Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Quantum Monte Carlo (QMC) methods are powerful for simulating quantum systems.
• Calculating forces in QMC has been computationally expensive, limiting its application.
• Efficient force calculations are crucial for studying material properties and dynamics.

Purpose of the Study:

• To develop an efficient algorithm for computing atomic forces in quantum Monte Carlo simulations.
• To enable the calculation of forces with computational cost comparable to total energy calculations.
• To facilitate the study of finite-temperature thermodynamic properties of materials using QMC.

Main Methods:

• Utilizing adjoint algorithmic differentiation for efficient force computation.
• Applying the space warp coordinate transformation in differential form.
• Implementing the algorithm for electronic systems, demonstrated with water molecules.

Main Results:

• An efficient algorithm for computing all 3M force components for a system of M atoms was developed.
• The computational effort for force calculation is comparable to that of total energy calculation.
• The method was illustrated with examples for electronic systems containing water molecules.

Conclusions:

• The developed algorithm significantly enhances the efficiency of force calculations in QMC.
• This advancement makes the calculation of finite-temperature thermodynamic properties of materials feasible with QMC.
• The technique opens new avenues for materials research and discovery.