Perdew-Wang correlation functionals

The equilibrium interconversion between an ethylene phosphite and a bicyclic spirophosphorane is shown to proceed by the insertion of the phosphite into the labile O-H bond of the hydroxyethyl ester. The mechanism is similar to the insertion of carbenes or nitrenes. Energy relationships of reaction intermediates were studied by MO RHF, MP2(full), MP4SDTQ, and DFT calculations. In most cases, they predicted that hydroxyethyl ethylene phosphates were more stable than the strained spirophosphoranes, which is not supported by the experimental evidence. The best correspondence to experimental data was obtained by DFT calculations with Perdew-Wang correlation functions <2003JST35>. 

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%. 

GGA functionals satisfy the uniform density limit. In addition, they satisfy several known, exact properties of the exchange-correlation hole. Two widely used nonempirical functionals that satisfy these properties are the Perdew-Wang (PW) functional [15] and the Perdew-Burke-Emzerhof (PBE) functional [16]. Because GGA functionals include more physical ingredients than the LDA functional, it is often assumed that GGA functionals should be more accurate than the LDA. This is quite often true, but there are exceptions. One example of such a situation is in the calculation of the surface energy of transition metals and oxides. 

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 ... 

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. 

Perdew and Wang have proposed an exchange functional similar to B88 to be used in connection with the PW91 correlation functional given below (eq. (6.30)). 

Becke, A. D., 1992b, Density Functional Thermochemistry. II. The Effect of the Perdew-Wang Generalized-Gradient Correlation Correction , J. Chem. Phys., 97, 9173. 

Thus it is of some interest to know if the Stoll ansatz is correct, especially since several other ansUtze have been developed and used as input to a spin-resolved pair correlation function. For example, Perdew and Wang (PW) [51,52] proposed a scaling relation... 

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