Gradient-corrected correlation

Similarly, there are local and gradient-corrected correlation functionals. For example, here is Perdew and Wang s formulation of the local part of their 1991 correlation functional ... 

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. 

Different functionals can be constructed in the same way by varying the component functionals—for example, by substituting the Perdew-Wang 1991 gradient-corrected correlation functional for LYP—and by adjusting the values of the three parameters. 

The corresponding gradient-corrected correlation functionals have even more complicated analytical forms and cannot be understood by simple physically motivated reasonings. We therefore refrain from giving their explicit expressions and limit ourselves to a more qualitative discussion of the most popular functionals. Among the most widely used choices is the correlation counterpart of the 1986 Perdew exchange functional, usually termed P or P86. This functional employs an empirical parameter, which was fitted to the... 

An alternative approach was offered by Lee, Yang, and Parr [19], who derived a gradient-corrected correlation functional ( LYP ) from the second-order density matrix in HF theory. Together with PW91, this functional is currently the most widely used correlation functional for molecular calculations. 

LYP gradient-corrected correlation functional by Lee, Yang and Parr... 

The interaction of the acetylene molecule with the (100) surface of copper was studied using the cluster model approach. All the calculations have been performed using the Density Functional Theory. The BLYP method included in the Gaussian 98 [30] package was used. This method combines the gradient corrected exchange functional of Becke [31] with the gradient corrected correlation functional of Lee et al [32]. 

Dynamical electron correlation effects are intrinsically included in DFT methods via the local and gradient-corrected correlation functionals. Most importantly, the nondynamlcal electron correlation effects have been partially accounted for via the exchange functionals (33,34). As a consequence, the multiconfiguration characters that often show up in traditional ab initio calculations using Hartree-Fock references could be sUghtly reduced in DFT methods. In other words, for approximating the true electronic stmctures of many-electron atoms and molecules... 

Ecovr is the gradient corrected correlation, namely the Lee-Yang-Parr (LYP) functional [31]... 

Commonly used gradient-corrected correlation functionals E include the Lee-Yang-Parr (LYP) functional, the Perdew 1986 correlation functional (P86 or Pc86), the Perdew-Wang 1991 parameter-free correlation functional (PW91 or PWc91), and the Becke correlation functional called Bc95 or B%. 

TTie gradient corrected correlation functional reads as (Savin et al., 1984) ... 

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