Coulomb/exchange -fitting

It should be noted that the RI and local approximations are not completely black box. For the RI approximation, one must choose an auxiliary basis set. In Table 4 we have used the coulomb/exchange-fitting (JK-fitting) auxiliary basis for the Hartree-Fock part of the computation, and the MP2-fitting auxiliary basis for the computation of the correlation energy. It is possible that further investigation might yield even more efficient auxiliary basis sets. 

Dgauss A1 DFT Coulomb and exchange fitting. Available for H(4s) through Xc lOs5p5d). 

Functional fonns based on the above ideas are used in the FIFD [127] and Tang-Toeimies models [129], where the repulsion tenn is obtained by fitting to Flartree-Fock calculations, and in the XC model [92] where the repulsion is modelled by an ab initio Coulomb tenn and a semi-empirical exchange-repulsion tenn Cunent versions of all these models employ an individually damped dispersion series for the attractive... 

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

Interactions between cationic micelles and uni- and divalent anions have been treated quantitatively by solving the Poisson-Boltzmann equation in spherical symmetry and considering both Coulombic and specific attractive forces. Predicted rate-surfactant profiles are similar to those based on the ion-exchange and mass-action models (Section 3), but fit the data better for reactions in solutions containing divalent anions (Bunton, C. A. and Moffatt, J. R. (1985) J. Phys. Chem. 1985, 89, 4166 1986,90, 538). 

The evaluation to the desired numerical accuracy of the density functional total energy has been a major obstacle to such calculations for many years. Part of the difficulty can be related to truncation errors in the orbital representation, or equivalently to basis set limitations, in variational calculations. Another part of the difficulty can be related to inaccuracies in the solution of Poisson s equation. The problem of maximizing the computational accuracy of the Coulomb self-interaction term in the context of least-squares-fitted auxiliary densities has been addressed in [39]. A third part of the difficulty may arise from the numerical integration, which is unavoidable in calculating the exchange and correlation contributions to the total energy in the density functional framework. 

This disparity between extended systems and molecules motivates the approach used in GTOFF. As summarized in the introduction (recall Eq. (9)), GTOFF does exchange-correlation fitting to reference quantities evaluated with the fitted spin densities that are the output of the variational Coulomb fitting procedure, a procedure called fit-to-fit . In that procedure, rather than use Eq. (62), we approximate further ... 

Notice now that we are proposing to model the whole core potential at once from now on we do not make any attempt to fit the pseudopotential, the Coulomb potential or the exchange potential separately. We assume that these three components may all be collected together and fitted by a suitably flexible single expansion method. 

A double -STO basis (8) was employed for the ns and np shells of the main group elements augmented with a single 3d STO function, except for Hydrogen where a 2p STO was used as polarization. The ns, np, nd, (n + l)s and (n + l)p shells of the transition metals were represented by a triple -STO basis (5). Electrons in shells of lower energy were considered as core and treated according to the procedure due to Baerends et al. (2). The total molecular electron density was fitted in each SCF-iteration by an auxiliary basis (9) of s, p, d, f and g STOs, centred on the different atoms, in order to represent the Coulomb and exchange potentials accurately. 

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