Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation...

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Theoretical Physics

Background:

• Kohn-Sham (KS) calculations are central to modern electronic structure theory.
• Existing methods like direct random phase approximation (dRPA) have limitations in accuracy for certain energy calculations.
• The adiabatic-connection fluctuation-dissipation (ACFD) theorem provides a rigorous framework for deriving correlation energy functionals.

Purpose of the Study:

• Introduce novel σ-functionals for the Kohn-Sham correlation energy.
• Improve the accuracy of energy calculations, particularly for chemical reactions and non-covalent interactions.
• Develop a computationally efficient approach that complements existing density functional theory methods.

Main Methods:

• Developed new correlation energy functionals based on the ACFD theorem, termed σ-functionals.
• Utilized eigenvalues of the frequency-dependent KS response function as input.
• Optimized functionals using reference datasets for atomization, reaction, transition state, and non-covalent interaction energies.
• Employed a post-self-consistent approach using orbitals and eigenvalues from standard KS calculations with the Perdew-Burke-Ernzerhof functional.

Main Results:

• σ-functionals achieve significantly higher accuracy than dRPA methods, comparable to high-level wave function methods.
• Reaction and transition state energies approach chemical accuracy (≈1 kcal/mol), with a mean absolute deviation of 1.25 kcal/mol for the W4-11RE set.
• Non-covalent binding energies are accurately predicted to within tenths of a kcal/mol.
• The post-self-consistent calculation is computationally efficient, faster than hybrid functional calculations.

Conclusions:

• The new σ-functionals represent a significant advancement in calculating correlation energies.
• The approach offers a highly accurate and computationally feasible alternative to existing methods.
• σ-functionals can be readily implemented in existing dRPA codes, facilitating widespread adoption.