Exchange-correlation enhancement factor

One way[43] to compare these GGA s (for spin-unpolarized systems) is to define the exchange-correlation enhancement factor Fxc(rs, s), by writing ... 

For high density system, the enhancement factor becomes unity, and exchange effects dominate over the correlation effects. When the density becomes lower, the enhancement factor kicks in and includes correlation effects into the exchange energies. The enhancement factor is not unique, but can be derived differently in different approximations. The most reliable ones are parameterizations of molecular Monte-Carlo data. Some well known, and regularly used, parameterizations have been made by Hedin and Lundqvist [29], von Barth and Hedin [22], Gun-narsson and Lundqvist [30], Ceperly and Adler [31], Vosko, Wilk, and Nusair [32], and Perdew and Zunger [27]. 

A more recent correlation functional is that of Lee, Yang, and Parr[54], which is often used in conjunction with Becke exchange to form BLYP. The enhancement factor for BLYP is plotted in Figure 12. The LYP functional starts from the Colle-... 

We were involved in one of such investigations of GGA functionals and want to summarize some results (see [33] and references therein). From the newly proposed GGA functionals (in addition to the standard PBE [6]) we mention the functional by Wu and Cohen (WC) [34], AMOS by Armiento and Mattssson [35] and PBEsol [36]. In GGA the exchange correlation energy can be expressed in terms of an enhancement factor Fxc... 

Because the unpolarized enhancement factor may be expressed in terms of its exchange and correlation components. Equation 14.9 separates into... 

The heat-transfer coefficient, k, for laminar flow in tubes can be enhanced by a factor of two- to sixfold using static mixer elements in the heat-exchanger tubes. The heat-transfer coefficient is correlated using the Nusselt, Prandtl, and Reynolds numbers. Table 9.21 gives constants for Koch SMX and SMXL mixers for... 

In this Section we try to understand the INS and NMR experiments on the basis of the SRI SB mean-field theory. Using a generalized RPA expression for the spin susceptibility and assuming that the AFM correlations are spatially filtered by various -dependent hyperfine form factors, we focus, in particular, on the spin dynamical properties in the paraphase of the t-t -J model. Our starting point is an RPA-like form for the exchange-enhanced spin susceptibility [5, 6, 65]... 

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