Mingos Rules Research Articles

New low symmetry low energy structures of 11-atom bare germanium clusters: A density functional theory study

Abstract The previously reported density functional theory (DFT) calculations at the hybrid B3LYP level on 11-vertex germanium clusters Ge 11 z ( z = - 2 , 0 , + 2 , + 4 ) have been extended to less symmetrical structures starting from lower symmetry (Cs or C2v) structures. In addition, normal modes of imaginary vibrational frequencies less than 100 cm−1 were followed that had been ignored in previous work. No new global minima were found for Ge 11 2 - and Ge 11 4 + . However, new structures with little or no symmetry obeying the Wade–Mingos rules were found for Ge11 and Ge 11 2 + having lower energies than any of the previously reported structures. Thus the new global minima for Ge11 and Ge 11 2 + were found to be a Cs capped [10]-deltahedron (3,4,4-tricapped square antiprism) and a C1 bicapped [9]-deltahedron, respectively.

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 BnHnz (n = 8 and 11, z = −2, −4, and −6) for comparison with isoelectronic germanium clusters Genz. 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 B8H82- and B11H112-, the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade−Mingos rules, namely the D2d bisdisphenoid and the C2v edge-coalesced icosahedron, respectively. Only in the case of B8H82- is there a second structure close (+2.6 kcal/mol) to the D2d bisdisphenoid global minimum, namely the C2v 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 B8H82-. Stable borane structures with 3-fold symmetr...

Vibrational frequencies of the homoleptic cobalt carbonyls: Co 4(CO) 12 and Co 6(CO) 16

The homoleptic cobalt carbonyls Co 4(CO) 12 and Co 6(CO) 16 are characterized by their equilibrium geometries, thermochemistry, and vibrational frequencies using density functional theory (DFT) methods with the B3LYP, BLYP, and BP86 functionals. The B3LYP predicted Co Co distances are 2.51 and 2.47 Å for the C 3v and T d structures, respectively, of Co 4(CO) 12. The global minimum for Co 4(CO) 12 has C 3v symmetry with three bridging and nine terminal carbonyls. The 2.51 and 2.52 Å Co Co distances suggest the single bond required for an 18-electron configuration for the metal atoms. This structure is close to an experimentally realized structure. A more symmetrical Co 4(CO) 12 structure with T d symmetry, analogous to that observed in the valence isoelectronic Ir 4(CO) 12 molecule, lies ∼28 kcal/mol higher in energy and exhibits a small imaginary vibrational frequency (∼ 40 i). It has a slightly shorter Co Co distance of 2.47 Å. Both Co 4(CO) 12 structures satisfy the 18-electron rule. The Co 6(CO) 16 structure has T d symmetry and satisfies the Wade–Mingos rules for an octahedral cluster. The ν(CO) carbonyl frequencies for both Co 4(CO) 12 and Co 6(CO) 16 computed with the BP86 functional are closer to the experimental values than those computed with the B3LYP and BLYP functionals. The structure of Co 6(CO) 16 is not known experimentally, but the BP86 functional predicts 2.56 Å (Co Co), 1.77 and 2.02 Å (Co C), and 1.66 and 1.20 Å (C O) for the bond distances.

Novel Main Group-Transition Metal Cluster Compounds Incorporating Antimony, Iron and Cobalt

The reaction of [{Cpx(CO)2Fe}SbCl2] [1a: Cpx = η5-C5H3tBu2-1,3 (Cp"); 1b: Cpx = η5-C5Me5 (Cp*)] with Na2[Fe(CO)4] or K[Co(CO)4] affords the novel antimony-transition metal cluster compounds [{μ3-SbFe(CO)2Cp"}3{Fe(CO)3}4] (2), [{Fe3(CO)9}{μ3-SbFe(CO)2Cp"}2] (3) and [{μ4-SbFe(CO)2Cp*}2{Co4(CO)10(μ-CO)}] (4). All products were characterised by X-ray structure analyses and other methods. Cluster 2 reveals a novel Sb3Fe4 core, which does not follow the Wade−Mingos rules. Cluster 3 forms a square-pyramidal nido-cluster. The Sb2Co4 cluster core of 4 derives from a pentagonal bipyramid and consists of apical Sb and equatorial Co atoms with one missing pentagonal core atom.

Bonding, structure, and energetics of gaseous E8(2+) and of solid E8(AsF6)2 (E = S, Se).

The attempt to prepare hitherto unknown homopolyatomic cations of sulfur by the reaction of elemental sulfur with blue S8(AsF6)2 in liquid SO2/SO2ClF, led to red (in transmitted light) crystals identified crystallographically as S8(AsF6)2. The X-ray structure of this salt was redetermined with improved resolution and corrected for librational motion: monoclinic, space group P2(1)/c (No. 14), Z = 8, a = 14.986(2) A, b = 13.396(2) A, c = 16.351(2) A, beta = 108.12(1) degrees. The gas phase structures of E8(2+) and neutral E8 (E = S, Se) were examined by ab initio methods (B3PW91, MPW1PW91) leading to delta fH theta[S8(2+), g] = 2151 kJ/mol and delta fH theta[Se8(2+), g] = 2071 kJ/mol. The observed solid state structures of S8(2+) and Se8(2+) with the unusually long transannular bonds of 2.8-2.9 A were reproduced computationally for the first time, and the E8(2+) dications were shown to be unstable toward all stoichiometrically possible dissociation products En+ and/or E4(2+) [n = 2-7, exothermic by 21-207 kJ/mol (E = S), 6-151 kJ/mol (E = Se)]. Lattice potential energies of the hexafluoroarsenate salts of the latter cations were estimated showing that S8(AsF6)2 [Se8(AsF6)2] is lattice stabilized in the solid state relative to the corresponding AsF6- salts of the stoichiometrically possible dissociation products by at least 116 [204] kJ/mol. The fluoride ion affinity of AsF5(g) was calculated to be 430.5 +/- 5.5 kJ/mol [average B3PW91 and MPW1PW91 with the 6-311 + G(3df) basis set]. The experimental and calculated FT-Raman spectra of E8(AsF6)2 are in good agreement and show the presence of a cross ring vibration with an experimental (calculated, scaled) stretching frequency of 282 (292) cm-1 for S8(2+) and 130 (133) cm-1 for Se8(2+). An atoms in molecules analysis (AIM) of E8(2+) (E = S, Se) gave eight bond critical points between ring atoms and a ninth transannular (E3-E7) bond critical point, as well as three ring and one cage critical points. The cage bonding was supported by a natural bond orbital (NBO) analysis which showed, in addition to the E8 sigma-bonded framework, weak pi bonding around the ring as well as numerous other weak interactions, the strongest of which is the weak transannular E3-E7 [2.86 A (S8(2+), 2.91 A (Se8(2+)] bond. The positive charge is delocalized over all atoms, decreasing the Coulombic repulsion between positively charged atoms relative to that in the less stable S8-like exo-exo E8(2+) isomer. The overall geometry was accounted for by the Wade-Mingos rules, further supporting the case for cage bonding. The bonding in Te8(2+) is similar, but with a stronger transannular E3-E7 (E = Te) bonding. The bonding in E8(2+) (E = S, Se, Te) can also be understood in terms of a sigma-bonded E8 framework with additional bonding and charge delocalization occurring by a combination of transannular n pi *-n pi * (n = 3, 4, 5), and np2-->n sigma * bonding. The classically bonded S8(2+) (Se8(2+) dication containing a short transannular S(+)-S+ (Se(+)-Se+) bond of 2.20 (2.57) A is 29 (6) kJ/mol higher in energy than the observed structure in which the positive charge is delocalized over all eight chalcogen atoms.

Structure and reactivity of δ4-cyclobutadiene and cisoid-δ4(5e)-butadienyl-substituted rhenium complexes formed by reaction of [ReBr2{δ2(4e)-alkyne}(δ-C5H5)] with alkynes or o-diphenylphosphinostyrene *

When cis-/trans-[ReBr2(CO)2(η-C5H5)] and PhC2Ph were heated together under reflux in toluene solution for 24 h the η4-cyclobutadiene-substituted complex [ReBr2(η4-C4Ph4)(η-C5H5)] 1 was formed in good yield via the intermediate [ReBr2{η2(4e)-PhC2Ph}(η-C5H5)]. A single-crystal X-ray diffraction study confirmed an overall pseudo-tetrahedral structure for 1, establishing a Br–Re–Br angle of 83.9°. Treatment of 1 with PPh3 or PMe3 (L) in the presence of AgBF4 afforded the cations [ReBr(L)(η4-C4Ph4)(η-C5H5)][BF4] 2 (L = PPh3) and 3 (L = PMe3). Reaction of 1 with an excess of Li[AlH4] gave the dihydride [ReH2(η4-C4Ph4)(η-C5H5)] 4 characterised by X-ray crystallography, whereas, 1 equivalent of Li[AlH4] afforded [ReH(Br)(η4-C4Ph4)(η-C5H5)] 5. In contrast with predictions from the Davis–Green–Mingos rules, reaction of 2 with Li[BHEt3] afforded 5 (major) and the minor product [ReH(PPh3)(η4-C4Ph4)(η-C5H5)]Br 6. Extended Hückel molecular orbital calculations suggested that protonation of 4 should give the cationic trihydride [ReH3(η4-C4Ph4)(η-C5H5)]+, however a novel ring-opening reaction occurred with CF3CO2H to give the crystallographically characterised η4-1,3-diene complex [ReH{OC(O)CF3}{η2,η2-Z,Z-PhCHC(Ph)C(Ph)C(Ph)H}(η-C5H5)] 7. When [ReBr2{η2(4e)-PhC2R}(η-C5H5)] (R = Me or Ph) was treated with AgBF4 (2 equivalents) and o-diphenylphosphinostyrene (dpps) a carbon–carbon coupling reaction between the co-ordinated alkyne and alkene part of the dpps ligand took place followed by a deprotonation reaction to give the cisoid-η4(5e)-butadienyl-substituted complexes [Re{C(Ph)-η3-C(R)CHCHC6H4PPh2-o}(η-C5H5)][BF4] 8 (R = Me) and 9 (R = Ph); the structure of 8 being confirmed by single-crystal X-ray crystallography. Treatment of 9 with K[BHBus3] led to the selective delivery of ‘H–’ to the ReCα carbon of the η4(5e)-butadienyl ligand and formation of the crystallographically identified d6 η4-1,3-diene complex [Re{η4-CH(Ph)C(Ph)CHCHC6H4PPh2-o}(η-C5H5)] 10. Interestingly, reaction of 10 with [Ph3C][BF4] led to regeneration of the parent cisoid-η4(5e)-butadienyl complex 9 confirming the relationship between η4(5e)-butadienyl and η4-1,3-diene ligands.