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.     

InnNa和InnNa+(n=2-8)的团簇结构和电子性质

在密度泛函理论B3LYP水平上, 对InnNa和InnNa+(n=2-8)团簇进行了结构优化和振动频率计算. 计算结果表明, InnNa(n=2、3、4、6)最稳定结构中的对称性分别为C2v、C3v、C4v和C2v, 而InnNa(n=5、7、8)的最稳定结构的对称性为C1点群. 从InnNa(n=4-8)的最稳定结构可以看出, Na原子均位于四个In原子形成的四边形面上. 对于InnNa+(n=2-8), 除了In2Na+、In4Na+和In7Na+, 其它结构都与其中性结构相似. 进一步计算InnNa(n=2-8)团簇的平均结合能、能量的二阶差分以及绝热电离能表明, InnNa(n=2-8)团簇能量的二阶差分呈现奇偶交替特征, In4Na和In6Na较其它团簇更为稳定, 而且理论计算得到的绝热电离能和实验结果吻合得很好.     

Stochastic search of the quantum conformational space of small lithium and bimetallic lithium-sodium clusters

In this paper we report the results obtained by an implementation and application of the simulated annealing optimization procedure to the exploration of the conformational space of small neutral and charged lithium clusters (Li(n)(q), n = 5, 6, 7; q = 0, +/-1) and of the bimetallic lithium/sodium clusters (Li5Na) in their lowest spin states. Our methodology eliminates the structure guessing procedure in the process of generating cluster configurations. We evaluate the quantum energy, typically with the Hartree-Fock Hamiltonian, of randomly generated points in the conformational space and use a modified Metropolis test in the annealing algorithm to generate candidate structures for atomic clusters. The structures are further optimized by analytical methods (gradient following) at the M?ller-Plesset second order perturbation theory level (MP2), in conjunction with basis sets including polarization functions with and without diffuse functions. High accuracy ab initio energies at the coupled clusters level, with single, double, and triple substitutions from the Hartree-Fock determinant (CCSD(T)), on the MP2 geometries were calculated and used to establish the relative stability of the isomers within each potential energy surface. Various cluster properties were computed and compared to existing values in order to validate our methods. Our results show excellent agreement with previous experimental and theoretical reports. Even at these small sizes, evidence for 10 new structures never reported before for the lithium clusters and four new structures for the bimetallic clusters is presented.     

Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.; et al. Nature 1979, 278, 332; Rayez, J. C.; et al., J. Chem. Phys. 1981, 75, 5393] indicated these molecules would have a shallow minimum and adopt symmetrical geometries that accord with the valence shell electron pair repulsion (VSEPR) rules for geometries defined by electron pairs surrounding a central point of attraction. These earlier calculations were all based upon Hartree-Fock (HF) calculations with a fairly small basis of atomic functions, except for the H3(-) ion for which configuration interaction (CI) calculations were carried out. A related paper [Hirao, K.; et al., Chem. Phys. 1983, 80, 237] carried out similar calculations on the same clusters, finding geometries similar to our earlier calculations. However, although that paper argued that the stabilization energy of negative ion clusters H(n)(-) is small, vibration frequencies for the whole set of clusters was not reported, and so a definitive assertion of a true equilibrium was not present. In this paper we recalculate the energetics of the ion induced dipole clusters using density function theory (DFT) B3LYP method calculations in a basis of functions (6-311++G(d,p)). By calculating the vibration frequencies of the VSEPR geometries, we prove that in general they are not true minima because not all the resulting frequencies correspond to real values. By searching the energy surface of the B3LYP calculations, we find the true minimum geometries, which are surprising configurations and are perhaps counterintuitive. We calculate the total energy and binding energy of the new geometries. We also calculate the bond paths associated with the quantum theory of atoms in molecules (QTAIM). The B3LYP/6-311++G(d,p) results, for each molecule, deliver bond paths that radiate between each polarized H2 molecule and the polarizing H(-) ion.     

A Gaussian-3 theoretical study of small silicon-lithium clusters: electronic structures and electron affinities of SinLi(-) (n = 2-8)

The molecular structures of neutral Si n Li ( n = 2-8) species and their anions have been studied by means of the higher level of the Gaussian-3 (G3) techniques. The lowest energy structures of these clusters have been reported. The ground-state structures of neutral clusters are "attaching structures", in which the Li atom is bound to Si n clusters. The ground-state geometries of anions, however, are "substitutional structures", which is derived from Si n+1 by replacing a Si atom with a Li (-). The electron affinities of Si n Li and Si n have been presented. The theoretical electron affinities of Si n are in good agreement with the experiment data. The reliable electron affinities of Si n Li are predicted to be 1.87 eV for Si 2Li, 2.06 eV for Si 3Li, 2.01 eV for Si 4Li, 2.61 eV for Si 5Li, 2.36 eV for Si 6Li, 2.21 eV for Si 7Li, and 3.18 eV for Si 8Li. The dissociation energies of Li atom from the lowest energy structures of Si n Li and Si atom from Si n clusters have also been estimated respectively to examine relative stabilities.     

Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si12-Si20

Ab initio all-electron molecular-orbital calculations are carried out to study the structures and relative stability of low-energy silicon clusters (Si(n),n = 12-20). Selected geometric isomers include those predicted by Ho et al. [Nature (London) 392, 582 (1998)] based on an unbiased search with tight-binding/genetic algorithm, as well as those found by Rata et al. [Phys. Rev. Lett. 85, 546 (2000)] based on density-functional tight-binding/single-parent evolution algorithm. These geometric isomers are optimized at the M?ller-Plesset (MP2) MP2/6-31G(d) level. The single-point energy at the coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] CCSD(T)/6-31G(d) level for several low-lying isomers are further computed. Harmonic vibrational frequency analysis at the MP2/6-31G(d) level of theory is also undertaken to assure that the optimized geometries are stable. For Si12-Si17 and Si19 the isomer with the lowest-energy at the CCSD(T)/6-31G(d) level is the same as that predicted by Ho et al., whereas for Si18 and Si20, the same as predicted by Rata et al. However, for Si14 and Si15, the vibrational frequency analysis indicates that the isomer with the lowest CCSD(T)/6-31G(d) single-point energy gives rise to imaginary frequencies. Small structural perturbation onto the Si14 and Si15 isomers can remove the imaginary frequencies and results in new isomers with slightly lower MP2/6-31G(d) energy; however the new isomers have a higher single-point energy at the CCSD(T)/6-31G(d) level. For most Si(n) (n = 12-18,20) the low-lying isomers are prolate in shape, whereas for Si19 a spherical-like isomer is slightly lower in energy at the CCSD(T)/6-31G(d) level than low-lying prolate isomers.     

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.     

Interaction of peroxyformic acid with water molecules: a first-principles study

The present article comprises a theoretical study of structures and energetics of the lowest energy conformers of peroxyformic acid (PFA) and its hydrated variants, viz. PFA...(H2O)n (n = 1-4), at the molecular level. We have employed two different ab initio quantum chemical methods, viz. restricted Hartree-Fock (RHF) and the second-order M?ller-Plesset (MP2) perturbation theory with the basis sets 6-31G(d,p) and 6-311++G(2d,2p). Modifications in the structure as well as vibrational frequencies of PFA brought about by successive addition of H2O molecules are also discussed. Cooperativity of hydrogen bonding in these clusters can be gauged through a detailed many body interaction energy analysis.     

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.     

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.     

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.     

Multiple isomers in the photoelectron spectra of small mono-niobium carbide clusters

We calculate the photoelectron spectrum of small mono-niobium carbide clusters (NbC(n)) using density functional theory for clusters with n = 2-7 and the symmetry adapted cluster configuration interaction method for the smallest clusters (n = 2-4). Theoretical spectra of a single structure cannot explain all peaks present in the spectrum measured by Zhai et al. [J. Chem. Phys. 115, 5170 (2001)]. However, we can match all peaks in the experimental spectra if we assume that the beam contains a combination of cyclic and linear structures. This finding is even more surprising given the fact that some of the excited metastable geometries have energies as large as 0.5 eV above the ground state. Our result is confirmed by both theoretical approaches. We suggest further experiments, using additional beam cooling, to corroborate this observation.     

First-principles investigation of finite-temperature behavior in small sodium clusters

A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na(n), in the size range of n=8-50 are carried out. The simulations are performed using density-functional molecular dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond-length fluctuation, deviation energy, etc., are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n=8 and 10 do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show an irregular pattern similar to the experimentally observed one for larger clusters [Schmidt et al., Nature (London) 393, 238 (1998)]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n=40-55. While Na(40) and Na(55) show well-developed peaks in the specific-heat curve, Na(50) cluster exhibits a rather broad peak, indicating a poorly defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); Breaux et al., Phys. Rev. Lett. 94, 173401 (2005)].     

Con(n=2～10)团簇的结构和磁性

采用密度泛函理论中的局域自旋密度近似(LSDA)和广义梯度近似(GGA)对Con(n=2～10)团簇的几何构型进行优化，并对能量、频率和磁性进行了计算,两种方法确定的基态构型完全一致,并从平均键长、平均配位数和对称性对磁性的影响进行了理论探讨.研究表明, Con(n=2～10)基态团簇的磁性在n=2～4时主要受平均键长的影响,在n=5～9时主要受平均配位数的影响,在n=10时受原子间距和平均配位数的相互影响,最终导致与Co8基态团簇具有相同的磁性.基态团簇在Co5和Co9出现了磁性局域最小点.     

Local lattice structure study of the octahedral (CrO6)9- clusters for Cr3+ ion doping in a variety of oxide crystals by simulating the corresponding EPR and optical spectra

On the basis of the 120 x 120 complete energy matrix, the local lattice structures of the octahedral (CrO6)9- clusters for Cr3+ ions doping in a variety of oxide crystals with D3d or C3v site symmetry have been studied by employing two distorted parameters, respectively. By simulating the calculated EPR and optical spectra data to the experimental results, the local lattice structure parameters are determined unambiguously. It is shown, by means of a series of calculations, that although the local lattice structures around the M (M = Al3+, Ga3+, Li+, Sc3+, etc.) ions in host crystals are obviously different, the local lattice structures of the octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ ions are similar and fluctuant in the vicinity of that of the Cr2O3. This may be ascribed to the fact that there is the similarly octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ and the Cr2O3 crystal. Our viewpoint is consistent with that of Gaudry et al. [Phys. Rev. B 2003, 67, 094108].     

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.     

(BN)n团簇的结构和稳定性

用HF方法、密度泛函理论的B3LYP以及微扰理论的MP2方法，在6—31G(d)基组 水平上，对(BN)n(n=1-16)团簇的各种可能结构进行了优化．讨论了环状与笼状稳 定团簇的几何构型、自然键轨道(NBO）、振动频率、结合能、核独立化学位移 (NICS)和能量二次差分，得到了(BN)n(n＝1-16)团簇结构的稳定性信息．比较了 HF，B3LYP以及MP2三种理论方法对(BN)n团簇的适应性所表现出的差异．     

CCSD calculations on C(14), C(18), and C(22) carbon clusters

The structure and energetics of the ring isomers of C(4n+2) (n=3-5) carbon clusters were studied by using coupled-cluster singles and doubles excitation theory to overcome the vast differences existing in the literature. The results obtained in the present study clearly indicate that C(14), C(18), and C(22) carbon rings have bond-length and bond-angle alternated acetylenic minimum energy structures. Contrarily, density functional theory calculations were unable to predict these acetylenic-type structures and they ended up with the cumulenic structures. It is found from the coupled-cluster studies that the lowest-energy ring isomer for the first two members of C(4n+2) series is a bond-angle alternated cumulenic D((2n+1)h) symmetry structure while the same for the remaining members is a bond-length and bond-angle alternated C((2n+1)h) symmetry structure. In C(4n+2) carbon rings, Peierls-type distortion, transformation from bond-angle alternated to bond-length alternated minimum energy structures, occurs at C(14) carbon ring.     

Pressure and size effects in endohedrally confined hydrogen clusters

Density functional theory is used to carry out a systematic study of zero-temperature structural and energy properties of endohedrally confined hydrogen clusters as a function of pressure and the cluster size. At low pressures, the most stable structural forms of (H(2))(n) possess rotational symmetry that changes from C(4) through C(5) to C(6) as the cluster grows in size from n=8 through n=12 to n=15. The equilibrium configurational energy of the clusters increases with an increase of the pressure. The rate of this increase, however, as gauged on the per atom basis is different for different clusters sizes. As a consequence, the size dependencies of the configurational energies per atom at different fixed values of pressure are nonmonotonic functions. At high pressures, the molecular (H(2))(n) clusters gradually become atomic or dominantly atomic. The pressure-induced changes in the HOMO-LUMO gap of the clusters indicate a finite-size analog of the pressure-driven metallization of the bulk hydrogen. The ionization potentials of the clusters decrease with the increase of pressure on them.     

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.