Premium
Topology of conical intersections and Jahn‐Teller crossing: Application to the standard model for XY 4 molecules in T 2 ground states
Author(s) -
Liotard D.,
Roche M.
Publication year - 1987
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540080613
Subject(s) - ground state , morse theory , hamiltonian (control theory) , classification of discontinuities , adiabatic process , jahn–teller effect , mathematics , smoothing , differentiable function , topology (electrical circuits) , physics , quantum mechanics , mathematical analysis , combinatorics , mathematical optimization , ion , statistics
The topological understanding of a potential function requires a knowledge of its critical points and indices. These concepts are mathematically meaningless if the potential function is not twice continuously differentiable. When conical intersections or Jahn–Teller crossings are encountered, the adiabatic potential, defined as the lowest eigenvalue of a Hamiltonian, can be smoothed everywhere. Moreover, the limiting properties of the smoothed critical points for vanishing values of a smoothing parameter lead to a unambiguous definition of a pseudo critical point of the limiting potential. Therefore, Morse theory is readily applicable to the ground state potential function in spite of the first order discontinuities. The regularization procedure is formally and numerically applied to the simplest Hamiltonian matrix of order 3 describing the Jahn–Teller effect of XY 4 molecules in the T 2 ground states. Various kinds of pseudo‐critical points are encountered and are shown to satisfy the Morse theory.