A simultaneous eigen valued expression to model the three coupled electronic states with triply and doubly degenerate seams together II

Abstract

AbstractIn part I a novel and yet complicated mathematical model to predict the presence of triply degenerate seam was presented and was illustrated its efficiency using some physical models. Here in this part, a discussion on the the model's ability to account for the triple degeneracy found in the potential energy surface is presented in addition to a discussion on the derivatives and its discontinuities and infiniteness at a specific point. Analytical evaluation of derivatives is possible in principle but in practice, numerical approximation to the exact derivatives is the only way out to solve this problem. Two examples (one being physical and the other being chemically realistic) are taken to the probe the above mentioned properties of the proposed simultaneous model. Integration of model function gives finite values everywhere irrespective of the point of degeneracy being present or not. This is just opposite to derivative evaluation.