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 αβ 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 −c∫ραρβ/(ρ(1+dρ−1/3))dr. It reproduces the αβ correlation energies of (He–Ar) to a very high accuracy. The correlation functional which represents σσ correlation is more complex, because the two particle Hartree–Fock density matrix is zero at electron coalescence. The functional must therefore depend upon (∇ρ)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 αβ correlation, and two i...

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