Excited state geometry calculations and the resonance Raman spectrum of hexamethylpyrromethene

Abstract

Abstract A Newton-Raphson procedure was developed for the geometry optimisation of excited states by time-dependent density functional theory (TD-DFT). The algorithm is formulated in internal coordinates and is based on finite differences to approximate the first- and second-order energy derivatives. Using this approach, the geometry of the first excited singlet state of hexamethylpyrromethene (HMPM) was partially optimised with respect to 21 selected internal coordinates at the TD-DFT level with the B3LYP functional and the 6-31G* basis set. The excited state displacements with respect to the ground state geometry were used to calculate the resonance Raman (RR) intensities of the normal modes by means of the transform theory. In general, the predicted enhancement pattern, illustrated by the comparison with the calculated non-resonant Raman spectrum, is in satisfactory agreement with the experimental RR and Raman spectra that were measured at 413 and 1064 nm excitation, respectively. However, relative RR intensities sensitively depend on subtle changes of the excited state geometry as documented by the RR spectra calculated at different steps of the geometry optimisation, which, due to the close proximity of the S1 and S2 potential energy surfaces in HMPM, only yields an approximate energy minimum structure. This specific property of HMPM is most likely the origin for the deviations between the calculated and experimental RR intensities noted for some of the normal modes. Nevertheless, TD-DFT provides a much better reproduction of the experimental data than the Hartree–Fock single-configuration interaction approximation.