However, as detailed in Refs. 25 and 26, all the required quantities can be reconstructed from the characteristic polynomial (CP) coefficients of the potential matrix. The fitting of PESs in regions of degeneracy via CP coefficients was first developed by Opalka and Domcke and has seen a renewal of interest. Let V (R) be the n×n adiabatic potential matrix for an n-state system, with on-diagonal elements V ii (R) corresponding to the adiabatic PESs E i (R). To separate out the parts that give rise to discontinuous derivatives at points of intersection, the potential matrix is decomposed into an average energy and splitting term: