Using Spatial Orbitals

Abstract

In many applications, especially for programming purposes, it is very important to rewrite theoretical expressions containing spinorbitals in terms of spatial orbitals. This is imperative for the sake of effective computation, since the number of spinorbitals is twice as large as the number of spatial orbitals. If the computational procedure manipulates with the full list of two-electron integrals, the time requirement of the calculation is proportional at least to the fourth power of the number of basis functions. Consequently, if the programming would be done in terms of spinorbitals, this would lead to a 2⁴ = 64-times longer run. The situation is usually worse, since the time requirement of a quantum chemical calculation including the approximate treatment of electron correlation is proportional to the (at least) 6th power of the number of orbitals.