Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids-A case study in...

Area of Science:

• Computational physics and chemistry
• Materials science
• Quantum mechanics

Background:

• Diffusion Monte Carlo (DMC) is an exact method for electronic structure calculations.
• The fermionic sign problem requires approximations, introducing variational errors.
• Systematically improvable trial wavefunctions are crucial for accurate DMC results.

Purpose of the Study:

• To develop a computational method for generating systematically improvable trial wavefunctions for DMC.
• To reduce and better control the fixed-node error in ab initio electronic structure calculations.
• To accurately determine the cohesive energy of periodic solids.

Main Methods:

• Utilizing the configuration interaction using a perturbative selection made iteratively (CIPSI) method.
• Generating trial wavefunctions with systematically improvable nodes.
• Employing a protocol to extrapolate results from finite supercells to the thermodynamic limit.

Main Results:

• Demonstrated improved fixed-node DMC energies for carbon diamond using large Slater-Jastrow expansions.
• Observed a monotonic and smooth decrease in fixed-node error with increasing determinants.
• Achieved cohesive energy extrapolation in close agreement with experimental values.

Conclusions:

• The presented method offers better control over the fixed-node error in DMC calculations.
• Systematically improvable nodes significantly enhance the accuracy of electronic structure calculations.
• Error cancellation is notable even at the single-determinant level for carbon diamond.