Orbital energy Kohn-Sham

By the way, through ensemble theory with unequal weights, Ref. [68] identifies an effective potential derivative discontinuity that links physical excitation energies to excited Kohn-Sham orbital energies from a ground-state calculation.)... 

The second [35], with the highest occupied Kohn-Sham orbital energy and is identified to be the negative of the first ionization potential... 

Chong DP, Gritsenko OV, Baerends EJ (2002) Interpretation of the Kohn-Sham orbital energies as approximate vertical ionization potentials, J. Chem. Phys, 116 1760-1772... 

In this section we are going to develop a different approach to the calculation of excitation energies which is based on TDDFT [69, 84, 152]. Similar ideas were recently proposed by Casida [223] on the basis of the one-particle density matrix. To extract excitation energies from TDDFT we exploit the fact that the frequency-dependent linear density response of a finite system has discrete poles at the excitation energies of the unperturbed system. The idea is to use the formally exact representation (156) of the linear density response n j (r, cu), to calculate the shift of the Kohn-Sham orbital energy differences coj (which are the poles of the Kohn-Sham response function) towards the true excitation energies Sl in a systematic fashion. 

Table 1. The lowest S - P excitation energies of various atoms. The experimental values (first column) [226] are compared with results calculated from Eq. (362) for the singlet and from Eq. (363) for the triplet (second column) and with ordinary Ascf values (third column). The LDA was employed for v c and the ALDA for the xc kernels. The corresponding Kohn-Sham orbital-energy differences Oo are shown in the last column (All values in rydbergs)...

The optimized effective potential was used for and the ALDA for the xc kernels. The corresponding Kohn-Sham orbital-energy differences coo are shown in the last column (All values in rydbergs)... 

Politzer and Abu-Aw wad61 studied the calculated single-particle energies for 12 smaller molecules and compared them with experimental ionization potentials. They found that the Kohn-Sham orbital energies were at least 2 eV too high... 

Why does the Kohn-Sham method accurately reproduce orbital energies only with the use of long-range corrected functionals The cause is clarified by looking into the dependence of orbital energies on the occupation number. It is established that Kohn-Sham orbital energies have the dependence on the occupation number (Tsuneda et al. 2010),... 

In Equation (11), S represents the overlap matrix, c the molecular orbital coefficient matrix, and e the Kohn-Sham orbital energies. The expansion coefficients of the approximate density, necessary for the construction of the Kohn-Sham matrix, are calculated by the minimization of... 

As the external potential does not have any special pole structure as a function of Lo, (4.61) implies that also n r,u)) has poles at the excitation energies, 17. On the other hand, xks has poles at the excitation energies of the non-interacting system, i.e. at the Kohn-Sham orbital energy differences e,-e,[cf.(4.63)]." "... 

The highest occupied Kohn-Sham orbital energy is equal to the exact first ionization energy. This is a property that is very desirable in qualitative MO theory in general and is often simply assumed in such theories. 

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