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Strategies for walking on potential energy surfaces using local quadratic approximations
Author(s) -
Simons Jack,
Nichols Jeff
Publication year - 1990
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.560382427
Subject(s) - hessian matrix , maxima and minima , stationary point , quadratic equation , directional derivative , sequence (biology) , potential energy , energy (signal processing) , point (geometry) , saddle point , key (lock) , local coordinates , second derivative , taylor series , physics , mathematics , mathematical analysis , computer science , geometry , classical mechanics , chemistry , quantum mechanics , biochemistry , computer security
An algorithm for locating stationary points corresponding to local minima and transition states on potential energy surfaces is further analyzed. This method utilizes local gradient and Hessian (i.e., first and second energy derivative) information to generate a series of “steps” that are followed to the desired stationary point. By designing the step sequence to move energetically downhill in all coordinates, local minima can be found. By stepping uphill along one local eigenmode of the Hessian while minimizing the energy along all other modes, one locates transition states. Key elements of this development are more efficient parameterization of the step vector in terms of quantities that permit the direction (i.e., uphill or downhill), and length of the step to be carefully controlled, and implementation of the ability to explore “side channels” as attractive options occur.