Exchange-correlation potential definition

The theorem holds if the exchange-correlation potential VXc equals the functional derivative of the exchange-correlation energy /iXc with respect to the electron density p - an operational definition, which is intrinsic to DFT. 

Table II presents the first excitation energies obtained from spin- polarized calculations [24]. As ground-state exchange-correlation potentials were used the extra term in Eq.(20) does not appear. This is, certainly, one of the reasons for the difference between the calculated and the experimental excitation energies. There is a definite improvement comparing with the nonspin-polarized results [13]. Still, in most cases the calculated excitation energies are highly overestimated. The results provided by the different local density approximations are quite close to each other. The best one seems to be the Gunnarson-Lundqvist-Wilkins approximation. (In non-spin-polarized case the Perdew-Zunger parametrization gives results closest to the experimental data[30].)...

Dalton s atomic theory, overview, 1 De Broglie equation, 23 Delocalization energy, definition, 174 Density functional theory chemical potential, 192 computational chemistry, 189-192 density function determination, 189 exchange-correlation potential and energy relationship, 191-192 Hohenberg-Kohn theorem, 189-190 Kohn-Sham equations, 191 Weizsacker correction, 191 Determinism, concept, 4 DFT, see Density functional theory Dipole moment, molecular symmetry, 212-213... 

After immediate suppressing of the A factor in all the terms and by considering the exchange-correlation potential with the formal definition ... 

Substituting this expression and the definition of the approximate exchange-correlation potential O Eq. 16.42 into O Eq. 16.41 yields ... 

The answer is yes, in a very general way, as has been discussed before [62,63]. Consider any parameter in the external potential, called y. For definiteness, we choose the internuclear separation in a diatomic molecule. Then the exchange-correlation energy depends parametrically on this quantity. Now imagine making an infinitesimal change in y. The differential change in is... 

In the definition of the KS potential the Hartree-potential vh and the exchange-correlation term are functionals of n(r, t), function of time and space. The Hartree potential however is defined as... 

As mentioned above, the nuclei are assumed to be fixed and are thus nothing more than sources of an external electrostatic potential in which the electrons move. If there is no magnetic field external to the molecule under consideration, and if external electric fields are time-independent, we arrive at the so-called electrostatic limit of relativistic density functional theory. Note that most molecular systems fall within this regime. In this case, one can prove the relativistic Hohen-berg-Kohn theorem using the charge density, p(r) = J f), only. This leads to a definition of an exchange-correlation functional -Exc[p( )]... 

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