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.     

Density functional theory study of eight-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 Ge8z(z=-6, -4, -2, 0, +2, +4) using nine initial geometries. For Ge8(2-) the D2d bisdisphenoid structure predicted by the Wade-Mingos rules is not computed to be the global minimum but instead lies 3.9 kcal mol-1 above the Td tetracapped tetrahedron global minimum predicted to exhibit spherical aromaticity. The hyperelectronic clusters Ge(8)4- and Ge8(6-) have nido B8H12 and square antiprism structures, respectively, as global minima in accord with the Wade-Mingos rules and experimental data on E(8)2+(E=Sb, Bi) cations. Hypoelectronic eight-vertex clusters isoelectronic and isolobal with Ge8, Ge8(2+) and Ge(8)4+ are not known experimentally. Their computed structures include smaller polyhedra having one or more capped triangular faces as well as more open non-polyhedral structures.     

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+).     

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.     

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.     

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.     

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-).     

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.     

Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21-Ge29

We performed a constrained search for the geometries of low-lying neutral germanium clusters Ge(N) in the size range of 21 < or = N < or = 29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N approximately 65.     

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.     

Limited occurrence of isocloso deltahedra with 9 to 12 vertices in low-energy hypoelectronic diferradicarbaborane structures

Theoretical studies show that the 10-vertex system Cp(2)Fe(2)C(2)B(6)H(8) is the only one of the 2n skeletal electron Cp(2)Fe(2)C(2)B(n-4)H(n-2) systems (n = 9, 10, 11, 12) for which a true isocloso deltahedron having a single degree 6 vertex is highly favored over alternative structures. This is demonstrated by the occurrence of only the 10-vertex isocloso deltahedron as the central Fe(2)C(2)B(6) polyhedron in all nine of the Cp(2)Fe(2)C(2)B(6)H(8) structures within 8 kcal/mol of the global minimum. Low energy isocloso structures are also observed for the 11-vertex Cp(2)Fe(2)C(2)B(7)H(9). However, interspersed with these isocloso structures are Cp(2)Fe(2)C(2)B(7)H(9) structures based on deltahedra having two or more degree 6 vertices. For the 12-vertex Cp(2)Fe(2)C(2)B(8)H(10), the six lowest energy structures all have central Fe(2)C(2)B(8) deltahedra with two degree 6 vertices, one for each iron atom. The Cp(2)Fe(2)C(2)B(8)H(10) structures having a central Fe(2)C(2)B(8) icosahedron with all degree 5 vertices lie at significantly higher energies, starting at 17.8 kcal/mol above the global minimum. The 9-vertex Cp(2)Fe(2)C(2)B(5)H(7) system appears to be too small for isocloso structures to be favorable, although three such structures are found at energies between 5.5 and 8.0 kcal/mol above the global minimum. Five Cp(2)Fe(2)C(2)B(5)H(7) structures based on the tricapped trigonal prism lie in an energy below the lowest energy isocloso structure. The lowest energy Cp(2)Fe(2)C(2)B(5)H(7) structure and two higher energy structures within 8.0 kcal/mol of the global minimum have central Fe(2)C(2)B(5) deltahedra with a degree 6 vertex for each iron atom.     

Deltahedral germanium clusters: insertion of transition-metal atoms and addition of organometallic fragments

Reactions of nine-atom deltahedral clusters of germanium with Ni(COD)2 and/or Ni(PPh3)2(CO)2 in ethylenediamine yielded the Ni-centered heteroatomic 10-atom clusters [Ni@(Ge9Ni-CO)]2- and [Ni@(Ge9Ni-en)]3-, as well as the empty 10-atom heteroatomic cluster [Ge9Ni-CO]3-. A ligand exchange reaction between [Ni@(Ge9Ni-CO)]2- and potassium phenylacetylide produced the organically functionalized species [Ni@(Ge9Ni-CCPh)]3-. The empty cluster [Ge9Ni-CO]3- is a bicapped square antiprism where one of the capping vertexes is the nickel atom. The other three clusters are tricapped trigonal prisms where an additional 10th vertex of monoligated nickel caps a triangular base of the trigonal prism. As a result of this, that base opens up, and the distances within it become nonbonding. This ensures that all atoms of the cluster are equidistant from the central nickel atom, i.e., the cluster is very close to spherical. All species were structurally characterized in crystalline compounds with [K-(2,2,2-crypt)]+ countercations. They were also characterized in solution by mass spectrometry, IR, and 13C NMR.     

原子团簇Ge11同分异体的密度泛函研究

用分子图形软件设计出多种Ge_11原子团簇模型,使用B3LYP密度泛函方法进行几何构型优化和振动频率计算,比较了14种同分异构体的总能量,得到了新的基态构型。锗原子团簇的大部分原子以三、四、五和六配位成键。在Ge11原子团簇中,双角反四棱柱衍生出来的构型能量较低,它是设计大分子锗原子团簇初始模型的重要结构单元。由三棱柱演变的构型能量居中。带心结构和共边构型带有高配位原子,其总能量较高,是不稳定的结构。     

A theoretical study on growth patterns of Ni-doped germanium clusters

Ni-doped germanium clusters have been systematically investigated by using the density functional approach. The growth-pattern behaviors, stabilities, charge transfer, and polarities of these clusters are discussed in detail. Obviously different growth patterns appear between small-sized Ni-doped germanium clusters and middle- or larger-sized Ni-doped germanium clusters. The Ni-convex or substituted Ge(n) frames for small-sized clusters as well as Ni-concaved or encapsulated Ge(n) frames for middle- or large-sized clusters are dominant growth patterns. The calculated fragmentation energies manifest that the magic numbers of stabilities are 5, 8, 10, and 13 for Ni-doped germanium clusters; the obtained relative stabilities exhibit that the Ni-encapsulated Ge(10) cluster is the most stable species of all different-sized clusters, which is in good agreement with available experimental observations of CoGe(10)(-). Natural population analysis shows that different charge-transfer phenomena depend on the sizes of the Ni-doped Ge(n) clusters. Additionally, the properties of frontier orbitals and the polarities of Ni-doped Ge(n) clusters are also discussed.     

石墨炉原子化器中原子化过程的研究(Ⅲ)——石墨炉中锗的原子化机理

有关锗的石墨炉原子吸收光谱分析,文献报道较少,对锗的原子化机理,亦有不同的看法^[1~3].本文基于右墨炉中锗原孚化行为的观察,对锗原子形成的过程进行了讨论,认为原子化过程中,并存着二种还原反应:GeO₂(s)+C→GeO(g)+CO(g),GeO₂(s)+CO→GeO(g)+CO₂,而锗原子的形成是GeO(g)热分解的结果。     

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.     

Interaction of diatomic germanium with lithium atoms: electronic structure and stability

Quantum chemical calculations were applied to investigate the electronic structure of mono-, di-, and trilithiated digermanium (Ge2Lin) and their cations (n=0-3). Computations using a multiconfigurational quasidegenerate perturbation approach based on complete active space self-consistent-field wave functions, and density functional theory reveal that Ge2Li has a 2B1 ground state with a doublet-quartet energy gap of 33 kcal/mol. Ge2Li2 has a singlet ground state with a 3Au-1A1 gap of 29 kcal/mol, and Ge2Li3 a doublet ground state with a 4B2-2A2 separation of 22 kcal/mol. The cation Ge2Li+ has a 3B1 ground state, being 13 kcal/mol below the open-shell 1B1 state. The computed electron affinities for diatomic germanium are EA(1)=1.9 eV, EA(2)=-2.5 eV, and EA(3)=-6.0 eV, for Ge2-, Ge2 (2-), and Ge2 (3-), respectively, indicating that only the monoanion is stable with respect to electron detachment, in such a way that Ge2Li is composed by Ge2-Li+ ions. An "atoms-in-molecules" analysis shows the absence of a ring critical point in Ge(2)Li. An electron localization function analysis on Ge2Li supports the view that the Ge-Li bond is predominantly ionic; however, a small covalent character could be anticipated from the analysis of the Laplacian at the Ge-Li bond critical point. The ionic picture of the Ge-Li bond is further supported by a natural-bond-order analysis and the Laplacian of the electron density. The calculated Li affinity value for Ge2 is 2.08 eV, while the Li+ cation affinity value for Ge2- is 5.7 eV. The larger Li+ cation affinity value of Ge2- suggests a Ge2-Li+ interaction and thus supports the ionic nature of Ge-Li bond. In GeLi4 and Ge2Li, the presence of trisynaptic basins indicates a three-center bond connecting the germanium and lithium atoms.     

Interaction of triatomic germanium with lithium atoms: electronic structure and stability of Ge3Lin clusters

Quantum chemical calculations were applied to investigate the electronic structure of mono-, di-, and tri- lithiated triatomic germanium (Ge3Lin) and their cations (n = 0-3). Computations using a multiconfigurational quasi-degenerate perturbation approach (MCQDPT2) based on complete active space CASSCF wavefunctions, MRMP2 and density functional theory reveal that Ge3Li has a 2A' ground state with a doublet-quartet gap of 24 kcal/mol. Ge3Li2 has a singlet ground state with a singlet-triplet (3A' '-1A1) gap of 30 kcal/mol, and Ge3Li3 a doublet ground state with a doublet-quartet (4A' '-2A') separation of 16 kcal/mol. The cation Ge3Li+ has a 1A' ground state, being 18 kcal/mol below the 3A' state. The computed electron affinities for triatomic germanium are EA(1) = 2.2 eV (experimental value is 2.23 eV), EA(2) = -2.5 eV, and EA(3) = -5.9 eV, for Ge3-, Ge32-, and Ge33-, respectively, indicating that only the monoanion is stable with respect to electron detachment, in such a way that Ge3Li is composed of Ge3-Li+ ions. An atoms in molecules (AIM) analysis shows the absence of a Ge-Ge-Li ring critical point in Ge3Li. An electron localization function (ELF) map of Ge3Li supports the view that the Ge-Li bond is predominantly ionic; however, a small covalent character could be anticipated from the Laplacian at the Ge-Li bond critical point. The ionic picture of the Ge-Li bond is further supported by the natural bond orbital (NBO) results. The calculated Li affinity value for Ge3 is 2.17 eV, and the Li+ cation affinity value for Ge3- amounts to 5.43 eV. The larger Li+ cation affinity of Ge3- favors an electron transfer, resulting in a Ge3-Li+ interaction.