Vincenzo Tschinke

A theoretical study of metal—ligand bond strengths (ML: L = OH, OCH3, SH, NH2, PH2, CH3, SiH3, CN and H) in the early transition metal systems Cl3ML (M = Ti, Zr and Hf) and late transition metal systems LCo(CO)4

Abstract The strength of metal—ligand bonds (ML: L = OH, OCH 3 , SH, NH 2 , PH 2 , CN, CH 3 , SiH 3 and H) in the early transition metal systems Cl 3 ML (M = Ti, Zr and Hf) and late transition metal systems LCo(CO) 4 have been calculated by a non-local density functional method. For the early transition metal systems the TiL bond in Cl 3 TiL was found to be quite polar, in particular for OCH 3 , OH and NH 2 . The order of the D (TiL) bond strength was calculated to be OH(453) > OCH 3 (427) > CN(410) > NH 2 (365) > SH(283) > CH 3 (268) > H(251) > SiH 3 (211) > PH 2 (191), where the numbers in parentheses are the bond energies in kJ mol −1 . The corresponding bond energies of the Cl 3 ZrL systems were calculated to be between 25 kJ mol −1 and 50 kJ mol −1 higher. An additional increase in the ML bond energy of 10 kJ mol −1 to 20 kJ mol −1 was calculated in going from M = Zr to M = Hf. The ML bonds in the late transition metal systems LCo(CO) 4 were calculated to be weaker and less polar than the corresponding bonds in Cl 3 TiL. The order for the bond strengths in LCo(CO) 4 , was calculated to be CN(304) > OH(232) > H(230) > SiH 3 (212) > SH(169) > CH 3 (160) > NH 2 (146) > PH 2 (145). The quite different order of stability for the ML bond strength in early and late transition metal systems was analysed in terms of electronic and steric factors.

On the different representations of the hole‐correlation functions in the Hartree–Fock and the Hartree–Fock–Slater methods and their influence on bond energy calculations

We have investigated the change in shape of the Hartree–Fock Fermi‐hole correlation function upon bond formation. Our analysis indicates that the molecular Fermi‐hole correlation function is on the whole considerably more diffuse than its atomic counterpart. It is shown that this imbalance gives rise to HF bond energies which in many instances are much smaller than the experimental values. The imbalance is related to the so‐called near degeneracy error, a well known feature of the HF method. It can be removed by introducing a limited configuration interaction calculation which ensures a proper dissociation limit as the bond is broken. The Fermi‐hole correlation function adopted by the Hartree–Fock–Slater method does not introduce the same imbalance between molecular and atomic hole functions. The calculated bond energies are, as a consequence, much larger and in better agreement with experiment. It is suggested that the Hartree–Fock–Slater method in part introduces correlation by avoiding the near degener...

A theoretical study on the strength of multiple metal-metal bonds in binuclear complexes and transition-metal dimers by a non-local density functional method

Abstract The strength of multiple metal-metal bonds in the metal dimers M 2 (M = Cr, Mo or W) and binuclear complexes M 2 (OH) 6 (M = Cr, Mo or W), M 2 Cl 4 (PH 3 ) 4 M = V, Cr, Mn, Nb, Mo, Tc, Ta, W or Re) has been studied by a non-local density functional theory. The method employed here provides metal-metal bond energies [ D (M-M)] in good accord with experiments for Cr 2 and Mo 2 , and predicts that W 2 of the three dimers M 2 (M = Cr, Mo or W) has the strongest metal-metal bond with D (W-W) = 426 kJ mol −1 and R (W-W) = 2.03 A. Among the binuclear complexes studied here we find the 3 d elements to form relatively weak metal-metal bonds (40–100 kJ mol −1 ), compared to the 4 d and 5 d elements with bonding energies ranging from 250 to 450 kJ mol −1 . The metal-metal bond for a homologous series is calculated to be up to 100 kJ mol −1 stronger for the 5 d complex, than for the 4 d complex. An energy decomposition of D (M-M) revealed that the σ-bond is somewhat stronger than each of the π-bonds, and one order of magnitude stronger than the δ-bond. For the same transition metal we find D (M-M) to be larger for M 2 (PH 3 ) 4 Cl 4 (M = Cr, Mo or W) than for M 2 (OH) 6 (M = Cr, Mo or W), and attribute this to a stronger π-interaction in the former series. While many of the findings here are in agreement with previous HFS studies, the order of stability D (3 d -3 d ) « D (4 d -4 d ) D (5 d -5 d ) differs from the order D (3 d -3 d ) « D (5 d -5 d ) D (4 d -4 d ) obtained by the HFS method, and the present method provides in general more modest values for D (M-M) than the HFS scheme.

Gradient corrections to the Hartree-Fock-Slater exchange and their influence on bond energy calculations

SummaryDensity functional approximations based on a local representation of the exchange energy tend to over-estimate bond energies. We show that the tendency is due to the incorrect form of the Fermi hole correlation function adopted by these methods. This function is adequate at the maxima of the radial density in isolated atoms, at the corresponding maxima of atoms in molecules, and at the saddle points of the molecular density in the bonding regions. However, the Fermi hole correlation function yields too low exchange energy contributions in absolute terms from the tails of the core shells and the valence density. On bond formation electron density is transferred from the tails of the atomic core shells to the density maximum of the valence shell. At the same time, parts of the atomic valence tails are transformed into the bonding region with a saddle point. In both cases the contributions from the tail regions to the exchange energy are under-estimated in the local approximation, with the result that the calculated bond energies are too large. Similar considerations can be used to explain why local exchange density functional methods under-estimate ionization potentials.The addition of non-local gradient correction terms to the local exchange functionals greatly improves calculated bond energies and ionization potentials by rectifying the qualitatively incorrect behaviour of the local Fermi hole correlation function in the tails of the core shells and the valence density. A detailed graphic analysis is provided of the contributions from non-local corrections to the calculated bond energies.

Density functional theory as a practical tool in organometallic energetics and dynamics

The dearth of reliable experimental data on bond dissociation energies is felt throughout the field of organometallic chemistry. Accurate theoretical studies should afford a much needed supplement to the sparse available experimental data on metal-ligand bond energies, necessary for a rational approach to the synthesis of new transition metal complexes.

An Evaluation of Local Electron Correlation Corrections and Non-Local Exchange Corrections to the Hartree-Fock-Slater Method from Calculations on Bond Energies and Electronic Spectra of Molecular Systems

We provide here a numerical evaluation of the Local-Spin-Density method1 as well as the semi-empirical density functional due to Becke2 in comparison with the well known Hartree-Fock-Slater (HFS) method3, based on calculated ionization potentials, bond energies and excitation energies of molecular systems. All calculations were with minor modifications carried out using the HFS-program due to Baerends et al.4

Quantitative Results and Qualitative Analysis by the Hartree-Fock-Slater Transition State Method

The challenge from transition metal chemistry has been met over the last twenty years with increasing success by theoretical chemists using a variety of methods ranging from calculations on the back of an envelope to computations on mainframe computers. The qualitative “back of the envelope” type of calculations have clearly had a profound influence not only on the field of transition metal chemistry as a whole, but also on practitioners of more extensive calculation schemes by forcing them to provide a qualitative analysis of the-(at best) quantitative results, and we present here a scheme, the generalized transition state method1, by which quantitative (or at least extensive) calculations can be subjected to a qualitative analysis.