Spin-polarized density functional theory energy function

The broken-symmetry approach was developed within the framework of unrestricted Hartree-Fock theory or spin-polarized density functional theory, i.e., Xa theory. " It is based on the assumption that the energy difference between the singlet and triplet states resulting from the interaction between two 5 = 1/2 spin centers is given by ... 

What is obviously needed is a generally accepted recipe for how atomic states should be dealt with in approximate density functional theory and, indeed, a few empirical rules have been established in the past. Most importantly, due to the many ways atomic energies can be obtained, one should always explicitly specify how the calculations were performed to ensure reproducibility. From a technical point of view (after considerable discussions in the past among physicists) there is now a general consensus that open-shell atomic calculations should employ spin polarized densities, i. e. densities where not necessarily... 

Since Equation 3.15 resembles the steady-state problem, it can be rigorously justified that Hit), Hit), (0 and the quasi-energy e are all uniqne fnnctionals of the electron density (spin densities in the spin-polarized theory) [65], with the latter being periodic in time. Thns, the qnasi-energy functional Equation 3.16 can be expressed as a functional of the density. 

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