Quantum Monte Carlo with very large multideterminant wavefunctions.

Area of Science:

• Computational Quantum Chemistry
• Quantum Monte Carlo Methods

Background:

• Large multideterminant wavefunctions are crucial for accurate quantum Monte Carlo (QMC) calculations.
• Efficient computation of derivatives of these wavefunctions is computationally intensive.
• Existing methods face challenges with the scale and complexity of multideterminant expansions.

Purpose of the Study:

• To develop and present an efficient algorithm for calculating the first two derivatives of large multideterminant wavefunctions.
• To reduce the computational cost associated with QMC calculations using extensive wavefunctions.
• To introduce a novel truncation scheme for multideterminant expansions.

Main Methods:

• Utilizes the Sherman-Morrison formula for updating the inverse Slater matrix.
• Implements optimizations by reducing column substitutions and enhancing scalar product calculations.
• Leverages the structure of identical spin-specific determinants to improve scaling.

Main Results:

• The algorithm demonstrates practical scaling with the total number of unique spin-specific determinants (Ndet↑+Ndet↓).
• Computational cost is significantly reduced, making calculations with up to one million determinants feasible.
• A new truncation scheme allows for larger expansions without prohibitive computational time increases.

Conclusions:

• The presented algorithm offers a substantial computational advantage for QMC calculations involving large multideterminant wavefunctions.
• Feasibility demonstrated through all-electron fixed-node diffusion Monte Carlo calculations on the chlorine atom.
• Calculations with ~750,000 determinants are shown to be computationally tractable.