A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schrodinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.

A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies.

The magnetic circular dichroism (MCD) properties of a spin-allowed transition from an orbitally nondegenerate ground state manifold A to an orbitally nondegenerate excited state manifold J in the presence of spin−orbit coupling (SOC) are derived for any S ≥ 1/2. Three physically distinct mechanisms are identified that lead to MCD intensity and depend on SOC between excited states which leads to a sum rule and SOC between the ground state and other excited states that leads to deviations from the sum rule. The model is valid for any symmetry of the magnetic coupling tensors and arbitrary transition polarizations. The S = 1/2 case is analytically solved, and the determination of linear polarizations from MCD saturation magnetization data is discussed. For all mechanisms the MCD intensity is proportional to the spin-expectation values of the ground state sublevels which are conveniently generated from a spin-Hamiltonian (SH). For Kramers systems with large zero-field splittings (ZFSs) this allows the contrib...

MCD C-Term Signs, Saturation Behavior, and Determination of Band Polarizations in Randomly Oriented Systems with Spin S ≥ 1/2. Applications to S = 1/2 and S = 5/2

Die elektronenarmen Ubergangsmetalle V, Nb, Ta, Mo, W und Re bilden in den hochsten Oxidationsstufen tetraederformige Thioanionen mit bemerkenswerten Eigenschaften. Die farbenprachtigen Thiometallate werden durch Festkorperreaktion oder in Losung aus den Oxometallaten erhalten. Aus Thiometallaten lassen sich durch neuartige intramolekulare Redox-Prozesse bei gleichzeitiger Kondensation Poly(thiometallate) mit gemischten Valenzen gewinnen. Die Metall-Schwefel-Bindung reagiert sowohl nucleophil als auch elektrophil; bei der Mo–S-Bindung ist diese Eigenschaft von biochemischem Interesse. Als Komplexliganden ermoglichen die Thiometallate die Erzeugung von Multi-Metall-Komplexen. Daruber hinaus zeichnen sie sich durch vielseitiges Koordinationsverhalten sowie einzigartige elektronische Eigenschaften aus; wegen der ausgepragten Elektronendelokalisation existieren Thiometallato-Komplexe mit unterschiedlicher Elektronenpopulation. MoS42- hat auserdem Bedeutung fur bioanorganische Fragen, z. B. das Nitrogenase-Problem und den Cu-Mo-Antagonismus.

Thioanionen der Übergangsmetalle: Eigenschaften und Bedeutung für Komplexchemie und Bioanorganische Chemie

The electronic structures of MnO−4, MnO2−4, MnO3−4, CrO2−4, CrO3−4, VO3−4, RuO4, RuO−4, RuO2−4, TcO−4 and MoO2−4 have been investigated using the Hartree-Fock-Slater Discrete Variational Method. The calculated ordering of the valence orbitals of all the comlexes is: t1, 4t2, 3a1, 1c, 3t2, with t1 the orbital of highest energy. The calculated single transition energies are in good agreement with experimental values and indicate the uniform assignment: t1 → 2e(v1), 4t2 → 2e(v2). t1 → 5t2(v3), and 4t2 → 5t2(v4). A/D values, calculated from the theory of magnetic circular dichroism (MDC) also support this assignment. Population analyses reveal that all complexes, whether d0, d1 or d2, have d-orbital populations close to those of the corresponding M2+ ions in which two electrons have been removed from the (n + 1)s orbital of M. This is also true of the excited states, such as t1 → 2e and 4t2 → 2e, where a transfer of charge from the ligands to the metal has previously been assumed. It is shown that, instead of a transfer of charge from ligands to metal, electronic excitation consists of a rearrangement of electron density both at the ligands and at the metal.

The electronic structures of tetrahedral oxo-complexes. The nature of the “charge transfer” transitions

A model is developed for the green-yellow emitting centre in PbMoO4 and PbWO4 in terms of an excited state which can be visualized as Pb3+-XO3−4, i.e. an electron localized at XO and an electron-hole at one of the surrounding Pb2+ ions. The different levels of the triplet excited state arise from splitting due to the small tetragonal distortion and spin-orbit interaction. Moreover, hyperfine interaction induces an additional splitting if the lead ion of the centre has a nuclear spin (207Pb, I = ½). In this way the four-level scheme, obtained empirically can be qualitatively understood. Hence, the two components of the emission are connected with the presence of two different kinds of lead isotopes: 207Pb with I = ½ and 204Pb, 206Pb, and 208Pb, with I = 0. The blue emission of PbWO4 can be ascribed to a charge transfer transition within the tungstate anion, as in the alkaline-earth scheelites.

Luminescence of lead molybdate and lead tungstate. II. discussion

Absorption and magnetic circular dichroism spectra have been measured for the tetrahedral d° ions MoS4 2-, MoO4 2-, WS4 2-, ReS4 -, VS4 3-, VO4 3- and OsO4 in the visible and ultra-violet spectral range. Comparison of the experimentally obtained MCD parameters with regard to their relative signs leads to the conclusion that probably the first two allowed longest wavelength electronic transitions of all these species have the same assignment (i.e., t 1 →2e and 3t 2 →2e, which seems likely on energetic grounds). An estimation of the MCD parameters by using eigenvectors from recently published molecular orbital treatments gave contradictory results.

E. Diemann

Papers

Magnetic circular dichroism and absorption spectra of d° tetrahedral oxyanions and thioanions: MoS42-, MoO42-, WS42-, ReS4-, VS43-, VO43- and OsO4