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Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion

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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. Physical Review B, 102, 081122® (2020)]. Here we provide an intuitive picture for the effect of nuclear quantum motion on exciton energies and find that zero-point nuclear quantum fluctuations can significantly affect the energies of low-lying excited states. We compute the vibration-induced corrections to exciton energies on a large set of diverse molecules 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 a benchmark set of molecules in the literature [Schreiber et al. Journal of Chemical Physics, 128, 134110 (2008)] 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.

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