Use of Block Hessians for the Optimization of Molecular Geometries

We test a strategy for using block Hessians for transition state geometry optimizations. The block Hessian matrix is constructed by mixing a small critical block of the accurate Hessian for key atoms involved in bond breaking and forming with large noncritical blocks of the low-level Hessian. The method is tested for transition state optimizations at the MC-QCISD/3 level for five reactive systems:  H + CH3OH, O + CH4, OH + CH4, NH2 + CH4, and H + C2H5OH. When the entire low-level Hessian was used, significant oscillations were observed during the optimizations for the first four systems, whereas the transition state for the last system was optimized to a wrong structure. The block Hessian strategy efficiently removed these pathological effects of using low-level Hessians, and therefore it provides a highly reliable method for optimizing transition state structures with reduced computational cost. The method is very general, and it is especially well suited for optimizing transition state structures and equilibrium structures of large systems at very high levels of theory.