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.

A quantum mechanical study of the interplay between the bright ππ*(S(π)) and the dark nπ*(S(n)) excited states of thymine in the gas phase is reported. TD-PBE0 calculations indicate that within a relevant region of the S(π) surface, connecting the Franck-Condon point with the planar and non-planar S(π) plateau, S(π) and S(n) are almost isoenergetic and that a S(π)→S(n) population transfer is therefore likely. This latter process has been studied by two complementary quantum dynamical approaches, a three-dimensional anharmonic (quartic) model, and a full-dimensional harmonic linear vibronic coupling model. Although providing slightly different quantitative indications, both approaches predict a very fast and effective S(π)→S(n) population transfer: already at 50 fs the S(n) state is significantly populated (20-40%) and this population persists or even increases on a longer time scale.

We present mixed quantum-classical simulation of the internal conversion between the lowest energy pipi* (S(La)) and npi* (S(n)) excited electronic states in adenine in the gas phase, adopting a quadratic vibronic model (QVC), parametrized with the help of PBE0 density functional calculations. Our approach is based on a hierarchical representation of the QVC Hamiltonian and a subsequent treatment of the most relevant coordinates at accurate time-dependent quantum level and of the other 'bath' modes at classical level. We predict an ultrafast transfer (-30 fs) of approximately 75% of the initial population excited on S(La) to S(n). Within an adiabatic picture, on the same timescale the wave packet concentrates almost completely on the lowest S1 state, where however it shows a very broad distribution with different characteristics (due to the different 'diabatic' character). It is shown that the proposed methodology offers a practicable route to describe the quantum dynamics of internal conversion processes in large semi-rigid systems.