Symmetry-adapted polynomial basis for global potential energy surfaces-applications to XY4 molecules

The nuclear potential energy surfaces (PES) used in quantum chemistry inherit the symmetry of the whole molecular system, and are therefore invariant under the action of the nuclear permutation-translation-rotation-inversion group. One can take advantage of this property, both theoretically and numerically. The present article is the prolongation of the works of Schmelzer and Murrell and of Collins and Parsons on the subject. It presents a simplified technique to obtain symmetry-adapted polynomial basis for global PES, together with algorithmic recipes that make the problem computationally tractable. The method is illustrated in detail on XY4 type of molecules for which a full description of the algebra of invariant polynomials under the full symmetry group of the molecule is given.