On the adiabatic to diabatic states transformation in the presence of a conical intersection: A most diabatic basis from the solution to a Poisson's equation. I

We report the first determination of a "most" diabatic basis for a triatomic molecule based exclusively on ab initio derivative couplings that takes careful account of the limitations imposed by the nonremovable part of those couplings. Baer [Chem. Phys. Lett. 35, 112 (1975)] showed that an orthogonal transformation from adiabatic states to diabatic states cannot remove all the derivative coupling unless the curl of the derivative coupling vanishes. Subsequently, Mead and Truhlar [J. Chem. Phys. 77, 6090 (1982)] observed that this curl does not, in general, vanish so that some of the derivative coupling is nonremovable. This observation and the historical lack of efficient algorithms for the evaluation of the derivative coupling led to a variety of methods for determining approximate diabatic bases that avoid computation of the derivative couplings. These methods neglect an indeterminate portion of the derivative coupling. Mead and Truhlar also observed that near an avoided crossing of two states the rotation angle to a most diabatic basis, i.e., the basis in which the removable part of the derivative coupling has been transformed away, could be obtained from the solution of a Poisson's equation requiring only knowledge of the derivative couplings. Here a generalization of this result to the case of a conical intersection is used to determine a most diabatic basis for a section of the 1¹A^′ and 2¹A^′ potential energy surfaces of HeH₂ that includes the minimum energy point on the seam of conical intersection.