Reducing the Cost of Energy Differences in Variational Monte Carlo with Spotlight Sampling

Area of Science:

• Computational chemistry
• Quantum mechanics
• Method development

Background:

• Variational Monte Carlo (VMC) is a powerful quantum mechanical method for calculating molecular energies.
• Predicting energy differences for local chemical changes with VMC can be computationally expensive, limiting its application to large systems.
• Existing methods like side-chaining and embedding offer partial solutions but may not scale optimally.

Purpose of the Study:

• To develop a novel approximate sampling scheme for VMC that significantly reduces computational cost.
• To achieve near-linear or sublinear cost scaling with system size for calculating local energy differences.
• To demonstrate the effectiveness of the proposed method on various chemical systems.

Main Methods:

• Introduction of spotlight sampling, an approximate sampling scheme for VMC.
• Utilizing an approximate fragmented Hamiltonian and correlated sampling techniques.
• Application of the method to calculate bond stretching energies in alcohols, hydrogen dimer chains, and molecules with delocalized π-systems.

Main Results:

• The spotlight sampling approach demonstrates near-linear cost scaling with system size.
• An explicit cost crossover was observed compared to standard VMC methods.
• The method proved effective across diverse molecular systems, including those with varying degrees of π-system delocalization.

Conclusions:

• Spotlight sampling offers a significant reduction in computational cost for VMC energy difference calculations.
• The method's near-linear scaling makes it suitable for larger and more complex chemical systems.
• This approach has the potential to accelerate computational chemistry research by enabling more efficient simulations.