Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum...

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Stochastic electronic structure methods, such as quantum Monte Carlo (QMC), face challenges in optimizing atomic coordinates and lattice parameters due to statistical errors in force and stress tensor measurements.
• Conventional gradient-based optimization methods are ill-suited for these noisy, stochastic results, especially when forces are unavailable or computationally expensive.
• Flat energy surfaces near minima exacerbate the difficulty of achieving sufficient statistical accuracy for reliable optimization.

Purpose of the Study:

• To explore Gaussian process-based techniques for sampling energy surfaces in stochastic electronic structure calculations.
• To reduce the sensitivity of optimization procedures to the inherent statistical noise of methods like QMC.
• To demonstrate the applicability of these techniques for optimizing systems with multiple parameters.

Main Methods:

• Utilized Gaussian process regression to model the energy surface.
• Employed Latin hypercube sampling for energy point selection, with sampling density scaling quadratically with the number of parameters.
• Applied the developed method to optimize a benzene molecule's geometry starting from a disordered state.

Main Results:

• Successfully applied Gaussian process techniques to overcome statistical error challenges in QMC optimization.
• Demonstrated effective optimization for systems involving tens of parameters.
• Achieved successful optimization of a benzene molecule, showcasing the method's potential for complex systems.

Conclusions:

• Gaussian process-based sampling offers a robust approach to handle statistical errors in stochastic electronic structure calculations.
• This method enhances the reliability and applicability of QMC and similar techniques for structural optimization.
• The demonstrated success with a benzene molecule indicates broad potential for materials science and computational chemistry applications.