Symmetric orthonormalization method

Lowdin s symmetric orthogonalization method is an often employed technique for the generation of orthonormal molecular basis sets. Since within most LCAO MO methods, density matrices are determined by AO basis set coefficients, and idempotency of density matrices is a property easily controlled on an orthonormal basis, Lowdin s transforma-... 

The greater the number of functions 4 J, belonging to the orthonormal set, the more completely and in more detail the spectrum of the /(-decay-induced excitations of a molecule can be calculated. Consequently, the method for calculating the wave functions of the daughter ion must be such that at a reasonable volume of calculation we would be able to construct a sufficiently large number of multielectron wave functions of excited states. The Hartree Fock method allows one to construct the wave functions of excited states as the combinations of determinants symmetrized in a certain way. Within this method the excitation is considered to be a transition of an electron from an occupied Hartree-Fock molecular orbital into a vacant one. 

The Lanczos method is based on generating the orthonormal basis in Krylov space Ki =span c, Ac, A c by applying the Gram-Schmidt orthogonaliza-tion process, described in Appendix A. In matrix notations this approach is associated with the reduction of the symmetric matrix A to a tridiagonal matrix and also with the special properties of T/,. This reduction (called also QT decomposition) is described by the formula... 

---