Intramolecular Dynamics: Proceedings of the Fifteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry Held in Jerusalem, Israel, March 29—April 1, 1982

549 Pages·1982·33.445 MB·English

by  Eli Pollak (auth.), Joshua Jortner, Bernard Pullman (eds.)

INTRAMOLECULAR DYNAMICS
THE JERUSALEM SYMPOSIA ON
QUANTUM CHEMISTRY AND BIOCHEMISTRY
Published by the Israel Academy of Sciences and Humanities,
distributed by Academic Press (N. Y.)
1st JERUSALEM SYMPOSIUM: The Physicochemical Aspects of Carcinogenesis
(October 1968)
2nd JERUSALEM SYMPOSIUM: Quantum Aspects of Heterocyclic Compounds in
Chemistry and Biochemistry (April 1969)
3rd JERUSALEM SYMPOSIUM: Aromaticity, Pseudo-Aromaticity, Antiaromaticity
(April 1970)
4th JERUSALEM SYMPOSIUM: The Purines: Theory and Experiment
(April 1971)
5th JERUSALEM SYMPOSIUM: The Conformation of Biological Molecules and
Polymers (April 1972)
Published by the Israel Academy of Sciences and Humanities,
distributed by D. Reidel Publishing Company (Dordrecht, Boston and London)
6th JERUSALEM SYMPOSIUM: Chemical and Biochemical Reactivity
(April 1973)
Published alld distributed by D. Reidel Publishing Company
(Dordrecht, Boston and London)
7th JERUSALEM SYMPOSIUM: Molecular and Quantum Pharmacology
(March/April 1974)
8th JERUSALEM SYMPOSIUM: Environmental EJfects on Molecular Structure and
Properties (April 1975)
9th JERUSALEM SYMPOSIUM: Metal-Ligand Interactions in Organic Chemistry
and Biochemistry (April 1976)
10th JERUSALEM SYMPOSIUM: Excited States in Organic Chemistry and
Biochemistry (March 1977)
11 th JERUSALEM SYMPOSIUM: Nuclear Magnetic Resonance Spectroscopy
in Molecular Biology (April 1978)
12th JERUSALEM SYMPOSIUM: Catalysis in Cllemistry ami Biochemistry
Theory and Experiment (April 1979)
13th JERUSALEM SYMPOSIUM: Carcinogenesis: fundamental Mechanisms
and Environmental Effects (April/May 1980)
14th JERUSALEM SYMPOSIUM: Intermolecular Forces (April 1981)
VOLUME 15
INTRAMOLECULAR
DYNAMICS
PROCEEDINGS OF THE FIFTEENTH JERUSALEM SYMPOSIUM ON
QUANTUM CHEMISTRY AND BIOCHEMISTRY HELD IN
JERUSALEM, ISRAEL, MARCH 29-ApRIL 1, 1982
Edited by
JOSHUA JORTNER
Department of Chemistry
Tel-Aviv University, Tel-Aviv, Israel
and
BERNARD PULLMAN
Universite Pierre et Marie Curie (Paris VI)
Institut de Biologie Physico-Chimique
(Fondation Edmond de Rothschild), Paris, France
D. REIDEL PUBLISHING COMPANY
DORDRECHT: HOLLAND / BOSTON: U.S.A.
LONDON: ENGLAND
library of Congress Cataloging in Publication Data
Jerusalem Symposium on Quantum Chemistry and Biochemistry
(l5th : 1982)
Intramolecular dynamics.
(The Jerusalem symposia on quantum chemistry and biochemistry;
v.15)
Includes index.
1. Molecular dynamics-Congresses. I. Jortner, Joshua.
II. Pullman, Bernard, 1919- . III. Title. IV. Series.
QD46lJ47 1982 541.2'2 82-18107
ISBN-13: 978-94-009-7929-1 e-ISBN-I3: 978-94-009-7927-7
DOl: 10.1007/978-94-009-7927-7
Published by D. Reidel Publishing Company,
P.O. Box 17,3300 AA Dordrecht, Holland.
Sold and distributed in the U.S.A. and Canada
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In all other countries, sold and distributed
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D. Reidel Publishing Company is a member of the Kluwer Group.
All Rights Reserved
Copyright © 1982 by D. Reidel Publishing Company, Dordrecht, Holland
Sotlcover reprint of the hardcover I st edition 1982
No part of the material protected by this copyright notice may be reproduced or
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TABLE OF CONTENTS
Preface
~x
E. POLLAK / Do Vibrationally Adiabatic Molecules Exist?
R. D. LEVINE / Algebraic Approach to Molecular Structure
and Dynamics 17
R. S. BERRY / Are Atoms and Small Molecules Almost the Same? 29
R. LEFEBVRE / Siegert Quantization and Intramolecular
Dynamics 55
F. A. GIANTURCO and A. PALMA / Rotational Rainbows in
Collisions Involving van der Waals Molecules 63
A. E. HANSEN / Interference Effects in Molecular Circular
Dichroism Spectra 89
M. BIXON / Classical Aspects of Wavepacket Dynamics 97
R. KOSLOFF / Comparison Between Classical and Quantum
Dynamical Chaos 107
M. S. CHILD / Local and Normal Vibrational States 115
M. L. SAGE / The Dynamics of Intramolecularly Coupled
Local Modes 129
J. BRICKMANN / Quantum Dynamics of Gaussian Wave Packets
in Anharmonic Vibrational Systems 139
R. B. GERBER, V. BUCH, and M. A. RATNER / Self-Consistent
Field and Statistical Wavefunction Methods for
Excited Vibrational States of Polyatomic
Molecules 171
W.-K. LIU, D. W. NOID, and M. L. KOSZYKOWSKI / Dynamical
Studies of Excited States in Triatomic Molecules 191
S. F. FISCHER / Intramolecular Vibrational Relaxation
of Polyatomic Molecules 205
L. YOUNG, C. A. HAYNAM, and D. H. LEVY / Intramolecular
Vibrational Relaxation and Photochemistry in
Weakly Bound Organic Dimers 219
vi TABLE OF CONTENTS
U. EVEN and J. JORTNER / Spectroscopy of Large Molecules ~n
Supersonic Expansions: Isolated Ultracold
Porphyrins 227
J. P. MAIER and F. THOMMEN / Intramolecular Relaxation of
Open-Shell Organic Cations 241
J. KOMMANDEUR, B. J. VAN DER MEER, and H. Th. JONKMAN /
Rotations and Electronic Decay 259
G. E. EWING / Vibrational Energy Flow in van der Waals
Molecules 269
R. ENGLMAN / Trajectories in Large Molecules: A Tunnelling
Contribution to Classical Motion 287
M. SHAPIRO / Dissociation and Intramolecular Dynamics 299
J. TROE / Inter- and Intramolecular Dynamics of
Vibrationally Highly Excited Polyatomic Molecules 311
J. LINDERBERG / Photochemical Rearrangement Reactions 325
S. LIFSON and P. S. STERN / The Morse Potential as a
Bridge Between Molecular Structure and Dynamics 341
F. A. MATSEN / An Optical Potential Model for
Isomerization in the Gas Phase 351
M. QUACK / The Role of Intramolecular Coupling and
Relaxation in IR-Photochemistry 371
J. STONE, E. THIELE, and M. F. GOODMAN / An Analytic
Approach to Time Averages and Chaotic Behavior
in Quantum Mechanics 391
M. J. DAVIS, R. E. WYATT, and C. LEFORESTIER / Classical
and Quantum Mechanical Studies of Molecular
Multiphoton Excitation and Dissociation 403
I. PROCACCIA / The Effect of Many Body Collective Phenomena
on the Rates of Chemical Reactions 429
K. F. FREED, H. METIU, E. HOOD, and C. JEDRZEJEK I Quantum
Mechanical Model of the Dynamics of Desorption
Processes 447
I. Z. STEINBERG and E. HAAS I Intramolecular Dynamics of
Polymer Molecules Studied by Longe-Range
Non-Radiative Energy Transfer 459
D. COWBURN, D. H. LIVE, A. J. FISCHMAN, and W. C. AGOSTA /
Dynamic Structure of Peptides Studied by
Multinucle.ar NMR 473
C. M. DOBSON / NMR Studies of Protein Dynamics 481
R. BERSOHN I Fast Non-Radiative Decay Rates in Metalloproteins 497
T ABLE OF CONTENTS vii
W. L. DUAX, M. D. FRONCKOWIAK, J. F. GRIFFIN, and D. C. ROHRER /
A Comparison Between Crystallographic Data and
Molecular Mechanics Calculations on the Side Chain
and Backbone Conformations of Steroids 505
W. K. OLSON / The Longe-Range Stiffness and Local Mobility
of Double-Stranded DNA 525
E. W. PROHOFSKY / Nonbonded Interactions and the Acoustic
Modes of the Double Helix 537
INDEX OF SUBJECTS 549
PREFACE
The Fifteenth Jerusalem Symposium reflected the high standards
of the former international scientific meetings, which convene once a
year at the Israel Academy of Sciences and Humanities in Jerusalem to
discuss a specific topic in the broad area of quantum chemistry and
biochemistry. The topic at this year's Jerusalem Symposium was intramo
lecular dynamics, a subject of central interest for theoreticians, che
mists and biologists.
During the last two decades, there has been remarkable pro
gress in our understanding of time dependent phenomena. The development
and application of the modern techniques of quantum mechanics and sta
tistical mechanics to excited-state dynamics and to chemical and biophy
sical systems constitutes a fast developing current research area. The
main theme of the Symposium was built around a conceptual framework for
the elucidation of photophysical and photochemical phenomena in atoms,
molecules, van der Waals complexes and clusters, condensed phases, poly
mers and biological supermolecules. The interdisciplinary nature of this
research field was deliberated by intensive and extensive interactions
between scientists from different disciplines and between theory and
experiment. This volume provides a record of the invited lectures at the
Symposium.
We wish to express our thanks and gratitude to all those who
have made this meeting possible and who have contributed significantly
to its success. In particular, we are indebted to Baron Edmond de
Rothschild, whose continuous and generous support makes him a true part
ner in this important endeavour, the Israel Academy of Sciences and
Humanities under whose auspices the Symposium was held and the members
of its administrative staff, Mrs Avigail Hyam and Mrs Miriam Yogev, who
gave valued assistance to the efficiency and excellence of the local
arrangements, and to the Hebrew University and especially to Professor
Raphael Mechoulam, the Rector, for the constant intellectual support in
this inspiring event.
Joshua Jortner
Bernard Pullman
ix
J. Jortner and B. Pullman (eds.), Intramolecular Dynamics, ix.
Copyright © 1982 by D. Reidel Publishing Company.
DO VIBRATIONALLY ADIABATIC EXIST?
~IDLECULES
*
Eli Pollak
Chemical Physics Department
Weizmann Institute of Science
Rehovot 76100, Israel
* .
Bergmann memorlal fellow
ABSTRACT
A quasi-classical model for resonance widths in the H+HH and H+MuH
collinear exchange reaction is presented. An important ingredient in
the model is the stability frequency of resonant periodic orbits. In
1 ight atom transfer reactiotl)we fi nd that these neriodic orbi ts are
stable although there is no static potential energy well on the surface.
This implies the existence of quasi-periodic bound orbits for these
systems. Classically these orbits may be called a vibrationally adiaba
tic molecule since the binding force is dynamic. The quantal analog of
the adiabatic molecule is investigated. We find good reason to believe
that the adiabatic molecule is also a quantal entity. Possible experi
mental verification of the adiabatic molecule is discussed.
INTRODUCTION
One of the striking quantal effects found in exact atom molecule
scattering computations is the resonance structure found in the energy
dependent transition probabilities. This feature was surprising since
it was found for reactions occurring on 'purely repulsive' potential
energy surfaces - surfaces that don't exhibit a minimum of the potential
energy .. It ~Ias though quite cl ear from the work of Levi ne and Wu1 that
these resonances are indeed associated with relatively (in comparison
with a vibrational period) long time delays. Quantum mechanically,
although no static well existed on the potential energy surface, a long
lived complex was formed. It was suggested, that the 'binding force'
holding the complex together was dynamic. In fact, one of the numerical
methods of solving the exact scattering problem involved the construction
of vibrationally adiabatic potential energy surfaces (using natural
collision coordinates). These surfaces exhibited, for vibrationally
excited states, wells in the interaction region. It was then proposed
by Levine and Wu1 that the mechanism responsible for the formation of
the complex was 'adiabatic trapping' in these adiabatic wells.
J. Jortner and B. Pullman (eds.), Intramolecular Dynamics, 1-16.
Copyright © 1982 by D. Reidel Publishing Company.
2 E.POLLAK
This point of view was confirmed qualitatively through the work of
Wyatt and coworkers2 • They showed that if the adiabatic well s were el i
minated then the resonance structure in the reaction probability also
disappeared. More quantitative evidence of the adiabatic trapping
mechanism came as a result of the work of Kaye and Kunpermann3, and
Babamov and Marcus4• Here the vibrationally adiabatic potential energy
surfaces were constructed by using the radial Delves coordinate systems.
Aga in, these surfaces exhibi ted well sin the interaction region. More
importantly though. the resonance energies could be correlated with the
virtual or bound states of the adiabatic wells.
The resonances presented a challenge to the semiclassical theory of
reactive scattering. Stine and Marcl,.Is6, in a unique calculation, were
able to show that the first resonance in the H3 system could be accounted
for, quantitatively. using a particular set of classical trajectories
that traversed the interaction region an increas ing number of times.
This was the first direct evidence and picture of the 'quantal complex'.
However. not only is such a computation very tedious (much more expensive
then the exact quantal computation), Duff and Truhlar7 demonstrated that
it is not generally aprlicable.
One of the major problems in the semiclassical analysis of the
resonances is fundamental. Consider the previous adiabatic ricture. If
the adiabatic approximation is exact then the semiclassical analog of the
resonance would be quasi-periodic motion on an invariant torus with
(half) integer action conditions on each of its (topologically) indepen
dent surfaces of section8• I n fact. resonances found for scatted n9 on
surfaces with well 10 have been correl ated successfully by Noid and
S9,
Koszykowski 11 with quasi-periodic motion. However, close scrutiny of
the H3 system forexampleby Costley and Pechukas12 has shown that except
for a very small energy region (lO-3eV) the symmetric stretch of the
hydrogen exchange reaction is always unstable. Child has also-under
taken a thorough search for quasi-periodic motion on the H3 surface
without any success13• We have shown14 that at 1 east for H3 an upper
bound on the quasi -peri odic portion of phase space is 0.1 %. What is
then the semiclassical analog of the quantal resonance?
Gutzwiller1s has shown that when no quasi-neriodic orbits exist one
should look at periodic orbits. We16 have shown that the quantal reso
nance energies of the H3 and FHH systems (and their isotopic analogues)
can be predicted with quantitative accuracy using resonant periodic
orbits with an integer action quantisation condition. Examples of such
orbits for the H3 system are shown in figure 1.
What about the resonance widths? In figure 2 we show the resonance
regions of the H+HH and H+MuH reactions on the same (Porter-Karplus II)
potential energy surfacel ? In H3 we find aporoximately the same width
at all energies while in HMuH there are order of magnitude variations.
In section II we provide a quasi-classical model of resonance widthsl8
which accounts for these Variations. Two ingredients enter the model.
One is the tunnelling probability through the adiabatic barriers in the