An Iterative Correction of Wavefunction Using a Residual Vector for Efficient Calculations of Ab Initio Energy

ABSTRACT This work presents an improved version of the residual vector correction (RVC) algorithm, designed to address the eigenproblem involved in electronic structure calculations. Instead of directly diagonalizing the entire Hamiltonian matrix, the proposed algorithm iteratively diagonalizes a 2 × 2 submatrix, focusing only on the relevant molecular orbitals. Molecular orbital energies are iteratively minimized along a residual vector, with the step size determined by diagonalizing the 2 × 2 submatrix. To obtain the subsequent eigenvalues, we employ Hotelling deflation, which constructs the necessary auxiliary Fock matrix. Since the size of the diagonalized matrix does not increase with the molecular system, this algorithm eliminates the cubic scaling dependence of computational efficiency on molecule size seen in direct diagonalization. Compared to the earlier version, the implementation within the Hartree–Fock framework shows that the current version is significantly more practical for the calculation of considerably large molecules. As demonstrated, the RVC method consistently surpasses existing iterative approaches in efficiency while maintaining high accuracy.