Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion: a mode-resolved picture and the effect of molecular size

TL;DR

This study demonstrates that including nuclear quantum motion in excited state calculations significantly improves their accuracy, reveals size-dependent effects, and allows mode-resolved analysis of vibrational contributions.

Contribution

It introduces a systematic first-principles methodology to quantify nuclear quantum effects on excited states, highlighting size dependence and mode-specific contributions.

Findings

Zero-point motion improves agreement with experimental excitation energies.

Red-shifts can reach up to 1.36 eV due to nuclear quantum effects.

Smaller molecules exhibit larger red-shifts, with specific vibrational modes dominating the effect.

Abstract

The energies of molecular excited states arise as solutions to the electronic Schr\"{o}dinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a red-shift of excited state energies. However, it is thus far unclear whether incorporating nuclear quantum motion in molecular excited state calculations leads to a systematic improvement of their predictive accuracy, making further investigation necessary. Here we present such an investigation by employing two first-principles methods for capturing the effect of quantum fluctuations on excited state energies, which we apply to the Thiel set of organic molecules. We show that accounting for zero-point motion leads to much improved agreement with experiment, compared to `static' calculations which only account for electronic effects, and the magnitude of the red-shift can become as large as 1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited state energies largely depends on the molecular size, with smaller molecules exhibiting larger red-shifts. Our methodology also makes it possible to analyze the contribution of individual vibrational normal modes to the red-shift of excited state energies, and in several molecules we identify a limited number of modes dominating this effect. Overall, our study provides a foundation for systematically quantifying the shift of excited state energies due to nuclear quantum motion, and for understanding this effect at a microscopic level.