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The transition metal hydride cations, TMH⁺ (TM = first transition metal row, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn), have been studied using valence bond (VB) theory to elucidate the bonding in these systems through VB concepts. Although the bonds appear extremely covalent by virtue of charge distribution, this appearance conceals key contributions to bonding, such as covalent-ionic resonance energy (RECS) and relaxation energy of the inactive electrons (ΔErelax(inactive)). The RECS term is seen to increase from ScH⁺ toward ZnH⁺, becoming significant in the late TMH⁺ molecules. The ΔErelax(inactive) term, which accounts for the nonbonding 3dⁿ electrons and the 3s²3p⁶ core electrons, is always significant. Furthermore, for all of the bonds from CrH⁺ to CuH⁺, the relaxation term makes a major contribution to the bond energy. It appears therefore, that in these TM−H⁺ bonds, the spin pairing of the bonding electrons can act as a trigger for the nonbonding and adjacent core electrons to relax their Pauli repulsion and thereby strengthen the binding of TM⁺ and H. As a result of the general weakness of TM bonds, the relaxation is expected to frequently be an important bonding contribution. The major function of the inactive and core electrons shows that the traditional role of “covalency” must be reassessed in a systematic manner.

REKS-type (Filatov, M.; Shaik, S. Chem. Phys. Lett. 1999, 304, 429) density functional calculations were carried out for the lowest energy singlet and triplet states of tetramethyleneethane (TME) diradical. The calculations indicate that the ground state of TME in the gas phase is the singlet state, whereas the triplet state should be metastable at low temperatures. The triplet state metastability derives from the energetic preference for the triplet state at the optimal triplet molecular geometry and from the extremely small (<0.05 cm^-1) spin−orbit coupling between the triplet and ground singlet states. REKS calculations predict that, in the vibrational spectra of the two states of TME, the modes corresponding to symmetric scissoring vibrations should have nearly the same frequencies of 357 cm^-1, in accord with the experimental observation of two modes of the same frequency of 335 cm^-1 in the vibrational structure of the photoelectron spectrum of the [TME]^- anion.

Density functional calculations using the B3LYP, BP86, and FT97 functionals with an extended basis set are employed to investigate the mechanisms of H2 oxidation by FeO⁺. Three mechanisms are considered, addition−elimination, “rebound”, and oxene-insertion. The oxene-insertion is characterized by high barriers and only second-order saddle points. The addition−elimination and “rebound” mechanisms are competitive and both exhibit two-state-reactivity (TSR) with a crossing between sextet and quartet states. TSR provides a low-energy path for bond activation and is predicted to be the dominant pathway at room temperature. Both TSR mechanisms are concerted:  the addition−elimination mechanism involves 2+2 addition in the bond activation step, while the rebound mechanism is effectively concerted involving the H-abstraction followed by a barrierless “rebound” of the H-radical. At elevated temperature (above a threshold of ³/2RT = 0.5 eV), the stepwise “rebound” mechanism starts to dominate and produces FeOH⁺ + H^• via a single-state-reactivity (SSR) on the sextet surface. Kinetic isotope effect calculations have been performed, and their comparison with the experimental data¹⁰ seems to be characteristic of TSR. Thus, the measured isotope effects probe the extent of H···H (D···D) cleavage in a mechanism whereby bond activation and spin-inversion occur in a concerted manner. Some predictions have been made regarding the factors that affect the mechanistic competition.

Crystallographic constants for the title compound are as follows: Mr= 384.5 + 204.3, triclinic, PĪ, a= 6.878 (2), b= 10.309 (4), c= 11.159 (7) Å, α =109.94 (4), β = 100.91 (4), γ = 105.64 (3)°, Z= 1, V= 680.8 Å3, Dc= 1.46 g cm−3, Dm= 1.40 g cm−3(flotation, aqueous KI), λ(MoKα) = 0.71069 Å, μ = 3.27 cm−1, F(000) = 304, RF= 0.085 for 1948 data with |F0| > 2.5 σ(F0). The complex crystallizes in mixed stacks of alternating donors and acceptors with a maximum of intrastack overlap and a minimum of interstack interactions. The degree of charge transfer is shown by a number of criteria to be essentially zero, in stark contrast to the complex of TTF with unsubstituted TCNQ. Comparison is made with the relatively few other complexes of derivatives of TTF and TCNQ which form mixed stack complexes.

A study of the spin−orbit coupling (SOC) mechanisms which couple the triplet ππ* state (T1) to the singlet ground state (S0) in ethylene is carried out at a variety of computational levels and basis sets, using the full Breit−Pauli (BP) SOC Hamiltonian, the one-electron mean-field (MF) operator, and the approximate one-electron operator based on an effective nuclear charge, Z*. The basis set and wave functions requirements needed for good quality SOC calculations are elucidated by studying the SOC interaction using single- and multireference CI as well as MCSCF wavefunctions, with basis sets ranging from the minimal STO-3G all the way to an extended one with quadruple ζ and polarization quality. Two archetype distortion modes of ethylene were considered:  a twist mode which changes the symmetry from D2h to D2 and then to D2d and pyramidalization modes which change the ethylene symmetry to C2v (syn-pyramidalization) or C2h (anti-pyramidalization), as well as Cs (i.e., a mono-pyramidalization distortion). It is found that both the twist and syn-pyramidalization distortions of ethylene promote a nonzero SOC interaction, which involves an interplay between one-center and two-center SOC terms. In the twist distortion, the interplay is strong because the one-center terms arise from a residual incomplete cancelation of the two on-site interactions. In contrast, in the syn-pyramidalization distortion the interplay is weak, because the one-center terms add up. Consequently, the syn-pyramidalization promotes SOC matrix elements which exceed 6 cm^-1, while the twist mode has a weaker SOC on the order of 2 cm^-1. Zero SOC is obtained for distortion which involve either a 90° twist, or an anti-pyramidalization. The monopyramidalization distortion leads to SOC which is ca. 50% of that which is generated by the syn-pyramidalization. A qualitative analysis based on symmetry and electronic structure enables to understand these trends. A simple physical model, which enables us to carry out the vectorial summation of SOC in a pictorial manner, is constructed and used to explain the trends in the twist and syn-pyramidalization modes.