ON MATRICES WHICH ANTICOMMUTE WITH A HAMILTONIAN, WITH APPLICATIONS TO THE ECLETRONIC SPECTRA OF CONJUGATED HYDROCARBONS

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1959

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Ohio State University

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Coulson and $Rushbrooke^{1}$ have shown how many of the properties of the $\pi$---electron system in a conjugated hydrocarbon may be described in terms of contour integrals involving the secular determinant. This method yields particularly elegant results when applied to the alternating $hydrocarbon^{2}$. It seems that the mathematically important feature of this theory is the existence of an operator anticommuting with the Hamiltonian. It is the operator which reverses the signs of all the unstarred coordinates while preserving the signs of the starred coordinates. The theory of operators which anticommute with a Hamiltonian is discussed as well as the theory of those which satisfy more general relations. The electronic spectra and bond-orders of a number of alternant hydrocarbons are interpreted by the aid of this theory.

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$^{1}$C. A. Coulson and G. S. Rushbrooke, Proc. Camb. Phil. Soc. 36 , 193-200 (1940). $^{2} $C. A. Coulson, Proc. Camb. Phil. Soc. 36 , 201--203 (1940).
Author Institution: Brandeis University

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