Accurate electron densities from quantum Monte Carlo calculations using real-space grids.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Accurate calculation of electronic energies and densities is crucial for understanding molecular and atomic properties.
• Quantum Monte Carlo (QMC) methods offer a powerful framework for high-accuracy electronic structure calculations.

Purpose of the Study:

• To compute accurate ground state energies and electronic densities for Li2, C, and N2 using diffusion Monte Carlo (DMC) in the fixed-node approximation.
• To demonstrate the advantages of an all-electron, real-space grid approach for calculating orbitals used in DMC.
• To investigate the impact of different density functionals on the calculated electronic densities.

Main Methods:

• Diffusion Monte Carlo (DMC) in the fixed-node approximation.
• Real-space grid approach for calculating orbitals and electronic densities.
• Binning technique for density calculation and regularization for artifact correction.
• Comparison of local density approximation and exact-exchange functionals.

Main Results:

• DMC ground state energies comparable to elaborate single-reference QMC methods.
• Accurate electronic densities obtained using the real-space grid approach.
• Demonstration of residual statistical artifacts in QMC densities and their correction via regularization.
• Observation of direction-dependent asymptotic decay in the carbon atom's electronic density.

Conclusions:

• The all-electron, real-space grid DMC method provides accurate energies and densities.
• Regularization effectively corrects statistical artifacts in QMC densities.
• The accurate density reveals directional differences in the carbon atom's decay, linking to the exact Kohn-Sham potential.