Broyden-Fletcher-Goldfarb-Shanno procedure

Any quasi-Newton method for the minimization of E can be applied. We use the Broyden-Fletcher-Goldfarb-Shanno [24] procedure. 

J. D. Head and M. C. Zerner, Chon. Phys. h-ll., 122, 264 (1985). A Broyden-Fletcher-Goldfarb-Shanno Optimiz.arion Procedure for Molecular Geometries. 

There are three Hessian matrix elements to be solved for, but only two equations to be satisfied, so there is not a unique solution for the and several recipes have been proposed to find improved that satisfy (15.73). One commonly used recipe is the Broyden, Fletcher, Goldfarb, Shanno (BFGS) procedure Leach, p. 229). 

J. Cioslowski and M. Kertesz, QCPE Bull., 7, 159 (1987). Davidon-Fletcher-Powell vs. Broyden-Fletcher-Goldfarb-Shanno Optimization Procedures in Semiempirical and Solid-State MNDO Calculations. 

D. K. Agrafiotis and H. S. Rzepa, /. Chem. Res. (S), 100 (1988). Evaluation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Variable Metric Method in Geometry Optimisation Using Semi-Empirical SCF-MO Procedures. 

By utilizing forces on FES, we can identify the SS and TS stmctures in solution with full optimization with respect to all coordinates of the solute molecules. For example, if we adopt the quasi-Newton method with the following Broyden-Fletcher-Goldfarb-Shanno (BFGS) procedure [26-29] for stractural optimization scheme in the FEG method, the i -F l)-th reactant structure is taken as,... 

The current best correction matrix Q is denoted by the acronym BFGS, coming from the four authors who independently proposed it Broyden, Fletcher, Goldfarb, and Shanno. It is the complementary formulation of the DFP. The procedure for getting it is reported here below. 

The BFGS (Broyden [42], Fletcher [124], Goldfarb [145], Shanno [379]) algorithm is an update procedure for the Hessian matrix that is widely used in iterative optimization [125]. The simpler Rm update takes the form... 

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