Calculated and observed excited singlet state absorption (Sn←S1) spectra of a series of diphenylpolyenes are presented. In diphenyloctatetraene and diphenylhexatriene, the S1 state is assigned as an 1Ag state, in agreement with results from two-photon spectroscopic studies. In diphenylbutadiene, we assign the S1 state as a 1Bu, although two-photon studies have indicated that 1Ag state lies slightly below the 1Bu. It appears that a 1Ag state is the lowest excited state of diphenylbutadiene in its ground state geometry, but when the excited states relax to their equilibrium configurations, the 1Bu becomes the S1. Good agreement between the PPP–CI calculations and experimental Sn←S1 spectra demonstrates the potential usefulness of this technique in assigning ππ* excited states of large molecules.

The effect of path curvature on kinetic energy in bound state systems has been investigated by solving the Schrödinger equation for a particle confined to an annular region of uniform width. In the one-dimensional limit of a narrow annulus the angular behavior of the particle can be described by linear motion with an effective potential. This potential is related to the radius of curvature R by Veff=−(h/2/2m)(1/4R2). Thus, for a particle confined to a narrow channel high path curvature produces an effective stabilizing influence. An interpretation of this phenomenon is offered and several examples are examined.

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The quantum mechanical behavior of a particle constrained between two confocal ellipses is investigated as a model for cyclic pi systems with nondegenerate energy levels. The solutions of the Schrödinger wave equation for this system are analytic: the Mathieu functions. Effects of boundary curvature and annulus constriction on the wave functions and eigenvalues are determined and discussed. Low lying states may exhibit tunneling in regions of negative angular kinetic energy. As examples of an application to chemical systems, the model is calibrated to reproduce low lying π–π* transitions in several substituted benzenes. The limiting one dimensional problem of a particle-on-an-ellipse is discussed.

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