Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics

Area of Science:

• Computational Chemistry
• Molecular Dynamics Simulations
• Statistical Mechanics

Background:

• Born-Oppenheimer molecular dynamics (BO-MD) is crucial for simulating molecular systems.
• Achieving accurate canonical (NVT) ensemble simulations with BO-MD requires strict self-consistent field (SCF) convergence at each step.
• This strict convergence can be computationally expensive, limiting the applicability of BO-MD.

Purpose of the Study:

• To develop and analyze an Extended Lagrangian Born-Oppenheimer (ELBO) molecular dynamics approach for NVT simulations.
• To assess the performance of ELBO-MD with different thermostats (Nosé, Andersen, Langevin).
• To compare ELBO-MD accuracy and efficiency against standard BO-MD under varying SCF convergence and time step conditions.

Main Methods:

• Development of an Extended Lagrangian formulation for Born-Oppenheimer molecular dynamics.
• Implementation and testing of Nosé, Andersen, and Langevin thermostats within the ELBO framework.
• Comparison of temperature distributions from ELBO-MD and standard BO-MD against analytical predictions under varied SCF convergence and time step parameters.

Main Results:

• ELBO-MD simulations accurately reproduce canonical (NVT) distributions, even with approximate SCF convergence.
• The ELBO approach often requires only a single diagonalization per time step for accurate results.
• Standard BO-MD formulations show unphysical fluctuations without high SCF convergence at each time step.

Conclusions:

• The thermostated Extended Lagrangian Born-Oppenheimer framework provides an accurate and computationally efficient method for NVT simulations.
• ELBO-MD significantly reduces the computational cost compared to regular BO-MD while maintaining accuracy.
• This method offers a practical approach for sampling molecular processes in the canonical ensemble.