Multi-determinantal wavefunction

We may ask now, whether the same procedure may be applied to density-functional theory, just by replacing the Fock operator by the corresponding Kohn-Sham operator. To this end we have to look at the minimization of the total energy with respect to the density of a multi-determinantal wavefunction 4. We write the density as ... 

Unfortunately, in many situation of interest, both static and dynamic electronic correlation need to be taken into account. This is particularly true for the study of processes involving excited electronic states as in UV spectroscopy or in photochemistry. In this case, methods capable of taking into account the dynamic electronic correlation on top of a multi-determinantal wavefunction of the MCSCF type are needed. These methods are usually called multi-reference methods. The two standard methods that are able to account for both the static and dynamic electronic correlation are the multi-reference configuration interaction (MRCI) and several variants of second-order multi-reference perturbation theory (MRPT). 

For a systematic study of many related systems, a practical but nevertheless reliable approach had to be identified. It is clear that the reactions of the type depicted in Fig. 8.5 inherently have some diradical and hence multi-determinantal character. Therefore, semiempirical, HF and MP2 methods are unsuitable approaches because a single-reference will not be able to describe all the species involved equally well. DFT may be an option but it is also single-reference however, as it is not the wavefunction that is the operand but the electron density, DFT may still do a reasonable job in describing these reactions. The simple take on this is that the density may be well-behaved even if the wavefunction is not. For instance, DFT has been proven to work exceptionally well for carbenes although singlet carbenes are... 

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