Atom - Molecule Collision Theory: A Guide for the Experimentalist

785 Pages·1979·24.325 MB·English

by  Richard B. Bernstein (auth.), Richard B. Bernstein (eds.)

ATOM -MOLECULE
COLLISION THEORY
A Guide for the Experimentalist
PHYSICS OF ATOMS AND MOLECULES
Series Editors:
P. G. Burke, The Queen's University of Belfast,
Northern Ireland and Daresbury Laboratory, Science Research Council,
Warrington, England
and
H. Kleinpoppen, Institute ofA tomic Physics, University ofS tirling, Scot/and
Editorial Advisory Board:
R.B. Bernstein (New York, U.S.A.) W. Hanle (Giessen, Germany)
J.C. Cohen-Tannoudji (Paris, France) W.E. Lamb, Jr. (Tucson, U.S.A.)
R.W. Crompton (Canbe"a, Australia) P.-O. Lowdin (Uppsala, Sweden)
J.N. Dodd (Dunedin, New Zealand) M.R.C. McDowell (London, U.K.)
G.F. Drukarev (Leningrad, U.S.S.R.) K. Takayanagi (Tokyo, Japan)
1976:
ELECTRON AND PHOTON INTERACTIONS WITH ATOMS
Edited by H. Kleinpoppen and M.R.C. McDowell
1978:
PROGRESS IN ATOMIC SPECTROSCOPY, Parts A and B
Edited by W. Hanle and H. Kleinpoppen
1979:
ATOM-MOLECULE COLLISION THEORY: A Guide for the Experimentalist
Edited by Richard B. Bernstein
In preparation:
COHERENCE AND CORRELATION IN ATOMIC COLLISIONS
Edited by H. Kleinpoppen and J.F. Williams
THEORY OF ELECTRON-ATOM COLLISIONS
By P.G. Burke and C.J, loachain
A Continuation Order Plan is available for this series. A continuation order will
bring delivery of each new volume immediately upon publication. Volumes are
billed only upon actual shipment. For further information please contact the
publisher.
ATOM -MOLECULE
COLLISION THEORY
A Guide for the Experimentalist
Edited by
Richard B. Bernstein
Columbia University
New York, New York
PLENUM PRESS· NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Main entry under title:
Atom-molecule collision theory.
(physics of atoms and molecules)
Includes index.
1. Collisions (Nuclear physics) I. Bernstein, Richard Barry, 1923-
QC794.6.C6A82 539.7'54 78-27380
lSBN-13: 978-1-4613-2915-2 e-lSBN-13: 978-1-4613-2913-8
DOT: 10.1007/ 978-1-4613-2913-8
First Printing - June 1979
Second Printing - April 1984
© 1979 Plenum Press, New York
Softcover reprint of the hardcover I st edition 1979
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
Contributors
R. B. Bernstein, Department of Chemistry, Columbia University, New York,
New York 10027
M. S. Child, Theoretical Chemistry Department, University of Oxford,
Oxford OXI 3TG, England
D. J. Diestler, Department of Chemistry, Purdue University, West Lafayette,
Indiana 49707
D. A. Dixon, Department of Chemistry, University of Minnesota, Minneapolis,
Minnesota 55455
W. R. Gentry, Department of Chemistry, University of Minnesota, Minneapolis,
Minnesota 55455
J. L. Kinsey, Department of Chemistry, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139
D. J. Kouri, Departments of Chemistry and Physics, University of Houston,
Houston, Texas 77004
P. J. Kuntz, Hahn-Meitner-Institut fUr Kernforschung, 1000 Berlin 39,
West Germany
R. D. Levine, Department of Physical Chemistry, The Hebrew University,
Jerusalem, Israel
J. C. Light, The James Franck Institute and The Department of Chemistry,
University of Chicago, Chicago, Illinois 60637
J. T. Muckennan, Chemistry Department, Brookhaven National Laboratory,
Upton, New York 11973
M. D. PattengiU, Chemistry Department. University of Kentucky. Lexington.
Kentucky 40506
H. Pauly, Max-Planck-Institut fUr Stromungsforschung, 3400 Gottingen,
West Germany
J. Reuss, Fysisch Laboratorium, Katholieke Universiteit, Nijmegen,
The Netherlands
H. F. Schaefer III, Department of Chemistry, University of California,
Berkeley, California 94720
D. H. Secrest, School of Chemical Sciences, University of Illinois, Urbana,
Illinois 61801
S. Stolte, Fysisch Laboratorium, Katholieke Universiteit, Nijmegen,
The Netherlands
D. G. Truhlar, Department of Chemistry, University of Minnesota,
Minneapolis, Minnesota 55455
R. E. Wyatt, Department of Chemistry, The University of Texas,
Austin, Texas 78712
v
Preface
The broad field of molecular collisions is one of considerable current
interest, one in which there is a great deal of research activity, both experi
mental and theoretical. This is probably because elastic, inelastic, and
reactive intermolecular collisions are of central importance in many of
the fundamental processes of chemistry and physics.
One small area of this field, namely atom-molecule collisions, is now
beginning to be "understood" from first principles. Although the more
general subject of the collisions of polyatomic molecules is of great im
portance and intrinsic interest, it is still too complex from the viewpoint
of theoretical understanding. However, for atoms and simple molecules
the essential theory is well developed, and computational methods are
sufficiently advanced that calculations can now be favorably compared
with experimental results.
This "coming together" of the subject (and, incidentally, of physicists
and chemists !), though still in an early stage, signals that the time is ripe for
an appraisal and review of the theoretical basis of atom-molecule collisions.
It is especially important for the experimentalist in the field to have a
working knowledge of the theory and computational methods required to
describe the experimentally observable behavior of the system. By now many
of the alternative theoretical approaches and computational procedures
have been tested and intercompared. More-or-Iess optimal methods for
dealing with each aspect are emerging. In many cases working equations,
even schematic algorithms, have been developed, with assumptions and
caveats delineated.
Thus a book on atom-molecule collision theory would encourage the
experimentalist in the field to make full use of the best available theoretical
computational methods in the interpretation and analysis of the data and
also in the design of new experiments.
The purpose, then, of this compendium is to serve as a state-of-the-art
"handbook," a timely, practical reference work for the user of atom-molecule
collision theory. It is indeed intended as A Guide for the Experimentalist.
Richard B. Bernstein
Department of Chemistry
Columbia University
New York, New York
vii
Contents
Chap. 1. Introduction to Atom-Molecule Collisions:
The Interdependency of Theory and Experiment
Richard B. Bernstein
1. General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. The Experimentalist's "Need to Know" ...................................... 3
3. Overview of Experiments in Atom-Molecule Collisions ............. . . . . . . . . . . . 8
3.1. Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2. Inelastic Scattering ................................................... 10
3.3. Electronic Excitation and Curve Crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4. Reactive Scattering ................................................... 13
4. Experimental Examples ................................................... 14
4.1. Elastic Scattering .................................................... 15
4.2. Rotationally Inelastic Scattering ...................... . . . . . . . . . . . . . . . . . . 19
4.3. Vibrationally Inelastic Scattering ....................................... 23
4.4. Electronic Excitation and Charge Transfer ............................... 24
4.5. Reactive Atom-Molecule Scattering. . . . . .. . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . 25
4.6. Collision-Induced Dissociation ......................................... 31
5. Information Content of Atom-Molecule Collision Cross Sections ............... 31
6. Future Theoretical Demands of the Experimentalist ........................... 34
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chap. 2. Interaction Potentials I: Atom-Molecule Potentials
Henry F. Schaefer III
1. Current State of Ab Initio Electronic Structure Theory .......... . . . . . . . . . . . . . . . 45
2. Philosophy: Judicious Synthesis of Theory and Experiment. . . . . . . . . . . . . . . . . . . . . 46
3. Brief Survey of Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1. Basis Sets ........................................................... 48
3.2. The Problem of Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.1. The Concept. . .. . . . . . . . .. . . . . . . . .. . . . . . . . . . .. . . . . . .. . .. . . . . . . . . . 50
3.2.2. Configuration Interaction (CI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4. Examples ............................................................... 52
4.1. Nonreactive ......................................................... 53
4.1.1. Li+ -H2 ................................................... ..... 53
4.1.2. He-H CO ..................................................... 54
2
4.2. Reactive............................................................. 55
4.2.1. H + H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2. Fluorine-Hydrogen Systems. . . . .. .. . .. . . . . .. . .. . . . . . . . . . . .. . . . . . . 58
4.2.3. N+ + H2 ...................................................... 65
ix
x Contents
4.2.4. H + Li2, F + Li2 ............................................... 67
4.2.5. H + CIH, H + BrH ............................................. 70
5. Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Chap. 3. Interaction Potentials II: Semiempirical Atom-Molecule
Potentials for Collision Theory
P. J. Kuntz
1. Introduction............................................................. 79
1.1. Potential Surfaces for Collision Theory .................................. 79
1.2. Requisites for the Potential Energy Surface and Its Representation . . . . . . . . . . . 80
1.2.1. Physical Requirements.. .. . . . . .. . .. . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . 80
1.2.2. Computational Requirements ..................................... 81
1.3. Selection of Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2. The Method of Diatomics-in-Molecules (DIM) ............................... 82
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.2. General Formulation ................................................. 83
2.2.1. Defining the Scope of the Problem ................................. 83
2.2.2. The DIM Basis Set .............................................. 84
2.2.3. The DIM Hamiltonian Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.2.4. The DIM Eigenvalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.3. A Specific Example: FH2 .......... . . .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 89
2.3.1. Define the Coordinate System. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.3.2. Define the Atomic Basis Functions and Fragment Matrices ... . . . . . . . . . 90
2.3.3. Define the Diatomic Basis and Fragment Matrices ................... 91
2.3.4. Compute the Rotated Fragment Matrices ........................... 93
2.3.5. Construct the Triatomic Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.3.6. Construct the Atomic Matrices B .................................. 95
2.3.7. Construct the Diatomic Matrices B ................................ 95
2.3.8. Find the DIM Eigenvalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.4. Simple Systems: An Alternative Formulation.. . ...... ..... . .. .. ... . .. .... 101
2.5. Coupling............................................................ 104
2.5.1. Spin-Orbit Coupling ............................................ 104
2.5.2. Nonadiabatic Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3. Methods Related to DIM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.1. The LEPS Method ................................................... 106
3.2. Method of Blais and Truhlar .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3. Valence-Bond Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.3.1. Porter-Karplus Surface for H3 .................................... 107
3.3.2. Valence-Bond Methods with Transferable Parameters ............... " 107
3.4. Simple Approach to Nonadiabatic Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
References. " . . . . . . . . . . . . . . . . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . 108
Chap. 4. Elastic Scattering Cross Sections I: Spherical Potentials
H. Pauly
1. Introduction............................................................. III
2. Intermolecular Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.1. The Concept of an Intermolecular Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113
Contents xi
2.2. General Behavior of the Intermolecular Potential............. ....... ...... 113
2.3. Potential Models Used in the Evaluation of Scattering Cross Sections.... .... 116
2.3.1. Basic Potential Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
2.3.2. Modifications of the Basic Potentials and Piecewise
Analytic Potentials .............................................. 118
2.3.3. The Simons-Parr-Finlan (SPF) Modified Dunham Expansion. . .. . . . .. 123
3. Definitions of the Quantities That Can Be Measured in Elastic-Scattering
Experiments. Influence of Experimental Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . .. 123
4. Classical Scattering Theory ................................................ 125
4.1. Basic Formulas ...................................................... 125
4.2. Differential Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 129
4.2.1. Small-Angle Scattering ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 129
4.2.2. Glory Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.2.3. Rainbow Scattering. . . . . . . . .. . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. 131
4.2.4. Large-Angle Scattering ...........................................• 131
4.2.5. Orbiting Collisions .............................................. 133
4.2.6. Summary of the Classical Results for the Differential Scattering Cross
Section and Limits of Validity .... ..................... ............ 136
4.3. Total Elastic Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. .. 138
4.4. Identical Particles .................................................... 140
4.5. First-Order Momentum Approximation and Results for the
Basic Potentials. . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. 140
5. Quantal Treatment ....................................................... 142
5.1. Introduction......................................................... 142
5.2. Stationary Scattering Theory and Partial-Wave Analysis ................... 143
5.3. Examples of Numerical Results... ...... ............ ... ........... ...... 147
5.3.1. Differential Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 147
5.3.2. Total Scattering Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 150
5.4. Resonance Scattering ................................................. 152
5.5. Identical Particles .................................................... 157
6. Semiclassical Approximation.. . . . . . .. .. . . . . . . . . .. . .. . . . . . . . . . . . . . . . . . . . .. .. 159
6.1. General Assumptions and Introductory Remarks. . . . . . . . . . . . . . . . . . . . . . . . .. 159
6.2. Special Features of the Differential Cross Section. . . . . . . . . . . . . . . . . . . . . . . . .. 161
6.2.1. Interference Effects.. ..... .. .. . . ........ ... . ... ........... ........ 161
6.2.2. Rainbow Scattering. . . . . . .. . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. .. 164
6.2.3. Orbiting Collisions .............................................. 166
6.2.4. Large-Angle Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 168
6.2.5. Glory Scattering. . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 169
6.2.6. Small-Angle Scattering (Forward Diffraction Peak) . . . . . . . . . . . . . . . . . .. 171
6.3. Special Features of the Total Elastic Scattering Cross Section ............... 172
6.4. Identical Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 177
6.5. High-Energy Approximation... .. ..... .... .... . . . . ... .. . ... .... ... .. ... 177
6.5.1. Brief Outline of the Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 177
6.5.2. Results for the Basic-Potential Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178
7. Methods for the Evaluation of Potentials from Experimental Scattering Data. . . . .. 179
7.1. General Survey........................... ..... .... ............. ...... 179
7.2. Semiclassical Inversion Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181
7.2.1. Determination of the Repulsive Part of the Potential from the
s-Phase as a Function of the Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 182
7.2.2. Determination of the Potential from the Phase Shift Function
or the Deflection Function at a Fixed Energy. . . . . . . . . . . . . . . . . . . . . . . . 183
7.2.3. Determination of the Phase Shift Function o(p) or the
Classical Deflection Function 0(P) from an Analysis of
Differential Cross Section Data. . . . . .. . . . . . . .. . . . . . .. . . . .. . . . . . . .. . 184