I forgot to write about a publication which appeared at the end of the last year. It is a logical continuation of the previous works of Sven Karsten on the semi-classical description of vibronic spectra. That is when both electronic and nuclear motion of a molecule is excited.
This time Sven has elaborated on the imaginary time-shifted correlation functions and applied a Matsubara approximation to a ring polymer which is residing partly on the excited potential energy surface and partly on the ground state one, as has been described in previous publication. This approximation filters out high-frequency vibrations of the ring polymer, leaving only the low-frequency “smooth” distortions. The idea is that the high-frequency counterpart is anyway cut by the Boltzmann distribution at the finite temperature. However, strictly speaking, one cannot call this approximation just Matsubara as there is an abrupt change in the ring due to different potentials it is evolving according to. That is why we call it Matsubara-like.
I hope that this approach upon the proper generalization to more complicated molecules will be a step towards reliable simulation of vibrionic spectra with semi-classical methods.