The Adiabatic-to-Diabatic Mixing Angle for the Inelastic Collision B($^{2}$P$_{1/2})$ + H$_{2}(j, n) \quad \leftrightarrow $ B($^{2}$P$_{3/2})$ + H$_{2}(j$', $n$')

The Born-Oppenheimer approximation breaks down when two adiabatic potential energy surfaces become sufficiently close. Under these conditions, the nuclear dynamics are governed by a set of coupled diabatic surfaces. Derivative coupling matrix elements can be used to compute the transformation from the adiabatic to the diabatic potential energy surfaces. A line integral along various contours through the vector field defined by the derivative coupling matrix elements is used to compute the adiabatic-to-diabatic mixing angle. In particular, we investigate the path independence of this coupling angle for the inelastic collision B($^{2}$P$_{1/2})$ + H$_{2}(j) \quad \leftrightarrow $ B($^{2}$P$_{3/2})$ + H$_{2}(j$') collision (1). (1) D.E. Weeks, T.A. Niday, and S.H. Yang, J. Chem. Phys, 125, 164301 (2006).