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By Ramon Carbo, Joseph M. Riera

We stay in a molecular global, nearly closed shell in nature, and accordingly Chemistry has been a technological know-how facing closed shell mol­ ecules. even if, the excessive measure of experimental sophistication reached some time past decade has made extra obvious the function of open shell constructions in chemical learn. A parallel phenomenon might be saw within the improvement of SCF thought, the place closed shell molecular calculations at any point of complexity compose the most physique of references which are acquired in Quantum Chemistry this day. along with the linkage among experimental and theoretical behaviour, there are, evidently, different purposes which are connected to an absence of molecular open shell calculations. between others, there has been no connec­ tionbetween closed or open shell theoretical remedies. during this demeanour, many computational good points utilized by closed shell connoisseurs haven't been prolonged to different computational components. because the paintings of Roothaan in 1960, the open shell molecular panorama has been, the­ oretically, a really closed one. additional improvement of SCF thought, which has ended in an outburst of multiconfigurational approaches, has paid no, or very faint, realization to the interconnection among those SCF idea complex positive aspects, the open shell framework and closed shell universal perform. an exceptional theoretical target, mostly talking, and specifically inside of SCF concept, might encompass a method which might be used to resolve a given chemical challenge, in the actual and approx­ imate limits of the theory.

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Example text

SjO;i>; l. iEP. The implications become more apparent if we consider the case where all eigenvalues have a common shifting parameter, say, A o;v has now a manyfold degeneracy and the eiThen, the eigenvalue A o,v genvectors have an accompanying arbitrariness. NOW, going back to the general case, where the matrix M is not necessarily diagonal with respect to the vectors {Io;p>}, PEP, and considering a new matrix T, with elements defined according to the expression 26 (10. III) t .. = O•• A ~J ~J .

Finally, the last point of interest has been the need to obtain a PE procedure capable of studying excited states: It should be mentioned, for instance, that the mainline of computational tasks until now been carried out on a Closed Shell basis. has The present formalism will take this last situation as a particular case within the general MCPE framework. 1. Closed Shell MCPESCF Theory A discussion of the framework proposed by Veillard and Clementi and its description from a simpler point of view zation purposes.

2 Wpq hlq>, which is a very well known expression in the monoconfigurational closed shell cases, where R = F. III. Eigenspace Manipulations 1. Introduction Although the formal results of this section can have multiple applications, they were originally studied for application to SCF theory, and even in their original form they can be used in the framework of a unique coupling operator formalism. In order to develop a useful theoretical background with immediate application to a computational algorithm, the most convenient procedure is to start with a generalized secular equation in matrix form (1.

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