A Broyden—Fletcher—Goldfarb—Shanno optimization procedure for molecular geometries

Abstract Most quantum-chemical calculations for geometries evaluate first derivatives of the energy with respect to nuclear positions analytically and then use update procedures to build up information on the second derivatives as they step along the potential energy surface toward a minimum (stable geometry) or simple saddle point (transition state). We describe here the use of the Broyden—Fletcher—Goldfarb—Shanno (BFGS) quasi-Newton update used in conjunction with a partial line search. We have found BFGS superior to the other update formulae we have examined. In a particular, it is superior to the Murtagh—Sargent (MS) scheme that is commonly used in geometry determinations. The advantage of the BFGS update over the MS scheme becomes especially dramatic for large molecular systems.