A dynamical correlation functional

The purpose of this work is to search for a justifiable form for a molecular dynamic correlation functional. A detailed examination of Colle and Salvetti's derivation of the LYP functional is presented. It is argued that the leading term is all important, and furthermore that it should account for alphabeta correlation. This term only depends upon the densities, and it has a truncation factor which is obtained from the size of the correlation hole. It is -cintegralrho(alpha)rho(beta)/(rho(1+drho(-1/3)))dr. It reproduces the alphabeta correlation energies of (He-Ar) to a very high accuracy. The correlation functional which represents sigmasigma correlation is more complex, because the two particle Hartree-Fock density matrix is zero at electron coalescence. The functional must therefore depend upon (delrho)(2). Using these and related arguments we have found a four parameter generalized gradient functional which appears to perform nearly as well as the LYP functional. However unlike the LYP functional, it has two identifiable terms for alphabeta correlation, and two identifiable terms for sigmasigma correlation. Together with our previously derived exchange functional, we have therefore obtained an exchange-correlation functional for molecular studies, the form for which can be more understandably justified. The performance of this new Generalized Gradient Approximation functional for molecular predictions is reported. It is a considerable improvement on the BLYP functional, and is in the category of an optimum Generalized Gradient functional. Finally the present status of the science of searching for exchange-correlation functions is reviewed. It is suggested that it may not be possible to find a local functional which is significantly more accurate for chemistry than the presently used Generalized Gradient Approximation functionals. (C) 2002 American Institute of Physics.