Kohn unrestricted formalism

T JKS see Kohn-Sham, unrestricted formalism uncoupled density functional theory (UDFT) 197... 

Figure 5-1. H2 potential curves computed within the restricted and unrestricted Hartree-Fock (RHF and UHF) and Kohn-Sham (RKS and UKS) formalisms. 

Hartree-Fock (UHF) formalism and suffers from the same drawbacks when dealing with open-shell systems [71]. This is especially important when attempting to study magnetic systems with many open shells. The unrestricted Kohn-Sham determinant corresponds necessarily to a mixture of the different possible multiplets in the electronic configuration represented by the Kohn-Sham determinant. 

Because the convenience of the one-electron formalism is retained, DFT methods can easily take into account the scalar relativistic effects and spin-orbit effects, via either perturbation or variational methods. The retention of the one-electron picture provides a convenient means of analyzing the effects of relativity on specific orbitals of a molecule. Spin-unrestricted Hartree-Fock (UHF) calculations usually suffer from spin contamination, particularly in systems that have low-lying excited states (such as metal-containing systems). By contrast, in spin-unrestricted Kohn-Sham (UKS) DFT calculations the spin-contamination problem is generally less significant for many open-shell systems (39). For example, for transition metal methyl complexes, the deviation of the calculated UKS expectation values S (S = spin angular momentum operator) from the contamination-free theoretical values are all less than 5% (32). 

The rectangular B matrix is used in the SCF procedure instead of the usual Ldwdin matrix. Hence this method can be employed either for Hartree-Fock or Kohn-Sham equations resolution in the Roothaan formalism. The extension to the unrestricted spin case is trivial. 

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