Computational strategies for the optimization of equilibrium geometries and transition‐state structures at the semiempirical level

Abstract

AbstractSeveral improvements have been made to the gradient algorithms commonly used to optimize equilibrium and transition‐state geometries at the semiempirical level. A gradient algorithm derived from a combination of a variable metric method (Davidon–Fletcher–Powell/Broyden–Fletcher–Goldfarb–Shanno) and Pulay's direct inversion in the iterative subspace method for geometry optimization (GDIIS) is compared with the variable metric method combined with an accurate linear search algorithm. The latter method is used routinely in the standard semiempirical program packages, MNDO, MOPAC, and AMPAC. The combined variable metric and GDIIS algorithm is also compared with GDIIS which uses a static metric. The performance of these algorithms is examined for a wide range of systems with respect to both choice of coordinate system (for cyclic molecules) and guess for the initial Hessian. The results show that the GDIIS method is up to ca. 40% more efficient than the variable metric combined with accurate line search algorithm: however, the exact savings vary depending on the coordinate system and initial Hessian. For noncyclic systems, variable‐metric GDIIS is usually equal or superior to static‐metric GDIIS, and consistently performs ca. 30% more efficiently than the variable metric combined with accurate line search algorithm. For the optimization of cyclic molecules, an improved estimate of the initial Hessian has increased the efficiency by at least a factor of two. Greater efficiencies (usually >40%) are also obtained when static‐metric GDIIS is used to refine the geometry after the initial application of a transition‐state search based on the variable metric combined with line search algorithm. On the basis of these results, we recommend several changes to the algorithms as currently implemented in the standard semiempirical program packages.