Quantum chemical calculations using the complete active space of the valence orbitals have been carried out for H_nCCH_n (n=0–3) and N₂. The quadratic force constants and the stretching potentials of H_nCCH_n have been calculated at the CASSCF/cc-pVTZ level. The bond dissociation energies of the C−C bonds of C₂ and HC≡CH were computed using explicitly correlated CASPT2-F12/cc-pVTZ-F12 wave functions. The bond dissociation energies and the force constants suggest that C₂ has a weaker C−C bond than acetylene. The analysis of the CASSCF wavefunctions in conjunction with the effective bond orders of the multiple bonds shows that there are four bonding components in C₂, while there are only three in acetylene and in N₂. The bonding components in C₂ consist of two weakly bonding σ bonds and two electron-sharing π bonds. The bonding situation in C₂ can be described with the σ bonds in Be₂ that are enforced by two π bonds. There is no single Lewis structure that adequately depicts the bonding situation in C₂. The assignment of quadruple bonding in C₂ is misleading, because the bond is weaker than the triple bond in HC≡CH.

Die dreieckigen Cluster [Zn₃Cp*₃]⁺ und [Zn₂CuCp*₃] wurden durch Addition der in situ generierten, elektrophilen und isolobalen Spezies [ZnCp*]⁺ und [CuCp*] an das Carmona-Reagens [Cp*ZnZnCp*] synthetisiert, wobei die Zn-Zn-Bindung des Letzteren erhalten blieb. Die Verwendung von nichtkoordinierenden fluorierten aromatischen Lösungsmitteln ist dabei essenziell. Die Bindungssituation der ligandenstabilisierten Cluster wurde mit quantenchemischen Methoden untersucht, wobei sich ein hohes Maß an σ-Aromatizität zeigte, ähnlich der Bindungssituation im Triwasserstoffkation [H₃]⁺. Die neuen Spezies dienen als molekulare Bausteine für Cu_nZn_m-Cluster (Nanomessing), die auch im LIFDI-Massenspektrum der neuen Verbindungen detektiert werden können.

The triangular clusters [Zn₃Cp*₃]⁺ and [Zn₂CuCp*₃] were obtained by addition of the in situ generated, electrophilic, and isolobal species [ZnCp*]⁺ and [CuCp*] to Carmona’s compound, [Cp*ZnZnCp*], without splitting the ZnZn bond. The choice of non-coordinating fluoroaromatic solvents was crucial. The bonding situations of the all-hydrocarbon-ligand-protected clusters were investigated by quantum chemical calculations revealing a high degree of σ-aromaticity similar to the triatomic hydrogen ion [H₃]⁺. The new species serve as molecular building units of Cu_nZn_m nanobrass clusters as indicated by LIFDI mass spectrometry.

The complexes OCBeCO₃ and COBeCO₃ have been isolated in a low-temperature neon matrix. The more stable isomer OCBeCO₃ has a very high CO stretching mode of 2263 cm⁻¹, which is blue-shifted by 122 cm⁻¹ with respect to free CO and 79 cm⁻¹ higher than in OCBeO. Bonding analysis of the complexes shows that OCBeO has a stronger OCBeY bond than OCBeCO₃ because it encounters stronger π backdonation. The isomers COBeCO₃ and COBeO exhibit red-shifted CO stretching modes with respect to free CO. The inverse change of CO stretching frequency in OCBeY and COBeY is explained with the reversed polarization of the σ and π bonds in CO.

The attempted synthesis of NHC-stabilized dicarbon (NHCCCNHC) through deprotonation of a doubly protonated precursor ([NHCCHCHNHC]²⁺) is reported. Rather than deprotonation, a clean reduction to NHCCHCHNHC is observed with a variety of bases. The apparent resistance towards deprotonation to the target compound led to a reinvestigation of the electronic structure of NHCCCNHC, which showed that the highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) gap is likely too small to allow for isolation of this species. This is in contrast to the recent isolation of the cyclic alkylaminocarbene analogue (cAACCCcAAC), which has a large HOMO–LUMO gap. A detailed theoretical study illuminates the differences in electronic structures between these molecules, highlighting another case of the potential advantages of using cAAC rather than NHC as a ligand. The bonding analysis suggests that the dicarbon compounds are well represented in terms of donor–acceptor interactions LC₂L (L=NHC, cAAC).

Heterometalldotierte Goldcluster sind durch nasschemische Synthese schwer zugänglich, und mit Hauptgruppenmetallen oder frühen Übergangsmetallen dotierte Cluster sind rar. Die Verbindungen [M(AuPMe₃)₁₁(AuCl)]³⁺ (M=Pt, Pd, Ni) (1–3), [Ni(AuPPh₃)_(8–2n)(AuCl)₃(AlCp*)_n] (n=1, 2) (4, 5) und [Mo(AuPMe₃)₈(GaCl₂)₃(GaCl)]⁺ (6) wurden selektiv durch Transmetallierung von [M(M′Cp*)_n] (M=Mo, E=Ga, n=6; M=Pt, Pd, Ni, M′=Ga, Al; n=4) mit [ClAuPR₃] (R=Me, Ph) hergestellt und mit Einkristallröntgenbeugung sowie ESI-MS charakterisiert. Mithilfe von DFT-Rechnungen wurden die Bindungsverhältnisse analysiert. Die Transmetallierung ist eine wirkungsvolle Syntheseroute hin zu heterometalldotierten Goldclustern, deren Aufbau der 18-Valenzelektronenregel für das Zentralmetallatom gehorcht und die mit dem Superatomkonzept auf Grundlage des Jellium-Modells übereinstimmen.

A theoretical study of Li₉₀P₉₀, which possesses a circular double-helix structure that resembles the Watson–Crick DNA structure, is reported. This is a new bonding motif in inorganic chemistry. The calculations show that the molecule might become synthesized and that it could be a model for other inorganic species which possess a double-helix structure.

Quantum chemical calculations show that the N-heterocyclic carbene (NHC)-stabilized silavinylidene, NHC^tBuCSiR₂ is a strongly bonded complex, which has a linear arrangement of the donor and acceptor moieties. The molecule is the energetically lowest lying isomer of the NHC-stabilized R₂CSi isomers and it is stable towards dimerization when R is a bulky substituent. The silavinylidene complex is the only species of the silylidene homologues NHC^tBuEE′R₂ (E, E′=C–Pb) which possesses a linear arrangement. The unusual bonding situation is explained in terms of donor–acceptor interactions between NHC^tBu as σ donor and CSiR₂ in the doubly excited singlet state 3a₁2b₂ which leads to a significantly shorter CSiR₂ bond compared with free CSiR₂.

Heterometal-doped gold clusters are poorly accessible through wet-chemical approaches and main-group-metal- or early-transition-metal-doped gold clusters are rare. Compounds [M(AuPMe₃)₁₁(AuCl)]³⁺ (M=Pt, Pd, Ni) (1–3), [Ni(AuPPh₃)_(8−2n)(AuCl)₃(AlCp*)_n] (n=1, 2) (4, 5), and [Mo(AuPMe₃)₈ (GaCl₂)₃(GaCl)]⁺ (6) were selectively obtained by the transmetalation of [M(M′Cp*)_n] (M=Mo, E=Ga, n=6; M=Pt, Pd, Ni, M′=Ga, Al, n=4) with [ClAuPR₃] (R=Me, Ph) and characterized by single-crystal X-ray diffraction and ESI mass spectrometry. DFT calculations were used to analyze the bonding situation. The transmetalation proved to be a powerful tool for the synthesis of heterometal-doped gold clusters with a design rule based on the 18 valence electron count for the central metal atom M and in agreement with the unified superatom concept based on the jellium model.

Quantum chemical calculations using density functional theory at the BP86/TZ2P level have been carried out to determine the geometries and stabilities of Group 13 adducts [(PMe₃)(EH₃)] and [(PMe₃)₂(E₂H_n)] (E=B–In; n=4, 2, 0). The optimized geometries exhibit, in most cases, similar features to those of related adducts [(NHC^Me)(EH₃)] and [(NHC^Me)₂(E₂H_n)] with a few exceptions that can be explained by the different donor strengths of the ligands. The calculations show that the carbene ligand L=NHC^Me (:C(NMeCH)₂) is a significantly stronger donor than L=PMe₃. The equilibrium geometries of [L(EH₃)] possess, in all cases, a pyramidal structure, whereas the complexes [L₂(E₂H₄)] always have an antiperiplanar arrangement of the ligands L. The phosphine ligands in [(PMe₃)₂(B₂H₂)], which has C_s symmetry, are in the same plane as the B₂H₂ moiety, whereas the heavier homologues [(PMe₃)₂(E₂H₂)] (E=Al, Ga, In) have C_i symmetry in which the ligands bind side-on to the E₂H₂ acceptor. This is in contrast to the [(NHC^Me)₂(E₂H₂)] adducts for which the NHC^Me donor always binds in the same plane as E₂H₂ except for the indium complex [(NHC^Me)₂(In₂H₂)], which exhibits side-on bonding. The boron complexes [L₂(B₂)] (L=PMe₃ and NHC^Me) possess a linear arrangement of the LBBL moiety, which has a BB triple bond. The heavier homologues [L₂(E₂)] have antiperiplanar arrangements of the LEEL moieties, except for [(PMe₃)₂(In₂)], which has a twisted structure in which the PInInP torsion angle is 123.0°. The structural features of the complexes [L(EH₃)] and [L₂(E₂H_n)] can be explained in terms of donor–acceptor interactions between the donors L and the acceptors EH₃ and E₂H_n, which have been analyzed quantitatively by using the energy decomposition analysis (EDA) method. The calculations predict that the hydrogenation reaction of the dimeric magnesium(I) compound L′MgMgL′ with the complexes [L(EH₃)] is energetically more favorable for L=PMe₃ than for NHC^Me.

The ground electronic state of C(BH)₂ exhibits both a linear minimum and a peculiar angle-deformation isomer with a central B-C-B angle near 90°. Definitive computations on these species and the intervening transition state have been executed by means of coupled-cluster theory including single and double excitations (CCSD), perturbative triples (CCSD(T)), and full triples with perturbative quadruples (CCSDT(Q)), in concert with series of correlation-consistent basis sets (cc-pVXZ, X=D, T, Q, 5, 6; cc-pCVXZ, X=T, Q). Final energies were pinpointed by focal-point analyses (FPA) targeting the complete basis-set limit of CCSDT(Q) theory with auxiliary core correlation, relativistic, and non-Born–Oppenheimer corrections. Isomerization of the linear species to the bent form has a minuscule FPA reaction energy of 0.02 kcal mol⁻¹ and a corresponding barrier of only 1.89 kcal mol⁻¹. Quantum tunneling computations reveal interconversion of the two isomers on a timescale much less than 1 s even at 0 K. Highly accurate CCSD(T)/cc-pVTZ and composite c∼CCSDT(Q)/cc-pCVQZ anharmonic vibrational frequencies confirm matrix-isolation infrared bands previously assigned to linear C(BH)₂ and provide excellent predictions for the heretofore unobserved bent isomer. Chemical bonding in the C(BH)₂ species was exhaustively investigated by the atoms-in-molecules (AIM) approach, molecular orbital plots, various population analyses, local mode vibrations and force constants, unified reaction valley analysis (URVA), and other methods. Linear C(BH)₂ is a cumulene, whereas bent C(BH)₂ is best characterized as a carbene with little carbone character. Weak B–B attraction is clearly present in the unusual bent isomer, but its strength is insufficient to form a CB₂ ring with a genuine boron–boron bond and attendant AIM bond path.

Quantum chemical calculations at the BP86/TZVPP//BP86/SVP level of theory have been performed for the isoelectronic series of compounds [(PPh₃)₂CEH₂]^q (E^q=Be, B⁺, C²⁺, N³⁺, O⁴⁺). The equilibrium geometries and bond dissociation energies were calculated and the nature of the CE bond was investigated with charge and energy decomposition methods. The dication [(PPh₃)₂CCH₂]²⁺ could become isolated as a salt compound with two counter ions [AlBr₄]⁻. The X-ray structure analysis of [(PPh₃)₂CCH₂]²⁺ gave bond lengths and angles that are in good agreement with the calculated data. The geometry optimization of [(PPh₃)₂COH₂]⁴⁺ gave [(PPh₃)₂COH]³⁺ as the equilibrium structure. Bonding analysis of [(PPh₃)₂CEH₂]^q shows that [(PPh₃)₂CBeH₂] and [(PPh₃)₂CBH₂]⁺ possess donor–acceptor bonds in which the σ and π lone-pair electrons of (PPh₃)₂C donate into the vacant orbitals of the acceptor fragment. The multiply charged compounds are better described as substituted olefins [(PPh₃)₂CCH₂]²⁺, [(PPh₃)₂CNH₂]³⁺, and [(PPh₃)₂COH]³⁺, which possess electron-sharing σ and π bonds that arise from the interaction between the triplet states of [(PPh₃)₂C]²⁺ and the respective fragment CH₂, (NH₂)⁺, and (OH)⁺. The multiply charged cations [(PPh₃)₂CCH₂]²⁺, [(PPh₃)₂CNH₂]³⁺, and [(PPh₃)₂COH]³⁺ are calculated to be stable toward dissociation.

The singlet potential-energy surface (PES) of the system involving the atoms H, X, and E (the (H, X, E) system) in which X=N–Bi and E=C–Pb has been explored at the CCSD(T)/TZVPP and BP86/TZ2P+ levels of theory. The nature of the XE bonding has been analyzed with charge- and energy-partitioning methods. The calculations show that the linear isomers of the nitrogen systems lin-HEN and lin-HNE are minima on the singlet PES. The carbon compound lin-HCN (HCN=hydrogen cyanide) is 14.9 kcal mol⁻¹ lower in energy than lin-HNC but the heavier group 14 homologues lin-HEN (E=Si–Pb) are between 64.8 and 71.5 kcal mol⁻¹ less stable than the lin-HNE isomers. The phosphorous system (H, P, E) exhibits significant differences concerning the geometry and stability of the equilibrium structures compared with the nitrogen system. The linear form lin-HEP of the former system is much more stable than lin-HPE. The molecule lin-HCP is the only minimum on the singlet PES. It is 78.5 kcal mol⁻¹ lower in energy than lin-HPC, which is a second-order saddle point. The heavier homologues lin-HPE, in which E=Si–Pb, are also second-order saddle points, whereas the bent-HPE structures are the global minima on the PES. They are between 10.3 (E=Si) and 36.5 kcal mol⁻¹ (E=Pb) lower in energy than lin-HEP. The bent-HPE structures possess rather acute bending angles H-P-E between 60.1 (E=Si) and 79.7° (E=Pb). The energy differences between the heavier group 15 isomers lin-HEX (X=P–Bi) and the bent structures bent-HXE become continuously smaller. The silicon species lin-HSiBi is even 3.1 kcal mol⁻¹ lower in energy than bent-HBiSi. The bending angle H-X-E becomes more acute when X becomes heavier. The drastic energy differences between the isomers of the system (H, X, E) are explained with three factors that determine the relative stabilities of the energy minima: 1) The different bond strength between the hydrogen bonds HX and HE. 2) The electronic excitation energy of the fragment HE from the X ²Π ground state to the ⁴Σ⁻ excited state, which is required to establish a E≡X triple bond in the molecules lin-HEX. 3) The strength of the intrinsic XE interactions in the molecules. The trends of the geometries and relative energies of the linear, bent, and cyclic isomers are explained with an energy-decomposition analysis that provides deep insight into the nature of the bonding situation.

The synthesis, characterization, and theoretical investigation by means of quantum-chemical calculations of an oligonuclear metal-rich compound are presented. The reaction of homoleptic dinuclear palladium compound [Pd₂(μ-GaCp*)₃(GaCp*)₂] with ZnMe₂ resulted in the formation of unprecedented ternary Pd/Ga/Zn compound [Pd₂Zn₆Ga₂(Cp*)₅(CH₃)₃] (1), which was analyzed by ¹H and ¹³C NMR spectroscopy, MS, elemental analysis, and single-crystal X-ray diffraction. Compound 1 consisted of two C_s-symmetric molecular isomers, as revealed by NMR spectroscopy, at which distinct site-preferences related to the Ga and Zn positions were observed by quantum-chemical calculations. Structural characterization of compound 1 showed significantly different coordination environments for both palladium centers. Whilst one Pd atom sat in the central of a bi-capped trigonal prism, thereby resulting in a formal 18-valence electron fragment, {Pd(ZnMe)₂(ZnCp*)₄(GaMe)}, the other Pd atom occupied one capping unit, thereby resulting in a highly unsaturated 12-valence electron fragment, {Pd(GaCp*)}. The bonding situation, as determined by atoms-in-molecules analysis (AIM), NBO partial charges, and molecular orbital (MO) analysis, pointed out that significant PdPd interactions had a large stake in the stabilization of this unusual molecule. The characterization and quantum-chemical calculations of compound 1 revealed distinct similarities to related M/Zn/Ga Hume–Rothery intermetallic solid-state compounds, such as Ga/Zn-exchange reactions, the site-preferences of the Zn/Ga positions, and direct MM bonding, which contributes to the overall stability of the metal-rich compound.

Quantum-chemical calculations at the BP86/TZVPP level have been carried out for the heavy Group 14 homologues of carbodiphosphorane E(PPh₃)₂, where E=Si, Ge, Sn, Pb, which are experimentally unknown so far. The results of the theoretical investigation suggest that the tetrelediphosphoranes E(PPh₃)₂ (1 E) are stable compounds that could become isolated in a condensed phase. The molecules possess donor–acceptor bonds Ph₃PEPPh₃ to a bare tetrele atom E, which retains its four valence electrons as two electron lone pairs. The analysis of the bonding situation and the calculation of the chemical reactivity indicate that the molecules 1 E belong to the class of divalent E(0) compounds (ylidones). All molecules 1 C–1 Pb have very large first but also very large second proton affinities, which distinguishes them from the N-heterocyclic carbene homologues, in which the donor atom is a divalent E(II) species that possesses only one electron lone pair. Compounds 1 E are powerful double donors that strongly bind Lewis acids such as BH₃ and AuCl in the complexes 1 E(BH₃)_n and 1 E(AuCl)_n (n=1, 2). The bond dissociation energies (BDEs) of the second BH₃ and AuCl molecules are only slightly less than the BDE of the first BH₃ and AuCl. The results of this work are a challenge for experimentalists.

Quantum chemical calculations at the BP86/TZVPP//BP86/SVP level are performed for the tetrylone complexes [W(CO)₅-E(PPh₃)₂] (W-1 E) and the tetrylene complexes [W(CO)₅-NHE] (W-2 E) with E=C–Pb. The bonding is analyzed using charge and energy decomposition methods. The carbone ligand C(PPh₃) is bonded head-on to the metal in W-1 C, but the tetrylone ligands E(PPh₃)₂ are bonded side-on in the heavier homologues W-1 Si to W-1 Pb. The WE bond dissociation energies (BDEs) increase from the lighter to the heavier homologues (W-1 C: D_e=25.1 kcal mol⁻¹; W-1 Pb: D_e=44.6 kcal mol⁻¹). The W(CO)₅C(PPh₃)₂ donation in W-1 C comes from the σ lone-pair orbital of C(PPh₃)₂, whereas the W(CO)₅E(PPh₃)₂ donation in the side-on bonded complexes with E=Si–Pb arises from the π lone-pair orbital of E(PPh₃)₂ (the HOMO of the free ligand). The π-HOMO energy level rises continuously for the heavier homologues, and the hybridization has greater p character, making the heavier tetrylones stronger donors than the lighter systems, because tetrylones have two lone-pair orbitals available for donation. Energy decomposition analysis (EDA) in conjunction with natural orbital for chemical valence (NOCV) suggests that the WE BDE trend in W-1 E comes from the increase in W(CO)₅E(PPh₃)₂ donation and from stronger electrostatic attraction, and that the E(PPh₃)₂ ligands are strong σ-donors and weak π-donors. The NHE ligands in the W-2 E complexes are bonded end-on for E=C, Si, and Ge, but side-on for E=Sn and Pb. The WE BDE trend is opposite to that of the W-1 E complexes. The NHE ligands are strong σ-donors and weak π-acceptors. The observed trend arises because the hybridization of the donor orbital at atom E in W-2 E has much greater s character than that in W-1 E, and even increases for heavier atoms, because the tetrylenes have only one lone-pair orbital available for donation. In addition, the WE bonds of the heavier systems W-2 E are strongly polarized toward atom E, so the electrostatic attraction with the tungsten atom is weak. The BDEs calculated for the WE bonds in W-1 E, W-2 E and the less bulky tetrylone complexes [W(CO)₅-E(PH₃)₂] (W-3 E) show that the effect of bulky ligands may obscure the intrinsic WE bond strength.

Quantum chemical calculations using DFT (BP86, M05-2X) and ab initio methods (CCSD(T), SCS-MP2) have been carried out on the borylene complexes (BH)L₂ and nitrogen cation complexes (N⁺)L₂ with the ligands L=CO, N₂, PPh₃, NHC_Me, CAAC, and CAAC_model. The results are compared with those obtained for the isoelectronic carbones CL₂. The geometries and bond dissociation energies of the ligands, the proton affinities, and adducts with the Lewis acids BH₃ and AuCl were calculated. The nature of the bonding has been analyzed with charge and energy partitioning methods. The calculated borylene complexes (BH)L₂ have trigonal planar coordinated boron atoms which possess rather short BL bonds. The calculated bond dissociation energies (BDEs) of the ligands for complexes where L is a carbene (NHC or CAAC) are very large (D_e=141.6–177.3 kcal mol⁻¹) which suggest that such species might become isolated in a condensed phase. The borylene complexes (BH)(PPh₃)₂ and (BH)(CO)₂ have intermediate bond strengths (D_e=90.1 and 92.6 kcal mol⁻¹). Substituted homologues with bulky groups at boron which protect the boron atom from electrophilic attack might also be stable enough to become isolated. The BDE of (BH)(N₂)₂ is much smaller (D_e=31.9 kcal mol⁻¹), but could become observable in a low-temperature matrix. The proton affinities of the borylene complexes are very large, particularly for the bulky adducts with L=PPh₃, NHC_Me, CAAC_model and CAAC and thus, they are superbases. All (BH)L₂ molecules bind strongly AuCl either η¹ (L=N₂, PPh₃, NHC_Me, CAAC) or η² (L=CO, CAAC_model). The BDEs of H₃B(BH)L₂ adducts which possess a hitherto unknown boronboron donor–acceptor bond are smaller than for the AuCl complexes. The strongest bonded BH₃ adduct that might be isolable is (BH)(PPh₃)₂BH₃ (D_e=36.2 kcal mol⁻¹). The analysis of the bonding situation reveals that (BH)L₂ bonding comes mainly from the orbital interactions which has three major contributions, that is, the donation from the symmetric (σ) and antisymmetric (π_||) combination of the ligand lone-pair orbitals into the vacant MOs of BH L(BH)L and the L(BH)L π backdonation from the boron lone-pair orbital. The nitrogen cation complexes (N⁺)L₂ have strongly bent LNL geometries, in which the calculated bending angle varies between 113.9° (L=N₂) and 146.9° (L=CAAC). The BDEs for (N⁺)L₂ are much larger than those of the borylene complexes. The carbene ligands NHC and CAAC but also the phosphane ligands PPh₃ bind very strongly between D_e=358.4 kcal mol⁻¹ (L=PPh₃) and D_e=412.5 kcal mol⁻¹ (L=CAAC_model). The proton affinities (PA) of (N⁺)L₂ are much smaller and they bind AuCl and BH₃ less strongly compared with (BH)L₂. However, the PAs (N⁺)L₂ for complexes with bulky ligands L are still between 139.9 kcal mol⁻¹ (L=CAAC_model) and 168.5 kcal mol⁻¹ (L=CAAC). The analysis of the (N⁺)L₂ bonding situation reveals that the binding interactions come mainly from the L(N⁺)L donation while L(N⁺)L π backdonation is rather weak.

The competitive 1,5-electrocyclization versus intramolecular 1,5-proton shift in imidazolium allylides and imidazolium 2-phosphaallylides has been investigated theoretically at the DFT (B3LYP/6-311 + +G**//B3LYP/6-31G**) level. 1,5-Electrocyclization follows pericyclic mechanism and its activation barrier is lower than that for the pseudopericyclic mechanism by ∼5–6 kcal mol⁻¹. The activation barriers for 1,5-electrocyclization of imidazolium 2-phosphaallylides are found to be smaller than those for their nonphosphorus analogues by ∼3–5 kcal mol⁻¹. There appears to be a good correlation between the activation barrier for intramolecular 1,5-proton shift and the density of the negative charge at C8, except for the ylides having fluorine substituent at this position (7b and 8b). The presence of fluorine atom reduces the density of the negative charge at C8 (in 7b it becomes positively charged) and thus raises the activation barrier. The ylides 7f and 8f having CF₃ group at C8, in preference to the 1,5-proton shift, follow an alternative route leading to different carbenes which is accompanied by the loss of HF. The carbenes Pr_7,8b–e resulting from intramolecular 1,5-proton shift have a strong tendency to undergo intramolecular S_N2 type reaction, the activation barrier being 7–28 kcal mol⁻¹. Copyright © 2011 John Wiley & Sons, Ltd.

Quantum chemical calculations using density functional theory at the BP86/TZVPP level and ab initio calculations at the SCS-MP2/TZVPP level have been carried out for the group 13 complexes [(NHC)(EX₃)] and [(NHC)₂(E₂X_n)] (E=B to In; X=H, Cl; n=4, 2, 0; NHC=N-heterocyclic carbene). The monodentate Lewis acids EX₃ and the bidentate Lewis acids E₂X_n bind N-heterocyclic carbenes rather strongly in donor–acceptor complexes [(NHC)(EX₃)] and [(NHC)₂(E₂X_n)]. The equilibrium structures of the bidentate complexes depend on the electronic reference state of E₂X_n, which may vary for different atoms E and X. All complexes [(NHC)₂(E₂X₄)] possess C_s symmetry in which the NHC ligands bind in a trans conformation to the group 13 atoms E. The complexes [(NHC)₂(E₂H₂)] with E=B, Al, Ga have also C_s symmetry with a trans arrangement of the NHC ligands and a planar CE(H)E(H)C moiety that has a EE π bond. In contrast, the indium complex [(NHC)₂(In₂H₂)] has C_i symmetry with pyramidal-coordinated In atoms in which the hydrogen atoms are twisted above and below the CInInC plane. The latter C_i form is calculated for all chloride systems [(NHC)₂(E₂Cl₂)], but the boron complex [(NHC)₂(B₂Cl₂)] deviates only slightly from C_s symmetry. The B₂ fragment in the linear coordinated complex [(NHC)₂(B₂)] has a highly excited (3)¹Σ_g⁻ reference state, which gives an effective B≡B triple bond with a very short interatomic distance. The heavier homologues [(NHC)₂(E₂)] (E=Al to In) exhibit a anti-periplanar arrangement of the NHC ligands in which the E₂ fragments have a (1)¹Δ_g reference state and an EE double bond. The calculated energies suggest that the dihydrogen release from the complexes [(NHC)(EH₃)] and [(NHC)₂(E₂H_n)] becomes energetically more favourable when atom E becomes heavier. The indium complexes should therefore be the best candidates of the investigated series for hydrogen-storage systems that could potentially deliver dihydrogen at close to ambient temperature. The hydrogenation reaction of the dimeric magnesium(I) compound [LMgMgL] (L=β-diketiminate) with [(NHC)(EH₃)] becomes increasingly exothermic with the trend B<Al<Ga<In.

Quantum chemical calculations have been performed for the dicoordinated carbon compounds C(PPh₃)₂, C(NHC_Me)₂, R₂CC=CR₂ (R=H, F, NMe₂), C₃O₂, C(CN)₂⁻ and N-methyl-substituted N-heterocyclic carbene (NHC_Me). The geometries of the complexes in which the dicoordinated carbon molecules bind as ligands to one and two AuCl moieties have been optimized and the strength and nature of the metal–ligand interactions in the mono- and diaurated complexes were investigated by means of energy decomposition analysis. The goal of the study is to elucidate the differences in the chemical behavior between carbones, allenes and carbenes. The results show that carbones bind one and two AuCl species in η¹ fashion, whereas allenes bind them in η² fashion. Compounds with latent divalent carbon(0) character can coordinate in more than one way, with the dominant mode indicating the degree of carbone or allene character. The calculated structures of the mono- and diaurated tetraaminoallenes (TAAs) reveal that TAAs exhibit a chameleon-like behavior: The bonding situation in the equilibrium structure is best described as allene [(R₂N)₂]CCC[(NR₂)₂] in which the central carbon atom is a tetravalent C^IV species, but the reactivity suggests that TAAs should be considered as divalent C⁰ compounds C{C[(NR₂)₂]}₂, that is, as “hidden” carbones. Carbon suboxide binds one AuCl preferentially in the η¹ mode, whereas the equilibrium structures of the η¹- and η²-bonded diaurated complex are energetically nearly degenerate. The doubly negatively charged isoelectronic carbone C(CN)₂²⁻ binds one and two AuCl very strongly in characteristic η¹ fashion. The N-heterocyclic carbene complex, [NHC_Me(AuCl)], possesses a high bond dissociation energy (BDE) for the splitting off of AuCl. The diaurated NHC adduct, [NHC_Me(AuCl)₂], has two η¹-bonded AuCl moieties that exhibit aurophilic attraction, which yield a moderate bond strength that might be large enough for synthesizing the complex. The BDE for the second AuCl in [NHC_Me(AuCl)₂] is clearly smaller than the values for the second AuCl in doubly aurated carbone complexes.

The synthesis and structural characterization of novel, metal-rich, highly coordinated compounds [Mo(M′R)₁₂] and [M(M′R)₈] (M: Pd, Pt, Mo; M′: Zn, Cd; R: Me=CH₃, Cp*=pentamethylcyclopentadienyl) are reported. Additionally, a description of the bonding situation of the new compounds by means of quantum-chemical calculations is presented including the Hg analogues. Reaction of [Pt(GaCp*)₄] with CdMe₂ results in the formation of the unprecedented all-Cd coordinated [Pt(CdMe)₄(CdCp*)₄] (1). Similarly, the treatment of the all-Zn coordinated [Pd(ZnMe)₄(ZnCp*)₄] with CdMe₂ affords the novel Zn/Cd mixed compound [Pd(CdMe)₄(ZnCp*)₄] (2). The related Zn/Cd mixed compound [Mo(ZnCp*)₃(CdMe)₉] (3) is prepared by reaction of [Mo(ZnCp*)₄(GaMe)₄] with an excess amount of CdMe₂. All compounds were analyzed by ¹H and ¹³C NMR spectroscopy, elemental analysis, and single-crystal X-ray diffraction. The bonding situation of these highly coordinated, metal-rich molecules 1–3 were studied by quantum-chemical calculations using density functional theory (DFT) at the BP86/TZ2P+ level, atoms-in-molecules (AIM) analysis, and energy-decomposition analysis (EDA), as well as the its natural orbitals for chemical valence variation (EDA-NOCV) and including the hypothetically all-Hg-coordinated analogues. The results point out that the radial interactions M–M′ in the icosahedral compounds that have twelve ligands are best described as classical electron-pair-sharing covalent bonds, whereas the dodecahedral species, which have eight ligands, exhibit metal–ligand donor–acceptor bonds. The attractive interactions between the metal–ligand fragments M′R by means of M′–M′ bonds are weaker but not insignificant. All complexes fulfill the 18-electron rule. The analysis clarifies the electronic structures as being distinctly different from typical endohedral clusters M@(M′′R)_n that exhibit strong peripheral M′′–M′′ interactions: The M′M′ bonds are not strong enough to yield stable (M′R)_n cages.

Quantum-chemical calculations using DFT and ab initio methods have been carried out for fourteen divalent carbon(0) compounds (carbones), in which the bonding situation at the two-coordinate carbon atom can be described in terms of donor–acceptor interactions LCL. The charge- and energy-decomposition analysis of the electronic structure of compounds 1–10 reveals divalent carbon(0) character in different degrees for all molecules. Carbone-type bonding LCL is particularly strong for the carbodicarbenes 1 and 2, for the “bent allenes” 3 a, 3 b, 4 a, and 4 b, and for the carbocarbenephosphoranes 7 a, 7 b, and 7 c. The last-named molecules have very large first and large second proton affinities. They also bind two BH₃ ligands with very high bond energies, which are large enough that the bis-adducts should be isolable in a condensed phase. The second proton affinities of the complexes 5, 6, and 8–10 bearing CO or N₂ as ligand are significantly lower than those of the other molecules. However, they give stable complexes with two BH₃ ligands and thus are twofold Lewis bases. The calculated data thus identify 1–10 as carbones LCL in which the carbon atom has two electron pairs. The chemistry of carbones is different from that of carbenes because divalent carbon(0) compounds CL₂ are π donors and thus may serve as double Lewis bases, while divalent carbon(II) compounds are π acceptors. The theoretical results point toward new directions for experimental research in the field of low-coordinate carbon compounds.

Quantum chemical calculations using DFT at the BP86/TZ2P level of theory are reported for the complexes (PH₃)₂ClM-L where L is an N-heterocyclic ligand and M a group-10 metal Ni, Pd and Pt. The ligands comprise pyridyl groups or carbenes derived from the pyridine, quinolidine or isoquinolidine systems wherein the nitrogen atom is either adjacent to the carbene carbon atom or it is in a remote (meta or para, or in the adjacent ring) position. Comparative calculations include the isomeric ligands of the well-known five-membered N-heterocyclic carbene. The nature of the metal–ligand interactions are investigated by energy decomposition analysis (EDA). The EDA results suggest that the nature of the metal–carbene bonds in the complexes shows little variation when the position of the nitrogen atom in pyridylidenes is adjacent (ortho) or remote (meta or para). It changes even very little when the nitrogen atom is in an adjacent ring to the cyclic carbene moiety. The most significant differences between the bond strengths come from the energy level of the σ-HOMO of the carbene ligand which depends largely on the position of the nitrogen atom. An energetically higher-lying σ lone-pair orbital of the carbene ligand yields stronger orbital interactions but also stronger electrostatic attraction because of better overlap with the metal nucleus. This holds also for the isomers of the five-membered N-heterocyclic carbenes. An excellent correlation is established between the ϵ(HOMO) values of the ligands and the metal–ligand interaction energies, ΔE_int.(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)

We report on the hydroboration of 1-[bis(trimethylsilyl)amino]-2,3-diethylborirene (3) with 9-borabicyclo[3.3.1]nonane (9-BBN), which led through ring-opening to an amino(vinyl)borane. The viscous borane was subsequently converted into a crystalline borate on treatment with MeLi. Both compounds were fully characterized by multinuclear NMR spectroscopy and in case of the latter by single-crystal X-ray diffraction analysis. To elucidate the reaction mechanism of the unexpected boron-carbon bond cleavage, DFT calculations of energy minima and transition states for the hydroboration were carried out.

Quantum-chemical calculations at the BP86/TZVPP level of theory have been carried out for compounds EL₂ for E=Si, Ge, Sn, where L is a five-membered cyclic ylidene or N-heterocyclic ylidene. The theoretical results provide evidence for the classification of the complexes as divalent E(0) compounds, where the bonding situation is best described in terms of donor–acceptor interactions between a bare atom E, which retains its valence electrons as two lone pairs, and two donor ligands LEL. The molecules are very strong donors, which may bind one or two Lewis acids. Divalent E(0) compounds have unusually high second proton affinities and they are strong σ donor ligands. The calculations predict that complexes of EL₂ with one or two BH₃ ligands are stable enough to become isolated in a condensed phase. It is also shown that the bond dissociation energies (BDEs) of transition-metal complexes [(CO)₅WD] and [(CO)₃NiD], where D=EL₂ are rather high. The BDE of some ligands D are higher than those of CO in the metal carbonyls.

Density functional calculations at the BP86/TZ2P level were carried out to understand the ligand properties of the 16-valence-electron(VE) Group 14 complexes [(PMe₃)₂Cl₂M(E)] (1ME) and the 18-VE Group 14 complexes [(PMe₃)₂(CO)₂M(E)] (2ME; M=Fe, Ru, Os; E=C, Si, Ge, Sn) in complexation with W(CO)₅. Calculations were also carried out for the complexes (CO)₅W–EO. The complexes [(PMe₃)₂Cl₂M(E)] and [(PMe₃)₂(CO)₂M(E)] bind strongly to W(CO)₅ yielding the adducts 1ME–W(CO)₅ and 2ME–W(CO)₅, which have C_2v equilibrium geometries. The bond strengths of the heavier Group 14 ligands 1ME (E=Si–Sn) are uniformly larger, by about 6–7 kcal mol⁻¹, than those of the respective EO ligand in (CO)₅W-EO, while the carbon complexes 1MC–W(CO)₅ have comparable bond dissociation energies (BDE) to CO. The heavier 18-VE ligands 2ME (E=Si–Sn) are about 23–25 kcal mol⁻¹ more strongly bonded than the associated EO ligand, while the BDE of 2MC is about 17–21 kcal mol⁻¹ larger than that of CO. Analysis of the bonding with an energy-decomposition scheme reveals that 1ME is isolobal with EO and that the nature of the bonding in 1ME–W(CO)₅ is very similar to that in (CO)₅W–EO. The ligands 1ME are slightly weaker π acceptors than EO while the π-acceptor strength of 2ME is even lower.

The equilibrium geometries and bond dissociation energies of 16-valence-electron(VE) complexes [(PMe₃)₂Cl₂M(E)] and 18-VE complexes [(PMe₃)₂(CO)₂M(E)] with M=Fe, Ru, Os and E=C, Si, Ge, Sn were calculated by using density functional theory at the BP86/TZ2P level. The nature of the ME bond was analyzed with the NBO charge decomposition analysis and the EDA energy-decomposition analysis. The theoretical results predict that the heavier Group 14 complexes [(PMe₃)₂Cl₂M(E)] and [(PMe₃)₂(CO)₂M(E)] with E=Si, Ge, Sn have C_2v equilibrium geometries in which the PMe₃ ligands are in the axial positions. The complexes have strong ME bonds which are slightly stronger in the 16-VE species 1ME than in the 18-VE complexes 2ME. The calculated bond dissociation energies show that the ME bonds become weaker in both series in the order C>Si>Ge>Sn; the bond strength increases in the order Fe<Ru<Os for 1ME, whereas a U-shaped trend Ru<Os<Fe is found for 2ME. The ME bonding analysis suggests that the 16-VE complexes 1ME have two electron-sharing bonds with σ and π symmetry and one donor–acceptor π bond like the carbon complex. Thus, the bonding situation is intermediate between a typical Fischer complex and a Schrock complex. In contrast, the 18-VE complexes 2ME have donor–acceptor bonds, as suggested by the Dewar–Chatt–Duncanson model, with one ME σ donor bond and two ME π-acceptor bonds, which are not degenerate. The shape of the frontier orbitals reveals that the HOMO−2 σ MO and the LUMO and LUMO+1 π* MOs of 1ME are very similar to the frontier orbitals of CO.

Quantum-chemical calculations with DFT (BP86) and ab initio methods [MP2, SCS-MP2, CCSD(T)] have been carried out for the molecules C(PH₃)₂ (1), C(PMe₃)₂ (2), C(PPh₃)₂ (3), C(PPh₃)(CO) (4), C(CO)₂ (5), C(NHC_H)₂ (6), C(NHC_Me)₂ (7) (Me₂N)₂CCC(NMe₂)₂ (8), and NHC (9), where NHC=N-heterocyclic carbene and NHC_Me=N-methyl-substituted NHC. The electronic structure in 1–9 was analyzed with charge- and energy-partitioning methods. The results show that the bonding situations in L₂C compounds 1–8 can be interpreted in terms of donor–acceptor interactions between closed-shell ligands L and a carbon atom which has two lone-pair orbitals LCL. This holds particularly for the carbodiphosphoranes 1–3 where L=PR₃, which therefore are classified as divalent carbon(0) compounds. The NBO analysis suggests that the best Lewis structures for the carbodicarbenes 6 and 7 where L is a NHC ligand have CCC double bonds as in the tetraaminoallene 8. However, the Lewis structures of 6–8, in which two lone-pair orbitals at the central carbon atom are enforced, have only a slightly higher residual density. Visual inspection of the frontier orbitals of the latter species reveals their pronounced lone-pair character, which suggests that even the quasi-linear tetraaminoallene 8 is a “masked” divalent carbon(0) compound. This explains the very shallow bending potential of 8. The same conclusion is drawn for phosphoranylketene 4 and for carbon suboxide (5), which according to the bonding analysis have hidden double-lone-pair character. The AIM analysis and the EDA calculations support the assignment of carbodiphosphoranes as divalent carbon(0) compounds, while NHC 9 is characterized as a divalent carbon(II) compound. The LC(¹D) donor–acceptor bonds are roughly twice as strong as the respective LBH₃ bond.

Quantum chemical calculations at the MP2/TZVPP//BP86/SVP level are reported for the first and second proton affinities (PAs) of divalent carbon-donor molecules. The molecules investigated are imidazol-2-ylidenes (“normal” NHCs) and the tautomeric imidazol-4/5-ylidenes (“abnormal” NHCs). PAs are also calculated for acyclic and cyclic carbodiphosphoranes, carbophosphoranesulfide, unsaturated and saturated carbodicarbenes, tetraaminoallenes and carbon suboxide. The results are discussed in terms of divalent carbon(II) compounds (carbenes) CR₂, which have one lone electron pair at carbon, and carbon(0) compounds CL₂, which have two lone pairs at carbon and two CL donor–acceptor bonds. Divalent C(0) compounds (carbones) not only have very high first PAs, but the second PA is also large and strong enough to isolate doubly protonated C(0) species as salts in a condensed phase. The first PA of divalent carbon(II) compounds (carbenes) are also large. However, they have much smaller second PAs than the divalent carbon(0) compounds. The divalent C(0) character of a compound is not always obvious when the bonding situation in the equilibrium geometry is considered. This is the case, for example, for tetraaminoallenes (TAAs). Protonation of TAAs changes the bonding situation of the central moiety from doubly bonded (R₂N)₂CCC(NR₂)₂ to a donor–acceptor description (R₂N)₂CC(H⁺)_nC(NR₂) [n=1, 2]. The atomic partial charge at the carbon donor atom does not correlate with the PA and the trend of the second PA may be quite different from the trend of the first. The trends of the first and second PA correlates quite well with the eigenvalues of the highest-lying carbon lone-pair orbitals.

The electronic structures and bonding patterns for a new class of radical cations, [H_nE-H-H-EH_n]⁺ (EH_n=element hydride, E=element of Groups 15–18), have been investigated by applying quantum-chemical methods. All structures investigated give rise to symmetric potential energy minimum structures. We envisage clear periodic trends. The HH bond length is shorter for elements toward the bottom of the periodic table of elements, and a short HH bond corresponds to accumulation of electron density in the central HH region. All [H_nE-H-H-EH_n]⁺ of Groups 15–17 are thermodynamically unstable towards loss of either H₂ or H. The barriers for these dissociations are rather low. The Group 18 congeners, except E=Xe, appear to be global minima of the respective potential energy surfaces. The findings are discussed in terms of H₂ bond activation, and a general mechanistic scheme for the standard reduction process 2H⁺ + 2e⁻ H₂ is given. Finally, it is proposed that some of the symmetric radical cations are likely to be observed in mass spectrometric or matrix isolation experiments.

Quantum-chemical calculations with DFT (BP86) and ab initio methods (MP2, SCS-MP2) were carried out for protonated and diprotonated compounds N-H⁺ and N-(H⁺)₂ and for the complexes N-BH₃, N-(BH₃)₂, N-CO₂, N-(CO₂)₂, N-W(CO)₅, N-Ni(CO)₃ and N-Ni(CO)₂ where N=C(PH₃)₂ (1), C(PMe₃)₂ (2), C(PPh₃)₂ (3), C(PPh₃)(CO) (4), C(CO)₂ (5), C(NHC_H)₂ (6), C(NHC_Me)₂ (7) (Me₂N)₂CCC(NMe₂)₂ (8) and NHC (9) (NHC_H=N-heterocyclic carbene, NHC_Me=N-substituted N-heterocyclic carbene). Compounds 1–4 and 6–9 are very strong electron donors, and this is manifested in calculated protonation energies that reach values of up to 300 kcal mol⁻¹ for 7 and in very high bond strengths of the donor–acceptor complexes. The electronic structure of the compounds was analyzed with charge- and energy-partitioning methods. The calculations show that the experimentally known compounds 2–5 and 8 chemically behave like molecules L₂C which have two LC donor–acceptor bonds and a carbon atom with two electron lone pairs. The behavior is not directly obvious when the linear structures of carbon suboxide and tetraaminoallenes are considered. They only come to the fore on reaction with strong electron-pair acceptors. The calculations predict that single and double protonation of 5 and 8 take place at the central carbon atom, where the negative charge increases upon subsequent protonation. The hitherto experimentally unknown carbodicarbenes 6 and 7 are predicted to be even stronger Lewis bases than the carbodiphosphoranes 1–3.