Optimization of Large Determinant Expansions in Quantum Monte Carlo

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Configuration Interaction (CI) methods are crucial for accurate electronic structure calculations.
• Quantum Monte Carlo (QMC) offers a powerful stochastic approach for large systems.
• Optimizing CI expansions within QMC remains computationally demanding.

Purpose of the Study:

• To introduce a novel, efficient method for optimizing large CI expansions in QMC.
• To leverage the transcorrelated (TC) framework for improved computational performance.
• To enhance the accuracy and reduce the computational cost of electronic structure calculations.

Main Methods:

• Replaced nonorthogonal variational optimization with orthogonal non-Hermitian optimization using the TC framework.
• Rewrote TC equations as an effective self-consistent Hermitian problem.
• Developed improved estimators to reduce statistical fluctuations.

Main Results:

• Achieved minimal memory requirements in QMC codes.
• Reduced statistical fluctuations by over an order of magnitude.
• Demonstrated sub-milli-Hartree convergence in 2-3 iterations for large wave functions (10^5-10^6 determinants).

Conclusions:

• The proposed TC-based QMC method offers a significant advancement in optimizing large CI expansions.
• This method provides a computationally efficient and accurate approach for electronic structure studies.
• The technique is effective for both effective core potential and all-electron calculations.