Constrained Newton approach adequate to direct self‐consistent field calculations in closed‐ and open‐shell configurations

The quadratically convergent approach to solve self‐consistent field (SCF) solutions for closed‐ and open‐shell configurations is derived from the Lagrange–Newton method with constraints of the molecular orbital orthonormality. The resulting Lagrangian supermatrix is expressed in a simple manner in terms of atomic orbital (AO) integrals. The present scheme realizes a decrease in computational cost when used with secondary memory to save the Lagrangian supermatrix. Furthermore, the direct SCF approach of the proposed scheme may be efficient to cut down computational cost when used with a preconditioner useful to improve slow convergence in each Lanczos iteration process. The present scheme converges nearly quadratically to a SCF solution when once a good starting point is chosen. The initial estimates of the Lagrange multipliers play a relatively minor role in the convergence rate. As an illustration of the proposed procedure ab initio calculations for the ground and excited states of CO and the ground sta...