Systematic Improvement of Molecular Excited State Calculations by Inclusion of Nuclear Quantum Motion

Many theoretical studies of excited state molecules aim to provide accurate solutions to the electronic Schrödinger equation in order to produce energies that can be compared to experiment. However, nuclear quantum motion, which is usually ignored, can also affect exciton energies, as we showed in a recent study [Alvertis et al. Phys. Rev. B, 102, 081122(R) (2020)]. Here we provide an intuitive picture for the effect of nuclear quantum motion on exciton energies and find that zero-point fluctuations can significantly affect the energies of excited states. We compute vibration-induced corrections to exciton energies by combining TDDFT with Monte Carlo sampling techniques based on finite difference methods. We show that incorporating nuclear zero-point energy effects can lead to corrections of up to 1.1 eV on computed exciton energies. We compare our results with the benchmark on the well-known Thiel molecular set, finding that the correction to excited state energies by incorporating nuclear quantum motion, and without any adjustable parameters, leads to vastly improved agreement with experimental results, while maintaining a low computational cost. We therefore establish nuclear quantum motion as a critical factor towards the accurate calculation of exciton energies.