Direct Givens rotation method based on error back-propagation algorithm for self-consistent field solution.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• The self-consistent field (SCF) procedure is fundamental for Hartree-Fock and Kohn-Sham density functional theory (DFT) calculations.
• Convergence of standard SCF methods is not theoretically guaranteed, necessitating alternative approaches.
• Direct minimization methods like augmented Lagrangian method (ALM) and second-order SCF (SOSCF) offer gradient-based solutions but have limitations.

Purpose of the Study:

• To propose a novel direct energy minimization algorithm for SCF calculations.
• To ensure orbital orthogonality and prevent variational collapse during SCF optimization.
• To provide an alternative to existing SCF algorithms with potentially improved convergence properties.

Main Methods:

• Developed a new SCF algorithm based on minimizing the ALM Lagrangian.
• Employed sequential Givens rotations between occupied and virtual orbitals for unitary transformations.
• Utilized the error back-propagation method to compute complex gradients for the Givens rotations.
• Compared the performance of the developed Direct Givens Rotation (DGR) method against established algorithms.

Main Results:

• The proposed DGR method effectively obtains SCF solutions through direct energy minimization.
• Sequential Givens rotations successfully maintain orbital orthogonality and prevent variational collapse.
• Illustrative applications demonstrated the method's features and compared its performance with Direct Inversion in Iterative Subspace (DIIS), SOSCF, and ALM.

Conclusions:

• The DGR method presents a viable and robust alternative for achieving SCF solutions in electronic structure calculations.
• The use of sequential Givens rotations offers a reliable way to handle unitary transformations and maintain orbital orthonormality.
• Further investigations into the DGR method's efficiency and applicability across various quantum chemical systems are warranted.