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Nature

Wave Mechanics and the Rotation of Homopolar Molecules

David M. Dennison

Published Feb 1, 1927• 2 citations
Publisher
DOI
10.1038/119316a0

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The eigenstates of the one-band Hamiltonian for a two-electron homopolar molecule can be exactly determined. The exact solution for the ground state and all its properties can thus be used as a standard to assess the accuracy and validity of several commonly used approximations: the normal molecular-orbital ground state, the Heitler–London states, the spin-density waves and the charge-density waves. The most general unrestricted self-consistent field approximations are studied in both the Hartree and Hartree–Fock approximations and are compared with one another as well as with the exact results. New and simple correlated states are also proposed and tested: a symmetrized spin-density wave and a symmetrized charge-density wave. These new states are easily obtained from the corresponding Hartree–Fock states, and whenever they exist, they are extremely good approximations to the exact ground state. General consequences and extensions to more complicated systems can be inferred from this study.

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Exact results on homopolar singlet excitation energies of the hubbard model for linear polyenes

Katsufumi Hashimoto

Abstract The Lieb–Wu equations for homopolar singlet excited states of the Hubbard model of linear polyenes are formulated in a form tractable by numerical calculation. They are solved to obtain exact excitation energies of the lowest two excited states, corresponding to the 1B and 1E states of the benzene molecule, for systems with up to 50 and 30 electrons, respectively. These results may be particularly useful for checking accuracy of approximate methods for the homopolar states for which the conventional CI method is very difficult to apply. Calculation is also carried out for the 1B+ ionic excited state involving a spin excitation, which corresponds to the 1B state of the benzene molecule. The length dependence of the excitation energies is examined and shown to have no N−1 dependence for large N, where N is the number of electrons. This supplements the result on the 1E ionic state obtained in our previous paper.

International Journal of Quantum Chemistry•Nov 1, 1986•21 citations
The eigenstates of the one-band Hamiltonian for a two-electron homopolar molecule can be exactly determined. The exact solution for the ground state and all its properties can thus be used as a standard to assess the accuracy and validity of several commonly used approximations: the normal molecular-orbital ground state, the Heitler–London states, the spin-density waves and the charge-density waves. The most general unrestricted self-consistent field approximations are studied in both the Hartree and Hartree–Fock approximations and are compared with one another as well as with the exact results. New and simple correlated states are also proposed and tested: a symmetrized spin-density wave and a symmetrized charge-density wave. These new states are easily obtained from the corresponding Hartree–Fock states, and whenever they exist, they are extremely good approximations to the exact ground state. General consequences and extensions to more complicated systems can be inferred from this study.
Abstract The Lieb–Wu equations for homopolar singlet excited states of the Hubbard model of linear polyenes are formulated in a form tractable by numerical calculation. They are solved to obtain exact excitation energies of the lowest two excited states, corresponding to the 1B and 1E states of the benzene molecule, for systems with up to 50 and 30 electrons, respectively. These results may be particularly useful for checking accuracy of approximate methods for the homopolar states for which the conventional CI method is very difficult to apply. Calculation is also carried out for the 1B+ ionic excited state involving a spin excitation, which corresponds to the 1B state of the benzene molecule. The length dependence of the excitation energies is examined and shown to have no N−1 dependence for large N, where N is the number of electrons. This supplements the result on the 1E ionic state obtained in our previous paper.