3RD-ORDER METHODS FOR MOLECULAR-GEOMETRY OPTIMIZATIONS

Third-order optimization methods that require the evaluation of the gradient and initial estimates for the second and third derivatives are described. Update algorithms for the Hessian and the third-derivative tensor are outlined. The direct inversion in the iterative subspace scheme is extended to third order and is combined with the third-order update procedures. For geometry optimization, an approximate third-derivative tensor is constructed from simple empirical formulas. Examples of application to Hartree-Fock geometry optimization problems are given.