Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Accurate calculation of electronic density at the nucleus is crucial for understanding atomic and molecular properties.
• Existing quantum Monte Carlo (QMC) methods face challenges in efficiency and implementation complexity for this specific property.

Purpose of the Study:

• To develop novel, highly efficient, and parameter-free quantum Monte Carlo (QMC) estimators for electronic density at the nucleus.
• To provide more accurate benchmark values for the electronic density at the nucleus for selected atoms and molecules.

Main Methods:

• Derivation of new QMC estimators based on the zero-variance and zero-bias principles.
• Application of these estimators in both variational and diffusion QMC frameworks.
• Calculation of electronic density at the nucleus for first-row atoms (Li-Ne), Argon, and diatomic molecules (B2, N2, F2).

Main Results:

• The developed QMC estimators are significantly simpler to implement and use, containing no adjustable parameters.
• These estimators demonstrate high efficiency compared to alternative methods.
• The study provides the most accurate available estimates for the electronic density at the nucleus for the targeted systems.

Conclusions:

• The new QMC estimators offer a substantial improvement in calculating electronic density at the nucleus.
• These methods are versatile, applicable to various QMC approaches and systems.
• The obtained accurate results serve as valuable benchmarks for future theoretical and experimental studies.