On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate modeling of electron correlation is crucial for predicting molecular properties.
• Existing density functional methods face challenges in capturing short-range dynamic correlation.
• The electron-electron cusp requires specific treatment in quantum chemical calculations.

Purpose of the Study:

• To develop novel, one-parameter, on-top density functionals for short-range dynamic correlation.
• To introduce the Opposite-spin exponential-cusp and Fermi-hole correction (OF) functional.
• To evaluate the performance of the OF functional combined with Restricted Open-shell Hartree-Fock (ROHF).

Main Methods:

• Derivation of separate density functionals for opposite-spin and parallel-spin electrons.
• Representation of the electron-electron cusp using an exponential function.
• Parameterization of the OF functional by fitting to experimental ionization energies and electron affinities of atoms He to Ar using ROHF.

Main Results:

• The ROHF-OF method demonstrates superior performance compared to completely renormalized coupled-cluster [CR-CC(2,3)] for ionization energies.
• ROHF-OF performance is comparable to or better than conventional density functional methods for ionization energies.
• While less impressive for electron affinities overall, ROHF-OF achieves a mean absolute error of only 3 kJ mol⁻¹ for third-row atoms.

Conclusions:

• The developed OF functional provides an accurate description of short-range dynamic correlation.
• ROHF-OF is a promising approach for calculating ionization energies, outperforming established methods.
• Further refinement may be needed for electron affinity predictions, though accuracy for third-row elements is notable.