Self-consistent field theory generation

Asakura and Oosawa (5) first identified depletion as a mechanism for generating an attractive interparticle potential. Numerous elaborations of their simple model followed, including sophisticated lattice and self-consistent field theories. Recently, Evans (27) resolved some inconsistencies in the evaluation of the effective pair potentid between the original niave model and the subsequent detailed analyses and achieved quantitative consistency between predictions and the detailed experiments employing bilayer membranes in a micropipette device. 

The unique density dependence of fluid properties makes supercritical fluids attractive as solvents for colloids including microemulsions, emulsions, and latexes, as discussed in recent reviews[l-4]. The first generation of research involving colloids in supercritical fluids addressed water-in-alkane microemulsions, for fluids such as ethane and propane[2, 5]. The effect of pressure on the droplet size, interdroplet interactions[2] and partitioning of the surfactant between phases was determined experimentally[5] and with a lattice fluid self-consistent field theory[6]. The theory was also used to understand how grafted chains provide steric stabilization of emulsions and latexes. 

Now we have written down a wave function appropriate for use in the case where H = h(i). In HF theory, we make some simplifications so many-electron atoms and molecules can be treated this way. By tacitly assuming that each electron moves in a percieved electric field generated by the stationary nuclei and the average spatial distribution of all the other electrons, it essentially becomes an independant-electron problem. The HF Self Consistent Field procedure (SCF) will be bent on constructing each x(x) to give the lowest energy. 

In advanced Slater theory, more than one Slater function is taken in a linear combination to generate the best approximation to particular atomic orbitals and we have seen that this best standard could be based on the degree of fit to the numerical radial functions or the linear combinations that returned the variation principle best eigenvalue. In such cases, these coefficients are undetermined until the best eigenvalues have been calculated and the overall requirement of normalization is imposed. This is a general problem, which leads us to the theory of the self-consistent field (57,58,61,62, 42,47,53) developed by Hartree in his early calculations (1) and to Chapter 5. 

Jensen, H. J. Aa., Jprgensen, R, Agren, H., and Olsen, J. (1988a). Second-order Mpller-Plesset perturbation theory as a configuration and orbital generator in multiconfiguration self-consistent field calculations. J. Chem. Phys., 88, 3834-3839. 

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