Kohn-Sham determinants

Savin, A., 1995, Beyond the Kohn-Sham Determinant , in Recent Advances in Density Functional Methods. Part I, Chong, D. P. (ed.), World Scientific, Singapore. 

The Kohn-Sham determinant is the single determinant which reproduces the electron density and minimises the kinetic energy [1,9].) They observed that for the Be atom, the Kohn-Sham orbitals were nearly indistinguishable from the HF orbitals, and on this evidence they claim that the problem of finding a physically meaningful wave function from an electron density is solved . Here, we merely note that there are a number of desirable features for our model ... 

A very different approach has been followed by Zhao et al. [54-57] who based their method on the constrained search definition of the Kohn-Sham kinetic energy. It follows from this definition that, from all Slater determinants which yield a given density, the Kohn-Sham determinant will minimize the kinetic energy. Suppose we have an exact density po- If one minimizes the Kohn-Sham kinetic energy under the constraint... 

Due to the spin polarization effect, the magnetic orbitals can be difficult to identify from a spin-unrestricted calculation. Since the total energy of a Kohn—Sham determinant is invariant under unitary transformations between the spin-up orbitals among each other and spin-down orbitals among each other, one can arrange each spin-up orbital to overlap at most with each spin-down orbital on the basis of the corresponding orbital transformation (COT) (88—90). Then, the molecular orbitals (MOs) are ordered into pairs of maximum similarity between spin-up and spin-down orbitals and can be separated into three groups (i) the MOs with spatial overlap close to one (doubly occupied MOs),... 

Denoting 0) as the unperturbed Kohn-Sham determinant, we have the following representation for the reference Kohn-Sham determinant... 

Hartree-Fock (UHF) formalism and suffers from the same drawbacks when dealing with open-shell systems [71]. This is especially important when attempting to study magnetic systems with many open shells. The unrestricted Kohn-Sham determinant corresponds necessarily to a mixture of the different possible multiplets in the electronic configuration represented by the Kohn-Sham determinant. 

Here 0) is tire unperturbed Kohn-Sham determinant, and /<( ) the anti-Hermitian operator... 

The second term in Eq. (2), AEp ui , refers to the repulsive interactions between the fragments, which are caused by the fact that two electrons with the same spin cannot occupy the same region in space. AEp ui is calculated by enforcing the Kohn-Sham determinant on the superimposed fragments to obey the Pauli principle by antisymme-trization and renormalization. The stabilizing orbital interaction term, which is... 

The minimum energy Kohn-Sham determinant is of closed shell type py orbital doubly occupied), but 6p 6p configurations also... 

The total wave function is a Slater determinant, which ui our situation should be called the Kohn-Sham determinant instead. The electronic density distribution of such a system is given by Eq. (11.7) and the density distribution po means exact i.e., correlated 100% (thanks to the wonder and unknown operator no). 

In fact, this is Kohn-Sham exchange energy [see Eq. (11.72)], because the Slater determinant wave function used to calculate it is the Kohn-Sham determinant not the Hartree-Fock one. 

The DFT exchange energy (E ) is calculated in the same way as in the Hartree-Fock method, but with the Kohn-Sham determinant The correlation energy Ec represents just a rest. 

Since the Kohn-Sham electrons do not interact, their wave function represents a single Slater determinant (caUed the Kohn-Sham determinant). 

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