The paper for deriving the titled formalism has been accepted by J. Chem. Theory Comput. This is the link of the paper. It is first-authored by Dr. Ekadashi Pradhan. Congratulations, Eka! Here are the excerpts of the reviewers' comments:

" ... this article in an important and lasting contribution to the literature on the JT effect ..."

"With a lot of recent theoretical and experimental spectroscopic interest in the topic, I feel this paper is extremely timely and a great advancement for the field."