Oscillator strength of symmetry-forbidden d-d absorption of octahedral transition metal complex: theoretical evaluation

The theoretical evaluation of the oscillator strength of a symmetry-forbidden d-d transition is not easy even nowadays. A new approximate method is proposed here and applied to octahedral complexes [Co(NH(3))(6)](3+) and [Rh(NH(3))(6)](3+) as an example. Our method incorporates the effects of geometry distortion induced by molecular vibration and the thermal distribution of such distorted geometries but does not need the Herzberg-Teller approximation. The calculated oscillator strengths of [Co(NH(3))(6)](3+) agree well with the experimental values in both (1)A(1g) → (1)T(1g) and (1)A(1g) → (1)T(2g) transitions. In the Rh analogue, though the calculated oscillator strengths are somewhat smaller than the experimental values, computational results reproduce well the experimental trends that the oscillator strengths of [Rh(NH(3))(6)](3+) are much larger than those of the Co analogue and the oscillator strength of the (1)A(1g) → (1)T(1g) transition is larger than that of the (1)A(1g) → (1)T(2g) transition. It is clearly shown that the oscillator strength is not negligibly small even at 0 K because the distorted geometry (or the uncertainty in geometry) by zero-point vibration contributes to the oscillator strength at 0 K. These results are discussed in terms of frequency of molecular vibration, extent of distortion induced by molecular vibration, and charge-transfer character involved in the d-d transition. The computational results clearly show that our method is useful in evaluating and discussing the oscillator strength of symmetry-forbidden d-d absorption of transition metal complex.