Construction of orthonormal vector sets for atoms and molecules by means of recursive variation

It is shown using a recursive variation method that the Schmidt orthonormalized vectors are optimal in the sense that the least squared distances are minimized, and that the use of maximal squared overlaps yields a Schmidt canonical orthonormalized vector set which corresponds to the Lowdin canonical vector set. By introducing the Krylov sequence, the method is applied to the derivation of a variational expression for the Lanczos vectors which tridiagonalize any self‐adjoint operator. The repeated use of two‐step variations is shown to derive a pseudopotential which is useful for the calculations of correlated pair functions.