Tests Demonstrate the Accuracy of the Q_im-Reaction Path Hamiltonian for Double-Well Tunneling Splittings for H-Atom...

Reduced dimensional models of tunneling have been a focus of theoretical chemistry since the birth of this field. The simplest model is the "reaction path" that connects a saddle point to the associated minima describing the reactant and the product. The widely used intrinsic reaction coordinate is a curved path that, perforce, contains a complex kinetic energy operator. In this paper, we examine a rectilinear reaction path, denoted the Q_im-path, and the associated 1d Hamiltonian. In the simplest version, the generally small Coriolis coupling terms are neglected. This Hamiltonian was introduced and shown to produce tunneling splittings of H- and D-transfer of malonaldehyde with good accuracy by Wang and Bowman in 2008. Here, we present further tests of this approach for tunneling splittings of H- and D-transfer for a number of molecules with symmetric double wells. These are tropolone, acetylacetone, malonaldehyde, and protonated oxalate anion, for which high-quality machine-learned potentials have been reported. Tests make use of the available benchmark results, including those from diffusion Monte Carlo calculations and, for tropolone, ring polymer instanton results. Extensions of the method for asymmetric double wells due to asymmetric isotope substitution and potential asymmetry, as well as to more than one degree of freedom, are reported.