Energies and derivative couplings in the vicinity of a conical intersection - 3. The 'most' diabatic basis

It is shown that in the immediate vicinity of an arbitrary conical intersection at R-x, all the derivative coupling, except for the small part due to the finiteness of the basis sets, is removable by the orthogonal transformation generated by the angle alpha(rho,theta,z) = lambda(theta)/2 + rho m(rho),(theta)/q(theta) + zm(z),(theta)/q(theta), where rho, theta,z are cylindrical polar coordinates centred at R-x,. Expressions for lambda(theta), q(theta),m(rho),(theta) and m(z)(theta) are given. The implications of this result for numerical studies that (i) determine the 'most' diabatic basis using Poisson's equation and (ii) assess approximate diabatization schemes are discussed.