Singly and doubly lithium doped silicon clusters: geometrical and electronic structures and ionization energies

The geometric structures of neutral and cationic Si(n)Li(m)(0/+) clusters with n = 2-11 and m = 1, 2 are investigated using combined experimental and computational methods. The adiabatic ionization energy and vertical ionization energy (VIE) of Si(n)Li(m) clusters are determined using quantum chemical methods (B3LYP/6-311+G(d), G3B3, and CCSD(T)/aug-cc-pVxZ with x = D,T), whereas experimental values are derived from threshold photoionization experiments in the 4.68-6.24 eV range. Among the investigated cluster sizes, only Si(6)Li(2), Si(7)Li, Si(10)Li, and Si(11)Li have ionization thresholds below 6.24 eV and could be measured accurately. The ionization threshold and VIE obtained from the experimental photoionization efficiency curves agree well with the computed values. The growth mechanism of the lithium doped silicon clusters follows some simple rules: (1) neutral singly doped Si(n)Li clusters favor the Li atom addition on an edge or a face of the structure of the corresponding Si(n)(-) anion, while the cationic Si(n)Li(+) binds with one Si atom of the bare Si(n) cluster or adds on one of its edges, and (2) for doubly doped Si(n)Li(2)(0/+) clusters, the neutrals have the shape of the Si(n+1) counterparts with an additional Li atom added on an edge or a face of it, while the cations have both Li atoms added on edges or faces of the Si(n)(-) clusters.     

Theoretical investigation of the large nonlinear optical properties of (HCN)n clusters with Li atom

Two new classes of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) clusters with the electride characteristic are formed in theory by the metal Li atom attaching to the (HCN)(n) (n = 1, 2, 3) clusters. Because of the interaction between the Li atom and the (HCN)(n) part, the 2s valence electron of the Li atom becomes a loosely bound excess electron. Our high-level ab initio calculations show that these new clusters with the excess electron have large first hyperpolarizabilities, for example, beta(0) = -15,258 au for (HCN)...Li and beta(0) = -3401 au for Li...(HCN) at the QCISD/6-311++G(3df,3pd) level (only beta(0) = -2.8 au for HCN monomer(26)). Obviously, the excess electron from the Li atom plays a crucial role in the large first hyperpolarizabilities of these clusters. The beta(0) value of (HCN)(n)...Li (beta(0) > 10(4) au, from sigma --> pi* transition) is larger than that of Li...(HCN)(n) (beta(0) > 10(3) au, from sigma --> sigma* transition) for n = 1, 2, or 3. In addition, two interesting rules have been observed. They are that |beta(0)| decreases with lengthening of the HCN chain for (HCN)(n)...Li clusters and that |beta(0)| increases as n increases for Li...(HCN)(n) clusters. In this paper, we discuss two classes of clusters that are highly similar to the electride structure model, of which the structural characteristics are that alkali metal atoms ionize to form cations and trapped electrons under the action of other polar molecules. Thus, the investigation on the large first hyperpolarizabilities of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) may prompt one to study the unusual nonlinear optical responses of some electrides.     

Adsorption of small Au(n) (n = 1-5) and Au-Pd clusters inside the TS-1 and S-1 pores

We used a hybrid quantum-mechanics/molecular-mechanics (QM/MM) approach to simulate the adsorption of Au(n)() (n = 1-5), AuPd, and Au(2)Pd(2) clusters inside the TS-1 and S-1 pores. We studied nondefect and metal-vacancy defect sites in TS-1 and S-1 for a total of four different environments around the T6 crystallographic site. We predict stronger binding of all clusters near Ti sites in Ti-substituted framework compared to adsorption near Si sites-consistent with the experimental finding of a direct correlation between the Ti-loading and the Au-loading on the Au/TS-1 catalysts with high Si/Ti ratio. The cluster binding is also stronger near lattice-metal vacancies compared to fully coordinated, nondefect sites. In all the cases, a trend of binding energy (BE) versus Au cluster size (n) shows a peak at around n = 3-4. Our results show that there is enough room for the attack of H(2)O(2) on the Ti-defect site even with Au(1-4) adsorbed-a result that supports the possibility of H(2)O(2) spillover from the Au clusters to the adjacent Ti-defect sites. Mulliken charge analysis indicates that in all the cases there is electron density transfer to adsorbed clusters from the zeolite lattice. In the case of both gas-phase and adsorbed Au-Pd clusters, all the Pd atoms were positively charged, and all the Au atoms were negatively charged due to the higher electron-affinity of Au. We also found a correlation between the BE and the charge transfer to the clusters (the higher the charge transfer to the clusters, the higher the BE), and a universal correlation was found for Au(2-5) when BE and charge transfer were plotted on a per atom basis. A relatively larger charge transfer to the adsorbed clusters was found for the Ti sites versus the Si sites, and for the defect sites versus the nondefect sites. The trends in the BE were corroborated using Gibbs free energy of adsorption (DeltaG(ads)), and the implications of DeltaG(ads) in sintering of Au clusters are also discussed. Our results confirm that electronic factors such as cluster-charging are potentially important support effects for the Au/TS-1 catalyst.     

Structures and stability of lithium monosilicide clusters SiLin (n = 4–16): What is the maximum number,magic number,and core number for lithium coordination to silicon?

In the coordination, hypervalent and cluster chemistry, three important characteristic properties are the maximum coordination number, magic number, and core coordination number. Yet, few studies have considered these three numbers at the same time for an ML(n) cluster with n larger than 8. In this article, we systematically studied the three properties of SiLi(n) (n = 4-16) clusters at the B3LYP/6-31G(d), B3LYP/6-311++G(2d), and CCSD(T)/6-311++G(3df)//B3LYP/6-311++G(2d) (for energy only) levels. Various isomeric forms with different symmetries were calculated. For each SiLi(n) (n = 4-9), silicon cohesive energy (cE) from SiLi(n) --> Si + Li(n) reaction, vertical ionization potential (vIP), and vertical electron affinity (vEA) were obtained for the lowest-energy isomer. We found that the maximum Li-coordination number of Si is 9, which is the largest number among the known MLi(n) clusters. All cE, vIP, and vEA values predicted that 6 is the magic Li-coordination number of Si. For small SiLi(n) (n < or = 6) clusters, Li atoms favor direct coordination to Si, whereas for larger SiLi(n) (n > or = 7) clusters, there is a core cluster that is surrounded by excessive Li atoms. The core Li-coordination number is 6 for SiLi(n) (n = 7,8), 7 for SiLi(n) (n = 9,10), 8 for SiLi(n) (n = 11-15) and 9 for SiLi(n) (n > or = 16). Through the calculations, we verified the relationship between the structure and stability of SiLi(n) with the maximum coordination number, magic number, and core coordination number.     

First-principles studies on the reactions of O2 with silicon clusters

The reactions of an O(2) molecule with the neutral and positively charged Si(n)(n = 3-16) clusters are studied with first-principles calculations. Neutral Si(n)(n = 4,5,6,7,10,14) and charged Si(n) (+)(n = 4,5,6,7,13,15) clusters show higher inertness to O(2) molecule adsorption, which is in good agreement with experimental results. Both charge transfer and hybridizations between Si and O play an important role in the dissociative adsorption of O(2) molecule. We find that the spin triplet-single conversion of O(2) molecule is always accompanied with O(2) dissociatively chemisorbed on the Si(n) clusters.     

Reactions of silicon atoms and small clusters with CO: experimental and theoretical characterization of SinCO (n=1-5), Si2(CO)2, c-Si2(mu-O)(mu-CSi), and c-Si2(mu-O)(mu-CCO) in solid argon

Reactions of silicon atoms and small clusters with carbon monoxide molecules in solid argon have been studied using matrix isolation infrared absorption spectroscopy. In addition to the previously reported SiCO monocarbonyl, Si(2)(CO)(2) and Si(n)CO (n=2-5) carbonyl molecules were formed spontaneously on annealing and were characterized on the basis of isotopic substitution and theoretical calculations. It was found that Si(2)CO, Si(3)CO, and Si(5)CO are bridge-bonded carbonyl compounds, whereas Si(4)CO is a terminal-bonded carbonyl molecule. The Si(2)(CO)(2) and Si(3)CO molecules photochemically rearranged to the more stable c-Si(2)(mu-O)(mu-CCO) and c-Si(2)(mu-O) (mu-CSi) isomers where Si(2) is inserted into the CO triple bond.     

CuCl3]- and [CuCl4]2- hydrates in concentrated aqueous solution: a density functional theory and ab initio study

In this work, structures and thermodynamic properties of [CuCl(3)](-) and [CuCl(4)](2-) hydrates in aqueous solution were investigated using density functional theory and ab initio methods. Contact ion pair (CIP) and solvent-shared ion pair (SSIP) structures were both taken into account. Our calculations suggest that [CuCl(3)(H(2)O)(n)](-) clusters might favor a four-coordinated CIP structure with a water molecule coordinating with the copper atom in the equatorial position for n = 3 and 4 in aqueous solution, whereas the four-coordinated SSIP structure with one chloride atom dissociated becomes more stable as n increases to 5. For the [CuCl(4)](2-) cluster, the four-coordinated tetrahedron structure is more stable than the square-planar one, whereas for [CuCl(4)(H(2)O)(n)](2-) (n ≥ 1) clusters, it seems that four-coordinated SSIP structures are slightly more favorable than CIP structures. Our calculations suggest that Cu(2+) perhaps prefers a coordination number of 4 in CuCl(2) aqueous solution with high Cl(-) concentrations. In addition, natural bond orbital (NBO) calculations suggest that there is obvious charge transfer (CT) between copper and chloride atoms in [CuCl(x)](2-x) (x = 1-4) clusters. However, compared with that in the [CuCl(2)](0) cluster, the CT between the copper and chloride atoms in [CuCl(3)](-) and [CuCl(4)](2-) clusters becomes negligible as the number of attached redundant Cl(-) ions increases. This implies that the coordination ability of Cl(-) is greatly weakened for [CuCl(3)](-) and [CuCl(4)](2-) clusters. Electronic absorption spectra of these different hydrates were obtained using long-range-corrected time-dependent density functional theory. The calculated electronic transition bands of the four-coordinated CIP conformer of [CuCl(3)(H(2)O)(n)](-) for n = 3 and 4 are coincident with the absorption of [CuCl(3)](-)(aq) species (～284 and 384 nm) resolved from UV spectra obtained in CuCl(2) (ca. 10(-4) mol·kg(-1)) + LiCl (>10 mol·kg(-1)) solutions, whereas the calculated bands of [CuCl(3)(H(2)O)(n)](-) in their most stable configurations are not when n = 0 - 2 or n > 4, which means that the species [CuCl(3)](-)(aq) exists in those CuCl(2) aqueous solutions in which the water activity is neither too low nor too high. The calculated bands of [CuCl(4)(H(2)O)(n)](2-) clusters correspond to the absorption spectra (～270 and 370 nm) derived from UV measurements only when n = 0, which suggests that [CuCl(4)](2-)(aq) species probably exist in environments in which the water activity is quite low.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

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.     

Electronic structure and thermochemical properties of silicon-doped lithium clusters Li(n)Si0/+, n = 1-8: new insights on their stability

A theoretical investigation on small silicon-doped lithium clusters Li(n)Si with n = 1-8, in both neutral and cationic states is performed using the high accuracy CCSD(T)/complete basis set (CBS) method. Location of the global minima is carried out using a stochastic search method and the growth pattern of the clusters emerges as follows: (i) the species Li(n)Si with n ≤ 6 are formed by directly binding one Li to a Si of the smaller cluster Li(n-1)Si, (ii) the structures tend to have an as high as possible symmetry and to maximize the coordination number of silicon. The first three-dimensional global minimum is found for Li(4)Si, and (iii) for Li(7)Si and Li(8)Si, the global minima are formed by capping Li atoms on triangular faces of Li(6)Si (O(h)). A maximum coordination number of silicon is found to be 6 for the global minima, and structures with higher coordination of silicon exist but are less stable. Heats of formation at 0 K (Δ(f)H(0)) and 298 K (Δ(f)H(298)), average binding energies (E(b)), adiabatic (AIE) and vertical (VIE) ionization energies, dissociation energies (D(e)), and second-order difference in total energy (Δ(2)E) of the clusters in both neutral and cationic states are calculated from the CCSD(T)/CBS energies and used to evaluate the relative stability of clusters. The species Li(4)Si, Li(6)Si, and Li(5)Si(+) are the more stable systems with large HOMO-LUMO gaps, E(b), and Δ(2)E. Their enhanced stability can be rationalized using a modified phenomenological shell model, which includes the effects of additional factors such as geometrical symmetry and coordination number of the dopant. The new model is subsequently applied with consistency to other impure clusters Li(n)X with X = B, Al, C, Si, Ge, and Sn.     

Synthesis, structures and stabilities of thioanisole-functionalised phosphido-borane complexes of the alkali metals

Treatment of the secondary phosphine {(Me(3)Si)(2)CH}PH(C(6)H(4)-2-SMe) with BH(3)·SMe(2) gives the corresponding phosphine-borane {(Me(3)Si)(2)CH}PH(BH(3))(C(6)H(4)-2-SMe) (9) as a colourless solid. Deprotonation of 9 with n-BuLi, PhCH(2)Na or PhCH(2)K proceeds cleanly to give the corresponding alkali metal complexes [[{(Me(3)Si)(2)CH}P(BH(3))(C(6)H(4)-2-SMe)]ML](n) [ML = Li(THF), n = 2 (10); ML = Na(tmeda), n = ∞ (11); ML = K(pmdeta), n = 2 (12)] as yellow/orange crystalline solids. X-ray crystallography reveals that the phosphido-borane ligands bind the metal centres through their sulfur and phosphorus atoms and through the hydrogen atoms of the BH(3) group in each case, leading to dimeric or polymeric structures. Compounds 10-12 are stable towards both heat and ambient light; however, on heating in toluene solution in the presence of 10, traces of free phosphine-borane 9 are slowly converted to the free phosphine {(Me(3)Si)(2)CH}PH(C(6)H(4)-2-SMe) (5) with concomitant formation of the corresponding phosphido-bis(borane) complex [{(Me(3)Si)(2)CH}P(BH(3))(2)(C(6)H(4)-2-SMe)]Li (14).     

Theoretical study of mixed silicon-lithium clusters Si(n)Li(p)(+) (n=1-6, p=1-2)

Theoretical study on the structures of neutral and singly charged Si(n)Li(p)((+)) (n=1-6, p=1-2) clusters have been carried out in the framework of the density functional theory (DFT) with the B3LYP functional. The structures of the neutral Si(n)Li(p) and cationic Si(n)Li(p)(+) clusters are found to keep the frame of the corresponding Si(n), Li species being adsorbed at the surface. The localization of the lithium cation is not the same one as that of the neutral atom. The Li(+) ion is preferentially located on a Si atom, while the Li atom is preferentially attached at a bridge site. A clear parallelism between the structures of Si(n)Na(p) and those of Si(n)Li(p) appears. The population analysis show that the electronic structure of Si(n)Li(p) can be described as Si(n)(p)(-)+pLi(+) for the small sizes considered. Vertical and adiabatic ionization potentials, adsorption energies, as well as electric dipole moments and static dipolar polarizabilities, are calculated for each considered isomer of neutral species.     

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.     

1,3-Disila-2-gallata- and -indataallenic Anions [>SiMSi<]-.Li+ (M = Ga, In): compounds featuring double bonds between elements of groups 13 and 14

The first compounds containing Si=Ga or Si=In double bonds, 1,3-disila-2-gallata- (2-) and -indataallenic anions (3-), were obtained in the form of lithium salts as dark red crystals by the reaction of bis(di-tert-butylmethylsilyl)dilithiosilane 1 with GaCl3 or InCl3. X-ray crystallographic analysis of 2-.[Li(thf)4]+ and 3-.[Li(thf)4]+ showed that the >SiMSi< frameworks (M = Ga, In) are not linear and the two Si=M bond lengths are about 9% shorter than typical Si-M single bonds. In the 29Si NMR spectra, the signals of the terminal Si atoms in 2- and 3- are greatly shifted upfield (2-: -79.9; 3-: -77.6 ppm). The NPA charge distribution for the model compound, [(Me3Si)2SiGaSi(SiMe3)2]- (4-) showed a large part of the negative charge localizing on the two terminal silicon atoms (-0.736 and -0.729). In addition, 2-.[Li(thf)4]+ reacted with MeI to give the corresponding iodogallane 5 nearly quantitatively. This result confirms that the allenic [>SiMSi<]- fragments are highly polarized.     

Electronic structures and thermochemical properties of the small silicon-doped boron clusters B(n)Si (n=1-7) and their anions

We perform a systematic investigation on small silicon-doped boron clusters B(n)Si (n=1-7) in both neutral and anionic states using density functional (DFT) and coupled-cluster (CCSD(T)) theories. The global minima of these B(n)Si(0/-) clusters are characterized together with their growth mechanisms. The planar structures are dominant for small B(n)Si clusters with n≤5. The B(6)Si molecule represents a geometrical transition with a quasi-planar geometry, and the first 3D global minimum is found for the B(7)Si cluster. The small neutral B(n)Si clusters can be formed by substituting the single boron atom of B(n+1) by silicon. The Si atom prefers the external position of the skeleton and tends to form bonds with its two neighboring B atoms. The larger B(7)Si cluster is constructed by doping Si-atoms on the symmetry axis of the B(n) host, which leads to the bonding of the silicon to the ring boron atoms through a number of hyper-coordination. Calculations of the thermochemical properties of B(n)Si(0/-) clusters, such as binding energies (BE), heats of formation at 0 K (ΔH(f)(0)) and 298 K (ΔH(f)([298])), adiabatic (ADE) and vertical (VDE) detachment energies, and dissociation energies (D(e)), are performed using the high accuracy G4 and complete basis-set extrapolation (CCSD(T)/CBS) approaches. The differences of heats of formation (at 0 K) between the G4 and CBS approaches for the B(n)Si clusters vary in the range of 0.0-4.6 kcal mol(-1). The largest difference between two approaches for ADE values is 0.15 eV. Our theoretical predictions also indicate that the species B(2)Si, B(4)Si, B(3)Si(-) and B(7)Si(-) are systems with enhanced stability, exhibiting each a double (σ and π) aromaticity. B(5)Si(-) and B(6)Si are doubly antiaromatic (σ and π) with lower stability.     

Structure, stability and spectral signatures of monoprotic carborane acid-water clusters (CBW(n), where n = 1-6)

The gas phase structure, stability, spectra, and proton transfer properties of monoprotic carborane acid-water clusters [CB(11)F(m)H(11-m)(OH(2))(1)]-(H(2)O)(n) (where m = 0, 5, and 10; n = 1-6) have been calculated using density functional theory (DFT) with the Becke's three-parameter hybrid exchange functional and Lee-Yang-Parr correlation functional (B3LYP) using 6-31+G* basis set. Results reveal that Eigen cation defects are found in CBW(n) (where n = 2-6) clusters and these clusters are significantly more stable than the non-Eigen geometry. In addition to the conventional hydrogen bond (H-bond) the role of dihydrogen bond (DHB) and halogen bond (XB) in the stabilization of these clusters can be observed from the molecular graphs derived from the atoms in molecules (AIM) analysis. Spectral information shows the features of Eigen cation and proton oscillation involved in the proton transfer process. The dissociation of proton from the perfluoro derivatives with two water molecules is more favorable when compared to the other derivatives.     

Structural evolution and stability of hydrogenated Li(n) (n = 1-30) clusters: a density functional study

The structure and electronic and optical properties of hydrogenated lithium clusters Li(n)H(m) (n = 1-30, m ≤ n) have been investigated by density functional theory (DFT). The structural optimizations are performed with the Becke 3 Lee-Yang-Parr (B3LYP) exchange-correlation functional with 6-311G++(d, p) basis set. The reliability of the method employed has been established by excellent agreement with computational and experimental data, wherever available. The turn over from two- to three-dimensional geometry in Li(n)H(m) clusters is found to occur at size n = 4 and m = 3. Interestingly, a rock-salt-like face-centered cubic structure is seen in Li(13)H(14). The sequential addition of hydrogen to small-sized Li clusters predicted regions of regular lattice in saturated hydrogenated clusters. This led us to focus on large-sized saturated clusters rather than to increase the number of hydrogen atoms monotonically. The lattice constants of Li(9)H(9), Li(18)H(18), Li(20)H(20), and Li(30)H(30) calculated at their optimized geometry are found to gradually approach the corresponding bulk values of 4.083. The sequential addition of hydrogen stabilizes the cluster, irrespective of the cluster size. A significant increase in stability is seen in the case of completely hydrogenated clusters, i.e., when the number of hydrogen atoms equals Li atoms. The enhanced stability has been interpreted in terms of various electronic and optical properties like adiabatic and vertical ionization potential, HOMO-LUMO gap, and polarizability.     

Stability of alkali-encapsulating silicon cage clusters

We report a computational study of the possibility to form alkali-encapsulating Si clusters A@Si(n) with n = 10 - 20. We predict and quantify the stability for lithium, sodium, and potassium atoms encapsulated in silicon cage. The structure and electronic properties are discussed. An electronic charge transfer from the alkali atom to the Si(n) cage is observed. The A@Si(n) cluster is formed of a positive charge located on the alkali surrounded by a negative one distributed on the whole Si cage. For each size the predicted stability of such structure is discussed and compared with that of surface-bound alkali isomers. The alkali-encapsulating Si clusters A@Si(n) are found to be stable but lying much higher in energy as compared to surface-bound alkali isomers.     

Equilibrium geometries and associated energetic properties of mixed metal-silicon clusters from global optimization

The structural properties of the cluster series Me(m)Si(7-m) (Me = Cu and Li, m < or = 6) are studied by density functional theory (DFT) employing a plane wave basis. The equilibrium geometries and energetic properties of these clusters are obtained by use of the simulated annealing procedure in conjunction with the Nosé thermostat algorithm. The lowest energy isomer thus obtained is analyzed by density functional theory at the B3LYP/6-311+G(d,p) level including all electrons. Pentagonal ground state structures derived from the D(5)(h) equilibrium geometries of both Si(7) and Cu(7) are obtained for Cu(m)Si(7-m) with m < 6. The Li(m)Si(7-m) clusters, in contrast, tend toward adsorption geometries where m Li atoms are attached to a Si(7-m)framework with pronounced negative charge. For both Li(m)Si(7-m) and Cu(m)Si(7-m), a marked decrease of the energy gap is found as the number of metal atom constituents increases.     

含碱金属分子簇体系的结构和NLO性质

采用MP2方法优化得到Li(HF)n(n=2~4)体系的三个环型结构. 使用高水平的从头算方法MP2/6-311++G(3df,3pd)计算了它们的偶极矩μ0、极化率α0和一阶超极化率β0. 得出了大的一阶超极化率的变化规律, 并揭示出额外电子是引起大一阶超极化率的主要原因.