Scaling spin-orbit integrals

As described in Sec. 3.1, each Hartree-Fock iteration involves the construction of the Fock matrix for a given density matrix, followed by the diagonalization of the Fock matrix to generate a set of improved spin orbitals and thus an improved density matrix. Formally, the construction of the Fock matrix requires a number of operations proportional to K4, where K is the number of atoms (because the number of two-electron integrals scales as Al4). For large systems, however, this quartic scaling with K (i.e., with system size) can be reduced to linear by special techniques, as will now be discussed. 

The energy levels of 3d 4p have been calculated In the sequence Y XIII —Ag XXI by the Slater-Condon method and Z-expansion formulas are given for the Slater and spin-orbit fitted parameters [8], as well as scaling factors between Hartree-Fock integrals and fitted parameters. 

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