Kohn orbital energies

In this formulation, the electron density is expressed as a linear combination of basis functions similar in mathematical form to HF orbitals. A determinant is then formed from these functions, called Kohn-Sham orbitals. It is the electron density from this determinant of orbitals that is used to compute the energy. This procedure is necessary because Fermion systems can only have electron densities that arise from an antisymmetric wave function. There has been some debate over the interpretation of Kohn-Sham orbitals. It is certain that they are not mathematically equivalent to either HF orbitals or natural orbitals from correlated calculations. However, Kohn-Sham orbitals do describe the behavior of electrons in a molecule, just as the other orbitals mentioned do. DFT orbital eigenvalues do not match the energies obtained from photoelectron spectroscopy experiments as well as HF orbital energies do. The questions still being debated are how to assign similarities and how to physically interpret the differences. 

Zhao, Q., R. C. Morrison, and R. G. Parr. 1994. From electron density to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies. Phys. Rev. A 50, 2138. 

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.)... 

Table 2. Orbital energies of the highest occupied Kohn-Sham orbital. The mean abst ute deviation from OPM is denoted by A...

The optimal energy for intra-orbit variation is attained at < [pop,(r) y ]. Because the functional N-representability condition is fulfilled, this value is an upper bound to (i.e., to the optimal energy within the Hohenberg-Kohn orbit as W/Hn, C ] =... 

The question arises of why not to carry out this energy minimization for an energy functional that has been defined from the outset in the Hohenberg-Kohn orbit. The answer is that if we wish to construct the exact energy density functional d [p(r) we must depart from some orbit-generating... 

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

The KS equations are obtained by differentiating the energy with respect to the KS molecular orbitals, analogously to the derivation of the Hartree-Fock equations, where differentiation is with respect to wavefunction molecular orbitals (Section 5.2.3.4). We use the fact that the electron density distribution of the reference system, which is by decree exactly the same as that of the ground state of our real system (see the definition at the beginning of the discussion of the Kohn-Sham energy), is given by (reference [9])... 

In Kohn-Sham DFT based approaches, expressions that are of similar structure as Eqs. (9a) and (9b) are obtained, but in the form of contributions from all occupied Kohn-Sham MOs The excited-state wavefunctions are at the same time formally replaced by the unoccupied MOs, and the many-electron perturbation operators /T(M41, etc. by their one-electron counterparts //(M-41, etc. Orbital energies e and ea formally substitute the total energies of the states (see later). Thus, similar interpretations of NMR parameters can be worked out in which the highest occupied MO-lowest unoccupied MO gap (HLG) plays a highly important role. It must be emphasized, though, that there is no one-to-one correspondence between the excited states of the SOS equations and the unoccupied orbitals which enter the DFT expressions, nor between excitation energies and orbital energy differences, i.e., there are no one-determinantal wavefunctions in Kohn-Sham DFT perturbation theory which approximate the reference and excited states. 

The orthogonal orbitals, which minimize the Kohn-Sham energy functional are obtained from the following set of one-electron equations21 for / = 1, N ... 

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