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

Shubhang Krishnakant Trivedi1, Phanish Suryanarayana1,2

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|February 23, 2026
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This summary is machine-generated.

We developed a new computational method for atomic structure calculations using the optimized effective potential (OEP) method within the random phase approximation (RPA). This spectral finite-element approach accurately models electronic structures and aids in developing advanced computational chemistry models.

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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.