Canonical Approach To Generate Multidimensional Potential Energy Surfaces

A new force-based canonical approach for the accurate generation of multidimensional potential energy surfaces is demonstrated. Canonical transformations previously developed for diatomic molecules are used to construct accurate approximations to the 3-dimensional potential energy surface of the water molecule from judiciously chosen (adopting the right coordinate system) 1-dimensional planar slices that are shown to have the same canonical shape as the classical Lennard-Jones potential curve. Spline interpolation is then used to piece together the 1-dimensional canonical potential curves, to obtain the full 3-dimensional potential energy surface of a water molecule with a relative error less than 0.01. This work provides an approach to greatly reduce the computational cost of constructing potential energy surfaces in molecules from ab initio calculations. The canonical transformation techniques developed in this work illuminate a pathway to deepening our understanding of chemical bonding.