The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• The conventional Roothaan-Hall (RH) method with direct inversion in iterative subspace (DIIS) acceleration for optimizing Hartree-Fock and Kohn-Sham energies has known limitations.
• These limitations include potential convergence failures and convergence to saddle points instead of true energy minima, impacting computational chemistry reliability.

Purpose of the Study:

• To introduce a novel, more reliable, and cost-efficient optimization method for Hartree-Fock and Kohn-Sham energies.
• To overcome the inherent flaws of the traditional RH/DIIS scheme, ensuring convergence to a true energy minimum.

Main Methods:

• A new trust-region based optimization algorithm is proposed.
• This method replaces the two-step RH/DIIS iteration with a single concerted step, leveraging Hessian information from previous iterations.
• The algorithm relies on matrix multiplications and exhibits linear scaling for large systems.

Main Results:

• The novel method demonstrates robustness and cost-efficiency in numerical examples.
• It successfully converges to energy minima even in cases where RH/DIIS fails or converges to saddle points.
• The algorithm ensures convergence to a true energy minimum by design.

Conclusions:

• The presented trust-region method offers a superior alternative for Hartree-Fock and Kohn-Sham energy optimization.
• It enhances the reliability and reduces the computational cost of electronic structure calculations.
• The linear scaling property makes it suitable for large-scale quantum chemistry and materials science applications.