Density Functional Computations of Vibrational Circular Dichroism Spectra beyond the Born-Oppenheimer Approximation

Transition-metal complexes provide rich features in vibrational circular dichroism (VCD) spectra, including significant intensity enhancements, and become thus useful in structural and functional studies of molecules. Quite often, however, the vibrational spectral bands are mixed with the electronic ones, and interpretation of such experiments is difficult. In the present study, we elaborate on the theory needed to calculate the VCD intensities beyond the Born-Oppenheimer (BO) approximation. Within a perturbation approach, the coupling between the electronic and vibrational states is estimated using the harmonic approximation and simplified wave functions obtainable from common density functional theory (DFT) computations. Explicit expressions, including Slater determinants and derivatives of molecular orbitals, are given. On a model diamine complex, the implementation is tested and factors affecting spectral intensities and frequencies are investigated. For two larger molecules, the results are in a qualitative agreement with previous experimental data. Typically, the electronic-vibrational interaction Hamiltonian coupling elements are rather small (∼0 to 10 cm^-1), which provides negligible contributions to vibrational frequencies and absorption intensities. However, significant changes in VCD spectra are induced due to the large transition magnetic dipole moment associated with the d-d metal transitions. The possibility to model the spectra beyond the BO limit opens the way to further applications of chiral spectroscopy and transition-metal complexes.