The approach to calculate improved, two-state, adiabatic-todiabatic transformation angles (also known as mixing angles), presented before (see Das et al., J Chem Phys 2010, 133, 084107), was used here while studying the F þ H 2 system. However, this study is characterized by two new features: (a) it is the first of its kind in which is studied the interplay between Renner-Teller (RT) and Jahn-Teller (JT) nonadiabatic coupling terms (NACT); (b) it is the first of its kind in which is reported the effect of an upper singular RT-NACT on a lower two-state (JT) mixing angle. The fact that the upper NACT is singular (it is shown to be a quasi-Dirac d-function) enables a semi-analytical solution for this perturbed mixing angle. The present treatment, performed for the F þ H 2 system, revealed the existence of a novel parameter, g, the Jahn-Renner coupling parameter (JRCP), which yields, in an unambiguous way, the right intensity of the RT coupling (as resembled, in this case, by the quasi-Dirac d-function) responsible for the fact that the final end-of-the contour angle (identified with the Berry phase) is properly quantized. This study implies that the numerical value of this parameter is a pure number (independent of the molecular system): g ¼ 2 ffiffi ffi 2 p =p (¼ 0.9003) and that there is a good possibility that this value is a novel characteristic molecular constant for a certain class of tri-atomic systems.
TheoryThe three-state model Our goal is to calculate well-behaved diabatic PESs for a triatomic system (in this case F þ H 2 ), and to do that we consider a plane that contains three atoms (A, B, and C) where a point in configuration space is described in terms of three (Cartesian) coordinates (r, R, and h). Here, r is the distance between two atoms (usually the atoms that form the diatomic molecule, BC), R is a distance between the third atom, A, and [a] A.