Shigeyuki Aono

Superconducting and other phases in organic high polymers of polyacenic carbon skeletons. I. The method of sum of divergent perturbation series

The instabilities of a normal molecular orbital state of polyacenic materials are studied within RPA with a g model for an electronic interaction. The condensed states predicted are singlet superconducting (SSC), charge density wave (CDW), and spin density wave (SDW) ones, and their phase diagram is shown. In contrast to usual one‐dimensional (1D) conductors, there reveals a wide range of superconducting state, which is not overcome by CDW transition. Weakness of Peierls distortion of the present model is also contrasted with the case of polyacetylene.

Superconducting and other phases in organic high polymers of polyacenic carbon skeletons. II. The mean field method

Ordered phases such as CDW, SDW, and the singlet superconductivity(SSC) are predicted by means of a mean field theory. The electronic Hamiltonian is linearized by introducing order parameters which are expected to arise, and these order parameters are determined self‐consistently. The behaviors of gap, transition temperature, and condensation energy are greatly different from those of BCS theory. The coexistence of the various phases is discussed. Aside from a very special case the single phase is most stable.

Instabilities of the Hartree–Fock solution and the vibrational mode in a molecule

The Hartree−Fock instability and the force constant formula for a normal coordinate of a molecule are discussed. (AIP)

Explicit construction and algebraic structures of Hückel propagators and their applications

Propagator theory is developed in the Huckel model. Analytical expressions of Huckel propagators for linear and ring molecules with and without bond alternation are obtained by analyzing the Dyson’s equation. Further, the propagators for molecules of complex topological structures are constructed in systematic ways with those for simpler linear and ring systems. By applying the partitioning technique to the Dyson’s equation, it is easily shown that the propagators of complex systems are formally brought into the same form as those for the simple ones with renormalized Coulomb and resonance integrals. Finally, some physical quantities are directly evaluated by the integration method proposed by Coulson.

Superconducting and other phases in polyacenic skeletons

Abstract Low temperature ordered states of polyacenic conductors are studied. Thermodynamic properties within a mean field theory contrast with the BCS formula. Special interest is concentrated on a superconductivity with the Littles mechanism because of the essential weakness of an electron-lattice interaction. The effective interaction intermediated by a side chain designed is still unfavorable for superconductivity.

Generator coordinate method based on coherent states. II. Calculation of vibrational states by the double circular orbit method

For pt.I see ibid., vol.14, no.18, p.3305-11 (1981). The double circular orbit method (DCOM) is proposed to extend the applicability of the generator coordinate method based on coherent states (COM) which has recently been developed by the authors. The efficiency of the DCOM is examined for the Morse, double minimum and cubic anharmonic potential systems and compared with that of the COM.

Generator coordinate method based on coherent states: calculation of nuclear bound and resonance states in molecules

Supplementing the well known variational expansions in terms of harmonic oscillator states and Glaubers (1963) coherent states, the authors show the existence of another type of expansion in terms of coherent states. Employing this expansion form, they derive, using the generator coordinate formalism, an orbit method similar to that recently developed by Davis and Helles (1979). Then they apply it to calculations of nuclear bound and resonance states in several anharmonic one-dimensional model potential systems (i.e., Morse, double-minimum and cubic anharmonic potential systems).

On the relation between the quantum scattering theory and the molecular orbital theories of chemical reactivity

The reaction amplitude [or transition (T‐)‐matrix element] in the quantum scattering theory is expressed, under the several approximations, by two terms which we call here the electronic‐transition (E) term and the nuclear‐overlap (N) term, respectively. It is shown that the E and N terms are closely related to the correlation‐diagram method and the perturbative method, both of which are familiar to chemists as the qualitative MO theories of chemical reactivity. We also show that as a merit of starting with the formal theory of scattering, the nonadiabatic effects are taken into account in our derivation, naturally and systematically. This fact enables us to extend our treatment to nonadiabatic chemical reactions and photochemical reactions.

Comment on ‘‘Theory of vibrational overtone line shapes of polyatomic molecules’’

Heller and Mukamel’s theory of the line shapes of overtone vibrations in polyatomic molecules is further explored. Local mode interactions are discussed. (AIP)

Generator coordinate method based on coherent states. III. Calculation of vibrational states in coupled oscillator systems

For pt.II see ibid., vol.16, no.16, p.2871 (1983). The circular orbit method (COM) which has been proposed in parts I and II is extended to coupled oscillator systems. The authors also develop a new method (they call it the phase correlation method (PCM)) which enables one to calculate a particular state manifold. They apply the COM and PCM to calculations of state energy in the Henon-Heiles and Barbanis potential systems and examine the efficiency of them.