K. Deguchi

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)

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.

On the localization of the resonance state wave function in the complex coordinate method

The localization of the resonance state wave functions is investigated in the complex coordinate method within the framework of a simple two‐state model. (AIP)

Generator coordinate method based on coherent states. IV. Adiabatic generator coordinate method in coupled oscillator systems

For pt.III see ibid., vol.17, p.1699 (1984). An adiabatic generator coordinate method (GCM) is derived and applied to calculations of vibrational states in the Henon-Heiles potential system. It seems that the adiabatic GCM is preferable to the standard adiabatic approach.