The following subject areas are covered: (1) total integral reactive cross sections and vibrationally resolved reaction probabilities for F + H2 = HF + H; (2) a theoretical study of inelastic O + N2 collisions; (3) body frame close coupling wave packet approach to gas phase atom-rigit rotor inelastic collisions; (4) wave packet study of gas phase atom-rigit motor scattering; (5) the application of optical potentials for reactive scattering; (6) time dependent, three dimensional body frame quantal wave packet treatment of the H + H2 exchange reaction; (7) a time dependent wave packet approach to atom-diatom reactive collision probabilities; (8) time dependent wave packet for the complete determination of s-matrix elements for reactive molecular collisions in three dimensions; (9) a comparison of three time dependent wave packet methods for calculating electron-atom elastic scattering cross sections; and (10) a numerically exact full wave packet approach to molecule-surface scattering

Kouri, Donald J.

English

NASA Technical Reports Server

Final Report on NASA Grant NASA-Ames NAG2-503
"Theoretical Studies of Molecular Collisions"
Donald J. Kouri, P.I.
Dept. of Chemistry
University of Houston
Houston, TX 77204-5641
(NASA-CR-188190) THEORETICAL STUDIES OF N~9~l-22846
MOLECULAR COLLISIONS Final Report (Houston
Univ.) 10 p CSCL 20H
Unclas
G3/72 0012360
https://ntrs.nasa.gov/search.jsp?R=19910013533 2020-03-19T17:55:47+00:00Z
I. Summary of Results and Publications
Although we were unable to complete all the research we had hoped to due to the
unforeseen budgetary problems which prevented our continuing for the third year of this
grant, tremendous progress was made in the development of new methods and their appli-
cations to the calculation of converged three-dimensional quantum scattering information.
This has enabled us to make detailed comparisons of converged 3-D quantum results to
analogous quasi-classical trajectory (QCT) results obtained by Dr. Rich Jaffe, in order
to assess the accuracy and reliability of the latter. Of greatest significance is the fact
that the first fully converged 3-D quantum cross sections over a wide range of energies
for the F + H->. —> HF + H reaction were obtained, and the results compared with QCT
and experimental cross sections. This is a landmark achievement, and it was found that
there are very significant quantum effects! These quantum effects are manifested in the
threshold energy regime, and in the dependence of the reactive cross sections on the initial
rotational state of the Hy molecule. It appears therefore that considerable care must be
exercised in simulating reactive scattering processes by the QCT method, especially under
threshold conditions, and when the experiment is probing low initial rotational states of
the reactant molecules.
In a related study of vibration-rotational inelastic scattering of JV2 by oxygen atoms,
O, over a very large energy range we found very large quantum effects in the thresholds for
producing vibrationally excited N2. The results showed that the QCT leads to vibrational
excitation at substantially lower total energies than the quantum results. This will have
a major effect on the energy transfer rates and the collisional line broadening of the NZ
under the conditions expected in the shock produced by the AOTV. Again, this indicates
that great care must be exercised in simulating molecular collision processes in the shock
wave associated with the AOTV.
We anticipate continuing this program of research in collaboration with Dr. Rich
Jaffe of NASA-Ames. For example, several powerful new methods for propagating quan-
tum wavepackets and for obtaining the most detailed state-to-state reactive scattering
amplitudes have been developed. We will continue to carry out calculations for the O + Ny
and F + Hi systems in order to complete the comparisons of exact quantum results with
Dr. Rich Jaffe's QCT results. In addition, we still expect to be able to compute reactive
scattering results for the extremely difficult, highly exoergic N + O^ —* NO + O reaction
for comparison to QCT results.
We turn now to a brief summary of the detailed results obtained under support of
NAG2-503. It is convenient to frame this in terms of the refereed publications resulting
from the grant support. There are a total of fourteen such papers.
1. Total Integral Reactive Cross Sections for F + H2 —> HF + H: Comparison of Con-
verged Quantum, Quasiclassical Trajectory and Experimental Results, D. Neuhauser, R. S.
Judson, R. L. Jaffe, M. Baer, and D. J. Kouri, Chem. Phys. Lett. 176. 546 (1991).
This paper reports a major breakthrough in the quantum theory of reactive scattering.
The first converged 3-D quantum complete reactive cross sections for this prototype of an
exoergic reaction yielding a population inversion are reported, both for H? in the v = 0,
.7 = 0 and v = 0, j = 1 initial (reactant) states. The comparison to QCT results shows very
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strong quantum effects in the threshold behavior and the dependence on initial rotational
state of the reactant H^ molecule. The comparison to experiment (combined with the
comparison to the QCT results) demonstrates that the potential (T5A due to Truhlar and
collaborators) is not sufficiently accurate to correctly describe the system. This is by far
the most important paper published under the grant, and a much more complete paper
will be prepared for submission in the coming months.
2. A Theoretical Study of Inelastic O + JV2 Collisions: Comparison of Classical with Exact
Quantum Results for Energies up to 2.6 eV and Selected Total Angular Momenta, R. S.
Judson, C.-K. Zhang, D. J. Kouri, and R. L. Jaffe, in preparation.
This paper is almost ready for submission to the Journal of Chemical Physics. Be-
cause of the large masses of the O atom and JV2 molecule, and the high collision energies
considered, one would have expected very good agreement between QCT and accurate 3-D
quantum results. In fact, due to the very stiff N2 bond, there are large quantum effects in
the vibrational excitation probabilities. Thus, the QCT threshold for vibrationally exciting
the 7V2 occurs much lower in energy that the quantum threshold. The energy difference in
the threshold is such that the QCT vibrational excitation rate constant should be orders
of magnitude larger than the quantum rate. It is found in both quantum and QCT results
that very large changes in TV^-rotational angular momentum occur, both for At; — 0 and
AT; 7^ 0 vibrational transitions. As would be expected from the repulsive nature of the
potential, rotational rainbow structure occurs in the final ^ -rotational state distributions.
This is seen in both the quantal and the QCT results. The peak of the rotational rainbow
typically occurs at a slightly larger final j-state in the quantum results than in the QCT
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results.
3. Time Dependent (Wavepacket) Quantum Approach to Reactive Scattering: Vibra-
tionally Resolved Reaction Probabilities for F + H2 —» HF + H, D. Neuhauser, M. Baer,
R. S. Judson, and D. J. Kouri, Chem. Phys. Lett. 169. 372 (1990).
This paper presents the first detailed state-to-state converged 3-D quantum reactive
scattering transition probabilities for the extremely difficult F + H^ —> HF + H reaction,
obtained with wavepackets. The results demonstrated that such state-to-state reactive
probabilities for such a system could be obtained at many collision energies from a single
wavepacket propagation.
4. Body Frame Close Coupling Wave Packet Approach to Gas Phase Atom-Rigid Rotor
Inelastic Collisions, Y. Sun, R. S. Judson, and D. J. Kouri, J. Chem. Phys. 90, 241 (1989).
This paper provided the foundation of the wavepacket propagation for inelastic scat^-
tering in 3-D in a rotating frame of reference, as well as the detailed proofs that one
could obtain the state-to-state 5-matrix at many energies. This is one of the papers that
provided tools for developing the general 3-D quantum wavepacket method for reactive
scattering.
5. Wavepacket Study of Gas Phase Atom-Rigid Rotor Scattering, Y. Sun and D. J. Kouri,
J. Chem. Phys. 89, 2958 (1988).
This paper was the demonstration calculation that accurate 3-D quantum 5-matrix
results for atom-diatom could be obtained by wavepacket methods. The formulation was
in a space fixed, center of mass reference frame, which was extended in paper 4 above to
a rotating frame.
6. The Application of Optical Potentials for Reactive Scattering: A Case Study, D.
Neuhauser, M. Baer, and D. J. Kouri, J. Chem. Phys. 93, 2499 (1990).
This paper gives a numerical study of the optical (absorbing) potential idea which was
used to enable converged quantum reactive scattering calculations to be done using much
smaller grid sizes. This greatly reduces the computational labor required. It also enables
one to decouple arrangements in such a way that nonreactive scattering coordinates can
be used.
7. Time Dependent, Three Dimensional Body Frame Quantal Wavepacket Treatment of
the H + HI Exchange Reaction on the Liu-Siegbahn-Truhlar-Horowitz (LSTH) Surface,
D. Neuhauser, M. Baer, R. S. Judson, and D. J. Kouri, J. Chem. Phys. 90, 5882 (1989).
The first full 3-D time dependent quantum wavepacket calculations for a chemical
reaction were reported in this paper. It used the crudest form of the method. Thus,
each single energy required a separate wavepacket propagation, and the results really
represented scattering of a spread of energies peaked at the nominal energy of interest.
However, state-to-state probabilities were obtained and the general ideas of the method
were shown to be sound. The system studied was the H + H2 exchange reaction (chosen
because accurate results were available for comparison to be sure our codes were working
correctly).
8. A Time-Dependent Wavepacket Approach to Atom-Diatom Reactive Collision Proba-
bilities: Theory and Application to the H -f- H^J = 0) System, D. Neuhauser, M. Baer,
R. S. Judson, and D. J. Kouri, J. Chem. Phys. 93, 312 (1990).
The basic theory of the version of the wavepacket method to be used in the subsequent
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study of the F + H% —> HF + H reaction was given in this paper, along with example
calculation results for the standard H + H2 exchange reaction. The paper is a synthesis of
the CCWP propagation method of paper 4, the absorbing potential of paper 6, new flux
methods for the final state analysis, and a projection operator procedure for reducing the
grid size in the reactant entrance channel. Only reaction probabilities could be gotten by
this method.
9. Time-Dependent Wavepacket for the Complete Determination of 5-matrix Elements
for Reactive Molecular Collisions in Three Dimensions, R. S. Judson, D. J. Kouri, D.
Neuhauser, and M. Baer, Phys. Rev. A 42, 351 (1990).
A more general method for 3-D reactive quantum wavepacket propagation is given that
is able to determine an entire column of the 5-matrix both for reactive and the accom-
panying nonreactive scattering. The method uses the body frame propagation, complex
absorbing potentials to reduce grid size, and interpolation method to change from the reac-
tant to a product space grid, and a final state analysis yielding the most detailed 5-matrix
elements. It was shown to work by application to the standard H -f H% exchange reaction.
10. The Application of Time-Dependent Wavepacket Methods to Reactive Scattering, D.
Neuhauser, M. Baer, R. S. Judson, and D. J. Kouri, Computer Phys. Commun. 63, 460
(1991).
A summary of the various methodologies in reactive scattering wavepacket calculations
is given. It combines essentially all the ideas of papers 8 and 9.
11. Time Dependent Treatment of Scattering: Integral Equation Approaches Using the
Time-Dependent Amplitude Density, D. K. Hoffman, O. Sharafeddin, R. S. Judson, and
D. J. Kouri, J. Chem. Phys. 92, 4167 (1990).
A totally new way to propagate wavepackets is developed making use of the time de-
pendent Lippmann-Schwinger integral equation. The objective is to develop a new class of
propagation schemes which may make the quantum wavepacket method even more power-
ful for treating reactive scattering. An auxiliary function, the time dependent amplitude
density, is introduced and shown to enable one to restrict consideration solely to the region
in space where the potential is nonzero. This can lead to smaller grid sizes.
12. Time Dependent Treatment of Scattering. II. Novel Integral Equation Approach to
Quantum Wavepackets, O. A. Sharafeddin, R. S. Judson, D. J. Kouri, and D. K. Hoffman,
J. Chem. Phys. 93, 5580 (1990).
Work on the integral equation based schemes for propagating quantum wavepackets is
continued by exploring novel ways to define reference and interaction Hamiltonians. The
radical choice of the potential as H0 and the kinetic energy as the perturbation is shown
to work and yield identical results to more standard choices!
13. A Comparison of Three Time Dependent Wavepacket Methods for Calculating Elec-
tron-Atom Elastic Scattering Cross Sections, R. S. Judson, D. B. McGarrah, O. A.
Sharafeddin, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 94, 3577 (1991).
The Chebychev propagation, Amplitude Density propagation (see paper 11), and a
new integral equation based method called the Modified Cayley propagation were compared
by calculating complete elastic scattering of an electron off a spherically symmetric target
(atom). All three methods worked well, with the Modified Cayley being the most efficient,
as well as stable.
14. A Numerically Exact Full Wavepacket Approach to Molecule-Surf ace Scattering, R. C.
Mowrey, Y. Sun, and D. J. Kouri, J. Chem. Phys. 91, 6519 (1989).
Wavepacket propagation involving the polar angle, 9, is problematic due to the fact
that the kinetic energy operator involves terms containing the factor (I/ sin 0). This leads
to roundoff errors in the computer that produce instability after a number of time steps
or applications of the Hamiltonian to a wavepacket. However, Wavepacket propagation on
a grid for all variables is very desirable if one wants to take maximum advantage of the
N Iog2 JV scaling of Fast Fourier Transforms with the number of grid points, N. This paper
presents such a method which is stable and accurate. Although applied here to molecule-
surface collisions, the same method can be applied to any 3-D quantum scattering problem.
II. Personnel Supported Under NAG2-503
1. Donald J. Kouri (PI)
2. Danny Neuhauser (postdoc)
3. Ching-Kuang Zhang (graduate student)
4. Richard S. Judson (postdoc)
5. Bernard Chang (postdoc)
6. Omar A. Sharafeddin (graduate student)
7. Ferrel Bowen (graduate student)
III. Enclosures
Reprints of thirteen refereed publications are included.
IV. Funds
All funds were expended.
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