ALBERT

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: Total cross sections for He scattering from isolated imperfections on surfaces are calculated using the Sudden approximation, and in some cases also by a numerically exact, time-dependent quantum-mechanical wave packet method. Systems studied include: CO adsorbates on Pt(111); mono-, di-, and trivacancies on Pt(111). The main results are: (1) the incidence angle and energy dependence of the cross section for He/[Pt(111)+CO] are very sensitive to the CO distance from the Pt plane. Interactions with the adsorbate image have little effect on the cross section. (2) The cross sections for clusters of vacancies are given within 10% or better, by the geometric sum of the monovacancy cross sections, the latter being treated as circles centered at each monovacancy. (3) The dependence of the cross section on the energy is sufficiently sensitive to distinguish between the "electron density hole'' and "electron density hump'' models for vacancies and vacancy clusters. (4) The Sudden approximation compares well with the exact quantum-mechanical results at typical experimental energies, when the incidence angle is not too far from the normal. These results indicate that experimental measurements of He scattering cross sections as a function of energy and incidence angle, combined with Sudden or wave packet scattering calculations, can provide detailed information on surface defects and their interactions with gas-phase atoms.

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: 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 scattering of He atoms from a CO molecule adsorbed on a Pt surface is studied theoretically by methods that include: (1) Numerically exact solutions of the time-dependent Schrödinger equation for the scattered wavepacket; (2) The sudden approximation; (3) Classical trajectories. The methods are used to obtain detailed insight into the collision dynamics, and to predict and understand interesting features in the angular intensity distribution of the scattered atoms. The analysis and interpretation of the exact quantum results is facilitated by calculations of the probability current density of the scattered particles. Some of the main results are: (i) The angular intensity distribution exhibits nonspecular maxima of two types: Several of the peaks are rainbow effects induced by the adsorbate, while others (at angles nearer to the specular) are Fraunhofer diffraction interferences. Both types of peaks contain useful, largely complementary, information on adsorbate geometry and on the He/adsorbate interaction. (ii) The angular intensity distribution is quantitatively sensitive to the adsorbate distance from the surface, suggesting possible determination of that distance from experimental data. (iii) The corrugation due to the adsorbate leads to scattering resonances associated with temporary trapping of the scattered atom at the defect site. This is a new effect of potential importance for experimental studies of atom/defect interactions. The results obtained here suggest that He scattering from isolated adsorbates exhibits distinct, substantial effects, measurement of which should yield very useful data on the adsorbates and on their interactions with gas-phase atoms.

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: We used a randomly corrugated hard wall model and the sudden approximation to analyze two experiments on atom scattering from disordered surfaces. In one, the structural surface disorder was caused by ion bombardment. In the other, the disorder was due to an incomplete overlayer of adsorbed atoms. We also present a study of the scattering of a rigid rotor by a randomly corrugated hard wall using the sudden approximation.

Notes: A quantum mechanical theory is presented for the low temperature diffusion of atomic hydrogen on metal surfaces, based on a band model for the hydrogen motion. The theory is applicable to the diffusion of many interacting particles obeying quantum statistics. At low coverage the hydrogen band motion is limited by collisions between adsorbates, giving rise to a decrease of the diffusion constant with concentration. Other aspects of the hydrogen–hydrogen interaction are introduced to explain the coverage dependence at higher adsorbate concentrations. Comparison with recent low temperature diffusion measurements for H, D, and T on W(110) show that the above model reproduces satisfactorily the main features of the experimental coverage dependence of diffusion. The usefulness and limitations of band treatment for heavy particle diffusion are discussed in the light of these results.

Notes: The use of hyperspherical coordinates within the semiclassical self-consistent-field model (SCSCF) is investigated for two-mode models, corresponding to nonbending CO2 and H2O. The hyperspherical coordinate set is highly collective; since the screening which is characteristic of collective coordinates should result in increased accuracy of SCF methods, it might be expected that these coordinates would lead to very good SCF results. Numerical tests show that indeed the hyperspherical SCF results are accurate and superior to SCF either in local- or in normal-mode coordinates, the improvement being larger for CO2 than for H2O. These calculations show as does recent work on HCN that proper choice of the coordinate system can lead to much improved SCF results.