Alternatives to the Broken Symmetry Approach

A natural starting point is to combine a multiconfigurational SCF approach to treat the static electron correlation and DFT for the remaining (mainly dynamic) electron correlation. It is, however, not easy to design functionals that only take into account this latter part of the electron correlation and do not consider (part of) the static correlation. Despite many efforts, there seems no deflnitive solution to the double counting problem. 

Restricted ensemble Kohn-Sham DFT Alternatively one can perform standard KS-DFT calculations on a collection of determinants with different occupations and take a weighted average of the individual energies to obtain an estimate of the mul-tideterminantal situation. To avoid the independent calculation of several KS determinants, a generalization of this approach was proposed by Filatov and Shaik based on the coupling operator technique developed by Roothaan for restricted open-shell Hartree-Fock. This restricted open-shell Kohn-Sham (ROKS) approach was later extended to situations where fractional occupation numbers are not imposed by the 

Constrained DFT The basic shortcomings of the BS approach can be summarized in two points. In the first place, the spin contamination, or the impossibility to represent the low-spin states with a single Kohn-Sham determinant. The second point is the fact that nearly all todays functionals tend to overestimate the delocalization of the spin density and overestimate the anti ferromagnetic character of the coupling. 

Constrained DFT (C-DFT) remedies, at least partially, the latter by putting restrictions on the spatial distributions of the a and electrons [27], Two fragments p and q are defined such that both include one magnetic center and the atoms around it. 

Subsequently, the density is optimized under the restrictions that Na Np = M  

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