probed using infrared spectroscopy in the CH stretch region (2800-3100 cm(-1)). Accompanying ab initio calculations at the MP2/6-311++G(2df,2p) level for the n = 1-3 clusters suggest that methane molecules prefer to attach to the chloride anion by single linear H-bonds and sit adjacent to one another. These conclusions are supported by the agreement between experimental and calculated vibrational band frequencies and intensities. Infrared spectra in the CH stretch region for Cl--(CH4)n clusters containing up to ten CH4 ligands are remarkably simple, each being dominated by a single narrow peak associated with stretching motion of hydrogen-bonded CH groups. The observations are consistent with cluster structures in which at least ten equivalent methane molecules can be accommodated in the first solvation shell about a chloride anion.     

Geometrical and electronic properties of neutral and charged cesium clusters Cs(n) (n=2-10): a theoretical study

We have investigated the structure and electronic properties of cesium clusters following all electron ab initio theoretical methods based on configuration interaction, second-order Moller-Plesset (MP2) perturbation theory, and density-functional theory. Becke's three-parameter nonlocal hybrid exchange-correlation functional (B3LYP) is found to perform best on the present systems with a split valence 3-21G basis function. We have calculated the optimized geometries of neutral and singly charged cesium clusters having up to ten atoms, their binding energy per atom, ionization potentials (IPs), and adiabatic electron affinity (EA). Geometry optimizations for all the clusters are carried out without imposing any symmetry restriction. The neutral clusters having up to six atoms prefer planar structure and three-dimensional structure is preferred only when the number of atoms in a cluster is more than six. There is a good agreement between the present theoretical and reported experimental IP values for the neutral clusters with cluster size n相似文献   

Geometries and electronic properties of the neutral and charged rare earth Yb-doped Si(n) (n = 1-6) clusters: a relativistic density functional investigation

The neutral and charged YbSi(n) (n = 1-6) clusters considering different spin configurations have been systematically investigated by using the relativistic density functional theory with generalized gradient approximation. The total bonding energies, equilibrium geometries, Mulliken populations (MP), Hirshfeld charges (HC), fragmentation energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps are calculated and discussed. The optimized geometries indicate that the most stable YbSi(n) (n = 1-6) clusters keep basically the analogous frameworks as the low-lying Si(n)(+1) clusters, while the charged species deviate from their neutral counterparts, and that the doped Yb tends to occupy the substitutional site of the neutral and charged YbSi(n) isomers. The relative stabilities are investigated in terms of the calculated fragmentation energies, exhibiting enhanced stabilities for the remarkably stable neutral and charged YbSi2 and YbSi5 clusters. Furthermore, the calculated MP and HC values show that the charges of the neutral and charged YbSi(n) clusters transfer from the Yb atom to Si(n) atoms and the Yb atom acts as an electron donor, and that the f orbitals of the Yb atom in the neutral and charged YbSi(n) clusters behave as core without involvement in chemical bonding. The calculated HOMO-LUMO gaps indicate that the YbSi2 and YbSi4+ clusters have stronger chemical stabilities. Comparisons of the Yb-doped Si(n) (n = 1-6) with available theoretical results of transition-metal-doped silicon clusters are made. The growth pattern is investigated also.     

Geometries and stabilities of Ag-doped Si n (n=1-13) clusters: a first-principles study

The structures of AgSi(n) (n=1-13) clusters are investigated using first-principles calculations. Our studies suggest that AgSi(n) clusters with n=7 and 10 are relatively stable isomers and that these clusters prefer to be exohedral rather than endohedral. Moreover, doping leaves the inner core structure of the clusters largely intact. Additionally, the plot of fragmentation energies as a function of silicon atoms shows that the AgSi(n) are favored to dissociate into one Ag atom and Si(n) clusters. Alternative pathways exist for n>7 (except n=11) in which the Ag-Si cluster dissociates into a stable Si(7) and a smaller fragment AgSi(n-7). The AgSi(11) cluster dissociates into a stable Si(10) and a small fragment AgSi. Lastly, our analysis indicates that doping of Ag atom significantly decreases the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital for n>7.     

Structures and infrared spectra of fluoride-hydrogen sulfide clusters from ab initio calculations: F(-)-(H2S)n, n = 1-5

Clusters formed between a fluoride anion and several hydrogen sulfide molecules have been investigated via ab initio calculations at the MP2 level of theory, using Dunning's augmented correlation consistent basis sets. Optimised geometries, vibrational frequencies, and enthalpy changes for the ligand association reactions are presented for clusters with up to five H2S ligands interacting with a F- anion. The minimum energy structure for the 1:1 F(-)-H2S complex features proton transfer from the H2S to the F- anion, forming a planar C(s) symmetry FH...SH- structure. For the F(-)-(H2S)2 cluster, the FH...SH- core remains and is solvated by a perturbed H2S ligand. For the larger F(-)-(H2S)(3-5) clusters, in addition to the FH...SH(-)-(H2S)n cluster forms, other minima featuring a 'solvated F-' anion are predicted. Calculated infrared spectra for the minima of each cluster size are presented to aid in assigning spectra from future experimental studies.