Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations

Area of Science:

• * Computational Chemistry
• * Theoretical Chemistry
• * Molecular Dynamics

Background:

• * Direct dynamics simulations offer atomistic insights into chemical systems without potential energy surface fitting.
• * Electronic structure theory provides a representation of the potential energy surface.
• * Approximating the Hessian is crucial for computational efficiency in direct dynamics.

Purpose of the Study:

• * To evaluate the efficacy of recently developed compact finite difference (CFD) schemes for Hessian approximation in direct dynamics.
• * To assess the computational speed-up and robustness of CFD schemes across various molecular systems.
• * To determine the accuracy and parametrical tunability of CFD approximations.

Main Methods:

• * Employing monodromy matrix equations of motion to test CFD schemes.
• * Performing direct dynamics simulations using both analytic potential energy surfaces and on-the-fly calculations.
• * Simulating molecular systems such as carbon dioxide and benzene.

Main Results:

• * CFD-based direct dynamics simulations achieved speed-ups of up to two orders of magnitude.
• * The CFD approximation demonstrated robustness in handling chaotic motion, diverse vibrational modes, and molecular couplings.
• * Parametrical tuning of CFD parameters allowed for system-specific accuracy optimization.

Conclusions:

• * CFD schemes significantly accelerate electronic structure theory Hessian direct dynamics simulations.
• * The CFD method is reliable for simulating complex molecular dynamics, including resonances and couplings.
• * Approximate Hessian updating via CFD offers a viable alternative to calculating the exact Hessian at each step, enhancing simulation efficiency.