Incorporating reduced axis system embedding into ab initio tunnelling-rotation Hamiltonians with curvilinear vibrational M?ller-Plesset perturbation theory

Large-amplitude vibrational motion influences the rovibrational structure of molecules that tunnel between multiple wells. Reaction path (RP) Hamiltonians, and curvilinear coordinates more generally, are useful for modelling pure vibrational motion in these systems and provide a practical framework for calculating accurate ab initio anharmonic vibrational energies and tunnelling splittings with perturbation theory. These computational tools also offer the means to address rotation-vibration coupling associated with large-amplitude motion in rotating molecules. In this paper, we incorporate the reduced axis system (RAS) frame embedding with RP Hamiltonians and second-order vibrational Moller-Plesset perturbation theory (VMP2). Because the RP-RAS Hamiltonian eliminates rotation-vibration momentum coupling everywhere along a one-dimensional reaction path, it is well suited for rovibrational VMP2 methods, the convergence of which relies critically on approximate vibration-vibration and vibration-rotation separability. The accuracy of this combined RP-RAS-VMP2 scheme is demonstrated by comparisons with numerically exact variational calculations and VMP2 parameters based on traditional Eckart embeddings for reduced-dimension models of torsional tunnelling in hydrogen peroxide and inversion tunnelling in cyclopropyl radical. The favourable computational scaling of VMP2 makes it a promising strategy for calculating accurate tunnelling-rotation parameters for medium-sized and larger molecules in full dimensionality.