Spectral finite-element formulation of the optimized effective potential method for atomic structure in the random phase approximation

2025/12/19 by Shubhang Krishnakant Trivedi, Trivedi, Shubhang Krishnakant, Phanish Suryanarayana +1
Materials Science · #Atomic Physics (physics.atom-ph) #Block Copolymer Self-Assembly #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Machine Learning in Materials Science #X-ray Diffraction in Crystallography

paper · doi:10.48550/arxiv.2512.17757

openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28

Abstract

We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs a polynomial mesh with element nodes placed according to the Chebyshev-Gauss-Lobatto scheme, high-order C⁰-continuous Lagrange polynomial basis functions, and Gauss-Legendre quadrature for spatial integration. We employ distinct polynomial degrees for the orbitals, Hartree potential, and RPA-OEP exchange-correlation potential. Through representative examples, we verify the accuracy of the developed framework, assess the fidelity of one-parameter double-hybrid functionals constructed with RPA correlation, and develop a machine-learned model for the RPA-OEP exchange-correlation potential at the level of the generalized gradient approximation, based on the kernel method and linear regression.

Citations

• Self-consistent random phase approximation and optimized hybrid functionals for solids
• Random Phase Approximation Correlation Energy using Real-Space Density Functional Perturbation Theory
• Exact exchange-correlation potentials and energies for learning density functionals
• Spectral scheme for atomic structure calculations in density functional theory
• On-the-fly machine learned force fields for the study of warm dense matter: application to diffusion and viscosity of CH
• Kohn-Sham accuracy from orbital-free density functional theory via Δ-machine learning
• Deep-learning approach for the atomic configuration interaction problem on large basis sets
• Radial Kohn-Sham problem via integral-equation approach
• Completing density functional theory by machine-learning hidden messages from molecules
• Benchmark Database of Transition Metal Surface and Adsorption Energies from Many-Body Perturbation Theory
• A spectral element method for fluid dynamics: Laminar flow in a channel expansion

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