Modeling the Vibronic Spectra of Transition Metal Complexes: The Ligand-Field Spectrum of [PtCl₄]²⁻

A framework for calculating the intensity distribution and vibrational fine structure in the polarized ligand-field spectrum of transition metal complexes using the Herzberg−Teller approach is introduced and used to model the spectrum of the [PtCl₄]²⁻ ion. The model uses geometries, vibrational frequencies, and transition moments generated using density functional calculations on the ground and excited states, which arise from spin-allowed reorganization of the d electrons. The model predicts the whole spectral trace, including the polarization, the difference in the frequency of the electronic origin, the band maximum and the vertical transition energy, and the temperature dependence of the band intensities and the frequencies of the band maxima. Excitation to the ¹A_2g state is accompanied by a vibrational progression in the breathing mode of the excited state, as observed experimentally. Excitation to both the ¹B_1g and ¹E_g states is accompanied by a loss of planarity and extended vibrational progressions in two modes, and the resulting spectra are inherently of low resolution.