Permutation invariant polynomial neural network approach to fitting potential energy surfaces. III. Molecule-surface interactions

The permutation invariant polynomial-neural network (PIP-NN) method for constructing highly accurate potential energy surfaces (PESs) for gas phase molecules is extended to molecule-surface interaction PESs. The symmetry adaptation in the NN fitting of a PES is achieved by employing as the input symmetry functions that fulfill both the translational symmetry of the surface and permutation symmetry of the molecule. These symmetry functions are low-order PIPs of the primitive symmetry functions containing the surface periodic symmetry. It is stressed that permutationally invariant cross terms are needed to avoid oversymmetrization. The accuracy and efficiency are demonstrated in fitting both a model PES for the H2 + Cu(111) system and density functional theory points for the H2 + Ag(111) system.