TRANSFER-MATRIX METHOD FOR SUBGRAPH ENUMERATION - APPLICATIONS TO POLYPYRENE FUSENES
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A frequently encountered problem in chemical applications is that of a weighted enumeration (or summation over) a class of extended subgraphs of a given system graph, which might represent a chemical structure. Some aspects of a powerful transfermatrix method are described for treating such graphtheoretic weighted enumeration problems. This method is seen to be particularly amenable for system graphs which are long in one direction and narrow in transverse directions. When the system graph is uniform (i.e., translationally symmetric) along one extended direction, asymptotic results can be readily extracted. A second point of emphasis here is that the weighted enumeration problems of the type studied here naturally arise in computing matrix elements over cluster expanded wave functions, though most applications so far framed in the literature differ from this. Size consistency and sizeextensivity aspects of this application are noted in terms of the transfermatrix approach. Polypyrene fusene strips of varying lengths are considered as applications of the transfermatrix methods for two weighted enumeration problems. Different graphtheoretic problems are noted to arise for loworder cluster expanded wave functions, such as in fact occur in both the HerndonSimpson and the PaulingWheland resonance theories. For higherorder wave function anstze the graphtheoretic problems would simply have more complicated weights and transfer matrices, which for the present examples are very small (i.e., 2 by 2 and 3 by 3). Copyright 1986 John Wiley & Sons, Inc.
