Ground-state multiplicities and d—d excitations of transition-metal complexes by effective Hamiltonian method

Magnetic and optical properties of transition-metal complexes are governed by the ground state and the low-energy excitation spectrum of the d-shell of the central transition metal ion. These spectra are successfully fit to the crystal field theory. We present here an account of the effective Hamiltonian method recently developed to calculate the ground state and the excitations of the d-shells of transition-metal complexes and report the results of its application to some complexes of particular interest. © 1996 John Wiley & Sons, Inc.     

Extended spin-boson model for nonadiabatic hydrogen tunneling in the condensed phase

A nonadiabatic rate expression for hydrogen tunneling reactions in the condensed phase is derived for a model system described by a modified spin-boson Hamiltonian with a tunneling matrix element exponentially dependent on the hydrogen donor-acceptor distance. In this model, the two-level system representing the localized hydrogen vibrational states is linearly coupled to the donor-acceptor vibrational mode and the harmonic bath. The Hamiltonian also includes bilinear coupling between the donor-acceptor mode and the bath oscillators. This coupling provides a mechanism for energy exchange between the two-level system and the bath through the donor-acceptor mode, thereby facilitating convergence of the time integral of the probability flux correlation function for the case of weak coupling between the two-level system and the bath. The dependence of the rate constant on the model parameters and the temperature is analyzed in various regimes. Anomalous behavior of the rate constant is observed in the weak solvation regime for model systems that lack an effective mechanism for energy exchange between the two-level system and the bath. This theoretical formulation is applicable to a wide range of chemical and biological processes, including neutral hydrogen transfer reactions with small solvent reorganization energies.     

Electronic structure and optical spectra of transition metal complexes by the effective Hamiltonian method

Summary A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF ₆ ^4– (M=Mn, Fe, Co, Ni) anions, Mn(FH) ₆ ²⁺ cation, CoCl ₆ ^4– anion, and a tetrahedral CoCl ₄ ^2– anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.     

Electrical transport and magnetic ordering in R 2Ti3Ge4 (R=Dy, Ho and Er) compounds

New R ₂Ti₃Ge₄ (R=Dy, Ho and Er) intermetallic compounds have been synthesized and characterized by X-ray diffraction and low temperature ac magnetic susceptibility, electrical resistivity and thermoelectric power measurements were carried out. The compounds crystallize in the parent, Sm₅Ge₄-type orthorhombic structure (space group Pnma) and lanthanide contraction is observed as one moves along the rare-earth series. The changeover from paramagnetic to antiferromagnetic phase happens at low temperatures and the ordering temperature scales with the de Gennes factor. The electrical resistivity is metallic with a negative curvature above 100 K. Thermopower displays a weak maximum at temperatures less than 50 K signifying the possible phonon and magnon drag effects.     

Crystal-field splittings and optical spectra of transition-metal mixed-ligand complexes by effective Hamiltonian method

Many of the important properties of transition-metal complexes depend on the low-energy excitation spectrum formed by d-electrons of the central transition-metal atom. The spectra of this type are usually fit to the well-known crystal field theory or to the angular overlap model. The result of the fitting is a set of parameters which are considered as characteristics of the electronic structure of the complex such as strength of the ligand field or types and extent of metal-ligand bonding. We present here a short account of the effective Hamiltonian method recently developed to calculate the splitting of the d-levels by the ligands and the resulting d-d spectra of transition-metal complexes together with some results of its application to the mixed-ligand complexes with the general formula ML₄Z₂, where M = V, Co, Ni; L = H₂O, NH₃, Py; and Z = H₂O, NCS−,C −l. Particular attention is paid to the V(H₂O)₄Cl₂ and Co(H₂O)₄Cl₂ compounds. The former seems to have tetragonal structure, whereas for the latter, our method predicts a spatially degenerate ground state for the tetragonal arrangement of the ligands. That must lead to the Jahn-Teller distortion, which is actually observed. © 1996 John Wiley & Sons, Inc.     

Elastic properties of the Ta–V system: bcc Ta0.33V0.67 and C15 TaV2

Resonant ultrasound spectroscopy was used to measure the elastic constants of bcc Ta_0.33V_0.67 over the temperature range 3.5–300?K; the results were compared to earlier measurements on C15 TaV₂. The temperature dependence of the polycrystalline shear modulus is completely different in the two phases; that of the bcc phase decreases with temperature whereas that of the C15 phases increases in an anomalous fashion. This difference is consistent with a model involving doubly-degenerate levels at the X point of the Brillouin zone in the C15 phase with the Fermi level lying near the doubly degenerate level. This model accounted for the unusual behaviour of the C15 phase. Debye temperatures were determined from the ultrasonic measurements: 295?K for the C15 phase and 315?K for the bcc phase.     

Transition metal complexes with open d-shell in semiempirical context. Application to analysis of Mössbauer data on spin–active iron(II) compounds

With use of cumulants of two-electron density matrices semiempirical methods are analyzed from a point of view of their suitability to describe qualitative features of electronic correlation important for calculation of electronic structure of the transition metal complexes (TMC). It is shown that traditional semiempirical methods relying upon the Hartree–Fock–Roothaan form of the trial wave function suffer from a structural deficiency not allowing them to distinguish the energies of the atomic multiplets of the TMCs' d-shells. On the other hand, the effective Hamiltonian of the crystal field (EHCF) previously proposed by the authors is shown to be suitable for further parameterization and has been successfully applied for calculations on polyatomic TMCs. Here we describe in details its recent modifications performed in relation to the SINDO/1 parameterization scheme and present the results of the calculations on spin-active Fe(II) complexes with nitrogen-containing polydentate ligands in relation with interpretation of the Mössbauer measurements performed on these complexes.     

Buffer-assisted proton-coupled electron transfer in a model rhenium-tyrosine complex

The mechanism for tyrosyl radical generation in the [Re(P-Y)(phen)(CO)3]PF6 complex is investigated with a multistate continuum theory for proton-coupled electron transfer (PCET) reactions. Both water and the phosphate buffer are considered as potential proton acceptors. The calculations indicate that the model in which the proton acceptor is the phosphate buffer species HPO(4)2- can successfully reproduce the experimentally observed pH dependence of the overall rate and H/D kinetic isotope effect, whereas the model in which the proton acceptor is water is not physically reasonable for this system. The phosphate buffer species HPO4(2-) is favored over water as the proton acceptor in part because the proton donor-acceptor distance is approximately 0.2 A smaller for the phosphate acceptor due to its negative charge. The physical quantities impacting the overall rate constant, including the reorganization energies, reaction free energies, activation free energies, and vibronic couplings for the various pairs of reactant/product vibronic states, are analyzed for both hydrogen and deuterium transfer. The dominant contribution to the rate arises from nonadiabatic transitions between the ground reactant vibronic state and the third product vibronic state for hydrogen transfer and the fourth product vibronic state for deuterium transfer. These contributions dominate over contributions from lower product states because of the larger vibronic coupling, which arises from the greater overlap between the reactant and product vibrational wave functions. These calculations provide insight into the fundamental mechanism of tyrosyl radical generation, which plays an important role in a wide range of biologically important processes.