APPLICATIONS OF THE CATASTROPHE THEORY (CT) IN THE STUDY OF THE SCF THEORY AND METHOD
Journal Title: Analele Universitatii din Bucuresti. Chimie - Year 2009, Vol 18, Issue 2
Abstract
The energetic SCF(selfconsistent field) functionals (the SCF energy(I), the rotational increment of the SCF energy(II) and the rotational gradient of of SCF Lagrange multipliers(III)) are fitted by the catastrophe structures(CSs), allowing applications of the of the catastrophe theory(CT) in the study of the SCF theory and method. Through (I)-(II), in the SCF theory, rise qualitatively distinct problems by CT. They reduce themselves to a unique general problem with the stages: (a) the finding of the polynomial form (I)-(III) possibly to be approximated by the catastrophe potentials(CPs) (or the unfoldings of the catastrophe); (b) the identification of the parameter α of the behaviour(or state) for (a); (c) the inducing of the k-jets and the corresponding CPs; (d) the research of the extremum (minimum) of the critical points of CSs that fit the hypersurfaces (I)-(III); (e) the computation and analysis of the integral quadratic error as a measure of the degree of the fitting of (I)-(III) by the CSs; (f) the interpretation of the general results (a)-(e) by the peculiarity of the SCF problem risen by (I)-(III).
Authors and Affiliations
V. Scridonesi-Calin, A. Mihailescu
Keywords
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