The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIR) which are attributed to different angular momentum states ℓ and we explicitly show that in alkaline collisions only four universal ℓ-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of ℓ-wave CIRs is studied. In particular we show that all the ℓ-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized K-matrix theory and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.

The potential energy surface of the unknown N3H3 molecule is investigated by using ab initio coupled-cluster and many-body perturbation theory. Five stable isomers of N3H3 are identified. In decreasing order of stability, these are triazene, triimide, cz's-triimide, triaziridine, and d-s-triaziridine. The infrared spectra of the principal isomers are predicted at the MBPT(2) level by using newly developed analytical second-derivative techniques and are compared to SCF predictions. The thermochemical quantities of enthalpy, entropy, Gibbs free energy, and heat capacity at constant volume are also computed. The predicted IR spectra and these thermochemical properties should aid experimental attempts to synthesize and isolate these compounds, some of which should be observable in low-temperature matrices.

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We perform an analytical investigation in the framework of generalized K matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular we present the unitarity bounds which emerge when considering a quasi one dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de-)excitations by means of CIRs. We analyze the CIR for d-waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.

Hiickel Theory and AromaticityAfter several years in disrepute, the simple Hiickel molecular orbital (HMO) method, when used with proper reference structures, now appears to give accurate predictions of aromaticity (1). To decide whether a molecule is aromatic, one first computes the Hiickel ir energy in the ordinary way (2), and then subtracts the energy of a reference structure. The molecule is aromatic, nonaromatic, or antiaromatic depending upon whether this difference is