Constrained nuclear–electronic orbital second-order Møller–Plesset perturbation theory

A multicomponent second-order Møller-Plesset perturbation theory (MP2) method is derived and implemented within the constrained nuclear-electronic orbital (CNEO) framework from a multicomponent generalization of the Hylleraas functional. The CNEO-MP2 method includes electronic-nuclear and nuclear correlation in the calculation of vibrationally averaged molecular properties. Nuclear quantum effects such as vibrational averaging, isotopic effects, and zero-point energy can be captured in a single calculation or geometry optimization with CNEO-MP2, eliminating the need to perform costly subsequent calculations to determine higher order force constants as required with many existing methods used to determine vibrational effects upon molecular properties. The CNEO-MP2 method is benchmarked on a test set of diatomic and small polyatomic molecules and ions. Herein, we present internuclear distances, bond angles, potential energy surfaces, and vibrational frequencies calculated with the CNEO-MP2 method to demonstrate that it correctly captures the effects of nuclear vibrational motion upon molecular properties.