Effective spectral densities for system-environment dynamics at conical intersections : S2-S1 conical intersection in pyrazine

A recently developed effective-mode representation is employed to characterize the influence of a multi-dimensional environment on the S2–S1 conical intersection in pyrazine, taken as a paradigm case of high-dimensional dynamics at a conical intersection. We consider a simplified model by which four modes are strongly coupled to the electronic subsystem while a number of weakly coupled tuning modes, inducing energy gap fluctuations, are sampled from a spectral density. The latter is approximated by a series of simplified spectral densities which can be cast into a continued-fraction form, as previously demonstrated in Hughes et al. (K.H. Hughes, C.D. Christ, I. Burghardt, J. Chem. Phys. 131 (2009) 124108). In the time domain, the hierarchy of spectral densities translates to truncated effective-mode chains with a Markovian or quasi-Markovian (Rubin type) closure. A sequential deconvolution procedure is employed to generate this chain representation. The implications for the ultrafast dynamics and its representation in terms of reduced-dimensional models are discussed.