Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: application to the ππ∗∕nπ∗ internal conversion in thymine.

We face with the general problem of defining a reduced number of effective collective coordinates to describe accurately the short-time nonadiabatic dynamics of large semirigid systems, amenable to a description in terms of coupled harmonic potential energy surfaces. We present a numeric iterative protocol to define a hierarchical representation of the Hamiltonian taking into account both linear and quadratic intra- and inter-state couplings (QVC, quadratic vibronic coupling model), thus generalizing the method introduced recently in the literature [E. Gindensperger, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 126, 034106 (2007)] for the linear vibronic coupling (LVC) model. This improvement allows to take into account the effect of harmonic frequency changes and Duschinsky mixings among the different electronic states, providing a route to upgrade the models for nonadiabatic harmonic systems to those nowadays routinely used for the simulation of vibronic spectra of adiabatic systems (negligible nonadiabatic couplings). We apply our method to the study of ππ∗ → nπ∗ internal conversion in thymine, analysing the differences in LVC and QVC predictions both for the absorption spectrum and the dynamics of electronic populations.