A trust-region augmented Hessian implementation for restricted and unrestricted Hartree-Fock and Kohn-Sham methods

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Roothaan-Hall self-consistent field (SCF) equations are fundamental for electronic structure calculations but notoriously difficult to converge for open-shell and antiferromagnetically coupled systems.
• Existing methods like direct inversion of the iterative subspace (DIIS) can struggle with convergence and may yield suboptimal solutions for complex molecular systems.

Purpose of the Study:

• To introduce and evaluate a new trust-region augmented Hessian approach (TRAH-SCF) for solving SCF equations in Hartree-Fock and Kohn-Sham methods.
• To assess the convergence behavior and solution quality of TRAH-SCF compared to DIIS variants for challenging molecular systems.

Main Methods:

• Implementation of a trust-region augmented Hessian approach (TRAH-SCF).
• Convergence benchmark studies on open-shell and antiferromagnetically coupled molecules.
• Comparison of TRAH-SCF with Pulay's and Kollmar's (K) DIIS methods.

Main Results:

• TRAH-SCF consistently achieves convergence even with stringent thresholds, requiring a modest number of iterations.
• TRAH-SCF often finds lower-energy, symmetry-broken solutions compared to DIIS and KDIIS, though with increased spin contamination in unrestricted calculations.
• While TRAH-SCF may require more iterations than DIIS/KDIIS for smooth convergence, its overall runtime remains competitive, especially with extended basis sets.

Conclusions:

• TRAH-SCF provides a robust and reliable method for converging SCF calculations, particularly for difficult systems where DIIS methods may fail or converge slowly.
• The method's ability to find lower-energy solutions, even if symmetry-broken, offers valuable insights into electronic structure.
• TRAH-SCF presents a competitive and effective alternative for advanced quantum chemical computations.