Gaussian exchange-correlation

Her workers to fit the exchange-correlation potential and the charge density (in the Coulomb potential) to a linear combination of Gaussian-typc functions. 

Ab initio density functional theory calculations were also carried out on the CH2=XH(A) and CH(A)=XH2 series of molecules. The basis set used was the CEP-TZDP+ described previously26 and is more extensive than the DZP basis set used in the CAS(4,4)-OVB calculations. In TZDP+ the valence electron wave function is expanded in a triple-zeta sp set of functions plus a double set of polarization d-type functions plus a set of diffuse sp-type functions. The B3LYP exchange-correlation functional20 as defined in the Gaussian 94 program set35 was used in all the DFT calculations. 

In this study of the 3d metal oxides (ScO - ZnO) the popular hybrid functional B3LYP was used. The Gaussian 94 [20] and Gaussian 98 [21] programs were used. In these, the B3LYP exchange-correlation functional is of the form [22] ... 

Here, h is the one electron matrix in the non-orthogonal Gaussian basis and G (P ) is the two electron matrix for Hartree-Fock calculations, but for DFT it represents the Coulomb potential. The term Exc is the DFT exchange-correlation functional (for Hartree-Fock Exc = 0), while Vmn represents the nuclear repulsion energy. In the orthonormal basis, these matrices are h = etc., where the overlap... 

Linear Combinations of Gaussian Type Orbitals (LCGTO-LSD) (22) Gaussian basis fits for density and exchange-correlation most similar to "ab initio" analytical integrals accurate total energy possible... 

Here a and b stand for orbital basis functions and c denotes Gaussian functions used in the fitting of the electron density or the exchange-correlation potential. Most of the time is spent in the computation of I. We can rewrite the original Obara and Saika formula (15) in a form suitable for computation of three-index integrals ... 

Integrals involving the exchange-correlation potential r,c or the exchange-correlation energy density cannot be evaluated analytically so that further sets of auxiliary functions are introduced. (In practice and 6,<, behave similarly so that a common set is used to fit both functions.) The exchange-correlation basis (XCB) also consists of Hermite Gaussians... 

Overlap, kinetic-energy, nuclear-attraction and two-electron-repulsion integrals can all be written in this general form. The matrix elements of the exchange-correlation contribution to the energy in Kohn-Sham theory cannot, however. They are so awkward that a second basis set (usually of the Gaussian or Delta type) must be introduced to permit the computation. This, however, lies beyond the scope of our present Review. 

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