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Researchers reduced the computational cost of Hilbert space variational Monte Carlo (HS-VMC) calculations from fifth to fourth order. This advancement improves efficiency for quantum chemistry simulations, especially for larger systems.

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Area of Science:

  • Computational Quantum Chemistry
  • Electronic Structure Theory
  • Method Development

Background:

  • Variational Monte Carlo (VMC) methods are powerful tools for electronic structure calculations.
  • Hilbert space VMC (HS-VMC) offers advantages but suffers from high computational scaling.
  • Traditional methods for reducing computational cost are ineffective with Jastrow factors in HS-VMC.

Purpose of the Study:

  • To reduce the formal cost scaling of Hilbert space variational Monte Carlo.
  • To develop a method effective in the presence of Hilbert space Jastrow factors.
  • To improve the efficiency of quantum chemistry simulations for larger systems.

Main Methods:

  • Developed a semi-stochastic approach to exploit the near-sparsity of the four-index tensor in HS-VMC.
  • Applied the method to single-Slater-Jastrow and Jastrow geminal power wave functions.
  • Tested on alkanes of increasing system size using a minimal basis set.

Main Results:

  • Reduced the formal cost scaling of HS-VMC from fifth to fourth order with respect to system size.
  • Demonstrated that accuracy and statistical uncertainty remain unaffected.
  • Achieved a total cost crossover at approximately 50 electrons for alkanes in a minimal basis.

Conclusions:

  • The developed semi-stochastic approach significantly enhances the efficiency of HS-VMC.
  • The improved scaling brings HS-VMC computational cost in line with real-space counterparts.
  • Further studies are needed to determine crossover points for different molecular geometries and basis sets.