Ensemble exchange-correlation potentials

Ami occupation numbers. The ensemble exchange-correlation potential... 

To solve the Kohn-Sham equations (13) one needs the ensemble exchange-correlation potential. In the following sections several approximate forms are discussed. 

In section 2 the theory of ensembles is reviewed. Section 3 summarizes the parameter-free theory of G par[ll]. The self-consistently determined ensemble a parameters of the ensemble Xa potential are presented. In section 4 spin-polarized calculations using several ground-state exchange-correlation potentials are discussed. In section 5 the w dependence of the ensemble a parameters is studied. It is emphasized that the excitation energy can not generally be calculated as a difference of the one-electron energies. The additional term should also be determined. Section 6 presents accurate... 

As we have seen in the previous sections the currently existing exchange-correlation potentials do not always perform well for ensemble-states. Recently, a simple Xa ensemble potential has been proposed [15]. In this section this potential is discussed and results for other atoms are presented. The form of the Xa ensemble exchange potential is... 

Fig. 4. Exchange-correlation potentials producing the accurate interacting ground state density of the C2 molecule at various bonding distances. The potential v c is the exchange-correlation potential for a ground state ensemble. The potential Vxc hole is an exchange-correlation potential that reproduces the same density for a single Slater determinant with a hole.

There is a growing interest in determining the exact exchange, exchange-correlation and Kohn-Sham potential in the knowledge of the density[31-35]. The present author has also proposed a method that enables one to calculate these potentials if the density is known [37]. This method can be applied to ensemble states without any difficulty [16]. 

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