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We applied the semiclassical initial value representation method to calculate energies, lifetimes, and wave functions of scattering resonances in a two-dimensional potential for O+O2 collision. Such scattering states represent the metastable O3* species and play a central role in the process of ozone formation. Autocorrelation functions for scattering states were computed and then analyzed using the Prony method, which permits one to extract accurate energies and widths of the resonances. We found that the results of the semiclassical wave packet propagation agree well with fully quantum results. The focus was on the 16O16O18O isotopomer and the anomalous isotope effect associated with formation of this molecule, either through the 16O16O+18O or the 16O+16O18O channels. An interesting correlation between the local vibration mode character of the metastable states and their lifetimes was observed and explained. New insight is obtained into the mechanism by which the long-lived resonances in the delta zero-point energy part of spectrum produce the anomalously large isotope effect. [ABSTRACT FROM AUTHOR]

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony’s method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm-1 for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5≤τn<100 ps are accurate to within 10%. A three-level model was used to investigate accuracies of different approximations for the reaction rate constant. It was shown that the majority of the metastable states in this system are either long lived (narrow resonances) which can be treated as stable, or short lived (broad resonances) which can be treated without the knowledge of their lifetimes. Only a few metastable states fall into the intermediate range where both energies and lifetimes are needed to model the kinetics. The recombination rate constant calculated with the SWP method at room temperature and pressure is in good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Electronic structure calculations are carried out for the S4 molecule at the CCSD(T)-F12a/VTZ-F12 level of theory to map out its potential energy surface, which possesses a double-well shape with a low-energy barrier. Two degrees of freedom are considered: the distance R and the gearing motion angle between the two weakly-perturbed S2 dimers, which form S4. Vibrational states are computed on this 2D-surface and assigned quantum numbers based on their energies and the shapes of their wave functions. Two progressions of vibrational states are identified: a long progression of easily assignable states that develop nodes along the 'channels' on the surface, and a shorter progression of states that develop nodes across the 'channels' and are much harder to assign, due to the double-well effect. Normal mode analysis indicates that these two modes in S4 represent a significant mixture of conventional bending and stretching motions. When the angle is increased, the lower frequency mode corresponds to stretching of the distance R, while the higher frequency mode corresponds to compression of R. Frequencies of the modes, ∼180 and ∼420 cm−1, are in a qualitative agreement with earlier ab initio studies of tetra-sulfur, and with sparse experimental data. [ABSTRACT FROM AUTHOR]

We report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence. [ABSTRACT FROM AUTHOR]

A benchmark study of the approximate approach to the optimal control of vibrational qubits, which was used in the original paper [J. Chem. Phys.126, 204102 (2007)], is presented. Two simplified assumptions are used in this method: A linear approximation for the dipole moment function and a harmonic approximation for the vibrational wave functions. Both assumptions are often used in spectroscopy and are known to work well for many molecules when the vibrational excitation is low. Here, we show that our method works well for the OH molecule, which exhibits a very anharmonic spectrum of vibrational eigenstates and a complicated dipole moment function. [ABSTRACT FROM AUTHOR]