ALBERT

Notes: Vibrational energies and eigenfunctions of Ar3, including some pertaining to highly excited states, are computed, and insights into their dynamical and structural properties are obtained. The method used employs the vibrational self-consistent-field (SCF) theory in hyperspherical coordinates as a first approximation. Exact results are obtained by configuration interaction, using the SCF states as an efficient basis. A focal point of the study is the effect of three-body potentials on the vibrational spectrum. Axilrod–Teller and other three-body potentials are used to examine this. It is found that the effect of three-body forces on the spectrum is substantial, and larger than effects due to uncertainties in the presently known two-body Ar–Ar potentials. This suggests that experimental spectroscopy of Ar3 may be used to determine reliable three-body forces among Ar atoms. It is also shown that the three-body double-dipole–quadrupole interaction, while less important than the Axilrod–Teller one, has a significant effect on the vibrational spectrum. Finally, a detailed analysis is made of the Ar–Ar distance distributions in the various states, of the structural distributions of Ar3, and of the properties of the wave functions. We find that the wave functions show well-ordered nodal patterns even for the highly excited large-amplitude states. Thus, these states do not correspond qualitatively to "liquid-like'' behavior of the cluster.

Notes: The effects of domain structure on the low-frequency conductivity response of a polymer electrolyte having low carrier concentration are investigated by modeling the domains as spheres. For zero leakage (no dc conductivity), the diffusion equation is solved exactly. The results are also extended approximately to the case of small but nonzero leakage by imposing physically reasonable approximate boundary conditions together with an ad hoc procedure for treating the diffusion in the less conductive exterior. Interaction between charge carriers in different domains is taken into account in the Maxwell–Garnet approximation and found to have only a small effect for physically reasonable parameter values. The predicted diffusive behavior is studied and the results are applied to examine the predicted behavior of the frequency-dependent conductivity.

Notes: We consider an anisotropic multidimensional barrier crossing problem, in the Smoluchowski (diffusion) limit. The anisotropy arises from either or both the shape of the potential energy surface and anisotropic diffusion. In such situations, the separatrix, which separates reactant and product regions of attraction, does not coincide with the ridge of the potential surface, which separates reactant and product wells, thus giving rise to a complicated time evolution. In the asymptotically long time limit, the time evolution is governed by crossing the separatrix and is exponential with a rate which may be obtained as a generalization of Kramers' theory to the anisotropic situation. In contrast, in long, though not asymptotically long times, the time evolution is dominated by repeated crossings of the ridge, and is nonexponential. Such nonexponential time evolution has been observed in many biochemical reactions, where many degrees of freedom and anisotropic diffusion processes lead to complicated dynamical behavior. Our model provides a simple prototype of such situations.

Notes: The vibrational predissociation dynamics of a collinear model of the I2(v)He cluster is studied by numerically exact time-dependent quantum mechanics, and by the time-dependent self-consistent field (TDSCF) approximation. The time evolution for the initial excitation levels v=5, 11, 22 is explored. Excellent agreement is found between the TDSCF and the exact evolution of the wave packet; in particular the approximation reproduces well the dephasing events in the dynamics, and the measurable predissociation lifetimes. The results are very encouraging as to the applicability of quantum TDSCF as a quantitative tool in the study of van der Waals predissociation dynamics.

Notes: The photodissociation dynamics of a collinear model of the van der Waals cluster Xe–HI is used as a testing ground for time-dependent self-consistent field (TDSCF) approximations. In this study, the quantum-mechanical TDSCF and a combined classical/quantal TDSCF (in which the light atom is treated quantum mechanically, the heavy atoms are treated classically) are compared to numerically exact wave packet calculations. Very good agreement is found between the TDSCF approximations and the exact result over the entire subpicosecond time duration of the process. In particular, all the properties related to the quantal degree of freedom in the combined quantal/classical TDSCF method reproduce almost perfectly the exact results. However, the classical mode in the hybrid approximation is somewhat less well described due to insufficient representation of energy transfer between the modes. The conclusions are very promising as to the applicability of TDSCF methods, in particular the hybrid quantal/classical scheme to more complex systems in which only a few degrees of freedom can be treated quantum mechanically.

Notes: A study has been made of the vibrational energy flow mechanisms and time scales pertaining to the overtone stretch excitations of methyl and acetylenic CH stretches in propyne. Classical trajectories are used to interpret the experimental data for the overtone linewidths, as well as to analyze the role that individual modes play in determining energy flow. The full anharmonic potential surface for these calculations, including all modes, has been developed from spectroscopic and structural information, including the linewidth data. The principal results are: (1) The trajectory calculations show a localization transition, corresponding to a switch over from normal-mode behavior for CH3 excitations up to v≅3 to a local-mode CH excitation within the CH3 moiety for excitations of v(approximately-greater-than)6, with transition behavior for v=4,5. (2) The acetylenic CH shows local-mode behavior from v=1. Extremely long lifetimes are found for the excitations of this mode, and the trajectories indicate that the experimental width is predominantly rotational. (3) The rocking and deformation modes are dominant receiving modes in the relaxation of the methyl stretch. (4) A shorter lifetime is calculated for the v=6 vs the v=5 or v=7 overtones of the methyl C–H stretch. Experimental results are qualitatively consistent with this prediction. The origin of this shorter lifetime is a band of resonances between the stretch excitation and combinations of rocking, deformation, and pseudorotation modes. (5) CH3 internal rotation figures importantly in the relaxation of some levels (v=5, 8 of CH3) where it "closes the energy gap'' for achieving resonant energy transfer. (6) For v=8 of the methyl CH, some direct energy transfer to both C–C(Triple Bond)C stretching modes is seen. The switching on of the stretches as receiving modes is a consequence of sufficiently strong interactions between the excited H and the C–C(Triple Bond)C chain, which take place at these high vibrational energies. (7) Evidence is found for long distance "through-space'' energy transfer due to long-range dipole–dipole forces. This transfer occurs from the acetylenic to the methyl CH stretches. This result is illustrated for the v=2 excitation of the acetylenichydrogen, and constitutes a direct demonstration of intramolecular long-distance, through-space v–v energy transfer. These results demonstrate the potential importance of large amplitude modes such as rocking and deformation as initial receiving modes for vibrational energy from excited CH overtones. On the time scale probed here (∼1 ps), despite the availability of many degrees of freedom, the transfer process is dominated by specific energy transfer channels and by the specific behavior of individual modes, rather than by statistical considerations, which will certainly prevail on longer time scales.

Notes: The self-consistent field (SCF) approximation for coupled anharmonic vibrations is applied to the calculation of vibrational energy levels (predissociation resonances) of collinear models of I2 (v)He and I2 (v)Ne, with vibrational quantum number v between 5 and 30. The predissociation lifetimes of these same states are obtained from a distorted wave Born approximation calculation with self-consistent field states taken as the initial states of the complex, and with correlation between the modes taken as the interactions leading to decay. Although the binding energies of the van der Waals complex are very small (order of several cm−1 ), the SCF eigenvalues are in remarkable agreement with the exact numerical values. The lifetimes obtained from the SCF-distorted wave Born approximation (DWBA) are compared with calculations in which the initial state is treated more simply, assuming separability of the modes involved. Results then show that the DWBA with SCF initial states is considerably more accurate than with the more primitive initial state choice. We conclude from these results that the self-consistent field method offers a very accurate description of large-amplitude vibrational motions in van der Waals clusters, with good quantitative results for both the energy levels and predissociation dynamics of these species.

Notes: The full anharmonic stretching and bending potential of CO2 is determined to high accuracy from the measured vibration/rotation spectrum. The calculation consists of two stages: first, a direct explicit inversion of the data within a semiclassical self-consistent-field (SCF) treatment of vibrational dynamics and second, a refinement of this result by a first-order perturbative approach that includes corrections to the SCF approximation, but assumes that the SCF-inverted potential shows only small deviations from the true surface. The final result is tested by comparison of the energy levels calculated exactly from the determined potential against the original experimental input. Based on this criterion of accuracy in reproducing experimental frequencies, the present inverted potential appears more accurate than previous potentials obtained from empirical fitting of the data. These results indicate that the perturbatively corrected SCF inversion method is a very powerful tool for obtaining potential energy surfaces directly from experimental data, with errors not exceeding several wave numbers.

Notes: We extend a model originally intended for the description of the scanning tunneling microscope (STM) current in molecular imaging of one-dimensional systems, to encompass the more general process of electron transfer between two reservoirs of states. In the STM problem, the reservoirs are naturally associated with the metal density of states of the electrodes. In the molecular electron transfer problem, the identification of the reservoirs with the Franck–Condon weighted density of vibrational states allows a number of fruitful connections with the theory of nonadiabatic electron transfer (ET) in molecules to be established. In this article, we present an exact procedure, based on Löwdin's partitioning technique, to determine the Green's function and the T matrix, relevant to the transport process. We obtain compact expressions for the conductance and the density of states in the limit of small applied voltage and low temperature, and discuss the important case where the molecular wire is described by a tight-binding Hamiltonian. Finally, we discuss some physical implications of the model.