Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born-Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrodinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 (2)A(') and 2 (2)A(') electronic states of H-3 obtained by solving a three-dimensional Poisson equation over the entire domain boolean OR of internal nuclear configuration space Q of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in boolean OR, the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over boolean OR of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrodinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full boolean OR domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure.