Local density approximation distributions

In the local density approximation it is assumed that at each point r in the inhomogeneous electron distribution (i.e. in the system of interest) where the density is p(r) then Vxc[p(r)] and Sxc p )) have the same values as in the homogeneous electron gas. In other words, the real electron density surrounding a volume element at position r is replaced by a constant electron density with the same value as at r. However, this constant electron density is different for each point in space (Figure 3.6). 

The local density approximation (LDA) is valid only in the region of slowly varying electron density. The LDA approximation is obviously an oversimplification of the actual density distribution and is well-known to lead to calculated bond and binding energies that are over-predicted. 

This density function provides the distribution of the particles centered around their lattice sites (Tarazona 1985). In this approach, the free energy is considered to be the functional F[p(r)] of the density distribution p(r) thus a general free energy functional can be expressed with the local density approximation as follows ... 

Faulkner, Wang and Stocks [2, 3] have analysed the distribution of charges in binary metallic alloys as obtained from LSMS calculations. They have studied large supercells with periodic boundary conditions containing hundreds of atoms and designed to simulate substitutional disorder. LSMS calculations are based on the local density approximation to the density functional theory [4, -5] and the muffin-tin approximation for the crystal potential thus the results of their analysis hold within the same approximations. Below we shall summarize and comment the conclusions obtained in Refs. [2, 3] that are relevant for our present concerns ... 

We test three theories for adsorption and capillary condensation in pores against computer simulation results. They are the Kelvin equation, and two forms of density functional theory, the local density approximation (LDA) and the (nonlocal) smoothed density approximation (SDA) all three theories are of potential use in determining pore size distributions for raesoporous solids, while the LDA and SDA can also be applied to mlcroporous materials and to surface area determination. The SDA is found to be the most accurate theory, and has a much wider range of validity than the other two. The SDA is used to study the adsorption of methane and methane-ethane mixtures on models of porous carbon in which the pores are slit-shaped. We find that an optimum pore size and gas pressure exists that maximizes the excess adsorption for methane. For methane-ethane mixtures we show the variation of selectivity with pore size and temperature. 

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