Development of a Highly Efficient Convergence Method for Self-Consistent Field Calculations combining Givens Rotation and Error Back-Propagation Algorithms

We have recently proposed a highly efficient convergence method for self-consistent (SCF) calculations combining Givens rotation and error back-propagation (EBP) algorithms, referred to as direct Givens rotation (DGR) method [J. Chem. Phys. 162, 014108 (2025)]. The Givens rotation corresponds to unitary transformations that guarantee the orthogonality of molecular orbitals. Complicated gradients constructed through sequential Givens rotations were computed using the EBP technique without deriving explicit forms. This article reviews the proposed DGR method and compares it with conventional methods such as the standard SCF procedure, the second-order SCF method, and the direct inversion in iterative subspace technique for H2O molecule. The DGR method exhibited a convergence speed comparable to that of the SOSCF method while achieving a lower and more reliable energy.