A new method for constructing multidimensional potential energy surfaces by a polar coordinate interpolation technique

An interpolation technique was developed for constructing ab initio potential energy surfaces (PES) around the equilibrium structure efficiently and accurately, using polar coordinates coupled with systematic generation of sample points on the hypersphere. Test calculations were performed for H2O and HCHO molecules, and interpolated PES and direct ab initio data were compared for randomly chosen 1000 points. Root mean square errors were found to be 4.8 × 10−5 (2.4 cm−1) for H2O and 1.7 × 10−4 (8.4 cm−1) for HCHO with respect to the maximum energy of 50 000 cm−1. The present approach was found to provide considerably more accurate PES than conventional methods.