Energy Derivatives in Real-Space Diffusion Monte Carlo

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Diffusion Monte Carlo (DMC) is a powerful quantum mechanical method.
• Calculating energy derivatives is crucial for understanding molecular properties and reaction pathways.
• The fixed-node approximation in DMC can introduce challenges in derivative calculations.

Purpose of the Study:

• To develop unbiased, finite-variance estimators for energy derivatives in real-space DMC.
• To address the problem of divergent variance in these calculations.
• To provide a consistent method for calculating derivatives that aligns with energy dependence on parameters.

Main Methods:

• Developed novel estimators for energy derivatives in real-space DMC within the fixed-node approximation.
• Employed regularization techniques for wave function parameter gradients, including a coordinate transformation method.
• Utilized a particle-in-a-box model to illustrate the algorithm and its effectiveness.

Main Results:

• Introduced unbiased, finite-variance estimators for energy derivatives.
• Demonstrated that the calculated derivatives are consistent with the energy dependence on parameters.
• Successfully regularized divergent variances using proposed methods.

Conclusions:

• The new estimators offer a robust way to compute energy derivatives in fixed-node DMC.
• The regularization techniques effectively mitigate the issue of divergent variances.
• This work advances the applicability of DMC for accurate property calculations.