[Paper Review] Static Correlation Density Functional Theory

Pablo Ramos, Michele Pavanello|arXiv (Cornell University)|Jun 16, 2019

Advanced Chemical Physics Studies30 references4 citations

TL;DR

This paper introduces a novel static correlation density functional theory framework that uses thermal (Fermi-Dirac) reference states instead of single Slater determinants in Kohn-Sham DFT, enabling accurate description of multireference systems. The key contribution is that the electronic Shannon entropy of the thermal state provides an excellent approximation to the static correlation functional, validated through benchmark systems including H₂⁺ and H₂ dissociation.

ABSTRACT

Over the years, several schemes have been proposed to describe multireference systems with Kohn-Sham Density Functional Theory. Problematic is the combination of two aspects: the Kohn-Sham reference wavefunction is usually taken to be a single Slater determinant, and approximate exchange-correlation functionals are typically derived form the local density approximation. In this work, we develop a theoretical framework that foregoes the single Slater determinant and instead employs thermal states as reference states for zero-temperature interacting systems. We provide convenient definitions of static and dynamic correlation functionals via an adiabatic connection approach. The formalism and computational results indicate that the entropic term of the thermal reference state is a good approximation to the static correlation functional. Hence, this work validates several reported results in the literature and motivates additional developments of static correlation density functionals.

Motivation & Objective

• Address the long-standing challenge of describing static correlation in standard Kohn-Sham DFT, which relies on single-reference wavefunctions.
• Overcome the limitations of approximate exchange-correlation functionals in multireference systems, particularly near degeneracy and bond dissociation.
• Develop a formal framework to separate static and dynamic correlation in DFT using adiabatic connection and thermal reference states.
• Validate the use of electronic entropy as a proxy for the static correlation functional, offering a practical and theoretically grounded approach.

Proposed method

• Propose a thermal reference state (Fermi-Dirac distribution) as the Kohn-Sham reference, replacing the single Slater determinant.
• Use an adiabatic connection approach to interpolate between the noninteracting thermal reference and the correlated interacting system.
• Define the static correlation functional via the entropic contribution of the thermal state, derived from the difference in free energy between reference and interacting systems.
• Compute the dynamic correlation energy as the residual correlation after subtracting the static component.
• Employ effective temperature τ as a tunable parameter to control orbital occupation smearing and probe static correlation effects.
• Use the Shannon entropy of the thermal state as a direct approximation to the static correlation functional, validated numerically.

Experimental results

Research questions

• RQ1 Can thermal reference states in Kohn-Sham DFT provide a better description of static correlation than single Slater determinant references?
• RQ2 Is the electronic Shannon entropy a valid and accurate proxy for the static correlation functional in multireference systems?
• RQ3 How does the adiabatic connection path based on thermal states improve the description of electron density and kinetic energy compared to standard DFT?
• RQ4 To what extent does including the entropic term in the functional reduce errors in bond dissociation curves, especially for challenging systems like H₂⁺?
• RQ5 Can current approximate exchange-correlation functionals still serve as effective dynamic correlation functionals when combined with the new static correlation functional?

Key findings

• The electronic Shannon entropy of a thermal reference state provides a strong approximation to the exact static correlation functional, particularly in multireference regimes.
• The use of thermal states improves the noninteracting kinetic energy in Kohn-Sham DFT, bringing it closer to the exact interacting value compared to pure-state references.
• The density difference between thermal and pure-state Kohn-Sham calculations serves as a reliable indicator of static correlation character in molecular systems.
• For H₂ dissociation, the inclusion of the static correlation functional via entropy improves the description of the dissociation curve, though the improvement is limited by self-interaction error.
• The method successfully reduces the detrimental effects of the missing step structure in the Kohn-Sham potential by allowing orbital occupation relaxation through Fermi-Dirac smearing.
• The framework validates prior observations that thermal states enhance accuracy in systems with strong static correlation, such as bond breaking and near-degenerate states.