Electronic Hamiltonian, wave functions, and energies, and derivative coupling between Born–Oppenheimer states in the vicinity of a conical intersection

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We derive the most general form of the first terms of the power-series expansion of the electronic Hamiltonian in the neighborhood of the conical intersection at the equilateral triangle configuration of the homonuclear triatomic system M3. Previous treatments of this problem had assumed that the derivative coupling between Born–Oppenheimer states could be transformed away by choosing a strictly diabatic basis of electronic states. It has recently been pointed out, however, that this is not possible, in general. Making full use of the symmetry of the problem, and also taking account of the molecular Aharonov–Bohm effect, we obtain explicitly the leading terms of the expansion for electronic energies and wave functions, and of the derivative coupling. In terms of the expansion parameter r, a measure of the distance from the equilateral triangle configuration, the derivative coupling can be transformed away through the first order, but in the second order, nonremovable terms appear which are expected to be important in some problems.