Investigating bonding in small silicon-carbon clusters: exploration of the potential energy surfaces of Si3C4, Si4C3, and Si4C4 using ab initio molecular dynamics

A theoretical investigation of the properties of the Si3C4, Si4C3, and Si4C4 clusters is reported. Systematic explorations of the potential energy surfaces of the three clusters are performed using a combination of ab initio molecular dynamics and local energy minimizations using density functional theory. A large number of isomers with a large variety of geometries has been found. The geometries, energies, and vibrational frequencies yielded are discussed. Furthermore, a quantitative analysis of the interatomic distances, angles, and coordination numbers observed, as well as the conclusions on the bonding properties, are presented. The cluster properties are then compared to those of solid SiC and of the smaller Si-C clusters (with size up to 6) obtained in a previous study. Analysis of our results and comparison with bulk properties show that even clusters as small as Si3C4, Si4C3, and Si4C4 exhibit properties similar to those of the amorphous bulk, in particular as for the structures and bonds formed by C atoms.     

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.     

Disparate effects of Cu and V on structures of exohedral transition metal-doped silicon clusters: a combined far-infrared spectroscopic and computational study

The growth mechanisms of small cationic silicon clusters containing up to 11 Si atoms, exohedrally doped by V and Cu atoms, are described. We find that as dopants, V and Cu follow two different paths: while V prefers substitution of a silicon atom in a highly coordinated position of the cationic bare silicon clusters, Cu favors adsorption to the neutral or cationic bare clusters in a lower coordination site. The different behavior of the two transition metals becomes evident in the structures of Si(n)M(+) (n = 4-11 for M = V, and n = 6-11 for M = Cu), which are investigated by density functional theory and, for several sizes, confirmed by comparison with their experimental vibrational spectra. The spectra are measured on the corresponding Si(n)M(+)·Ar complexes, which can be formed for the exohedrally doped silicon clusters. The comparison between experimental and calculated spectra indicates that the BP86 functional is suitable to predict far-infrared spectra of these clusters. In most cases, the calculated infrared spectrum of the lowest-lying isomer fits well with the experiment, even when various isomers and different electronic states are close in energy. However, in a few cases, namely Si(9)Cu(+), Si(11)Cu(+), and Si(10)V(+), the experimentally verified isomers are not the lowest in energy according to the density functional theory calculations, but their structures still follow the described growth mechanism. The different growth patterns of the two series of doped Si clusters reflect the role of the transition metal's 3d orbitals in the binding of the dopant atoms.     

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.     

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.     

Theoretical Study on the Structure and Stability of Si4X（X=Li, Be, B, C, N, O, F） Clusters

1 INTRODUCTION Silicon is an important kind of semiconductormaterial having been used to produce many sorts ofapparatus, digital and linear integrated circuit andLarge Scale Integrated circuit (LSI), and its clustershave drawn many scientists’ atten…     

Electronic structure and properties of isoelectronic magic clusters: Al13X (X=H,Au,Li,Na,K,Rb,Cs)

The equilibrium structure, stability, and electronic properties of the Al(13)X (X=H,Au,Li,Na,K,Rb,Cs) clusters have been studied using a combination of photoelectron spectroscopy experiment and density functional theory. All these clusters constitute 40 electron systems with 39 electrons contributed by the 13 Al atoms and 1 electron contributed by each of the X (X=H,Au,Li,Na,K,Rb,Cs) atom. A systematic study allows us to investigate whether all electrons contributed by the X atoms are alike and whether the structure, stability, and properties of all the magic clusters are similar. Furthermore, quantitative agreement between the calculated and the measured electron affinities and vertical detachment energies enable us to identify the ground state geometries of these clusters both in neutral and anionic configurations.     

Electronic and structural investigations of gold clusters doped with copper: Aun-1Cu- (n=13-19)

We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.     

Electronic structure and thermochemical properties of small neutral and cationic lithium clusters and boron-doped lithium clusters: Li(n)(0/+) and Li(n)B(0/+) (n = 1-8)

The stability, electronic structure, and thermochemical properties of the pure Li(n) and boron-doped Li(n)B (n = 1-8) clusters in both neutral and cationic states are studied using electronic structure methods. The global equilibrium structures are established, and their heats of formation are evaluated using the G3B3 and CCSD(T)/CBS methods based on the density functional theory geometries. Theoretical adiabatic ionization energies (IE(a)) for the Li(n) clusters are in good agreement with experiment: Li(2) (G3B3, 5.21 eV; CCSD(T), 5.14 eV; expt, 5.1127 ± 0.0003 eV), Li(3) (4.16, 4.11, 4.08 ± 0.10), Li(4) (4.76, 4.68, 4.70 ± 0.05), Li(5) (4.11, 4.06, 4.02 ± 0.10), Li(6) (4.46, 4.32, 4.20 ± 0.10), Li(7) (4.07, 3.99, 3.94 ± 0.10), and Li(8) (4.49, 4.31, 4.16 ± 0.10). The Li(4) experimental IE(a) has been revised on the basis of the Franck-Condon simulations. Species Li(5)B, Li(6)B(+), Li(7)B, and Li(8)B(+) exhibit high stability as compared to their neighbors, which can be understood by considering the magic numbers of the phenomenological shell model (PSM).     

Investigation of Structures and Stabilities of AlmPn and AlmP(m+n=2～6)Clusters by DFT

The geometries,electronic states and energies of Alm Pn （ m + n = 2 ～ 6）neutral and anionic clusters have been investigated using the density functional theory（DFT）method of Becke’s three-parameter hybrid exchange functional with the nonlocal correlation of B3LYP. Structural optimization and frequency analyses are performed with the basis of 6-311G（ d）. The calculations predict the existence of a number of previously unknown isomers（i. e. ,Al3P_ and AlmPn （ m + n.5））. The calculations have also predicted that small AlP and（AlP）2 clusters adopt two-and three-dimensional structures characteristic of Si2 and Si4 clusters,while the structures of the larger AlP clusters are different completely from those of Sin clusters with the same electrons. The results show that the structures with the singlet have higher symmetries,while those with the doublet have lower symmetries. The vertical detachment energy of AlmPn （ m + n = 2 ～ 6）are also discused and the adiabatic electron affinities of AlmPn（m + n = 2 ～ 6）and also discussed at the same level. The results agree satisfactorily with the anion photoelectron spectroscopy of aluminum phosphide clusters reported recently by Gomez et al.     

Si4X(X=C,N,O,Si,P,S)原子簇结构的理论研究

在密度泛函B3LYP/6-311G*水平上, 对具有C3v对称的Si4X (X = C, N, O, P, S)原子簇进行了几何构型优化计算, 并讨论它们的热力学稳定性、动力学活性、Mulliken布居、SiX键长、占据价轨道的对称性以及HOMO能级位置等周期递变规律。     

Computational investigation of TiSin (n=2-15) clusters by the density-functional theory

The geometries, stabilities, and electronic properties of TiSin (n=2-15) clusters with different spin configurations have been systematically investigated by using density-functional theory approach at B3LYP/LanL2DZ level. According to the optimum TiSin clusters, the equilibrium site of Ti atom gradually moves from convex to surface, and to a concave site as the number of Si atom increases from 2 to 15. When n=12, the Ti atom in TiSi12 completely falls into the center of the Si outer frame, forming metal-encapsulated Si cages, which can be explained by using 16-electron rule. On the basis of the optimized geometries, various energetic properties are calculated for the most stable isomers of TiSin clusters, including the average binding energy, the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap, fragmentation energy, and the second-order difference of energy. It is found that at size n=6,8,12 the clusters are more stable than neighboring ones. According to the Mulliken charge population analysis, charges always transfer from Si atoms to Ti atom. Furthermore, the HOMO-LUMO gaps of the most stable TiSin clusters are usually smaller than those of Sin clusters.     

Copper doping of small gold cluster cations: influence on geometric and electronic structure

The effect of Cu doping on the properties of small gold cluster cations is investigated in a joint experimental and theoretical study. Temperature-dependent Ar tagging of the clusters serves as a structural probe and indicates no significant alteration of the geometry of Au(n) (+) (n = 1-16) upon Cu doping. Experimental cluster-argon bond dissociation energies are derived as a function of cluster size from equilibrium mass spectra and are in the 0.10-0.25 eV range. Near-UV and visible light photodissociation spectroscopy is employed in conjunction with time-dependent density functional theory calculations to study the electronic absorption spectra of Au(4-m)Cu(m) (+) (m = 0, 1, 2) and their Ar complexes in the 2.00-3.30 eV range and to assign their fragmentation pathways. The tetramers Au(4) (+), Au(4) (+)[middle dot]Ar, Au(3)Cu(+), and Au(3)Cu(+)[middle dot]Ar exhibit distinct optical absorption features revealing a pronounced shift of electronic excitations to larger photon energies upon substitution of Au by Cu atoms. The calculated electronic excitation spectra and an analysis of the character of the optical transitions provide detailed insight into the composition-dependent evolution of the electronic structure of the clusters.     

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.     

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.     

Al7Ag and Al7Au clusters with large highest occupied molecular orbital-lowest unoccupied molecular orbital gap

The candidate structures for the ground-state geometry of the Al(7)M (M = Li, Cu, Ag, and Au) clusters are obtained within the spin-polarized density functional theory. Absorption energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level have been calculated to investigate the effects of doping. Doping with Ag or Au can lead to a large HOMO-LUMO gap, low electron affinity, and increased ionization potential of Al(7) cluster. In the lowest-energy structure of the Al(7)Au cluster, the Al atom binding to the Al(6)Au acts monovalent and the other six Al atoms are trivalent. Thus, the Al(7)Au cluster has 20 valence electrons, and its enhanced stability may be due to the electronic shell closure effect.     

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.     

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.     

SinP+m(n+m=5)结构和稳定性的理论研究

在实验的基础上 ,利用量子化学方法对 Sin P+ m( n+m=5 )的各种可能构型进行几何构型优化 ,预测各团簇的稳定结构 ,从中得出各个团簇稳定构型之间的基本关系 ,当 n>m时 ,团簇的稳定构型与 Si+ n 相似 ,而当 n相似文献   

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.