Cellular Method and the Calculation of Molecular Wavefunctions. I. A Generalized Method of Images

It is argued that the potential approximation and local physical viewpoint of the Cellular method, which is virtually obsolete in band theory, are well suited to the very different problem of calculating molecular orbitals. But the mathematics of the method, which are suspect even in metals, fail completely for covalent bonds. After discussing and illustrating these formal problems, we propose a technique for generating a highly overcomplete basis set in each cell from a Green's function for that cell, by placing source distributions on the neighboring atoms. The experience of the classical ``Method of Images'' suggests that a few point sources will be quite adequate to generate the wavefunction, so that the method is well suited to actual calculations. This is demonstrated in the succeeding paper where the technique is applied to the alkali molecules.