B3-LYP exchange-correlation functional

TABLE 4.2 Enejgetic Indices for the Organic Molecules Under Study as Computed Within the Density Functional Theory With B3-LYP Exchange-Correlation (Hypercube, 2002) AU Values in Electron-Volts (eV) (Putz et al., 2010)... 

Table 2-7. Acronyms and abbreviations used for approximate exchange, correlation, and exchange-correlation functionals discussed in this work and corresponding to their common use in the literature. In some cases, the same label is applied for exchange, correlation, or exchange-correlation functionals (PW91 for instance). In some cases, the labels used in the text are obtained as combinations of the ones included here B3LYP denotes the combination of the B3 exchange- and LYP correlation functionals, for instance...

The keyword for a given density-functional method is formed by concatenating the symbols for its exchange and correlation functionals. For example, combining the Becke three-term (B3) exchange functional with the Lee-Yang-Parr (LYP) correlation functional leads to the popular B3LYP density functional method. 

Becke three-parameter exchange functional (B3) and the Lee-Yang-Parr correlation functional (LYP), A.D. Becke, J. Chem. Phys., 98 (1993) 5648 C. Lee, W. Yang and R.G. Parr, Phys. Rev. B, 37 (1988) 785. Also, see R.H. Hertwig and W. Koch, Chem. Phys. Lett., 268 (1997) 345, concerning the various implementations of B3LYP. 

The DFT methods described above are pure DFT methods. Another important class of methods is called hybrid DFT. In these methods the exchange functional is replaced by a linear combination of the Hartree-Fock exchange term and a DFT exchange functional. In addition, the various exchange and correlation functionals may themselves be constructed as linear combinations of the various available methods. For example, the popular hybrid DFT method, B3-LYP, is defined as follows (58). 

TABLE 4.7 The Same Quantities of Table 4.6 As Computed Within Various Ab Initio Approaches By Density Functional Theory Without Exchange-Correlation (noEX-C), and With B3-LYP, B3-PW91, and Becke97 Exchange-Correlations, and by Hartree-Fock method. All With Minimal (STO-3G) Basis Sets (Putz, 2010a)... 

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. 

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