The Lee-Yang-Parr Correlation Potential

Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density Chengteh Lee, Weitao Yang and Robert G. Parr Physical Review B 37 (1988) 785-789 

The great challenge is to develop improved functionals for molecular studies, and a great deal of effort is currently going into such studies. 

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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. 

B3LYP = Becke s 3-parameter hybrid functional using the nonlocal correlation functional due to Lee, Yang, and Parr BP = nonlocal exchange correlation functional due to Becke and Perdew DF = Dirac-Fock DIIS = direct inversion of iterative subspace KS = Kohn-Sham LDA = local density approximation LSDA = local spin density approximation (R)ECP = (relativistic) effective core potential TM = transition metal. 

The form of F(p, Vp) varies and often contains empirical parameters. F(p, Vp) is frequently termed a gradient or non-local correction, since the potential is computed not only as a funcion of the location but also as a function of the Laplacian of the charge density, Vp(r). Of course, even these nonlocal functionals are perfectly local in a mathematical sense. The development of nonlocal exchange functionals is dominated by Becke, who has published a number of increasingly refined mathematical expressions for F(p, Vp) since 1983 (B). Nonlocal correlation functionals have been proposed by Perdew (P), Lee, Yang, and Parr (LYP), and Perdew and Wang (PW). The most commonly used nonlocal functional combinations are BP, BLYP and BPW. Earlier correction schemes like the self-interaction correction by Stoll, PreuB, and Pavli-dou (SPP) have been found to be inferior to the gradient-corrected functionals in most cases and seldom appear in the literature. 

Lee CT, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation energy formula into a functional of the electron density. Phys Rev B 37 785 Leligny H, Monier JC (1975) Structure de CdCl2 4H2O. Acta Cryst B 31 782-732 Li J, Fisher CL, Chen JL, Bashford D, Noodleman L (1996) Calculation of redox potentials and pKa values of hydrated transition metal cations by a combined density functional and continuum dielectric theory. Inorg Chem 35 4694-4702... 

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