A real-space stochastic density matrix approach for density functional electronic structure.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Real-space grid methods enhance electrostatics and density functional electronic structure modeling.
• Current linear-scaling real-space solvers face computational and storage challenges due to matrix operations.

Purpose of the Study:

• To introduce an alternative stochastic method for solving the one-electron density matrix directly in real space.
• To address the computational overhead associated with traditional wave function grid methods.

Main Methods:

• Developed an orbital-free, stochastic approach to compute the one-electron density matrix.
• Utilized model calculations in one dimension to demonstrate method features, including density matrix nodes.
• Employed stabilization of a Feynman-Kac functional integral to enforce particle number and idempotency constraints.

Main Results:

• The stochastic method shows potential for efficient electronic structure modeling.
• Demonstrated near-locality of random walks for simultaneous density matrix updates across processors.
• Successfully illustrated method applicability through one-dimensional model calculations.

Conclusions:

• The proposed stochastic method offers a promising alternative to traditional real-space solvers.
• This orbital-free approach is well-suited for future parallel computing environments.
• The method simplifies constraint enforcement compared to extensive matrix operations.