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 significantlyinfluence various molecular properties and therefore need to be considered in the-oretical predictions, especially for systems containing hydrogen atoms. The con-strained nuclear-electronic orbital (CNEO) framework is a recently developed theo-retical method that can accurately and efficiently account for these effects. In thiswork, we derive and implement analytic dipole derivatives within CNEO densityfunctional theory, enabling the evaluation of infrared (IR) intensities of molecularvibrations under double harmonic approximation. By comparing the results withthose obtained from conventional density functional theory calculations, we find thatnuclear quantum effects have considerable impacts on infrared intensities.