Modified weighted density approximations

To improve upon these defects, one has to go beyond the LDA The (modified) weighted density approximation [189] retains the correct asymptotic behaviour of and improves the response properties of metal clusters [162, 165]. A different route to improvement provides the self-interaction correction (SIC) of Perdew Zunger [37], where the spurious self-interaction of the LDA is compensated by additional terms in the ground-state potential [166] and in the effective perturbing potential as well [167] (Full-SIC[... 

The simulation results for coexistence properties are from Hoover and Ree [24] and the value of L is from the work of Ohnesorge et al. [135], The result from Barker s SCF theory [94] is from the leading term (order a ) in an expansion of the mean square displacement in powers of a = (p p/p) - 1 and may be an underestimate of the true value from that theory, SCF, self-consistent field LJD, Lennard-Jones and Devonshine MWDA, modified weighted-density approximation GELA, generalized effective liquid approximation FMF, fundamental measures functional. 

Mederos, L., Velasco, E., and Navascues, G. Phase diagram of colloidal systems. 1998. Langmuir 14 5652. Wang, D.C., and Gast, A.P. CrystaUization of power-law fluids A modified weighted density approximation model with a sohd reference state. 1999. 7. Ghem. Phys. 110 2522. 

Styrene udi the same technique This is slightly below the normal vdue. l/ ] values determined indirectly by the lyrplication of the modified mioothed density model are, however, considerably lower ( 0.03 . This model is known to give low values even for linear polymers but the error is approximately a factor of two. It can be made to yield correct values by changing the constant involved (Cm in Flory s notation) to force a fit with exact perturbation theory valid at low chain expansions Use of the modified smoothed density model on those branched polymers of high molecular weight (0 2 34.5°) shown in Fig. 7 would also lead to abnormally low, values (<0.1), in contrast to the normd values found directly from A2 near 6. The low j values are determined from the equation,... 

For a dilute solution, also, p is not greatly different from the density po of the pure solvent, and since this and its molecular weight Jlfo are constant, it follows from equation (32.32) that the concentration (molarity) of any aolvte in a dilute solution is approximately proportional to its mole fraction. It is possible, therefore, to modify equation (32.25) in the following manner. In the first place, if the solution is dilute, and particularly if it contains no electrolytes, the activity coefficient factor may be taken as unity, so that equation (32.25) reduces to (32.26). If the mole fractions are replaced by the corresponding molarities, utilizing equation (32.32), it is found that... 

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