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

Abstract

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.

Low-lying excited states of natural carotenoids viewed by ab initio methods

“…We mainly followed the protocol which has earlier been proposed for unsubstituted polyenes by the same authors 40 . DMRGSCF calculations were carried out in the active space including the entire π-system to avoid an additional bias in its selection.…”

“…Another approach is to replace commonly used perturbation theories such as complete active space second-order perturbation theory (CASPT2) 41 or N-electron valence state second-order perturbation theory (NEVPT2) 6,31,42 by driven similarity renormalization group (DSRG) perturbation theory (DSRG-MRPT2). 40 While DSRG-MRPT2 itself is not capable of completely removing a "poor" reference problem, it produces excitation energies which are closer to the experimental data than the NEVPT2 ones. Moreover, it has a much better computational scaling with respect to the number of active orbitals, therefore, in principle, it could pave the way to "double" active space calculations with post-SCF MRPT2 treatment for long polyenes.…”

“…0.8 eV for octatetraene 19 ). While relaxed geometries of the ground state (1A − g ) and the 1B + u state can be optimized relatively easy by means of (TD)-DFT and these geometries (and excitation energies calculated on them) are in excellent agreement with DMRG self-consistent field (DMRGSCF) results, 40 geometries of the "covalent" states have to be obtained from MCSCF (or DMRGSCF) optimization. This optimization requires numerical gradients from stateaveraged DMRGSCF and, despite the sufficient simplification due to the differentiation by the state weight, 43 remains a very time-consuming process for natural polyenes.…”

“…Density matrix renormalization group (DMRG) [33][34][35][36][37] is capable of dealing with such large active spaces and thus is extremely well-suited for treatment of static correlation in linear polyenes. 5,6,[38][39][40] However, further post-SCF perturbative treatment remains a significant computational bottleneck.…”

“…Nevertheless, the main goal of this paper is to explore the applicability of DSRG-MRPT2 to natural carotenoids in "normal" active spaces, thus expanding the previous work 40 on linear unsubstituted polyenes.…”