Energy extrapolation schemes for adaptive multi-scale molecular dynamics simulations.

Area of Science:

• Computational Chemistry
• Molecular Dynamics Simulations
• Theoretical Chemistry

Background:

• Molecular dynamics (MD) simulations generate extensive data, but calculating potential energies at every point is computationally expensive.
• Adaptive multi-scale MD simulations often require potential energy values only for post-simulation analysis.
• Efficient extrapolation methods are crucial for minimizing computational cost in MD simulations.

Purpose of the Study:

• To evaluate and compare simple extrapolation schemes for potential energy values from MD trajectories.
• To identify the most accurate and computationally efficient method for energy extrapolation.
• To assess the performance of extrapolation schemes across varying system sizes and simulation levels (MM/QM).

Main Methods:

• Utilized Taylor series and central finite difference approximations for energy extrapolation.
• Tested schemes on MD trajectories of molecular systems with varying sizes.
• Simulations were performed at Molecular Mechanics (MM) and Quantum Mechanics (QM) levels using velocity-Verlet integration.

Main Results:

• First and second order Taylor expansions showed errors increasing with system size.
• Second order central finite difference approximation demonstrated size-independent accuracy and good energy estimation.
• Fourth order central finite difference was not always feasible and offered no significant accuracy improvement over the second order method.

Conclusions:

• The second order central finite difference approximation is the optimal method for extrapolating potential energy from MD trajectories.
• This method provides accurate energy estimates with minimal computational cost, comparable to simpler Taylor series methods.
• The findings are validated through application in adaptive multi-scale simulation analysis.