DFT Techniques to Calculate Excitations

Another promising method was recently proposed by A. Gorling [28]. The so-called generalized adiabatic connection Kohn-Sham formalism is no longer 

It is also possible to calculate excitation energies from the ground-state energy functional. In fact, it was proved by Perdew and Levy [30] that every extremum density rii r) of the ground-state energy functional Ey[n] yields the energy Ei of a stationary state of the system. The problem is that not every excited-state density, rii r), corresponds to an extremum of Ev n], which implies that not all excitation energies can be obtained from this procedure. 

The last member of the first group of methods was proposed by Ziegler, Rauk and Baerends in 1977 [31] and is based on an idea borrowed from multiconfiguration Hartree-Fock. The procedure starts with the construction of many-particle states with good symmetry, by taking a finite superposition of states 

By taking the expectation value of the Hamiltonian in the state we arrive 

This method works quite well in practice, and was frequently used in quantum chemistry till the advent of TDDFT. We should nevertheless indicate two of its limitations i) The decomposition (4.85) is not unique and the system of linear equations can be under- or overdetermined, ii) The whole procedure of the recipe is not rigorously founded. 

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