Solvent polarizability modulated the electronic state of conjugated long-chain polyene molecules by DFT

•The differences of Infrared and Raman activity of β-carotene vibration modes.•Discussed the vibration modes that could not be distinguished in experiment.•Combined the frontier molecular orbital energy with the sum-over-state method to qualitatively analyze the polarizability.•The mechanism of polarizability field modulated the electronic state. As a typical organic conjugated long-chain polyene molecule, the study of β-carotene’s molecular structure in local environments is of great significance. Quantum chemical calculations of β-carotene in different polarization fields were carried out with density functional theory (DFT). The lowest energy structure of the ground state had a centrosymmetric structure, and the bond length of β-carotene was between 1.084 and 1.549 Å. The influence of the polarization field on the electronic state of β-carotene mainly manifested in the Raman intensity, frontier molecular orbital energy, dipole moment, and polarizability. With the decrease of the solvent polarizability, the Raman intensity, dipole moment, and polarizability of β-carotene decreased. Conversely, the highest occupied molecular orbital (HOMO) – the lowest unoccupied molecular orbital (LUMO) gap increased. The difference between the infrared (IR) activity and Raman activity of β-carotene was studied by vibration analysis, and the Raman peaks that could not be distinguished during experiments were decomposed and assigned.