Excited state corrections to looped adiabatic-to-diabatic transformation phases

The difference between the full revolution adiabatic-to-diabatic transformation angle, or the loop-integrated nonadiabatic coupling term, and the Berry phase is calculated perturbationally, when one or more excited states are coupled into a ground doublet. The difference is in general non-zero, but has no definite sign. A molecule distorted from a Renner-Teller situation serves as an illustration.