Analytic evaluation of dipole derivatives in constrained nuclear–electronic orbital framework: Impact of nuclear quantum effects on infrared intensities

Nuclear quantum effects, such as zero-point energy and tunneling, can significantly influence various molecular properties and, therefore, need to be considered in theoretical predictions, especially for systems containing hydrogen atoms. The constrained nuclear-electronic orbital (CNEO) framework is a recently developed theoretical method that can accurately and efficiently account for these effects. In this work, we derive and implement analytic dipole derivatives within CNEO density functional theory, enabling the evaluation of infrared intensities of molecular vibrations under the double harmonic approximation. By comparing the results with those obtained from conventional density functional theory calculations, we find that nuclear quantum effects have a considerable impact on infrared intensities.