Multiresolution potential energy surfaces for vibrational state calculations

A compact and robust many-mode expansion of potential energy surfaces (PES) is presented for anharmonic vibrations of polyatomic molecules, where the individual many-mode terms are approximated with various different resolutions, i.e., electronic structure methods, basis sets, and functional forms. As functional forms, the following three representations have been explored: numerical values on a grid, cubic spline interpolation, and a Taylor expansion. A useful index is proposed which rapidly identifies important many-mode terms that warrant a high resolution. Applications to water and formaldehyde demonstrate that the present scheme can increase the efficiency of the PES computation by a factor of up to 11 with the errors in anharmonic vibrational frequencies being no worse than ~ 10cm⁻¹.