Conical intersections electronic Hamiltonian

Electronic Hamiltonian, conical intersections, spin-orbit interaction, 559 Electronic states ... 

Molecular aspects of geometric phase are associated with conical intersections between electronic energy surfaces, W(Q), where Q denotes the set of say k vibrational coordinates. In the simplest two-state case, the W Q) are eigen-surfaces of the nuclear coordinate dependent Hermitian electronic Hamiltonian... 

Yarkoni [108] developed a computational method based on a perturbative approach [109,110], He showed that in the near vicinity of a conical intersection, the Hamiltonian operator may be written as the sum a nonperturbed Hamiltonian Hq and a linear perturbative temr. The expansion is made around a nuclear configuration Q, at which an intersection between two electronic wave functions takes place. The task is to find out under what conditions there can be a crossing at a neighboring nuclear configuration Qy. The diagonal Hamiltonian matrix elements at Qy may be written as... 

We follow Thompson and Mead [13] to discuss the behavior of the electronic Hamiltonian, potential energy, and derivative coupling between adiabatic states in the vicinity of the D31, conical intersection. Let A be an operator that transforms only the nuclear coordinates, and A be one that acts on the electronic degrees of freedom alone. Clearly, the electronic Hamiltonian satisfies... 

In this section, we describe an approach which, in addition to the implicit inclusion of the GP, takes into account all the non-adiabatic couplings between the two conically intersecting electronic surfaces. In this case, within the adiabatic representation, the nuclear Hamiltonian has the following form ... 

C. A. Mead, Electronic Hamiltonian, wave functions, and energies, and derivative coupling between Born-Oppenheimer states in the vicinity of a conical intersection, J. Chem. Phys. 78 807 (1983). 

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