Abstract
Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function. Hessian-based predictor-corrector integrators are a widely used approach for calculating the trajectories of moving atoms in direct dynamics simulations. We employ a monodromy matrix to propose a tool for evaluating the accuracy of integrators in the trajectory calculation. We choose a general velocity Verlet as a different object. We also simulate molecular with hydrogen(CO
2
) and molecular with hydrogen (H
2
O) motions. Comparing the eigenvalues of monodromy matrix, many simulations show that Hessian-based predictor-corrector integrators perform well for Hessian updates and non-Hessian updates. Hessian-based predictor-corrector integrator with Hessian update has a strong performance in the H
2
O simulations. Hessian-based predictor-corrector integrator with Hessian update has a strong performance when the integrating step of the velocity Verlet approach is tripled for the predicting step. In the CO
2
simulations, a strong performance occurs when the integrating step is a multiple of five.