Knowledge about excited states of carotenoids is essential for understanding photophysical processes underlying photosynthesis. However, due to the presence of a large number of optically dark states, experimental study of the excited-state manifold is limited to a significant extent. In this paper, we apply high-level ab initio quantum chemical methods to study the low-lying excited states of polyenes containing from 8 to 13 conjugated double bonds, which serve as a model for natural carotenoids. Vertical and adiabatic excitation energies from the ground 1Ag – state to the excited 2Ag –, 1Bu +, and 1Bu – states were evaluated by means of density matrix renormalization group (DMRG) with NEVPT2 perturbative correction. The energies of all excited states are highly sensitive to nuclear geometry, especially the 2Ag – state. Thus, the 2Ag – and 1Bu + states interchange their relative positions upon geometry relaxation, while the vertical excitation energy to the 2Ag – state is rather high. At the same time, the 1Bu – state energy is shown to be higher than other studied excited states at any geometry. With relaxed geometries of the excited states, absorption and transient absorption spectra were calculated within the Franck–Condon approximation bridging the gap between experimental spectroscopic data and computational results.

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.

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Low-lying excited states of carotenoids (the optically dark 2A g − and bright 1B u + ) are deeply involved in energy transfer processes in photosynthetic antennas, such as light harvesting and non-photochemical quenching. Though any ab initio modeling of these phenomena has to rely on precise energies of the carotenoid electronic states, the accurate evaluation of these states remains a challenging problem due to their different natures. The paper aims to study the accuracy of the excitation energies of the low-lying excited states of certain open-and closed-chain carotenoids obtained by a state-of-the-art multireference approach for electronic structure calculation. Here, density matrix renormalization group SCF (DMRGSCF) and a perturbative approach based on driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2) were used to treat the static and dynamic correlation, respectively. Nuclear geometries of the electronic states were optimized with DFT-based approaches. It is demonstrated that spin-flip TD-DFT can replace multiconfigurational methods for the geometry optimization of the 2A g − state but not for the calculation of the excitation energy. Adiabatic excitation energies to the 1B u + state were shown to be within a margin of 1000 cm −1 with an appropriate flow parameter value. Adiabatic excitation energies to the 2A g − state for the open-chain carotenoids lie within a range of experimental values (taking into account the broad range of experimental estimates); for the closed-chain ones, the error does not exceed 2000 cm −1 . Ab initio stationary (1A g − → 1B u + ) and transient (2A g − → 1B u +) absorption spectra were modeled for violaxanthin and lycopene, and these spectra showed good agreement with the experimental ones both in terms of the vibronic structure and the transition energies.