Density functional theory study of 10-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge10z germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 12 different initial configurations. The D4d 4,4-bicapped square antiprism found experimentally in B10H102- and other 10-vertex clusters with 22 skeletal electrons is calculated for the isoelectronic Ge102- to be the global minimum by more than 15 kcal/mol. The global minima found for electron-rich clusters Ge104- and Ge106- are not those known experimentally. However, experimentally known structures for nido-B10H14 and the pentagonal antiprism of arachno-Pd@Bi104+ are found at higher but potentially accessible energies for Ge104- and Ge106-. The global minimum for Ge10 is the C3v 3,4,4,4-tetracapped trigonal prism predicted by the Wade-Mingos rules and found experimentally in isoelectronic Ni@Ga1010-. However, only slightly above this global minimum for Ge10 (+3.3 kcal/mol) is the likewise C3v isocloso 10-vertex deltahedron found in metallaboranes such as (eta6-arene)RuB9H9 derivatives. Structures found for more electron-poor clusters Ge102+ and Ge104+ include various capped octahedra and pentagonal bipyramids. This study predicts a number of 10-vertex cluster structures that have not yet been realized experimentally but would be interesting targets for future synthetic 10-vertex cluster chemistry using vertex units isolobal with the germanium vertices used in this work.     

Density functional theory study of twelve-atom germanium clusters: conflict between the Wade-Mingos rules and optimum vertex degrees

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge(12)(z) bare germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 11 initial configurations. The Wade-Mingos rules are seen to have limited value in rationalizing the results since they frequently require vertex degrees higher than the optimum vertex degree of 4 for germanium. Thus the expected I(h) regular icosahedron is no longer the global minimum for Ge(12)(2-) although it remains a low energy structure for Ge(12)(2-) lying only 5.6 kcal mol(-1) above a bicapped arachno structure conforming to the Wade-Mingos rules. The three lowest energy structures for Ge(12)(4-) within 11 kcal mol(-1) are a prolate (elongated) polyhedron with six quadrilateral faces and eight triangular faces, the dual of the bisdisphenoid with four trapezoidal and four pentagonal faces, and a polyhedron with two quadrilateral and 16 triangular faces related but not identical to the polyhedron found in the known tetracarbon carboranes R(4)C(4)B(8)H(8). The lowest energy structures for the neutral Ge(12) are seen to be distorted versions of the icosahedron and the bicapped 10-vertex arachno lowest energy structures for Ge(12)(2-). The low energy structures for the even more hypoelectronic Ge(12)(2+) and Ge(12)(4+) are even more unusual including a hexacapped octahedron, a tetracapped square antiprism, and a double cube for Ge(12)(2+) and a C(2v) structure with a central unique degree 6 vertex for Ge(12)(4+).     

Density functional study of 8- and 11-vertex polyhedral borane structures: comparison with bare germanium clusters

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the polyhedral boranes B(n)H(n)(z) (n = 8 and 11, z = -2, -4, and -6) for comparison with isoelectronic germanium clusters Ge(n)(z). The energy differences between the global minima and other higher energy borane structures are much larger relative to the case of the corresponding bare germanium clusters. Furthermore, for both B(8)H(8)(2-) and B(11)H(11)(2-), the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade-Mingos rules, namely the D(2)(d) bisdisphenoid and the C(2)(v) edge-coalesced icosahedron, respectively. Only in the case of B(8)H(8)(2-) is there a second structure close (+2.6 kcal/mol) to the D(2)(d) bisdisphenoid global minimum, namely the C(2)(v) bicapped trigonal prism corresponding to the "square" intermediate in a single diamond-square-diamond process that can lead to the experimentally observed room temperature fluxionality of B(8)H(8)(2-). Stable borane structures with 3-fold symmetry (e.g., D(3)(h), C(3)(v), etc.) are not found for boranes with 8- and 11-vertices, in contrast to the corresponding germanium clusters where stable structures derived from the D(3)(d) bicapped octahedron and D(3)(h) pentacapped trigonal prism are found for the 8- and 11-vertex systems, respectively. The lowest energy structures found for the electron-rich boranes B(8)H(8)(4-) and B(11)H(11)(4-) are nido polyhedra derived from a closo deltahedron by removal of a relatively high degree vertex, as predicted by the Wade-Mingos rules. They relate to isoelectronic species found experimentally, e.g., B(8)H(12) and R(4)C(4)B(4)H(4) for B(8)H(8)(4-) and C(2)B(9)H(11)(2-) for B(11)H(11)(4-). Three structures were found for B(11)H(11)(6-) with arachno type geometry having two open faces in accord with the Wade-Mingos rules.     

Density functional theory study of 11-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(11)(z) (z = -6, -4, -2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge(11)(2-) set is an elongated pentacapped trigonal prism distorted from D(3)(h) to C(2v) symmetry. However, the much more spherical edge-coalesced icosahedron, also of C(2v) symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B(11)H(11)(2-) and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D(3)(h) pentacapped trigonal prisms are the global minima for the electron-rich structures Ge(11)(4-) and Ge(11)(6-). For Ge(11)(4-) the C(5v) 5-capped pentagonal antiprism analogous to the dicarbollide ligand C(2)B(9)H(11)(2-) is of significantly higher energy (approximately 28 kcal/mol) than the D(3h) global minimum. The C(2v) edge-coalesced icosahedron is also the global minimum for the electron-poor Ge(11) similar to its occurrence in experimentally known 11-vertex "isocloso" metallaboranes of the type (eta(6)-arene)RuB(10)H(10). The lowest energy polyhedral structures computed for the more hypoelectronic Ge(11)(4+) and Ge(11)(6+) clusters are very similar to those found experimentally for the isoelectronic ions E(11)(7-) (E = Ga, In, Tl) and Tl(9)Au(2)(9-) in intermetallics in the case of Ge(11)(4+) and Ge(11)(6+), respectively. These DFT studies predict an interesting D(5h) centered pentagonal prismatic structure for Ge(11)(2+) and isoelectronic metal clusters.     

Density functional theory study of nine-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(9)(z) clusters (z = -6, -4, -3, -2, 0, +2, and +4) starting from three different initial configurations. Double-zeta quality LANL2DZ basis functions extended by adding one set of polarization (d) and one set of diffuse (p) functions were used. The global minimum for Ge(9)(2)(-) is the tricapped trigonal prism expected by Wade's rules for a 2n + 2 skeletal electron structure. An elongated tricapped trigonal prism is the global minimum for Ge(9)(4)(-) similar to the experimentally found structure for the isoelectronic Bi(9)(5+). However, the capped square antiprism predicted by Wade's rules for a 2n + 4 skeletal electron structure is only 0.21 kcal/mol above this global minimum indicating that these two nine-vertex polyhedra have very similar energies in this system. Tricapped trigonal prismatic structures are found for both singlet and triplet Ge(9)(6)(-), with the latter being lower in energy by 3.66 kcal/mol and far less distorted. The global minimum for the hypoelectronic Ge(9) is a bicapped pentagonal bipyramid. However, a second structure for Ge(9) only 4.54 kcal/mol above this global minimum is the C(2)(v)() flattened tricapped trigonal prism structure found experimentally for the isoelectronic Tl(9)(9)(-). For the even more hypoelectronic Ge(9)(2+), the lowest energy structure consists of an octahedron fused to two trigonal bipyramids. For Ge(9)(4+), the global minimum is an oblate (squashed) pentagonal bipyramid with two pendant Ge vertices.     

Endohedral beryllium atoms in germanium clusters with eight and fewer vertices: how small can a cluster be and still encapsulate a central atom?

Structures of the beryllium-centered germanium clusters Be@Ge(n)(z) (n = 8, 7, 6; z = -4, -2, 0, +2) have been investigated by density functional theory to provide some insight regarding the smallest metal cluster that can encapsulate an interstitial atom. The lowest energy structures of the eight-vertex Be@Ge(8)(z) clusters (z = -4, -2, 0, +2) all have the Be atom at the center of a closed polyhedron, namely, a D(4d) square antiprism for Be@Ge(8)(4-), a D(2d) bisdisphenoid for Be@Ge(8)(2-), an ideal O(h) cube for Be@Ge(8), and a C(2v) distorted cube for Be@Ge(8)(2+). The Be-centered cubic structures predicted for Be@Ge(8) and Be@Ge(8)(2+) differ from the previously predicted lowest energy structures for the isoelectronic Ge(8)(2-) and Ge(8). This appears to be related to the larger internal volume of the cube relative to other closed eight-vertex polyhedra. The lowest energy structures for the smaller seven- and six-vertex clusters Be@Ge(n)(z) (n = 7, 6; z = -4, -2, 0, +2) no longer have the Be atom at the center of a closed Ge(n) polyhedron. Instead, either the Ge(n) polyhedron has opened up to provide a larger volume for the Be atom or the Be atom has migrated to the surface of the polyhedron. However, higher energy structures are found in which the Be atom is located at the center of a Ge(n) (n = 7, 6) polyhedron. Examples of such structures are a centered C(2v) capped trigonal prismatic structure for Be@Ge(7)(2-), a centered D(5h) pentagonal bipyramidal structure for Be@Ge(7), a centered D(3h) trigonal prismatic structure for Be@Ge(6)(4-), and a centered octahedral structure for Be@Ge(6). Cluster buildup reactions of the type Be@Ge(n)(z) + Ge(2) → Be@Ge(n+2)(z) (n = 6, 8; z = -4, -2, 0, +2) are all predicted to be highly exothermic. This suggests that interstitial clusters having an endohedral atom inside a bare post transition element polyhedron with eight or fewer vertices are less than the optimum size. This is consistent with the experimental observation of several types of 10-vertex polyhedral bare post transition element clusters with interstitial atoms but the failure to observe such clusters with external polyhedra having eight or fewer vertices.     

Polyhedral structures with three-, four-, and five fold symmetry in metal-centered ten-vertex germanium clusters

Studies using density functional theory (DFT) at the hybrid B3LYP level indicate that the relative energies of structures with three-fold, four-fold, and five-fold symmetry for centered 10-vertex bare germanium clusters of the general type M@Ge(10) (z) depend on the central metal atom M and the skeletal electron count. For M@Ge(10) clusters with 20 skeletal electrons the DFT results agree with experimental data on the isoelectronic centered 10-vertex bare metal clusters. Thus the lowest energy structure for Ni@Ge(10), isoelectronic with the known Ni@In(10) (10-), is a C(3v) polyhedron derived from the tetracapped trigonal prism. However, Zn@Ge(10) (2+) is isoelectronic with the known cluster Zn@In(10) (8-), which has the lowest energy structure, a D(4d) bicapped square antiprism. For the clusters Ni@Ge(10) (2-), Cu@Ge(10) (-), and Zn@Ge(10) that have 22 skeletal electrons the lowest energy structures are the D(4d) bicapped square antiprism predicted by the Wade-Mingos rules. For the clusters Ni@Ge(10) (4-), Cu@Ge(10) (3-), and Zn@Ge(10) (2-) that have 24 skeletal electrons the lowest energy structures are C(3v) polyhedra with 10 triangular faces and 3 quadrilateral faces derived from a tetracapped trigonal prism by extreme lengthening of the edges of the capped triangular face of the underlying trigonal prism. For the clusters Cu@Ge(10) (5-) and Zn@Ge(10) (4-) that have 26 skeletal electrons the lowest energy structures are the D(5d) pentagonal antiprisms predicted by the Wade-Mingos rules and the C(3v) tetracapped trigonal prism as a somewhat higher energy structure. However, for the isoelectronic Ni@Ge(10) (6-) the relative energies of these two structure types are reversed so that the C(3v) tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D(5d) pentagonal prism and D(4d) bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.     

Endohedral beryllium atoms in ten-vertex germanium clusters: effect of a small interstitial atom on the cluster geometry

Ten-vertex clusters are unusually versatile because polyhedra with 3-, 4-, and 5-fold symmetry are possible and are found in experimentally known structures. Such clusters therefore provide useful probes for subtle effects on cluster structure such as changing the electron count or introducing an interstitial atom. In this connection, DFT shows that one of the smallest possible interstitial atoms, namely beryllium, has relatively little effect on the structures of Be@Ge(10)(z) (z = +2, 0, -2, -4) clusters. Thus the same C(3v) and D(4d) polyhedra are found as the lowest energy structures for the isoelectronic pairs Be@Ge(10)(2+)/Ge(10) and Be@Ge(10)/Ge(10)(2-). Even for the more complicated potential energy surfaces of the Be@Ge(10)(2-)/Ge(10)(4-) and Be@Ge(10)(4-)/Ge(10)(6-) systems, the lowest energy structures are remarkably similar. Thus the same C(2v) structures are the global minima for both Be@Ge(10)(2-) and Ge(10)(4-). Similarly, the same slipped pentagonal prism structures are the global minima for both Be@Ge(10)(4-) and Ge(10)(6-).     

Effects of halogen substitution on the properties of eight- and nine-vertex closo-boranes

The symmetry constrained geometries of the eight- and nine-vertex polyhedral boranes and haloboranes BnXnz (n = 8 and 9; X = H, F and Cl; z = -2, -1 and 0) were optimized at the B3LYP/6-311+G(d) level and their nucleus-independent chemical shifts (NICS) were calculated using the GIAO method with Kohn-Sham orbitals. Substitution of halogens on borane cages was found to significantly impact not only the geometric but also magnetic properties. Multiple fluorine substituents cause a deviation from the Wade-Mingos skeletal electron rules in B8F8(2-), resulting in a distortion from the expected D2d bisdisphenoid to a C2v nido type bicapped trigonal prism. However, all of the nine-vertex cages B9X9z retain the D3h tricapped trigonal prismatic structure of B9H9(2-). The presence of halogen substituents was found to enhance the three-dimensional diatropic ring currents within the dianionic borane cages B8X8(2-) and B9X9(2-). For the neutral structures the NICS values indicate BnFn to be aromatic, BnCln to be essentially non-aromatic, and BnHn to be antiaromatic (n = 8, 9).     

Cobalt-centered ten-vertex germanium clusters: the pentagonal prism as an alternative to polyhedra predicted by the Wade-Mingos rules

One of the most exciting recent (2009) discoveries in metal cluster chemistry is the pentagonal prismatic Co@Ge(10)(3-) ion, found in [K(2,2,2-crypt)](4)[Co@Ge(10)][Co(1,5-C(8)H(12))(2)]·toluene and characterized structurally by X-ray diffraction. The complete absence of triangular faces in the pentagonal prismatic structure of Co@Ge(10)(3-) contradicts expectations from the well-established Wade-Mingos rules, which predict polyhedral structures having mainly or entirely triangular faces. A theoretical study on Co@Ge(10)(z) systems (z = -5 to +1) predicts a singlet D(5h) pentagonal prismatic global minimum for the trianion Co@Ge(10)(3-) in accord with this experimental result. Redox reactions on this pentagonal prismatic Co@Ge(10)(3-) trianion generate low-energy pentagonal prismatic structures for Co@Ge(10)(z) where z = 0, -1, -2, -4, and -5 having quartet, triplet, doublet, doublet, and triplet spin states, respectively. Similar theoretical methods predict a singlet C(3v) polyhedral structure for the monoanion Co@Ge(10)(-), similar to previous theoretical predictions on the isoelectronic neutral Ni@Ge(10) and the structure realized experimentally in the isoelectronic Ni@In(10)(10-) found in the K(10)In(10)Ni intermetallic. Redox reactions on this C(3v) polyhedral Co@Ge(10)(-) monoanion generate low energy C(3v) polyhedral structures for Co@Ge(10)(z) where z = 0, -2, -3, and -4 having doublet, doublet, triplet, and quartet spin states, respectively.     

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.     

Molecules for materials: germanium hydride neutrals and anions. Molecular structures,electron affinities,and thermochemistry of GeHn/GeHn- (n = 0-4) and Ge2Hn/Ge2Hn(-) (n = 0-6)

The GeH(n) (n = 0-4) and Ge(2)H(n) (n = 0-6) systems have been studied systematically by five different density functional methods. The basis sets employed are of double-zeta plus polarization quality with additional s- and p-type diffuse functions, labeled DZP++. For each compound plausible energetically low-lying structures were optimized. The methods used have been calibrated against a comprehensive tabulation of experimental electron affinities (Chemical Reviews 102, 231, 2002). The geometries predicted in this work include yet unknown anionic species, such as Ge(2)H(-), Ge(2)H(2)(-), Ge(2)H(3)(-), Ge(2)H(4)(-), and Ge(2)H(5)(-). In general, the BHLYP method predicts the geometries closest to the few available experimental structures. A number of structures rather different from the analogous well-characterized hydrocarbon radicals and anions are predicted. For example, a vinylidene-like GeGeH(2) (-) structure is the global minimum of Ge(2)H(2) (-). For neutral Ge(2)H(4), a methylcarbene-like HG?-GeH(3) is neally degenerate with the trans-bent H(2)Ge=GeH(2) structure. For the Ge(2)H(4) (-) anion, the methylcarbene-like system is the global minimum. The three different neutral-anion energy differences reported in this research are: the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). For this family of molecules the B3LYP method appears to predict the most reliable electron affinities. The adiabatic electron affinities after the ZPVE correction are predicted to be 2.02 (Ge(2)), 2.05 (Ge(2)H), 1.25 (Ge(2)H(2)), 2.09 (Ge(2)H(3)), 1.71 (Ge(2)H(4)), 2.17 (Ge(2)H(5)), and -0.02 (Ge(2)H(6)) eV. We also reported the dissociation energies for the GeH(n) (n = 1-4) and Ge(2)H(n) (n = 1-6) systems, as well as those for their anionic counterparts. Our theoretical predictions provide strong motivation for the further experimental study of these important germanium hydrides.     

Chemical bonding topology of ternary transition metal-centered bismuth cluster halides: from molecules to metals

The bismuth polyhedra in ternary transition metal-centered bismuth cluster halides may form discrete molecules or ions, infinite chains, and/or infinite layers. The chemical bonding in many of these diverse structures is related to that in deltahedral boranes exhibiting three-dimensional aromaticity by replacing the multicenter core bond in the boranes with two-center two-electron (2c-2e) bonds from the central transition metal to the nearest neighbor bismuth vertices. Examples of discrete molecules or ions include octahedral MBi(6)(micro-X)(12)(z)()(-) (X = Br, I; M = Rh, Ir, z = 3; M = Ru, z = 4) with exclusively 2c-2e bonds and pentagonal bipyramidal RhBi(7)Br(8) with a 5c-4e bond in the equatorial pentagonal plane indicative of M?bius aromaticity. The compound Ru(3)Bi(24)Br(20) contains a more complicated discrete bismuth cluster ion Ru(2)Bi(17)(micro-Br)(4)(5+), which can be dissected into a RuBi(5) closo octahedron and a RuBi(8) nido capped square antiprism bridged by a Ru(2)Bi(4)(micro-Br)(4) structural unit. In RuBi(4)X(2) (X = Br, I), the same Ru(2)Bi(4)(micro-Br)(4) structural unit bridges Bi(4) squares similar to those found in the known Zintl ion Bi(4)(2)(-) to give infinite chains of Ru(2)Bi(4) octahedra. The electron counts of the RuBi(5), RuBi(8), and Ru(2)Bi(4) polyhedra in these structures follow the Wade-Mingos rules. A different infinite chain structure is constructed from fused RhBi(7/2)Bi bicapped trigonal prisms in Rh(2)Bi(9)Br(3). This Rh(2)Bi(9)Br(3) structure can alternatively be derived from alternating Rh(2/2)Bi(4) octahedra and Rh(2/)(2)Bi(5) pentagonal bipyramids with electron counts obeying the Wade-Mingos rules. Related chemical bonding principles appear to apply to more complicated layer structures such as Pt(3)Bi(13)I(7) containing Kagomé nets of PtBi(8/2) cubes and Ni(4)Bi(12)X(3) containing linked chains of NiBi(6/3)Bi capped trigonal prisms.     

The importance of dihydrogen complexes HnGe(H2)+ (n=0,1) to the chemistry of cationic germanium hydrides: advanced theoretical and mass spectrometric analysis

Investigations of [Ge,Hn]-/0/- (n = 2,3) have been performed using a four-sector mass spectrometer. The results reveal that the complexes HnGe(H2)+ (n = 0,1) play an important role in the unimolecular dissociation of the metastable cations. Theoretical calculations support the experimental observations in most instances, and the established view that the global minimum of [Ge,H2]+ is an inserted structure may need reexamination; CCSD(T,full)/cc-pVTZ//CCSD(T)/6-311 ++ G(d,p) and B3LYP/cc-pVTZ studies of three low-lying cation states (2A1 HGeH+, 2B2 Ge(H2)+ and 2B1 Ge(H2)+) indicate a very small energy difference (ca. 4 kcal mol(-1)) between 2A1 HGeH+ and 2B2 Ge(H2)+; B3LYP favours the ion-molecule complex, whereas coupled-cluster calculations favour the inserted structure for the global minimum. Single-point multireference (MR) averaged coupled-pair functional and MR-configuration interaction calculations give conflicting results regarding the global minimum. We also present theoretical evidence indicating that the orbital-crossing point implicated in the spin-allowed metastable dissociation HGeH+* --> Ge(H2)+* --> Ge+ + H2 lies above the H-loss asymptote. Thus, a quantum-mechanical tunneling mechanism is invoked to explain the preponderance of the H2-loss signal for the metastable ion.     

The role of "external" lone pairs in the chemical bonding of bare post-transition element clusters: the Wade-Mingos rules versus the jellium model

The jellium sphere model of a volume of electrons, counterbalanced by a positive charge throughout the sphere, leads to an energy level sequence corresponding to special stabilities of bare post-transition element clusters with 20 valence electrons such as the known P4 and clusters with 40 valence electrons such as the known Ge9(4-), Ni@In10(10-), and In11(7-). In this model the otherwise "external" lone pairs on the vertex atoms participate at least indirectly in the skeletal bonding. Furthermore, this model predicts the most favorable polyhedra and electron counts in some cases to be quite different than those predicted by the Wade-Mingos rules of polyhedral borane chemistry.     

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.     

Theoretical study of the structural and electronic properties of SimGen and SimGen- (s = m + n <or= 7) clusters

Ground-state structures, vibrational frequencies, HOMO-LUMO energy gap, electron affinities, and cluster mixing energy of binary semiconductor clusters SimGen in the range s = m + n 相似文献   

Closo-alanes (Al4H4, AlnHn+2, 4 <or= n <or= 8): a new chapter in aluminum hydride chemistry

Anion photoelectron spectroscopy and density functional theory were employed to study aluminum hydride clusters, AlnHm- (4 相似文献   

VFe3S4 single and double cubane clusters: synthesis, structures, and dependence of redox potentials and electron distribution on ligation and heterometal

Both vanadium and molybdenum cofactor clusters are found in nitrogenase. In biomimetic research, many fewer heterometal MFe3S4 cubane-type clusters have been synthesized with M = V than with M = Mo because of the well-established structural relationship of the latter to the molybdenum coordination unit in the enzyme. In this work, a series of single cubane and edge-bridged double cubane clusters containing the cores [VFe3(mu3-S)4]2+ and [V2Fe6(mu3-S)6(mu4-S)2]2+ have been prepared by ligand substitution of the phosphine clusters [(Tp)VFe3S4(PEt3)3]1+ and [(Tp)2V2Fe6S8(PEt3)4]. The single cubanes [(Tp)VFe3S4L3]2- and double cubanes [(Tp)2V2Fe6S8L4]4- (L= F-, N3-, CN-, PhS-) are shown by X-ray structures to have trigonal symmetry and centrosymmetry, respectively. Single cubanes form the three-member electron transfer series [(Tp)VFe3S4L3]3-,2-,1-. The ligand dependence of redox potentials and electron distribution in cluster cores as sensed by 57Fe isomer shifts (delta) have been determined. Comparison of these results with those previously determined for the analogous molybdenum clusters (Pesavento, Berlinguette, and Holm Inorg. Chem. 2007, 46, 510) allows detection of the influence of heterometal M on the properties. At constant M and variable L, redox potentials are lowest for pi-donor ligands and largest for cyanide and relate approximately with decreasing ferrous character in clusters with constant charge z = 2-. At constant L and z and variable M, EV > E(Mo) and delta(av)V < delta(av)Mo, demonstrating that M = Mo clusters are more readily oxidized and suggesting a qualitative relation between lower potentials (greater ease of oxidation) and ferrous character.