Permutationally invariant polynomial potential energy surfaces for tropolone and H and D atom tunneling dynamics

We report permutationally invariant polynomial (PIP) fits to energies and gradients for 15-atom tropolone. These include standard, augmented, and fragmented PIP bases. Approximately, 6600 energies and their associated gradients are obtained from direct-dynamics calculations using DFT/B3LYP/6-31+G(d) supplemented by grid calculations spanning an energy range up to roughly 35 000 cm^-1. Three fragmentation schemes are investigated with respect to efficiency and fit precision. In addition, several fits are done with reduced weight for gradient data relative to energies. These do result in more precision for the H-transfer barrier height. The properties of the fits such as stationary points, harmonic frequencies, and the barrier to H-atom transfer are reported and compared to direct calculations. A previous 1D model is used to obtain the tunneling splitting for the ground vibrational state and qualitative predictions for excited vibrational states. This model is applied to numerous fits with different barrier heights and then used to extrapolate the H and D atom tunneling splittings to values at the CCSD(T)-F12 barrier. The extrapolated values are 2.3 and 0.14 cm^-1, respectively for H and D. These are about a factor of two larger than experiment, but within the expected level of agreement with experiment for the 1D method used and the level of the electronic structure theory.