M. Atanasov, T. C. Brunold, H. U. Güdel and C. Daul
Charge-Transfer Spectra and Bonding in Tetrahedral Mn^VI, Cr^V, and V^IV and Mn^VII, Cr^VI, and V^V Oxo Anions
Inorg. Chem. 37, 4589-4602 (1998)                 

Abstract: Density functional theory (DFT) calculations on the tetrahedral Mn^VI, Cr^V, and V^IV(d¹) oxo anions in their ground and lowest excited d-d and O M charge transfer (CT) states are reported and used to assign the electronic absorption spectra by reference to the spectra of the isoelectronic Mn^VII, Cr^VI, and V^V (d⁰) and the Mn^V and Cr^IV (d²) anions. Calculated geometrical shifts along the totally symmetric metal-ligand vibration (a₁) for electronic excitations are in agreement with data deduced from experimental vibronic fine structures, supporting the proposed assignments. Using a CT model including (as different from DFT) configuration interaction (CICT), it is shown that the CT excited states of MnO₄^2- at 17000, 23300, and 28200 cm^–1 are due to d^{2 3}A₂(2e²), ¹E(2e²), and ³A₂(2e²) final states combining with a single hole (L) on the ligand 1t₁ and 4t₂ orbitals, respectively. The higher 10Dq and smaller B values for the d²L(d¹) states compared to those of the d² systems correlate with the shortening of the metal-ligand bond accompanying the removal of electrons from the antibonding d orbitals, leading to an increase in covalency and a change in the ordering of CT states for Cr^V with ³T₂(2e¹5t₂¹)L (10Dq) at a higher energy than ¹E(2e²)L (8B + 2C) as compared to Cr^IV with nearly degenerate ³T₂(2e¹5t₂¹) and ¹E(2e²) terms. This allows one to estimate the energy of the ³A₂(2e²)L ¹E(2e²)L transition from the CT (d²L) spectrum of Cr^V(d¹), which could not be observed for Cr^IV. From a comparison of calculated and experimental oscillator strengths and Huang-Rhys factors (S) for the lowest CT band in the V^V, Cr^VI, and Mn^VII (d⁰) and the V^IV, Cr^V, and Mn^VI (d¹) oxo anions, it is shown that the increase in covalency from left to right in this series is accompanied by a reduction in band intensity and S for the progression in the a₁ vibration. An explanation of this result in terms of ionic contributions to the metal-ligand bond increasing from Mn^VI to Cr^V and V^IV is proposed. Intensities of "d-d" transitions display the opposite trend; increasing covalency leads to stronger mixing between d d and CT excited states and thus an increase in intensity.