Toward more accurate natural orbital functional approximations: Including 4-index cumulant contributions

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate modeling of bond breaking is a challenge in reduced density matrix functional theory (RDMFT).
• Existing functionals struggle with fragment properties like delocalization index and local spin at dissociation.
• Natural orbital functionals (NOFs) offer a promising avenue for improvement.

Purpose of the Study:

• To develop an improved natural orbital functional for accurate bond breaking in RDMFT.
• To address the limitations of existing functionals in reproducing fragment properties at dissociation.
• To enhance the reliability of RDMFT for strongly correlated systems.

Main Methods:

• Revisiting natural orbital functional construction by correcting the cumulant contribution of the PNOF5 functional.
• Enforcing physical constraints on the cumulant related to local spin and delocalization index at dissociation.
• Purifying one- and two-electron reduced density matrices using P, Q, and GN-representability conditions.

Main Results:

• The updated functional shows improved behavior in strongly correlated regimes.
• Energies computed for dissociating molecules (N2, NO+, O2, S2, CO) precisely match complete active space self-consistent field (CASSCF) energies.
• The method successfully reproduces key fragment properties at the dissociation limit.

Conclusions:

• The developed method provides a pathway for systematically improving NOFs for reliable bond-breaking calculations in RDMFT.
• The approach enhances the accuracy of RDMFT for systems exhibiting strong correlation.
• This work offers a more robust computational tool for studying molecular dissociation.