Self-consistent field calculations,

Raffenetti, R.C. Pre-processing two-electron integrals for efficient utilization in many-electron self-consistent field calculations. Chem. Phys. LeUera 20 335-338, 1973. 

Parr, R. G., and Mulliken, R. S., J. Chem. Phys. 18, 1338, LCAO self-consistent field calculation of the n electron energy levels of cis and trans-lf3-butadiene. ... 

Alexander approach to spherical geometries, while making the connection between tethered chains and branched polymers. The internal structure of tethered layers was illuminated by numerical and analytical self-consistent field calculations, and by computer simulations. 

These surfaces are all based on some combination of ab initio electronic structure calculations plus fitting. The AD and BM surfaces are based respectively in whole or in part on extended-basis-set single-configuration self-consistent-field calculations, whereas the RB and RBST calculations are based on calculations including electron correlation by Moller-Plesset fourth-order perturbation theory. For the rigid-rotator calculations R., the intramolecular internuclear distances R- and R ... 

Wright, L. R., and R. F. Borkman. 1980. Ab Initio Self-Consistent Field Calculations on Some Small Amino Acids. J. Am. Chem. Soc. 102, 6207-6210. 

We have just explained that the wave equation for the helium atom cannot be solved exacdy because of the term involving l/r12. If the repulsion between two electrons prevents a wave equation from being solved, it should be clear that when there are more than two electrons the situation is worse. If there are three electrons present (as in the lithium atom) there will be repulsion terms involving l/r12, l/r13, and l/r23. Although there are a number of types of calculations that can be performed (particularly the self-consistent field calculations), they will not be described here. Fortunately, for some situations, it is not necessary to have an exact wave function that is obtained from the exact solution of a wave equation. In many cases, an approximate wave function is sufficient. The most commonly used approximate wave functions for one electron are those given by J. C. Slater, and they are known as Slater wave functions or Slater-type orbitals (usually referred to as STO orbitals). 

Calculations of vibrational frequencies in a three-center bond as a function of Si—Si separation were performed by Zacher et al. (1986), using linear-combination-of-atomic-orbital/self-consistent field calculations on defect molecules (H3Si—H—SiH3). The value of Van de Walle et al. for H+ at a bond center in crystalline Si agrees well with the value predicted by Zacher et al. for a Si—H distance of 1.59 A. 

A selection of the predictions of the equilibrium structure of DPPC bilayers as found by numerical self-consistent-field calculations is given in the following figures. In a series of articles, the SCF predictions for such membranes were published, starting in the late 1980s. As discussed above, we will update these early predictions for the theory outlined above with updated parameter sets. The calculations are very inexpensive with respect to the CPU time, and thus variations of the parameter-set will also provide deeper insight into the various subtle balances that eventually determine the bilayer structure - the mechanical properties as well as the thermodynamic properties. 

In this review, we have presented a molecular picture of the lipid bilayer system in relation to its permeation properties, as it appears from simulations and from self-consistent field calculations. Of course, it was not possible to go into all the details. In fact, the practicalities are always much more complicated, and the fine details are only of interest to the experts. 

Wierzbicki, A., and Bowman, J. M. (1988), GVSCF A General Code to Perform Vibrational Self-Consistent Field Calculations, Comp. Phys. Comm. 51,225. 

Other experiments have been reported by Flinn, based on chemical arguments using self-consistent field calculations on various charge states in tin. Lees and Flinn (16) also conclude that AR/R is positive, although they do not give the magnitude for this term. Similar conclusions have been arrived at by Ruby and co-workers who also conclude from chemical evidence that AR is positive. 

The problem of the sign of AR/R for the divalent tin compounds was investigated by Lees and Flinn (16). In the relationship between the quadrupole splitting and chemical shift for the stannous compounds, two distinct correlations became apparent—compounds with a linear covalent bond, and compounds with a predominantly planar bond. Furthermore, there exists a linear relationship between the number of 5 p electrons and the chemical shift and hence the total 5 electron density. Using free tin ion wave functions in a self-consistent field calculation, they showed that the direct eflEect of adding 5 electrons is considerably... 

Yanai, T., Kurashige, Y., Ghosh, D., Chan, G.K-L. Accelerating convergence in iterative solutions of large active-space self-consistent field calculations. Int. J. Quantum Chem., 2009, 109, 2178-90. 

Fig. 4.2. Charge distribution and surface potential in a jellium model, (a) Distribution of the positive charge (a uniform background abruptly drops to zero at the boundary) and the negative charge density, determined by a self-consistent field calculation. (b) Potential energy as seen by an electron. By including all the many-body effects, including the exchange potential and the correlation potential, the classical image potential provides an adequate approximation. (After Bardeen, 1936 see Herring, 1992.)...

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