Fragment Rotational Distributions Research Articles

Imaging the State-Specific Vibrational Predissociation of the C2H2−NH3Hydrogen-Bonded Dimer

The state-to-state vibrational predissociation (VP) dynamics of the hydrogen-bonded ammonia-acetylene dimer were studied following excitation in the asymmetric CH stretch. Velocity map imaging (VMI) and resonance-enhanced multiphoton ionization (REMPI) were used to determine pair-correlated product energy distributions. Following vibrational excitation of the asymmetric CH stretch fundamental, ammonia fragments were detected by 2 + 1 REMPI via the B1E'' <-- X1A1' and C'1A1' <-- X1A1' transitions. The fragments' center-of-mass (c.m.) translational energy distributions were determined from images of selected rotational levels of ammonia with one or two quanta in the symmetric bend (nu2 umbrella mode) and were converted to rotational-state distributions of the acetylene co-fragment. The latter is always generated with one or two quanta of bending excitation. All the distributions could be fit well when using a dimer dissociation energy of D0 = 900 +/- 10 cm(-1). Only channels with maximum translational energy <150 cm(-1) are observed. The rotational excitation in the ammonia fragments is modest and can be fit by temperatures of 150 +/- 50 and 50 +/- 20 K for 1nu2 and 2nu2, respectively. The rotational distributions in the acetylene co-fragment pair-correlated with specific rovibrational states of ammonia appear statistical as well. The vibrational-state distributions, however, show distinct state specificity among channels with low translational energy release. The predominant channel is NH3(1nu2) + C2H2(2nu4 or 1nu4 + 1nu5), where nu4 and nu5 are the trans- and cis-bend vibrations of acetylene, respectively. A second observed channel, with much lower population, is NH3(2nu2) + C2H2(1nu4). No products are generated in which the ammonia is in the vibrational ground state or the asymmetric bend (1nu4) state, nor is acetylene ever generated in the ground vibrational state or with CC stretch excitation. The angular momentum (AM) model of McCaffery and Marsh is used to estimate impact parameters in the internal collisions that give rise to the observed rotational distributions. These calculations show that dissociation takes place from bent geometries, which can also explain the propensity to excite fragment bending levels. The low recoil velocities associated with the observed channels facilitate energy exchange in the exit channel, which results in statistical-like fragment rotational distributions.

A full-dimensional quantum dynamical approach to the vibrational predissociation of Cl2–He2

A full-dimensional, fully coupled wave packet method is proposed and applied to investigate the vibrational predissociation dynamics of the Cl2(B,v')-He2 complex. Simulations are carried out for the resonance states associated with the v'=10-13 initial vibrational excitations of Cl2, and the results are compared with the available experimental data. A good agreement with experiment is achieved for the resonance lifetimes (typically within experimental error) and the Cl(2) fragment rotational distributions. The mechanism of dissociation of the two He atoms is found to be dominantly sequential, through the Deltav'= -2 channel. The probabilities obtained for the Deltav'= -1 dissociation channel are, however, overestimated due to the use of absorbing boundary conditions combined with finite grid effects. It is suggested that a mechanism of energy redistribution through the couplings between the van der Waals modes of the two weak bonds takes place in the Deltav'= -1 dissociation. This mechanism is consistent with the resonance lifetimes and Cl2 rotational distributions predicted. The favorable comparison with most of the experimental data supports the reliability of the potential used to model Cl2(B,v')-He2, at least in the present range of v' levels.

Quantum calculations on the vibrational predissociation of NeBr2: Evidence for continuum resonances

Quantum mechanical calculations on the vibrational predissociation dynamics of NeBr2 in the B electronic state have been performed and the results compared with both experimental data and other computational studies. For vibrational levels with v⩽20 we find that the vibrational state dependence of the predissociation lifetimes is in qualitative agreement with experimental measurements, as are the calculated Br2 fragment rotational distributions. For higher vibrational levels, the B←X excitation profiles are well represented by a sum of two Lorentzian line shapes. We attribute this result to the presence of long-lived resonances in the dissociative continuum that are reminiscent of long-lived dissociative trajectories in previous classical studies of NeBr2.

A combined experimental-theoretical study of the vibrational predissociation and product rotational distributions for high vibrational levels of He79Br2

Pump-probe spectra of HeBr2 in vibrational states v′=10 and 39 through 48 of the B electronic state are reported and the fragment rotational distributions from vibrational predissociation of the cluster are extracted from the measured E(0g+)←B(3Π0u+) spectra of Br2. The experimental results are compared to theoretical calculations on the B←X spectra using atom-atom model potentials and performing a thermal average over transitions that contribute to the net excitation. Very good agreement between experiment and theory is obtained, except in the region of v′=44, where the Δv=−1 channel closes, and in the region of v′=48 where the Δv=−2 channel closes. For v′=43, and v′=44, the agreement is less satisfactory because the dynamics are extremely sensitive to details of the potential energy surface due to threshold effects associated with the Δv=−1 channel closing. Similar sensitivity to the potential due to the Δv=−2 channel closing impairs the agreement between experiment and theory for v′=48. Below v′=43, the rotational distributions for Δv=−1 and Δv=−2 are quite similar. Above v′=43 the peaks of the rotational distributions for Δv=−2 move to higher values of j. These results are compatible with the theoretical conclusion that dissociation shifts from a direct mechanism to one involving intramolecular vibrational distribution in the region of the closing of the Δv=−1 channel. Although the simple additive potential model used in this work succeeds in reproducing most of the experimental data for this system, further improvements in the potential energy surface will be required to achieve precise agreement between experiment and theory for large Br-Br separations.

Three-dimensional infinite order sudden quantum theory for indirect photodissociation processes. Application to the photofragment yield spectrum of NOCl in the region of the T1(13A″) ←S(11A′) transition. Fragment rotational distributions and thermal averages

The analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation, developed in paper I, is applied to study the indirect photodissociation of NOCl through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum functions. The transition is taken as polarized in the plane of the molecule; symmetric top wave functions are used for both the initial and intermediate bound states; and simple semiempirical model potentials are employed for each state. The theory provides analytical expressions for the photofragment yield spectrum for producing particular final fragment ro-vibrational states as a function of the photon excitation energy. Computations are made of the photofragment excitation spectrum of NOCl in the region of the T1(13A″) ←S0(11A′) transition for producing the NO fragment in the vibrational states nNO=0, 1, and 2. The computed spectra for the unexcited nNO==0 and excited nNO=2 states are in reasonable agreement with experiment. However, some discrepancies are observed for the singly excited nNO=1 vibrational state, indicating deficiencies in the semiempirical potential energy surface. Computations for two different orientations of the in-plane transition dipole moment produce very similar excitation spectra. Calculations of fragment rotational distributions are performed for high values of the total angular momentum J, a feature that would be very difficult to perform with close-coupled methods. Computations are also made of the thermally averaged rotational energy distributions to simulate the conditions in actual supersonic jet experiments.

Fragment rotational distributions from the dissociation of NeBr2: Experimental and classical trajectory studies

The Br2 fragment rotational distributions that result from the vibrational predissociation of NeBr2 in the B electronic state have been measured for several initial vibrational levels. In each case, the rotational distributions extend to the effective energetic limit determined by the amount of energy available (Eavl) for disposal into the fragment rotational and translational degrees of freedom. Analysis of the data allows refinement of the NeBr2 dissociation energy; we find that D0=70.0±1.1 cm−1 for the X electronic state, v=0. Both Δv=−1 and −2 dissociation events have been examined. For dissociation pathways with approximately the same value of Eavl the Δv=−2 pathways are observed to have a higher fraction of the fragment energy in rotational excitation. The overall shape of the Δv=−1 distributions are insensitive to the value of Eavl, suggesting that a Franck–Condon model for the dissociation may have some validity, though quantitative quantum mechanical calculations demonstrate that this model does not reproduce the large degree of fragment rotational excitation. Two classical models for the dissociation also fail to reproduce the extent of fragment rotational distribution. This result is discussed in light of previous experimental and theoretical investigations, focusing on the apparent agreement of classical models with the IBr fragment rotational distributions that result from the dissociation of NeIBr.

Three-dimensional analytical infinite order sudden quantum theory for triatomic photodissociation: Dependence on initial rotational and vibrational state and on thermal averages for NOCl dissociation on T1(1 3A″) surface

Our previously developed analytical infinite order sudden quantum theory of triatomic photodissociation is generalized to compute fragment internal energy distributions when the initial triatomic rotational state has K≠0. The dependence of product rotational energy distributions on initial rotational and vibrational state is illustrated through model computations for the direct NOCl photodissociation from the ground to the T1(1 3A″) potential energy surface. The calculations consider all J,K≤9 and employ a repulsive potential that is fit to ab initio computations. Comparisons of fragment rotational distributions with previous semiclassical approximations further elucidate the role of the mapping of the initial state bending wave function onto the fragment rotational distributions and the influence of parent rotations on this mapping. The infinite order sudden quantum-mechanical distributions exhibit a more complex structure, but upon thermal averaging they are already transformed at T=3 K into fairly broad rotational distributions. The present theory readily permits the calculations of energy distributions for initial states of high J and K.

Photodissociation dynamics of formaldehyde: H2 (v,J) vector correlations

Several bipolar moments of the H2 (v,J) correlated angular momentum and velocity distribution produced from the photodissociation of formaldehyde near the threshold for dissociation have been measured by analysis of Doppler-resolved LIF line shapes. It is determined that the fragment H2 〈v⋅J〉 correlation is not at the limit of v⊥J, but is closer to the limit of v⊥J than to v∥J. The rotation of the excited H2CO during the 10−7–10−8 s before dissociation does not completely wash out the lab-frame vector correlations. Anisotropy parameters as large as 0.85 and as small as −0.41 have been measured; these are outside the limits imposed by classical models of parent rotation. A quantum mechanical model for parent rotation is introduced that accounts for the large magnitude of the measured anisotropy parameters. Photolysis on the rR0(0) line of the 43 band produces fragments with β&amp;lt;0 while photolysis on the same rotational transition of the 2141 band produces fragments with β&amp;gt;0. It is not known if the different anisotropies are caused by differences in the parent transition dipole moment or by differences in the dissociation dynamics. The simple impulsive model that reproduces the fragment rotational distributions and product quantum-state correlations does not adequately describe the measured H2 (v,J) vector correlations.

Three-dimensional analytic quantum theory for triatomic photodissociations. II. Angle dependent dissociative surfaces and rotational infinite order sudden approximation for bent triatomics

We extend to triatomic molecules with bent initial bound states our analytical quantum theory of triatomic photodissociations. The theory uses basis functions for the initial bound state wave function that are product functions in the natural normal (or local) modes appropriate to that state and a continuum wave function that is a product function in the natural scattering coordinates appropriate to the dissociative surface. This choice of wave functions produces three-dimensional nonseparable transition amplitudes which are reduced to analytical forms by introduction of the infinite order sudden and Airy approximations for the continuum wave function and a quadrature formula for the integral over bending motions. The present theory also lifts some assumptions that had been introduced previously to simplify the theory for isotropic repulsive potentials. Thus, we use the exact nonlinear relation between the bound state bending angle and the scattering angle to remove the previous small angle approximation that is shown to lead to inaccuracies in some cases. We also study the ramifications of the fact that the bound state bending vibration is generally a linear combination of pure bend and both bond stretches in the transformation between normal modes and scattering coordinates. Inclusion of this bend–stretch coupling, ignored in our previous analytical work and in many theories of triatomic photodissociation that employ expansions of the bound state wave function in a basis set expressed in dissociative surface scattering coordinates, is shown to have profound influence on computed fragment rotational distributions. The bend–stretch couplings serve often to wash out the additional high frequency oscillations that appear in prior approximate treatments in which these couplings are ignored. This then leads to fragment rotational distributions that contain only those oscillations resulting from the map of the initial bound state bending vibration. Comparison is made with three-dimensional close coupled and DVR calculations for the photodissociation of HCN from the bent C̃1A′ state. Calculations are also presented for initial states of high rotational angular momenta.

Rotational rainbows in the vibrational predissociation of ICl–He complexes

Strongly peaked ICl fragment rotational distributions are observed following vibrational predissociation of ICl–He B state complexes containing two or three quanta of ICl vibrational excitation. The nascent rotational distributions of the ICl product exhibit two distinct maxima, occurring at j=7 and j=16. A theoretical analysis demonstrates that the two maxima are due to rotational rainbows, arising from the He atom scattering off of the I and Cl ends of the ICl molecule. The vibrational predissociation of ICl–He B(vB=2) is simulated with a semiclassical scattering theory which is analogous to that developed by Schinke [J. Chem. Phys. 85, 5049 (1986)] for direct photodissociation. Vibrational predissociation is modeled as a rotationally inelastic ‘‘half-collision,’’ following deactivation of the ICl vibration. The final rotational angular momentum of the ICl fragments is determined from exact classical trajectories and in a sudden limit on a model potential energy surface. The calculated ICl product rotational distribution, like the experimentally observed distributions, is bimodal.

The effect of parent internal motion on photofragment rotational distributions: Vector correlation of angular momenta and C2v symmetry breaking in dissociation of AB2 molecules

A semiclassical calculation is presented that fully accounts for the angular momentum disposal in photodissociation of triatomic molecules. Rotational distributions are calculated for O2(3Σ−g) produced by the visible photolysis of ozone, O2(1Δg) by the UV photolysis of ozone, and OH by the 157 nm dissociation of water, to illustrate the effects of parent internal motion on fragment rotational distributions in the dissociation of C2v geometry molecules. A simple, but realistic, impulsive model of the energy release is used to describe the dissociation dynamics. The calculations are carried out for parent molecules at room temperature, as well as at the low temperatures characteristic of molecular beams. The contributions to the diatomic fragment rotational distribution from both parent triatom rotation and zero-point bending vibration are computed. Comparison of the calculated distributions with experimentally measured distributions indicates that the spread in rotational and bending vibrational angular momenta of the parent molecule can account for all or nearly all of the spread in final J of the diatomic photofragment. However, the rotational distributions of the diatomic photofragment reveal a strong vector correlation between the diatom angular momentum produced by the dissociative energy release, and the angular momentum associated with the in-plane rotation. The correlation is such that only half of all the photofragment states allowed by energy and angular momentum conservation are actually produced with appreciable probability. Of two energy degenerate photofragment states, corresponding to breaking of one or the other nominally equivalent bonds in the AB2 molecule, the one with the smaller orbital angular momentum/recoil linear momentum is strongly favored. This is explained by larger Franck–Condon overlap in the photoexcitation for the state of lower recoil angular momentum. The correlation involves selection of which of the two nominally equivalent bonds will break in the photodissociation of an AB2 triatom of C2v geometry, and thus represents a symmetry breaking mechanism in such a photodissociation.