Toward an Accurate Ab Initio Description of Low-Lying Singlet Excited States of Polyenes

The low-lying excited states of carotenoids play a crucial role in many important biophysical processes such as photosynthesis. Most of these excited states are strongly correlated, which makes them both challenging for a qualitative ab initio description and an engaging model system for trying out emerging multireference methods. Among these methods, driven similarity renormalization group (DSRG) and its perturbative version (DSRG-MRPT2) are especially attractive in terms of both accuracy and moderate numerical complexity. In this paper, we applied density matrix renormalization group (DMRG) followed by DSRG-MRPT2 for the calculation of vertical and adiabatic excitation energies into the 2A_g^-, 1B_u^-, and 1B_u⁺ electronic states of polyenes containing from 8 to 13 conjugating double bonds acting as a model for natural carotenoids. It was shown that the DSRG flow parameter should be adjusted to ensure both the energy convergence with respect to it and the agreement with the experimental data. With the increased flow parameter, the proposed combination of methods provides a reasonable agreement with the experiment. The deviations of the adiabatic excitation energies are less than 1000 cm^-1 for the 2A_g^- and less than 3000 cm^-1 for the excited states of the B_u symmetry, which in terms of accuracy significantly outperforms the N-electron valence state perturbation theory. At the same time, DSRG-MRPT2 is shown to be robust with respect to variation of quality of the DMRG reference wave function such as the orbital optimization or the number of electronic states in the averaging.