Premium
Finding transition states when second‐order Jahn–Teller instability occurs
Author(s) -
Simons Jack
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560480306
Subject(s) - hessian matrix , curvature , instability , jahn–teller effect , eigenvalues and eigenvectors , symmetry (geometry) , physics , symmetry breaking , distortion (music) , second derivative , geometry , quantum mechanics , mathematics , mathematical analysis , ion , amplifier , optoelectronics , cmos
When second‐order Jahn–Teller couplings become strong along “streambeds” on potential energy surfaces, instability reflected in negative curvature along a symmetry‐lowering distortion coordinate can take place. The point where such negative curvature sets in is usually not a transition state because the gradient of the potential is usually large there. In this paper, it is demonstrated how to use the local energy, local gradient, local Hessian, and knowledge of how quickly the curvature for the symmetry‐breaking mode evolves along the streambed (i.e., the derivative of this curvature) to predict how far to move in the symmetry‐breaking mode in search of the desired transition state. It is shown that the Hessian matrix evaluated at the symmetry‐broken geometry suggested by this analysis has only one negative eigenvalue. Because this analysis is based on a local approximation to the potential, its predictions are, of course, approximate. As such, they only “suggest” the proper direction and magnitude that one should “step” to move toward a transition state. © 1993 John Wiley & Sons, Inc.