Correlation functions structural parameters from

Having determined the effect of the diffusive interfaces on the structure parameters, we now turn to the calculation of H and K in microemulsions. In the case of oil-water symmetry three-point correlation functions vanish and = 0. In order to calculate K from (77) and (83) we need the exphcit expressions for the four-point correlation functions. In the Gaussian approximation... 

MNDOC has the same functional form as MNDO, however, electron correlation is explicitly calculated by second-order perturbation theory. The derivation of the MNDOC parameters is done by fitting the correlated MNDOC results to experimental data. Electron correlation in MNDO is only included implicitly via the parameters, from fitting to experimental results. Since the training set only includes ground-state stable molecules, MNDO has problems treating systems where the importance of electron comelation is substantially different from normal molecules. MNDOC consequently performs significantly better for systems where this is not the case, such as transition structures and excited states. 

The nonlocal diffuse-layer theory near Eam0 has been developed283 with a somewhat complicated function oLyjind of solvent structural parameters. At low concentrations,/ ) approaches unity, reaching the Gouy-Chapman Qatc- 0. At moderate concentrations, deviations from this law are described by the effective spatial correlation range A of the orientational polarization fluctuations of the solvent. 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

Having obtained two simultaneous equations for the singlet and doublet correlation functions, X and, these have to be solved. Furthermore, Kapral has pointed out that these correlations do not contain any spatial dependence at equilibrium because the direct and indirect correlations of position in an equilibrium fluid (static structures) have not been included into the psuedo-Liouville collision operators, T, [285]. Ignoring this point, Kapral then transformed the equation for the singlet density, by means of a Laplace transformation, which removes the time derivative from the equation. Using z as the Laplace transform parameter to avoid confusion with S as the solvent index, gives... 

As implied by the name, a correlated wavefunction takes into account at least some essential parts of the correlated motion between the electrons which results from their mutual Coulomb interaction. As analysed in Section 1.1.2 for the simplest correlated wavefunction, the helium ground-state function, this correlation imposes a certain spatial structure on the correlated function. In the discussion given there, two correlated functions were selected a three-parameter Hylleraas function, and a simple Cl function. In this section, these two functions will be represented in slightly different forms in order to make their similarities and differences more transparent. 

The EHCF formalism allows us to separate electronic variables in the (/-shell, which require correlated and quantum description from the electrons in the rest of the complex. Then the EHCF assumes the HFR approximation for the electronic wave function of the /-system in order to establish the necessary parameters of the electronic structure. According to [37] (see also Section 1.7.2) the total electronic energy of the n-th state of a system with the wave function of eq. (2.103) is... 

---