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Space-warp coordinate transformation for efficient ionic force calculations in quantum Monte Carlo.

Kousuke Nakano1, Abhishek Raghav2, Sandro Sorella1

  • 1International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy.

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Quantum Monte Carlo (QMC) methods offer accurate wave functions. This study benchmarks QMC force calculations, finding Lattice-Regularized Diffusion Monte Carlo with space-warp transformation improves efficiency and accuracy for materials science applications.

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Area of Science:

  • Computational Quantum Chemistry
  • Materials Science
  • Condensed Matter Physics

Background:

  • Ab initio quantum Monte Carlo (QMC) methods are advanced computational techniques for highly accurate many-body wave functions.
  • While QMC excels at calculating ground-state energies in physics and chemistry, atomic force calculations are still under development.
  • Accurate QMC force evaluation is crucial for generating machine-learning force-field potentials, yet efficient algorithms remain debated.

Purpose of the Study:

  • To benchmark the accuracy of all-electron variational Monte Carlo (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC) forces.
  • To evaluate the impact of the space-warp coordinate transformation (SWCT) on QMC force calculation efficiency and scaling.
  • To compare different approximations for LRDMC force calculations, specifically Reynolds (RE) and variational-drift (VD).

Main Methods:

  • Benchmarking VMC and LRDMC forces for various mono- and heteronuclear dimers (Z ≤ 35).
  • Calculation of forces with and without the space-warp coordinate transformation (SWCT).
  • Application of regularization techniques to address infinite variance issues in force calculations.
  • Comparison of LRDMC forces using Reynolds (RE) and variational-drift (VD) approximations.

Main Results:

  • Lattice-regularized diffusion Monte Carlo (LRDMC) energies yield equilibrium bond lengths and harmonic frequencies closer to experimental values than VMC.
  • LRDMC forces with the Reynolds (RE) approximation show improvement over VMC forces, justifying the higher computational cost.
  • The space-warp coordinate transformation (SWCT) renders the computational cost ratio between QMC energy and forces independent of atomic number (Z).
  • LRDMC forces with variational-drift (VD) approximations also improve accuracy but significantly increase computational cost in all-electron calculations.

Conclusions:

  • Lattice-regularized diffusion Monte Carlo (LRDMC) provides more accurate results for molecular properties compared to variational Monte Carlo (VMC).
  • The Reynolds (RE) approximation for LRDMC forces offers a viable path for improved accuracy beyond VMC, despite increased computational expense.
  • The space-warp coordinate transformation (SWCT) is essential for efficient QMC force calculations, enabling scalability comparable to energy calculations.