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Optimization of equilibrium geometries and transition structures
Author(s) -
Schlegel H. Bernhard
Publication year - 1982
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.540030212
Subject(s) - quartic function , eigenvalues and eigenvectors , conjugate gradient method , energy minimization , ab initio , inverse , derivative (finance) , second derivative , matrix (chemical analysis) , computation , polynomial , mathematics , minification , algorithm , computational chemistry , mathematical optimization , physics , geometry , mathematical analysis , chemistry , quantum mechanics , pure mathematics , chromatography , financial economics , economics
A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initio MO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one‐dimensional minimization using a quartic polynomial is carried out, followed by an n ‐dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initio SCF – MO calculations.