Ab initio classical trajectories on the Born-Oppenheimer surface: Updatingmethods for Hessian-based integrators

For the integration of the classical equations of motion in the Born-Oppenh eimer approach, each time the energy and gradient of the potential energy s urface are needed, a properly converged wave function is calculated. If Hes sians (second derivatives) can be calculated, significantly larger steps ca n be taken in the numerical integration of the equations of motion without loss of accuracy. Even larger steps can be taken with a Hessian-based predi ctor-corrector algorithm. Since updated Hessians are used successfully in q uasi-Newton methods for geometry optimization, it should be possible to imp rove the performance of trajectory calculations using updated Hessians. The Murtagh-Sargent (MS) update, the Powell-symmetric-Broyden (PSB) update and Bofill's update (a weighted combination of MS and PSB) were tested, and Bo fill's update was found to be the best. Slightly smaller step sizes were ne eded with Hessian updating to maintain good conservation of the energy, but this was more than compensated by the reduction in total computational cos t. An overall factor of 3 in speed-up was obtained for trajectories of syst ems containing 4 to 6 heavy atoms computed at the HF/3-21G level. (C) 1999 American Institute of Physics. [S0021-9606(99)30443-8].