Self-consistent field theory symmetry

The obvious disadvantage of this simple LG model is the necessity to cut off the infinite expansion (26) at some order, while no rigorous justification of doing that can be found. In addition, evaluation of the vertex function for all possible zero combinations of the reciprocal wave vectors becomes very awkward for low symmetries. Instead of evaluating the partition function in the saddle point, the minimization of the free energy can be done within the self-consistent field theory (SCFT) [38 -1]. Using the integral representation of the delta functionals, the total partition function, Z [Eq. (22)], can be written as... 

J. Paldus, Hartree-Fock Stability and Symmetry Breaking. In R. Garbo and M. Klobukowski (Eds.) Self-Consistent Field Theory and Applications (Elsevier, Amsterdam, 1990), pp. 1-45. 

The general form of the expansion is dictated by very general symmetry considerations the specific coefficients for the example of a polymer blend can be derived from the self-consistent field theory. For a... 

The self-consistent field theory phase diagram is also likely to be inaccurate at low relative molecular mass, because, like any mean-field theory, it neglects fluctuations. The effect of fluctuations is to stabilise the disordered phase somewhat (Fredrickson and Helfand 1987) in addition the seeond-order transition predicted for the symmetrical diblock is replaced by a first-order transition and, for asymmetrical diblocks, there are first-order transitions directly from the disordered into the hexagonal and lamellar phases. In addition it seems likely that fluctuations tend to stabilise high symmetry states such as the gyroid (Bates et al. 1994). 

At the age of 23, Felix Bloch published an article called Uberdie QuantemnechanikderElektronen in Kristallgittem" in Zeitschrift filr Physik, 52, 555 (1928) (only two years after Schrodinger s historic publication) on the translational symmetry of the wave function. This was also the first application of LCAO expansion. In 1931, Leon Brillouin published a book entitled Quantenstatistik (Springer Verlag, Berlin), in which the author introduced some of the fundamental notions of band theory. The first at initio calculations for a polymer were made by Jean-Marie Andre in a paper Self-consistent field theory for the electronic structure of polymers , published in the Journal of Chemical Physics, 50, 1536 (1969). 

It is evident that the approach described so far to derive the electronic structure of lanthanide ions, based on perturbation theory, requires a large number of parameters to be determined. While state-of-the-art ab initio calculation procedures, based on complete active space self consistent field (CASSCF) approach, are reaching an extremely high degree of accuracy [34-37], the CF approach remains widely used, especially in spectroscopic studies. However, for low point symmetry, such as those commonly observed in molecular complexes, the number of CF... 

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

Configuration Interaction Density Functional Theory Equation of Motion CCSD Multiconfiguration-SCF Moller Plesset 2nd Order Multireference Cl Multistate CASPT2 Restricted Active Space SCF Restricted Hartree Fock Symmetry Adapted Cluster-CI Self Consistent Field Singlestate CASPT2... 

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