Perturbative approach to potential surface inversion for bound and half-scattering problems

A recently proposed inverse perturbation with singular value decomposition (IPSVD) method to correct potential energy surfaces (PES) of bound molecular systems is generalized in two significant ways. Firstly, in the current generalization, any given primitive PES of a bound system can in principle serve as a zeroth order (starting) PES which can be corrected to approach the desired PES by successive use of the perturbative inversion method. Secondly, the perturbative approach is further generalized and the mathematical equations are derived for correcting dissociative PES of half-scattering problems by using experimentally measured product state distribution of the fragments or spectrum as input variables. The specific mathematical treatments for the above two generalizations are explicitly given and discussed in the paper. An example is shown by application to HCN bound state potential energy surface.