Becke functional

Nonlocal DFT with the Becke-88 functional for exchange (Ref. 107) and the Perdew-86 functional for correlation (Ref. 108). 

Nevertheless, the different values of the multiplication factor in Eq. (4.460) can explain the various forms of exchange energy coefficients and forms above. Moreover, following this conceptual line the above Becke 88 functional (4.451) can be further rearranged in a so-called Xa-Becke88 form (Lee Zhou, 1991) ... 

BH HLYP Exchange functional with equal-weighted contributions of Hartree-Fock, local spin density, and Becke functionals and Lee, Yang, and Parr s correlation functionals... 

In the widely used Becke functional [15] for the exchange, for instance, the function g(x) is given by... 

Perez-Jordy J M and Becke A D 1995 A density functional study of van der Waals forces rare gas diatomics Chem. Phys. Lett. 233 134... 

Professor Axel Becke of Queens University, Belfast has been very actively involved in developing and improving exchange-correlation energy functionals. For a good recent overview, see ... 

Becke A D 1995 Exchange-correlation approximations in density-functional theory Modern Eiectronic Structure Theory vol 2, ed D R Yarkony (Singapore World Scientific) pp 1022-46... 

Becke-Lee-Yang-Parr gradient-corrected functional for use with... 

BLYP Becke correlation functional with Lee, Yang, Parr exchange Gradient-corrected... 

B3LYP Becke-style 3-Parameter Density Functional Theory Through 2nd derivatives (using the Lee-Yang-Parr correlation functional) ... 

Becke formulated the following gradient-corrected exchange functional based on the LDA exchange functional in 1988, which is now in wide use ... 

Pure DFT methods are defined by pairing an exchange functional with a correlation functional. For example, the well-known BLYP functional pairs Becke s gradient-corrected exchange functional with the gradient-corrected correlation functional of Lee, Yang and Parr. 

Hartree-Fock theory also includes an exchange term as part of its formulation. Recently, Becke has formulated functionals which include a mixture of Hartree-Fodc and DFT exchange along with DFT correlation, conceptually defining... 

A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, /. Chem. Phys., 98, 5648 (1993). 

Here is a KS-LCAO calculation on water at the experimental geometry of 95.7pm and 104.5°. I chose the BLYP functional this comprises Becke s 1988... 

Another functional form (not a correction) proposed by Becke and Roussel (BR) has the form... 

It should be noted that several of the proposed functionals violate fundamental restrictions, such as predicting correlation energies for one-electron systems (for example P86 and PW91) or failing to have the exchange energy cancel the Coulomb self-repulsion (Section 3.3, eq. (3.32)). One of the more recent functionals which does not have these problems is due to Becke (B95), which has the form... 

Models which include exact exchange are often called hybrid methods, the names Adiabatic Connection Model (ACM) and Becke 3 parameter functional (B3) are examples of such hybrid models defined by eq. (6.35). The <, d and parameters are determined by fitting to experimental data and depend on the form chosen for typical values are a 0.2, d 0.7 and c 0.8. Owing to the substantially better performance of such parameterized functionals the Half-and-Half model is rarely used anymore. The B3 procedure has been generalized to include more filling parameters, however, the improvement is rather small. 

Mays, R.W., Beck, K.A.. Nelson, W.J. (1994). Organization and function of the cytoskeleton in polarized epithelial cells a component of the protein sorting machinery. Curr. Opin. Cell Biol. 6, 16-24. 

Chee MS, Bankeir AT, Beck S, Bohni R, Brown CM, Cerny R, Horsnel T, Hutchinson CAI, Kouzarides T, Martignetti JA, Preddie E, Satchwell SP, Tomlinson P, Weston KM, Barrel BG (1990) Analysis of the protein-coding content of the sequence of human cytomegalovirus strain AD169, Curr Top Microbiol Immunol 154 125-170 Chiu TK, Davies DR (2004) Structure and function of HIV-1 integrase. Curr Top Med Chem 4 965-977... 

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