Diabatic Seam Space Sampling for Hydrogen Tunneling Systems with Nuclear–Electronic Orbital Theory

Abstract Hydrogen tunneling is central to many chemical and biological processes. Herein, we introduce the vibronic-SHAKE (V-SHAKE) approach to comprehensively sample energy-conserving molecular configurations enabling hydrogen tunneling. A constrained form of nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) dynamics, where the tunneling hydrogen nucleus is quantized, is used to sample geometries in the diabatic seam space corresponding to the intersection of the reactant and product NEO-DFT diabatic vibronic surfaces. V-SHAKE is applied to hydrogen and deuterium tunneling in 4-cyanobutanolate and (Z)-4-hydroxybut-3-en-2-one. The vibronic coupling is found to vary significantly in the diabatic seam space, mainly due to changes in the donor–acceptor distance. The reaction coordinate and gradient of the vibronic coupling at the minimum energy crossing point are nearly orthogonal and are dominated by motions stabilizing the product relative to the reactant or decreasing the donor–acceptor distance, respectively. V-SHAKE provides fundamental insights and qualitative support for assumptions underlying rate theories.