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Improved Monte Carlo estimators for the one-body density.

Roland Assaraf¹, Michel Caffarel, Anthony Scemama

¹Laboratoire de Chimie Théorique, CNRS-UMR 7616, Université Pierre et Marie Curie Paris VI, Case 137, 4 Place Jussieu, 75252 Paris Cedex 05, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

Summary

A new Monte Carlo method significantly reduces statistical errors for calculating the one-body density (rho(r)). This approach enables accurate electronic density computations, even in unexplored regions of simulations.

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Area of Science:

Computational Physics
Quantum Chemistry

Background:

Monte Carlo methods are widely used in physics and chemistry.
Calculating the one-body density (rho(r)) is crucial for understanding electronic structure.
Existing methods for density estimation can suffer from statistical errors and limitations in spatial coverage.

Purpose of the Study:

To introduce a novel and simplified Monte Carlo estimator for the one-body density.
To demonstrate the advantages of this new estimator over traditional methods.
To enable accurate density calculations across all spatial regions, including those not sampled by the simulation.

Main Methods:

Development of an alternative Monte Carlo estimator for rho(r).
Comparison of the new estimator with the standard delta-function regularization on a grid.
Application of the method to calculate electronic densities for the Helium atom and the water dimer.

Main Results:

The new Monte Carlo estimator exhibits a simpler form and broader applicability.
Significant reduction in statistical errors compared to conventional regularization techniques.
Accurate calculation of electronic densities is achieved at any point in space, irrespective of simulation sampling.

Conclusions:

The proposed Monte Carlo estimator offers a statistically superior and more versatile approach for determining one-body densities.
This method enhances the accuracy and spatial reach of density calculations in various Monte Carlo simulations.
The technique is validated by successful applications to atomic and molecular systems.