Spin Density Wave and Charge Transfer Wave in Long Conjugated Molecules*

A general theory on the solutions of the Hartree-Fock equation different from the conventional diamagnetic solution is developed in relation to the stability or instability problem of the Hartree-Fock ground state. Classification and properties of the solutions, in particular, degeneracy of the ground state, are discussed. A method is developed to construct the other solutions of the Hartree-Fock equation from a standard solution utilizing deformation of the Dirac density matrix. The general theory is applied to long conjugated molecule polyene without bond alternation. It is shown that, when the length of polyene exceeds certain critical lengths, the conventional diamagnetic ground state becomes unstable to spin density and number density fluctuations. Then, new solutions of two different types with undulatory spin density or charge density distribution and lower ground state energies than the conventional solution appear. These solutions have finite energy gap between the excited and the ground states even in the limit of infinite length, providing a new explanation for the convergence of the maximum absorption wavelength in polyenes.