Experimental and theoretical characterization of MSi16(-), MGe16(-), MSn16(-), and MPb16(-) (M = Ti, Zr, and Hf): the role of cage aromaticity

Silicon (Si), germanium (Ge), tin (Sn), and lead (Pb) clusters mixed with a group-4 transition metal atom [M = titanium (Ti), zirconium (Zr), and hafnium (Hf)] were generated by a dual-laser vaporization method, and their properties were analyzed by means of time-of-flight mass spectroscopy and anion photoelectron spectroscopy together with theoretical calculations. In the mass spectra, mixed neutral clusters of MSi(16), MGe(16), and MSn(16) were produced specifically, but the yield of MPb(16) was low. The anion photoelectron spectra revealed that MSi(16), MGe(16), and MSn(16) neutrals have large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps of 1.5-1.9 eV compared to those of MPb(16) (0.8-0.9 eV), implying that MSi(16), MGe(16), and MSn(16) are evidently electronically stable clusters. Cage aromaticity appears to be an important determinant of the electronic stability of these clusters: Calculations of nucleus-independent chemical shifts (NICSs) show that Si(16)(4-), Ge(16)(4-), and Sn(16)(4-) have aromatic characters with negative NICS values, while Pb(16)(4-) has an antiaromatic character with a positive NICS value.     

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.     

杂硼原子簇XB6+ (X=C,Si, Ge,Sn, Pb)的稳定性和芳香性

利用从头算MP2方法和密度泛函理论B3LYP和B3PW91方法, 研究了杂硼原子簇XB₆⁺ (X=C, Si, Ge, Sn, Pb)的结构、稳定性及化学键合情况. 对C, Si, Ge, B使用6-311+G(d)基组, 对Sn和Pb使用LANL2DZ赝势基组. 研究结果表明, 具有C_s对称性的假平面XB₆⁺ (X=C, Si, Ge, Sn, Pb)结构是势能面上的全域极小点, 其稳定性要高于C_6v对称性的锥形结构和C₂对称性的假锥形结构. 在B3LYP水平上, 对这些异构体的势能面的极小点进行了自然键轨道(NBO)的分析; 对最稳定构型的最高占据分子轨道(HOMO)和最低空轨道(LUMO)能级差、分子轨道(MO)和核独立化学位移(NICS)进行了计算和讨论. 分析了杂原子和硼原子间、相邻硼原子间的键合情况, 讨论了最稳定构型的芳香性质.     

Structure and bonding energy analysis of cationic metal-ylyne complexes of molybdenum and tungsten, [(MeCN)(PMe3)4M≡EMes]+ (M = Mo, W; E = Si, Ge, Sn, Pb): a theoretical study

The molecular and electronic structures and bonding analysis of terminal cationic metal-ylyne complexes (MeCN)(PMe(3))(4)M≡EMes](+) (M = Mo, W; E = Si, Ge, Sn, Pb) were investigated using DFT/BP86/TZ2P/ZORA level of theory. The calculated geometrical parameters for the model complexes are in good agreement with the reported experimental values. The M-E σ-bonding orbitals are slightly polarized toward E except in the complex [(MeCN)(PMe(3))(4)W(SnMes)](+), where the M-E σ-bonding orbital is slightly polarized toward the W atom. The M-E π-bonding orbitals are highly polarized toward the metal atom. In all complexes, the π-bonding contribution to the total M≡EMes bond is greater than that of the σ-bonding contribution and increases upon going from M = Mo to W. The values of orbital interaction ΔE(orb) are significantly larger in all studied complexes I-VIII than the electrostatic interaction ΔE(elstat). The absolute values of the interaction energy, as well as the bond dissociation energy, decrease in the order Si > Ge > Sn > Pb, and the tungsten complexes have stronger bonding than the molybdenum complexes.     

Theoretical studies on the band structures of superconducting solid compounds: Nb3X (X=Si, Ge, Sn, Pb)

The band structures of several analogous superconducting A-15 type solid compounds, Nb3X (X=Si, Ge, Sn, Pb), have been calculated by use of the tight-binding method within the Extended Huckel approximation (EHT). By analysis of their energy bands, densities of states and crystal orbital overlap populations, the dependence of the superconducting transition temperatures (Tc) on the electronic structures and bondings is qualitatively elucidated.     

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, trimethylgermyl, trimethylstannyl, and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene X. Some regularities

The changes in the vibrational frequencies of 1-tert-butyl and 1,2-di-tert-butyl derivatives of 3,3-dimethylcyclopropene brought about by substitution of the central carbon atom (X) of the tert-butyl moieties by Si, Ge, Sn, or Pb atoms are examined. The most important decrease in the vibrational frequencies implicating the X(CH(3))(3) moieties is noted for substitution of X=C by Si. The substitutions of Si by Ge or Ge by Sn or Sn by Pb are not accompanied by the pronounced frequency shifts observed for the C-->Si transition. An explanation is given for trends in these vibrational frequencies for the transitions X=C-->Si-->Ge-->Sn-->Pb. It is concluded that there are lower limiting values of the vibrational frequencies of a molecular moiety which are approached when the mass of its isovalent atom is increased. This leads to the formation of cluster regions in the vibrational spectra for the frequencies of the SnC(3) and PbC(3) moieties.     

Structure and electronic properties of PbnM (M=C, Al, In, Mg, Sr, Ba, and Pb; n=8, 10, 12, and 14) clusters: theoretical investigations based on first principles calculations

A systematic theoretical study of the PbnM (M=C, Al, In, Mg, Sr, Ba, and Pb; n=8, 10, 12, and 14) clusters have been investigated to explore the effect of impurity atoms on the structure and electronic properties of lead clusters. The calculations were carried out using the density functional theory with generalized gradient approximation for exchange-correlation potential. Extensive search based on large numbers of initial configurations has been carried out to locate the stable isomers of PbnM clusters. The results revealed that the location of the impurity atom depends on the nature of interaction between the impurity atom and the host cluster and the size of the impurity atom. Whereas, the impurity atoms smaller than Pb favor to occupy the endohedral position, the larger atoms form exohedral capping of the host cluster. The stability of these clusters has been analyzed based on the average binding energy, interaction energy of the impurity atoms, and the energy gap between the highest occupied and lowest unoccupied energy levels (HLG). Based on the energetics, it is found that p-p interaction dominates over the s-p interaction and smaller size atoms interact more strongly. The stability analysis of these clusters suggests that, while the substitution of Pb by C or Al enhances the stability of the Pbn clusters, Mg lowers the stability. Further investigations of the stability of PbnM clusters reveal that the interplay between the atomic and electronic structure is crucial to understand the stability of these clusters. The energy gap analysis reveals that, while the substitution of Mg atom widens the HLG, all other elements reduce the gap of the PbnM clusters.     

[MAl5]+(M=Si,Ge,Sn,Pb)体系结构和稳定性的理论研究

利用B3LYP和CCSD(T)(单点)方法, 研究了含Si, Ge, Sn, Pb的六原子体系[MAl₅]⁺中各个异构体的结构及稳定性. 研究结果表明, 尽管与[CAl₅]⁺一样也具有18个价电子, 但[MAl₅]⁺(M=Si, Ge, Sn, Pb)体系并不存在具有平面五配位结构的异构体, 其能量的全局极小点为具有C_s对称性的蝶形异构体Int1, 这是由于中心原子M(Si, Ge, Sn, Pb)较大的体积显著破坏了[MAl₅]⁺中平面五配位结构的稳定性所致.     

Experimental and theoretical investigation on binary semiconductor clusters of Bi/Si, Bi/Ge, and Bi/Sn

Bi(m)M(n)- (M = Si, Ge, Sn) binary cluster anions are generated by using laser ablation on mixtures of Bi and M (M = Si, Ge, Sn) samples and studied by reflectron time-of-flight mass spectrometer (RTOF-MS) in the gas phase. Some magic number clusters are present in the mass spectra which indicate that they are in stable structures. For small anions (m + n < or = 6), their structures are investigated with the DFT method and the energetically lowest lying structures are obtained. For the binary anionic clusters with the same composition containing Si, Ge, and Sn, they share similar geometric and electronic structure in the small size except that BiSi3-, BiSi5-, Bi2Si2-, Bi2Si3-, and Bi4Sn2- are different for the lowest energetic structures, and the ground states for all the anions are in their lowest spin states. The calculated VDE (vertical detachment energy) and binding energy confirm the obviously magic number cluster of BiM4- (M = Si, Ge, Sn), which agrees with the experimental results.     

Probing the electronic structure,chemical bonding,and excitation spectra of [CuE]+/0/− (E = 14 group element) diatomics employing DFT and ab initio methods

The electronic structure, chemical bonding, and excitation spectra of neutral, cationic, and anionic diatomic molecules of Cu and 14 group elements formulated as [CuE]^+/0/? (E = C, Si, Ge, Sn, Pb) were investigated by density functional theory (DFT) and time‐dependent (TD)‐DFT methods. The electronic and bonding properties of the diatomics analyzed by natural bond orbital (NBO) analysis approch revealed a clear picture of the chemical bonding in these species. The spatial organization of the bonding between Cu and E atoms in the [CuE]^+/0/? (E = Si, Ge, Sn, Pb) molecules can easily be recognized by the cut‐plane electron localization function representations. Particular emphasis was given on the absorption spectra of the [CuE]^+/0/? which were simulated using the results of TD‐DFT calculations employing the hybrid Coulomb‐attenuating CAM‐B3LYP functional. The absorption bands have thoroughly been analyzed and assignments of the contributing principal electronic transitions associated to individual excitations have been made. © 2012 Wiley Periodicals, Inc.     

Mechanism of abstraction reactions of dimetallenes (R2X=XR2; X = C, Si, Ge, Sn, Pb) with halocarbons: a theoretical study

Potential energy surfaces for the abstraction reactions of dimetallenes with halocarbons have been studied using density functional theory (B3LYP). Five dimetallene species, (SiH(3))(2)X=X(SiH(3))(2), where X = C, Si, Ge, Sn, and Pb, have been chosen in this work as model reactants. The present theoretical investigations suggest that the relative dimetallenic reactivity increases in the order C=C < Si=Si < Ge=Ge < Sn=Sn < Pb=Pb. That is to say, for halocarbon abstractions there is a very clear trend toward lower activation barriers and more exothermic reactions on going from C to Pb. Moreover, for a given dimetallene, the overall barrier heights are determined to be in the order CF(4) > CCl(4) > CBr(4) > CI(4). That is, the heavier the halogen atom (Y), the more facile its abstraction from CY(4). Halogen abstraction is always predicted to be much faster than the abstraction of a CY(3) group irrespective of the dimetallene or halocarbon involved. Our model conclusions are consistent with some available experimental findings. Furthermore, both a configuration mixing model based on the work of Pross and Shaik and bonding dissociation energies can be used to rationalize the computational results. These results allow a number of predictions to be made.     

Theoretical and experimental investigation on the electronic properties of the shuttlecock shaped and the double-decker structured metal phthalocyanines, MPc and M(Pc)2 (M = Sn and Pb)

The molecular geometries, electronic structures, and excitation energies of tin and lead phthalocyanine compounds, SnPc, PbPc, Sn(Pc)(2), and Pb(Pc)(2), were investigated using the B3LYP method within a framework of density functional theory (DFT). The geometries of SnPc, PbPc, Sn(Pc)(2), and Pb(Pc)(2) were optimized under C(4v), C(4v), D(4d), and D(4d) molecular symmetries, respectively. The excitation energies of these molecules were computed by the time-dependent DFT (TD-DFT) method. The calculated results for the excited states of three compounds other than the unknown Pb(Pc)(2) corresponded well with the experimental results of electronic absorption spectroscopy. The non-planar C(4v) molecular structure of SnPc and PbPc influences especially on the orbital energy of the HOMO-1 through mixing of the s-type atomic orbital of the central metal atom to the π system of the Pc ring in an anti-bonding way; however, the HOMO and the LUMO have little effect of the deviation from the planar structure because they have no contribution from the atomic orbital of the central metal. This orbital mixing pushes up the orbital energy of the HOMO-1, and reduces the energy of the metal-to-ligand charge transfer band of SnPc and PbPc. The calculated results also reproduced well the excitation profile of Sn(Pc)(2), which was quite different from that of SnPc. The strong interactions between the π-type orbitals of two Pc moieties altered the electronic structure resulting in the characteristic excitation profile of Sn(Pc)(2). In addition, this caused a reduction of about 0.8 eV in the ionization potential as compared to usual MPcs including SnPc, which was consistent with the experimental results.     

Evolution of the electronic properties of Snn- clusters (n=4-45) and the semiconductor-to-metal transition

The electronic structure of Sn(n) (-) clusters (n=4-45) was examined using photoelectron spectroscopy at photon energies of 6.424 eV (193 nm) and 4.661 eV (266 nm) to probe the semiconductor-to-metal transition. Well resolved photoelectron spectra were obtained for small Sn(n) (-) clusters (n< or =25), whereas more congested spectra were observed with increasing cluster size. A distinct energy gap was observed in the photoelectron spectra of Sn(n) (-) clusters with n< or =41, suggesting the semiconductor nature of small neutral tin clusters. For Sn(n) (-) clusters with n> or =42, the photoelectron spectra became continuous and no well-defined energy gap was observed, indicating the onset of metallic behavior for the large Sn(n) clusters. The photoelectron spectra thus revealed a distinct semiconductor-to-metal transition for Sn(n) clusters at n=42. The spectra of small Sn(n) (-) clusters (n< or =13) were also compared with those of the corresponding Si(n) (-) and Ge(n) (-) clusters, and similarities were found between the spectra of Sn(n) (-) and those of Ge(n) (-) in this size range, except for Sn(12) (-), which led to the discovery of stannaspherene (the icosahedral Sn(12) (2-)) previously [L. F. Cui et al., J. Am. Chem. Soc. 128, 8391 (2006)].     

锗分族元素二元团簇及其与Co形成的团簇离子

通过比较激光烧蚀E1/E2 (代表Ge/Sn， Ge/Pb和Sn/Pb) 和Co/E (E为Ge、Sn、Pb)混合样品形成的二元团簇负离子飞行时间质谱分布和谱峰的相对强度及形成的幻数团簇离子峰，发现E1/E2二元团簇离子中原子量大的锗分族元素在团簇离子中占主要组分，而原子量小的元素则少量掺杂，其组成和分布特点说明其结构和性质与纯E团簇离子相似，可能的结构为该类负离子团簇所有原子都在笼结构的骨架上；对于二元团簇离子GeSn9－、GePb9－和SnPb9－其结构可能是双帽反四棱柱构型，只是每个原子均为骨架的一部分.而对激光烧蚀过渡金属钴与锗分族元素的混合物的研究发现，反应形成了丰富的Co/E二元合金团簇负离子，分析发现该类簇离子为钴内包覆于E(锗分族元素)笼状结构.幻数离子CoGe10－、CoSn10－和CoPb10－可能具有双帽四角反棱柱结构，而CoPb12－可能具有二十面体构型，钴原子均为笼状结构的中心.     

Theoretical investigations of the reactivities of cationic six-membered carbene analogues of group 14 elements

The potential energy surfaces for the chemical reactions of cationic six-membered group 14 heavy carbene species have been studied using density functional theory (B3LYP/LANL2DZ) and CCSD (CCSD/LANL2DZ//B3LYP/LANL2DZ) methods. Five six-membered group 14 cationic heavy carbene species, [HC(CMeNPh)2E:](+), where E = C, Si, Ge, Sn, and Pb, have been chosen as model reactants in this work. Also, four kinds of chemical reaction, C-H bond insertion, multiple bond cycloaddition, dimerization, and O-H bond insertion, have been used to study the chemical reactivities of these group 14 cationic carbene species. Basically, our present theoretical work predicts that the larger the angle NEN bond angle and the smaller the singlet-triplet splitting of the carbene, the lower its activation barriers will be and, in turn, the more rapid are its chemical reactions with other species. Moreover, the theoretical investigations suggest that the relative carbenic reactivity decreases in the order C > Si > Ge > Sn > Pb. That is, the heavier the group 14 atom (E), the more stable is its cationic carbene toward chemical reaction. As a result, we predict that the cationic six-membered group 14 carbene species (E = C, Si, Ge, Sn, and Pb) should be stable, readily synthesized, and isolated at room temperature. Our computational results are in good agreement with the available experimental observations. Furthermore, the singlet-triplet energy splitting of the carbene, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict its reactivities. The results obtained allow a number of predictions to be made.     

Experimental and theoretical characterization of aluminum-based binary superatoms of AL12X and their cluster salts

The geometric and electronic structures of aluminum binary clusters, AlnX (X = Si and P), have been investigated, using mass spectrometry, anion photoelectron spectroscopy, photoionization spectroscopy, and theoretical calculations. Both experimental and theoretical results show that Al12Si has a high ionization energy and low electron affinity and Al12P has a low ionization energy, both with the icosahedral structure having a central Si or P atom, revealing that Al12Si and Al12P exhibit rare-gas-like and alkali superatoms, respectively. Experiments confirmed the possibility that the change in the total number of valence electrons on substitution could produce ionically bound binary superatom complexes, the binary cluster salts Al12P+ F- and Al12B- Cs+.     

Au12M (M=Na,Mg, Al,Si, P,S, Cl)团簇的结构、稳定性和电子性质

采用基于密度泛函理论的第一性原理方法系统地研究了Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇的结构、稳定性和电子性质.对团簇的平均结合能、镶嵌能、垂直离化势、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、电荷布居分析、自然键轨道(NBO)进行了计算和讨论.对于Au12M(M=Na,Mg,Al)团簇,它们形成了内含M原子的最稳定的笼状结构.然而对于Au12M(M=Si,P,S,Cl)团簇,它们却形成了以M元素为顶点的稳定锥形结构.在这些团簇中发现Au12S团簇相对是最稳定的,这是由于Au12S团簇形成了稳定的满壳层的电子结构.自然电荷布居分析表明:对于所有的Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇电荷总是从Au原子转向M原子.自然键轨道和HOMO分析表明Au12M团簇中发生了Au原子的s-d轨道和M原子的p轨道间的杂化现象.     

A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Ge(n) and CuGe(n) (n = 2-13) clusters have been systematically investigated by using density-functional approach. According to optimized CuGe(n) geometries, growth patterns of Cu-capped Ge(n) or Cu-substituted Ge(n+1) clusters for the small- or middle-sized CuGe(n) clusters as well as growth patterns of Cu-concaved Ge(n) or Ge-capped CuGe(n-1) clusters for the large-sized CuGe(n) clusters are apparently dominant. The average atomic binding energies and fragmentation energies are calculated and discussed; particularly, the relative stabilities of CuGe10 and Ge10 are the strongest among all different sized CuGe(n) and Ge(n) clusters, respectively. These findings are in good agreement with the available experimental results on CoGe10- and Ge10 clusters. Consequently, unlike some transition metal (TM)Si12, the hexagonal prism CuGe12 is only low-lying structure; however, the basket-like structure is located as the lowest-energy structure. Different from some TM-doped silicon clusters, charge always transfers from copper to germanium atoms in all different sized clusters. Furthermore, the calculated highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gaps are obviously decreased when Cu is doped into the Ge(n) clusters, together with the decrease of HOMO-LUMO gaps, as the size of clusters increases. Additionally, the contribution of the doped Cu atom to bond properties and polarizabilities of the Ge(n) clusters is also discussed.     

Search for lowest-energy structure of Zintl dianion Si(12)(2-), Ge(12)(2-), and Sn(12)(2-)

We perform an unbiased search for the lowest-energy structures of Zintl dianions (Si(12)(2-), Ge(12)(2-), and Sn(12)(2-)), by using the basin-hopping (BH) global optimization method combined with density functional theory geometric optimization. High-level ab initio calculation at the coupled-cluster level is used to determine relative stabilities and energy ranking among competitive low-lying isomers of the dianions obtained from the BH search. For Si(12)(2-), all BH searches (based on independent initial structures) lead to the same lowest-energy structure Si(12a)(2-), a tricapped trigonal prism (TTP) with C(s) group symmetry. Coupled-cluster calculation, however, suggests that another TTP isomer of Si(12c)(2-) is nearly isoenergetic with Si(12a)(2-). For Sn(12)(2-), all BH searches lead to the icosahedral structure I(h)-Sn(12a)(2-), i.e., the stannaspherene. For Ge(12)(2-), however, most BH searches lead to the TTP-containing Ge(12b)(2-), while a few BH searches lead to the empty-cage icosahedral structure I(h)-Ge(12a)(2-) (named as germaniaspherene). High-level ab initio calculation indicates that I(h)-Ge(12a)(2-) and TTP-containing Ge(12b)(2-) are almost isoenergetic and, thus, both may be considered as candidates for the lowest-energy structure at 0 K. Ge(12a)(2-) has a much larger energy gap (2.04 eV) between highest occupied molecular orbital and lowest unoccupied molecular orbital than Ge(12b)(2-) (1.29 eV), while Ge(12b)(2-) has a lower free energy than I(h)-Ge(12a)(2-) at elevated temperature (>980 K). The TTP-containing Si(12a)(2-) and Ge(12b)(2-) exhibit large negative nuclear independent chemical shift (NICS) value (approximately -44) at the center of TTP, indicating aromatic character. In contrast, germaniaspherene I(h)-Ge(12a)(2-) and stannaspherene I(h)-Sn(12a)(2-) exhibit modest positive NICS values, approximately 12 and 3, respectively, at the center of the empty cage, indicating weakly antiaromatic character.     

Theoretical Investigation of Binary and Ternary Metal Clusters derived from [Y10M]n— Zintl Ions

The pseudo element concept is applied to isolated Zintl anions [Y₁₀M]^n—, where M is Ni or Zn, and Y is a third group element, which is replaced by a fourth group element X. The aim of the theoretical study is to identify stable binary metal atom clusters and to test the robustness of the Zintl concept. DFT and RIMP2 methods are employed for this purpose. All low‐energy isomers of [X₁₀M]^m+ show structures known from corresponding Zintl anions. A partial replacement of only six third group elements, however, may lead to different low‐energy topologies. The cohesive energy of the clusters X₁₀Ni (X = Si, Ge, Sn, Pb) is significantly higher than that of the bare X₁₀ species, binding energy of the Ni atom amounts to about 5 eV.