Hartree-Fock method similarity transformations

This study was started in order to find out whether one could find meaningful complex eigenvalues in the Hartree-Fock scheme for a transformed Hamiltonian in the method of complex scaling. This problem was intensely discussed at the 1981 Tarfala Workshop in the Kebnekaise area of the Swedish mountains. It was found that, if the many-electron Hamiltonian undergoes a similarity transformation U which is a product of one-electron transformations u - as in the method of complex scaling - then the Fock-Dirac operator p as well as the effective Hamiltonian Heff undergo one-electron similarity... 

The Kohn-Sham equation is also transformed into a matrix equation on the basis of the Roothaan method in Sect. 2.5. Similar to the Hartree-Fock equation, the Kohn-Sham-Roothaan equation is written as... 

While the localized orbital concept was first formulated for closed shell molecular orbital wavefunctions, the method is by no means so limited. For a restricted open shell Hartree-Fock wavefunction, the subset of doubly occupied orbitals may be transformed in a manner analogous to that described above. Similarly, the sets of a and orbitals in an unrestricted Hartree-Fock wavefunction are separately invariant, and the set of active orbitals in a FORS (fully... 

The use of the orbital concept in the Hartree-Fock (HE) and Kohn-Sham (KS) methods leads to similar variational equations a coupled set of eigenvalue equations with a hermitian operator (See for example [7, 25]). This system of integro-differential equations is transformed into a matrix problem when we use a basis set. In both methods, one has to solve a generalized eigenvalue equation ... 

---