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

Area of Science:

• Computational chemistry
• Quantum mechanics
• Electronic structure theory

Background:

• The optimized effective potential (OEP) method is crucial for accurate electronic structure calculations.
• The random phase approximation (RPA) provides a systematic way to include electron correlation effects.
• Combining OEP and RPA presents computational challenges.

Purpose of the Study:

• To develop a novel spectral finite-element formulation for the OEP method within the RPA.
• To create an accurate and efficient computational framework for atomic structure calculations.
• To explore the application of machine learning to refine the RPA-OEP exchange-correlation potential.

Main Methods:

• Spectral finite-element framework utilizing Chebyshev-Gauss-Lobatto nodes.
• High-order C0-continuous Lagrange polynomial basis functions for spatial discretization.
• Gauss-Legendre quadrature for accurate numerical integration.
• Distinct polynomial degrees for orbitals, Hartree potential, and RPA-OEP potential.

Main Results:

• Verification of the spectral finite-element framework's accuracy through representative examples.
• Assessment of the fidelity of double-hybrid functionals incorporating RPA correlation.
• Development of a machine-learned model for the RPA-OEP exchange-correlation potential using kernel methods and linear regression.

Conclusions:

• The developed spectral finite-element method provides an accurate and efficient approach for OEP-RPA calculations.
• The framework enables reliable assessment of advanced density functionals.
• Machine learning offers a promising avenue for approximating complex exchange-correlation potentials in quantum chemistry.