Full and fragmented permutationally invariant polynomial potential energy surfaces for trans and cis N-methyl...

We report full and fragmented potential energy surfaces (PESs) for N-methyl acetamide that contain the cis and trans isomers and the saddle points separating them. The full PES uses Permutationally Invariant Polynomials (PIPs) in reduced symmetry which describe the three-fold symmetry of each methyl rotor. A more efficient PES is an extension of the fragmented PIP approach we reported recently. In this approach, the set of Morse variables is partitioned and the fragmented PIP basis is the union of the PIP basis for each set of variables. This approach is general and can be used with neural network fits. The fits are done using roughly 250 000 electronic energies and gradients obtained from direct dynamics, using the B3LYP/cc-pVDZ level of theory. The full PIP basis in 66 Morse variables, with a maximum polynomial order of 3, contains 8040 linear coefficients. The fragmented PIP basis, also with a maximum polynomial order of 3, contains 6121 coefficients. The root-mean-square errors of both PESs are roughly 100 cm^-1 for energies and 15 cm^-1/bohr per atom for gradients, for energies up to roughly 45 000 cm^-1, relative to the trans minimum. Energies and normal mode frequencies of the cis and trans isomers for the full and fragmented PESs agree well with direct calculations. The energies of the two saddle points separating these minima are precisely given by both PESs. Diffusion Monte Carlo calculations of the zero-point energies of the two isomers are also reported.