We formulate the Sawada model in coordinate suace and apply it to the n-electrons in a large conjugated molecule.
In this letter we investigate the possibility of existence of a high isolated collective mode in a large conjugated molecule. The analysis is based on the Sawada model for the electron gas.
The Sawada method [l] for the dense electron gas is based on a model Hamiltonian which cpntains only terms corresponding to the scattering of a particle-hole into another particle-hole and the creation or annihilation of two particle-holes. Direct or exchange interactions between two particles or two holes are neglected. The second assumption of the Sawada model is that the particlehole operators tiP ates a particle an8~~at!%~~~ aYE; 2~%2~complex conjugates satisfy boson commutation relations. The model was justified on the grounds that in the diagrammatic expansion it gives only bubble diagrams and thereby reproduces the results of Gell-Mann and Brueckner [Z] for the dense electron gas. However, the model has a wider range of applicability since the basic assumptions involved are approximately valid whenever the number of particle-holes in the exact ground state and in the low-lying excited states is small compared to the total number of electrons in the system. This may in particular be true in a finite system where the single particle level spacing is of the order of magnitude of the interaction matrix elements, as is the case for the z-electrons in a conjugated molecule. Since the system under investigation is finite and inhomogeneous the problem must be formulated in coordinate space. The analysis proceeds in accordance with the basic assumptions outlined above. We start from the Hamiltonian * Supported in part by the Advanced Research Projects Agency. National Science Foundation, and the Office of Naval Research. * The determinant changes sign somewhere bettveen [S] E. Clar. Polycyclic Hydrocarbons.
Vol. II (Academ-2.7 eV and 2.8 eV.