A second-order unconstrained optimization method for canonical-ensemble density-functional methods.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Kohn-Sham Density-Functional Theory (KS-DFT) is a cornerstone of electronic structure calculations.
• Accurate treatment of fractional electron occupations is essential for describing certain molecular systems and phenomena.
• Existing optimization methods may struggle with systems exhibiting fractional occupations.

Purpose of the Study:

• To introduce a novel second-order converging method of ensemble optimization (SOEO).
• To develop a general framework for optimizing both orbitals and occupation numbers simultaneously.
• To investigate the behavior of SOEO with various exchange-correlation functionals and molecular systems.

Main Methods:

• SOEO employs a second-order Newton-Raphson approach for energy minimization.
• Occupation numbers are constrained between 0 and 2 using occupation angles and trigonometric functions.
• The method controls the total number of electrons via second-order restrictions, adaptable for grand-canonical ensembles.
• Dissociation curves for diatomic carbon and calculations on chromium dimer were performed.

Main Results:

• SOEO favors symmetry-broken pure-state solutions with exact exchange functionals due to unphysical contributions from fractional occupations.
• Ensemble solutions are preferred by functionals without exact exchange at larger interatomic distances.
• SOEO successfully converges to ensemble solutions for complex systems like the chromium dimer.

Conclusions:

• SOEO provides a robust and general method for electronic structure calculations involving fractional electron occupations.
• The choice of exchange-correlation functional significantly impacts the nature of the optimized electronic state (pure vs. ensemble).
• SOEO demonstrates applicability to a range of molecular systems, advancing computational chemistry capabilities.