An efficient approach to ab initio Monte Carlo simulation.

Area of Science:

• Computational Physics
• Materials Science
• Quantum Chemistry

Background:

• Accurate calculation of equilibrium averages is crucial for understanding material properties.
• Traditional methods like ab initio molecular dynamics can be computationally expensive.
• Density functional theory (DFT) provides accurate potentials but is computationally intensive.

Purpose of the Study:

• To develop a more efficient computational scheme for calculating equilibrium averages.
• To reduce the computational cost associated with accurate potentials like DFT.
• To enhance the efficiency of Markov chain Monte Carlo (MCMC) methods.

Main Methods:

• Implementation of a Nested Markov chain Monte Carlo (NMC) scheme.
• Utilizing Metropolis sampling with an inexpensive reference potential to decorrelate configurations.
• On-the-fly optimization of the reference system's thermodynamic state (inverse temperature β(0)).
• Application to shocked states of argon using local density approximation.

Main Results:

• Achieved significant decorrelation of configurations, reducing the number needed for ensemble averages.
• Enhanced acceptance probabilities by factors of 1.2-28 compared to unoptimized NMC.
• Demonstrated that optimization compensates for reference potential shortcomings, especially with lower-quality potentials.
• Showcased optimized NMC efficiency competitive with standard ab initio molecular dynamics in the canonical ensemble.

Conclusions:

• Optimized NMC offers a computationally efficient alternative for calculating equilibrium averages with accurate potentials.
• The on-the-fly optimization strategy is key to maximizing the method's performance.
• This method holds promise for simulating complex systems where accurate potentials are required but computationally prohibitive.