Exchange potential Hartree-Fock

The SCF-Xa-SW method makes the following major assumptions. First one replaces the nonlocal Hartree-Fock exchange potential with the Xa local exchange potential that corresponds to the average exchange potential of a free electron gas. The exchange potential is related to the local electronic density by... 

From the application of the free-electron approximation in the Hartree-Fock exchange potential... 

This method is an extension of the Sharp-Hornton method for producing the local effective Hartree-Fock exchange potential (Sharp and Hornton 1953),... 

This integral equation simply produces the same effect as the localization of the nonlocal Hartree-Fock exchange potential. 

In the ab initio DFT, the exact exchange (EXX) potential and frequently its hybridization with the Hartree-Fock exchange potential is used as the exchange potential. The EXX potential that Gorling and Levy developed is a Kohn-Sham orbital-dependent potential (Gorling and Levy 1994 Ivanov et al. 1999),... 

This equation is based on the OEP method, as recognized from its similarity to Eq. (7.40). Even though the EXX potential produces valence orbital energies that are exactly similar to those of the Hartree-Fock exchange potential, it provides core orbital energies that are much different from the Hartree-Fock ones. Combining... 

Nikolic G, Shimazaki T, Yoshihiro A (eds) (2011) Fourier transforms, Gaussian and Fourier Transform (GFT) method and screened Hartree-Fock exchange potential for first-principles band structure calculations. 15-36... 

Hence for two different pairs of ki and k2 vectors giving the same K vector, we should get the same value of (ki Viex k2). In Fig. 1, we keep the K vector fixed but vary the ki and k2 pair. HFEGE and AAFEGE (as examples of V iex) give straight lines, as they depend on fixed K vector, but use of the Hartree-Fock exchange potential Vex (5)... 

There is an ongoing effort to improve the density functionals. Becke interpolated in linear sums between DFT and Hartree-Fock exchange potentials to agree with the experiments and accurate calculations. The most popular of these potentials is a three-parameter hybridization between Hartree-Fock and local exchange by Becke (B3). The potential also includes correlation potentials based on correlation theory of Lee, Yang, and Parr (LYP). This method is thus referred to as B3LYP. 

It was empirically found that, in a calculation of the electron structure of crystals with nonlocal exchange, the integration of the Hartree-Fock exchange potential over the direct lattice requires a so-called exchange-interaction radius to be introduced. The exchange-interaction radius cannot be arbitrarily large but must correspond to the used number of points k in the Brillouin zone. 

Lelj, F., C. Adamo, and V. Barone. 1994. Role of Hartree-Fock exchange in density functional theory. Some aspects of the conformational potential energy surface of glycine in the gas phase. Chem. Phys. Lett. 230, 189. 

For the special case that the exchange-correlation potential is the Hartree-Fock exchange, Eqs. (26) and (30) are identical. 

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