Gaussian local density approximations

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

Figure 12 Boxes fringe visibility as a function of Bragg excitation frequency. Error bars uncertainty due to four measurements. We observe a clear double-peaked spectrum, which is finite-time broadened. Solid line double peaked Gaussian fit. The peaks are found at 139 10 Hz, near the expected Bogoliubov local density approximation average excitation energy (138 5 Hz).

LCGTO linear combination of Gaussian-type orbitals LDA local density approximation... 

The calculations were performed with the linear combination of Gaussian type orbital density functional theory (LCGTO-DFT) deMon2k (Koster et al. 2006) code. In O Fig. 16-1, the crosses refer to all-electron polarizabilities calculated with the local density approximation (LDA) employing the exchange functional from Dirac (1930) in combination with the correlation functional proposed by Vosko, Wilk and Nusair (VWN) (Vosko et al. 1980). The stars denote polarizabilities obtained with the gradient corrected exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996). 

Kitaura, K., C. Satoko, and K. Morokuma (1979). Total energies of molecules with the local density functional approximation and Gaussian basis sets. Chem. Phys. Lett. 65, 206-11. 

For the calculations we used the Munich version of the linear combination of Gaussian-type orbital density functional (LCGTO-DF) code. ° The computationally economic local spin-density approximation (LSDA) to the exchange-correlation functional has been successfully used in chemical applications since the seventies. This functional (employed here in the parameterization suggested by Vosko, Wilk, and Nusair, has been shown to describe accurately impor-... 

Lee, C., Parr, R. G. (1987). Gaussian and other approximations to the first-order density matrix of electronic system, and the derivation of various local-density-fimctional-theories. Phys. Rev. A 35,2377-2383. 

In the mean-field treatment one approximates the square average (c ) by If we choose for the description of the mean local density (cm(r)) a Gaussian function, with a radius of gyration Rg and the maximum at the center of gravity rc... 

As the SIBFA approach relies on the use of distributed multipoles and on approximation derived form localized MOs, it is possible to generalize the philosophy to a direct use of electron density. That way, the Gaussian electrostatic model (GEM) [2, 14-16] relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. It offers the possibility of a continuous electrostatic model going from distributed multipoles to densities and allows a direct inclusion of short-range quantum effects such as overlap and penetration effects in the molecular mechanics energies. 

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