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An approximate form of the molecular orbital theory of unsaturated hydrocarbon molecules in their ground states is developed. The molecular orbitai equations rigorously derived from the correct many-electron Hamiltonian are simplified by a series of systematic approximations and reduce to equations comparable with those used in the semiempirical method based on an incompletely defined one-electron Hamiltonian. The two sets of equations differ, however, in that those of this paper include certain important terms representing electronic interaction. The theory is used to discuss the resonance energies, ionization potentials, charge densities, bond orders and bond lengths of some simple hydrocarbons. The electron interaction terms introduced in the theory are shown to play an important part in determining the ionization potentials. It is also shown that the uniform charge density theorem, proved by Coulson and Rushbrooke 1 for the simpler theory, holds also for the self-consistent orbitals derived by the method of this paper. 1.INTRoDucTIoN.-One of the methods most extensively used in the quantummechanical study of the mobile electrons of conjugated molecules is the semiempirical molecular orbital theory developed by Hiickel,2 Lennard-Jones,3 Coulson and Longuet-Higgins 4 and others. According to this well-known theory, the mobile electrons can be treated as occupying a set of delocalized molecular orbitals (not more than two electrons in each), these orbitals being eigenfunctions of a one-electron Hamiltonian representing the kinetic energy, the field of the nuclei and the smoothed-out distribution of the other electrons. The total energy of the mobile electrons is then obtained by adding together the energies of the individual electrons. By approximating the orbitals as linear combinations of atomic orbitals centred on the various atoms and estimating certain integrals empirically, the theory can be put in a simple form enabling it to be applied to a wide range of molecules.Although it has the merit of great simplicity, the Hiickel procedure has serious defects. These are connected with the difficulty of giving a precise definition of the one-electron Hamiltonian. Strictly the problem should be formulated in terms of the complete many-electron Hamiltonian in which the interelectronic repulsions are included explicitly. If the one-electron Hamiltonian is supposed to incIude a term allowing for the screening effect of other electrons, then interelectronic interactions will be counted twice in the total energy. These considerations have led some authors to develop more precise theories of mobile electrons based on the correct many electron Hamiltonian. Hall5 has proposed an alternative interpretation of the empirical theory in which the parameters are closely related to the ionization potentials of an excited state in which all mobile electrons have the same spin. Most of the more refined theories, however, have been of a nonempirical nature, obtaining energy levels and other molecular properties by direct calculatio...

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A general method is proposed for quantum-mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self-consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

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The lower excited electronic states of some unsaturated hydrocarbon radicals and ions are discussed in terms of molecular orbital theory, taking account of electron interaction. The following results emerge: In the absorption spectrum of an alternant radical there should appear two long wavelength bands. These arise jointly from excitations of electrons into and out of the singly occupied orbital. The lower frequency band should be weak, and the higher frequency band relatively strong. The existence of a low-lying quartet level is also predicted. The absorption spectra of the corresponding anion and cation should be closely related, the lowest two excited states being for both types of ion a triplet and a singlet. The singlet-triplet separation in the ions should be roughly equal to the separation of the two low-lying doublets of the radical. These generalizations are supported by the experimental data for certain triaryl-methyl systems.