|
Items in cart [0] |
Questions? Call 888-624-8373 |
PAPERBACK PDF BOOK Free Resources |
||||||||||||||||
|
||||||||||||||||
|
|
|||||||||||||||
| ||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 88
5
Molecular Physics
Molecular physicists apply the tools of physics to the problems of
chemistry in order to obtain quantitative pictures of the structure of
molecules, to learn how molecules interact and react, and to gain
understanding of more complex states of matter such as liquids.
Molecular and atomic physics share many experimental techniques,
and their styles of research are similar in the depth of analysis and the
desire for complete understanding of the phenomena in terms of the
basic laws of physics.
Molecular physics straddles the border between physics and chem-
istry. In universities, the work is pursued in both physics and chemis-
try departments. In Europe the majority of the research is carried out
in institutes of physics and physics departments; in the United States
the research is most often carried out in chemistry departments.
Research in the United States is funded by physics programs as well as
by chemistry programs. We have attempted to portray here the
activities in molecular physics that lie closest to the physics-chemistry
interface.
THE NEW SPECTROSCOPY
Within the last decade laser spectroscopy has been combined with
innovative molecular-beam techniques to create and study a multitude
of new molecular species. For the first time, molecular physicists are
88
OCR for page 89
MOLECULAR PHYSICS 89
able to prepare virtually any desired simple molecule in any desired
quantum state. (See Figure 5.1.) Our understanding of molecular
structure is advancing so rapidly that progress is not merely quantita-
tive, it is qualitative. Traditional concepts of molecular structure are
being challenged, in some cases set aside. An underlying unity between
molecular structure and dynamics, long regarded as disparate areas, is
beginning to emerge. The generation of archival data transition
frequencies, intensities, molecular constants, potential energy sur-
faces continues its central role in spectroscopic research, but this,
too, is being revolutionized by tunable lasers and modern data-
processing methods. Altogether, these developments have stimulated
an explosive growth in fields such as chemical kinetics, photophysics,
and photochemistry and in a host of applications including combustion
and plasma diagnostics, atmospheric monitoring, and laser develop-
ment.
New Views of Electronic Structure
Laser spectroscopy has made it possible for the first time to examine
systematically large classes of related molecular species, including
species such as ions and radicals that can be produced only in trace
quantities. By way of illustration, we shall briefly describe some new
views of electronic structure that are emerging from the study of three
of these novel species: Rydberg molecules (highly excited molecules),
long-range molecules, and open-core molecules.
In a Rydberg molecule, one electron is in an orbit whose radius is
much larger than the core molecular ion. The energy levels form a
hydrogenlike pattern, but there are deviations from this pattern that
can be measured with high precision. The deviations arise because the
core is not a point charge: it has an extended nonspherical shape, and
it is polarizable. Furthermore, the core vibrates and rotates. Fre-
quently, these nuclear motions are fast compared with the orbital
motion of the Rydberg electron. The Born-Oppenheimer approxima-
tion (nuclear motions slow compared with electronic motion), the basis
of the traditional understanding of molecular structure in terms of
potential energy surfaces, no longer applies. Fortunately, a highly
successful theoretical framework for understanding Rydberg mole-
cules has been created (multichannel quantum defect theory, men-
tioned in Chapter 4 in the section on Atomic Structure). The molecular-
level structure can be viewed in terms of a slow electron repeatedly
scattering from a molecular ion. The spectroscopy of Rydberg mole-
cules, however, contains far more information, and yields a far clearer
OCR for page 90
90 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
B - STATE
Molecular
Potent ial
Tunneling
zI;
~/~
JProbe Laser
~/ I. ?_ __~...~_
~ uas i bound
~,`~
Sodium
~ Molecu lar
Pump Lager ~Laser
X . VITO
Pump Laser
5800 A
C} ~~ ~
Phot 0 d lode
Signal
1
1 ~ ~
E=22.4
/ E=o(Arb
a:/
B -STAT E
Energy Level' E
~ / E-33.8
W
1 ~\
E- 25.9
Probe Laser Frequenc y
- V >> O
Probe Laser
5 500 A
Hea t pipe" ,
Na2 Later
o
8000 A
Four-M irror
Rlog Resonator
OCR for page 91
MOLECULAR PHYSICS 91
picture, than one could hope to attain from low-energy electron
scattering by molecular ions.
Molecules in high vibrational states for which the nuclei spend most
of their time far apart, typically five atomic diameters or more, have
distinctive properties and form a class known as long-range molecules.
Their properties can be understood from the properties of the isolated
atoms, for instance the atomic polarizabilities and quadrupole mo-
ments. The attractive forces between atoms can be determined from
the molecular-energy-level pattern of long-range molecules more pre-
cisely than by any other means, not only for ground states but also for
excited states. This knowledge of the long-range forces is invaluable
because it is these forces that control the rates of atom-atom recom-
bination, transport coefficients in gases, and the cross sections for
atom-atom inelastic collisions.
The third species, molecules in open-core states, is characterized by
having one atom with a partially filled inner shell, for instance a
transition-metal or rare-earth atom. The compact core of the open-shell
atom can be regarded as an atomic ion that is perturbed by the rest of
the molecule. The core, which is highly anisotropic because of its
angular momentum, serves as a probe of its chemical environment,
much as a nucleus in nuclear magnetic resonance. A myriad of
low-lying electronic states can exist even in simple diatomic molecules.
(Samarium monoxide, for instance, has over 1000 electronic states
below 3 eV.) The study of open-core molecules provides a comprehen-
sive picture for the electronic charge distribution in these states. The
picture reveals the underlying simplicity of the atomic-ion-in-molecule
electronic structure that lies concealed beneath an extremely complex
energy level structure.
FIGURE 5.1 New Views of Molecules. Lasers and laser spectroscopy make it possible
to study molecular states never before observable. The illustration shows one of many
examples: a technique for studying molecules in states in which they are vibrating
violently. The formation and breaking of bonds in chemical reaction generally proceeds
through states like these.
The sodium dimer molecule, Nat, is studied in this experiment using two tunable dye
lasers, and the molecule itself forms a third laser. The first laser (''the pump'') excites
molecules in the "heatpipe" to an A state, one of the electronic states that might be
studied by conventional spectroscopy. The excited molecules, which are in a laser
resonator, form a laser (the Nat laser), which causes them to radiate into a state with high
vibrational energy. The resulting long-range molecule is then studied with a probe laser
that explores the region of the electronic B state, where the molecules are about to fall
apart or dissociate the quasi-bound region. (It is in this region that atoms in a gas form
into molecules.) The rate at which the molecules dissociate is found from the width of the
spectral lines measured by the probe laser. Different states have very different line
widths, as shown in the bottom figure, revealing very different rates. The Nat laser is one
by-product of the research on molecular structure; many new laser systems have been
discovered in the course of such studies.
OCR for page 92
92 A TOMIC, MOLECULAR, AND OPTICAL PHYSICS
A natural connection links open-core molecules to the structure
revealed by x rays in high-energy electron-molecular scattering, as
described in Chapter 4 in the section on Atomic Dynamics. The same
details of the electric field near the nucleus are sampled: in open-core
molecules the probe is a natural vacancy; in the scattering experiments
the probe is a short-lived inner-shell vacancy.
Electronic-Structure Theory: Ab Ir~itio Calculations
Molecular-structure calculations have advanced so rapidly in recent
years that it is now possible to calculate virtually any observable
property of any small system. The accuracy can be high for example,
10 parts per million for the ionization energy of H2 though typically
the computed properties are not so accurate as those obtained by
experiment. Nevertheless, the computed properties are often sufficient
for diagnostic purposes and to supplement empirical data. Moreover,
in many cases they provide the theoretical background needed for
interpretation of experiments. Calculated constants such as spin-orbit
couplings or electric dipole moments are valuable for identifying the
electron configuration of an electronic state; oscillator strengths can
sometimes be calculated more accurately than they can be measured.
Hydrogen-Bonded Molecules
Midway between the strong chemical forces that create chemical
bonds and the weak forces of van der Waals interactions there exists a
class of forces that is responsible for molecular aggregates and poly-
mers. The most important of these are hydrogen and ion-dipole
bonding, for they govern the properties of substances vital to life
ranging from water to DNA. The microscopic properties of the
hydrogen bond the structures of H-bonded aggregates, the energy
levels, the bonding and dissociation energies are at last beginning to
be understood.
Most experimental work in the field of hydrogen bonding has focused
on liquids and solids, for it is in these systems that H bonding is most
important. Hydrogen bonds are very sensitive to the environment,
however, and so liquid and solid systems are not well suited for
studying them. To understand the bonds clearly, it is essential to study
them in the gaseous state where the H-bonded complexes exist as free,
unperturbed entities.
Traditional infrared spectroscopy of gaseous complexes reveals only
broad unresolved bands, similar to the spectra obtained from liquids.
OCR for page 93
MOLECULAR PHYSICS 93
In the last 10 years, however, microwave spectroscopy and molecular-
beam resonance spectroscopy have succeeded in revealing the struc-
ture of the ground states of H-bonded dimers and, in some cases, have
also yielded information on dipole moments and dissociation energies.
The richest lode of information, however, has come from infrared
rotation-vibration spectroscopy. For example, the spectrum of the
hydrogen fluoride dimer, which is held together by the hydrogen bond,
displays all the important vibrational modes in great detail. As a result,
a clear picture has been constructed of the potential barriers that
separate its conformations.
Through high-resolution microwave and infrared spectroscopy of
hydrogen-bonded complexes, accurate models of the pair potential for
H bonding, and also for van der Waals bonding, can be constructed.
This pair potential governs many of the phenomena of condensed-
phase chemistry: bulk association, conformation and steric effects,
salvation, solubility, and physisorption.
The ultimate impact of this work will extend to biology, for H
bonding is vital to many biological processes. It plays a key role in the
structure and formation of biomolecules and accounts for the activity
of some toxic substances. The anesthetic activity of substituted
fluorocarbons is believed to be due to H bonding. It has been
discovered that biomolecules can exhibit semiconduction when doped
with electron acceptors in which H bonding plays a role. Semiconduc-
tion is believed to be important in intercellular communication and in
the control of cell proliferation. Calculations of all of these processes
require accurate data on the structure of the H-bonded complexes.
These data are becoming available.
Vibrational Structure of Polyatomic Molecules
The vibrational motions of a molecule are traditionally described in
terms of normal modes simple combinations of the nuclear displace-
ment that execute simple harmonic motion at frequencies known as
normal-mode frequencies. If the vibrational motion is sufficiently large,
one expects motions to occur at multiples of the normal-mode frequen-
cies known as overtones.
In the past, the normal-mode picture adequately explained the
vibrational fundamentals and low overtones found in the 500-4000
cm-i region of traditional infrared absorption spectroscopy. Higher
overtones and combinations were generally too weak to detect, and
there was no reason to question the normal-mode picture. Recently,
highly sensitive laser techniques have been developed for recording
OCR for page 94
94 ATOMIC, MOLECULAR, AND OPTICAL PHYSIC.S
pure vibrational spectra in the visible-wavelength region. Perhaps the
greatest surprise from this work was the discovery that the normal-
mode picture can break down completely at modest levels of excita-
tion, typically 10,000 cm-'.
One might expect that when vibrational amplitudes are so large that
enharmonic effects are important, energy is transferred from a normal
mode to the entire molecule, and the molecule simply heats up.
However, it has been discovered that the energy can appear to be
localized in a single band. For molecules containing one or more C H.
O—H. or N H bonds, the vibrational spectrum near 20,000 cm- is
dominated by highly localized vibrations in high-frequency, unusually
enharmonic, bond-stretching motions. The normal mode structure is
replaced by a local-mode structure, in which the vibration appears as
a large-amplitude stretching motion of a single bond.
The observation of local-mode structures in the spectra of large
polyatomic molecules has ignited excitement about the possibility of
inserting energy into a specific bond. This has led to controversy about
the possibility of inferring the rates for redistributing vibrational energy
within a molecule from the widths of high-overtone spectral features.
High-resolution spectroscopic studies have revealed that many of these
features have sharp and assignable vibration-rotational fine structure,
in contradiction to predictions based on classical mechanical calcula-
tions. In contrast to the situation for diatomic molecules, it is impos-
sible to determine a potential energy surface for polyatomic molecules
from the observed rotation-vibration levels, except near the equilib-
rium structure, where the normal mode approximation is useful.
Several new semiclassical and variational schemes for obtaining more
complete potential surfaces from spectral data have been proposed.
The explosive growth of multiple-laser techniques for systematically
obtaining high-quality, readily assignable spectral data for highly
excited rotation-vibration levels is causing a complete rethinking of the
problem of how polyatomic molecules vibrate.
MOLECULAR PHOTOIONIZATION AND
ELECTRON-MOLECULE SCATTERING
Understanding the joint motion of electrons and nuclei in molecular
fields is the essence of molecular physics. The dynamics of these
motions underlie the spectroscopy, the physical transformations, and
even the chemical changes in molecular systems. One strategy for
studying these dynamics is to photoionize the molecule or to scatter
electrons from it. Such experiments can provide physical insight into
OCR for page 95
MOLECULAR PHYSICS 95
the processes occurring during molecular excitation and the escape of
the electron through the anisotropic molecular field. The approach is
straightforward in concept, but extracting a clear picture of the
dynamics requires formidable experimental and theoretical tools. Ma-
jor progress toward these goals during the last decade has yielded new
understandings of electron motion in anisotropic molecular fields and
the interchange of energy between electronic and nuclear modes.
Moreover, recently developed techniques such as resonant multipho-
ton excitation portend accelerated progress in the future.
Molecular Photoionization
Photoionization is a powerful probe of the rotation-vibration-
electronic dynamics of molecules. The photoelectrons, which are
excited into well-defined optical ionization channels, carry to the
detector information on the quantum state of the residual ion as well as
on the dynamics of the photoionization process. Experimental devel-
opments including intense synchrotron light sources, pulsed dye lasers,
and detectors of unprecedented sensitivity have led to rapid advances.
It is now feasible to perform triply differential photoionization studies
in which the wavelength, the photoelectron energy, and the ejection
angle are independently varied. Previously measurements were only
possible at fixed wavelengths from line sources; today the measure-
ments can be carried out anywhere from the visible to the x-ray region.
These experimental advances have been accompanied by the develop-
ment of complementary theoretical methods.
Molecular photoionization studies are broad in scope. Here we
discuss three topics of particular interest: autoionization, shape reso-
nances, and resonant multiphoton ionization.
Molecular Autoionization Dynamics
Autoionization affects all molecular photoionization spectra, often
producing dramatic spectral features. In the simplest case, autoioniza-
tion occurs when a discrete state with positive total energy is coupled
by a perturbation to the continuum of free-particle states. The pertur-
bation allows the electron to escape. Autoionizing states usually
consist of an excited Rydberg electron and an excited ion, which are
bound together by their Coulomb attraction. Autoionization takes
place during a close collision of the Rydberg electron with the ion: the
excitation energy of the ion is transferred to the Rydberg electron,
allowing it to escape from the ionic field. (Autoionization is the inverse
OCR for page 96
96 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
of dielectronic recombination, a process discussed in Chapter 4 in the
section on Atomic Dynamics.) A close encounter is essential, since
only when the Rydberg electron is near the ion core can it participate
fully in the dynamics of the ion and exchange energy efficiently with it.
A molecule can store the energy needed to ionize a Rydberg electron
in any of its three modes—electronic, vibrational, or rotational. The
most direct means of storing electronic energy is to create a hole in an
inner molecular orbital, often by promoting an inner electron into a
Rydberg state. Various combinations of vibrational and rotational
excitation can accompany photoexcitation of Rydberg states; it is the
existence and interplay among these alternative modes, or channels,
that leads to the unique properties of molecular autoionization.
The most accurate and penetrating theoretical analysis of molecular
autoionization has been carried out within the theoretical framework of
multichannel quantum defect theory (MQDT). MQDT simultaneously
treats the interactions between and within different excitation chan-
nels. The input to a MQDT calculation is a small set of physical
parameters quantum defects and dipole amplitudes that character-
ize the short-range interactions between the excited electron and the
core. From these few parameters, MQDT can yield values for many
quantities that are directly related to the observables, for instance total
photoionization cross sections, vibrational branching ratios, and
photoelectron angular distributions. The complete elucidation of the
autoionization spectrum of molecular hydrogen is one of the major
triumphs of MQDT.
Shape Resonances in Molecular Fields
A shape resonance is a quasi-bound state in which a particle is
temporarily trapped by a centrifugal potential barrier, that is, by the
shape of the potential. In the case of molecular photoionization, the
ejected photoelectron is partially blocked by a centrifugal barrier near
the edge of the molecule so that, on the average, it must traverse the
molecule several times before it eventually escapes the molecular core
by quantum-mechanical tunneling through the barrier.
During the last 10 years shape resonances have become recognized
as an important general class of phenomena in molecular physics, for
a large variety of molecular properties have been found to be affected
by them: x-ray and VUV absorption spectra, photoelectron branching
ratios and angular distributions, non-Franck-Condon vibrational ef-
fects in molecular photoionization, elastic electron scattering, and
OCR for page 97
MOLECULAR PHYSICS 97
vibrational excitation by electron impact, to name some of the most
prominent.
Shape resonances provide a unifying link among different states of
matter and among the various processes mentioned above. Because the
resonances are localized in the strong potential of the molecular core
they suffer only secondary effects owing to changes in the molecular
environment. Hence, the same manifold of shape resonances in the
photoionization cross sections of the free molecule is frequently
observed during adsorption on a surface, condensation into a solid, or
under completely different excitation conditions such as in electron
scattering. To cite one example, there are four prominent shape
resonances in the sulfur L-shell photoabsorption spectrum of gaseous
SF6. These are indistinguishable from the shape resonances in the
spectrum of solid SF6, and they also emerge in elastic electron-SF6
scattering. This property of shape resonances has proven useful for
studying the orientation and adsorption-site interactions of
physisorbed molecules and for interpreting prominent features in
spectra of ionic crystals.
Progress in understanding shape resonances has been profoundly
influenced theoretically by the development of methods for treating
molecular continuum states and experimentally by the harnessing of
synchrotron radiation to study photoionization dynamics as a contin-
uous function of wavelength, electron ejection angle, and electron
kinetic energy. An excellent example in the strong interplay of theory
and experiment is the prediction and confirmation of large changes in
vibrational branching ratios and in photoelectron angular distributions
induced by shape resonance. These arise because shape resonances are
so sensitive to the internuclear separation that they behave differently
in the individual vibrational ionization channels.
Shape resonances are a powerful probe of short-range excitation
dynamics in molecules. They provide an important link among mole-
cules in different physical states and among different physical pro-
cesses. Our current knowledge is merely the tip of the iceberg. The
expansion, refinement, and unification of these recent developments
will provide an important theme in molecular physics in the coming
years.
Resonant Multiphoton Ionization
In multiphoton ionization, a molecule absorbs several quanta of
radiation to reach the ionization continuum. Intense, tunable radiation,
which can be provided by modern dye lasers, is essential for inducing
OCR for page 98
98 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
mult~photon ionization. Resonant multiphoton excitation via a single
rotation-vibration level of an intermediate molecular state can dramat-
ically simplify the spectrum, eliminating entire groups of rotational and
vibrational states. Resonant multiphoton ionization reveals the
photoionization dynamics of excited states that are fully specified
quantum mechanically. Photoionization branching ratios, photo-
electron angular distributions, alignment, and fragmentation all the
important properties in single-photon ionization can now be studied
by photoionization of excited molecular states. Resonant multiphoton
ionization provides a means to probe dipole-forbidden ionization
channels, including whole manifolds of autoionizing states that have
never been observed. Collisional effects on the resonant intermediate
state can be studied, for instance by observing changes in the
photoelectron angular distributions. Because the total energy of the
several photons can readily exceed the energy of a single one, states of
much greater energy can also be probed. There are many other
applications, such as continuum-continuum transitions and nonlinear
and nonresonant effects, but these few examples should suggest the
great potential of this emerging stream of research.
Electron-Molecule Collisions
The electron-molecule continuum is highly structured, containing
transient negative-molecular-ion states that reveal themselves by a rich
pattern of resonances in electron-molecule scattering measurements.
Electron-molecule resonances are in many ways analogous to electron-
atom resonances, but the molecular resonances possess additional
structure because of the underlying nuclear dynamics. Moreover, the
electron-molecule interaction is inherently anisotropic. It is anisotropic
not only close to the molecule where the strong screened nuclear
attractive potential dominates but also at large electron-molecule
separations where the permanent dipole, quadrupole, and higher
moments of the molecule give rise to the long-range terms in the
interaction potential. Even the weak polarization interaction that
characterizes the adiabatic response of the bound molecular electrons
to an approaching electron is anisotropic.
During an electron-molecule collision the nuclei are free to move,
though the time scale of this motion is much longer than that typical of
bound electrons. The fact that nuclei are separated from one another
by distances of the order of atomic dimensions essentially guarantees
that the average electron-molecule interaction is strong over a fairly
OCR for page 99
MOLECULAR PHYSICS 99
large region of space. This frequently gives rise to the potential
resonances that were described in Chapter 4 in the section on Atomic
Dynamics. The interplay of the electron transit, the lifetime of a
resonance, and the various nuclear response times presents a theoret-
ical challenge that is just beginning to be met.
The most important advances in our understanding of electron-
molecule collision phenomena are in those aspects of the target that are
unique to molecules. For electron energies near a resonance, the
appropriate electronic wave function for small electron-molecule sep-
arations is that of the transient negative ion; the nuclei move in a
distorted potential field. As the electron leaves the complex, the
molecule is left in a coherent superposition of states. It has been found
from the measurements and from the study of semiclassical models that
the resonant structure due to nuclear motion is extremely sensitive to
details in the theoretical description. This sensitivity has provided both
a clear picture of the dynamics and a precise test of the ab initio
description. The experiments have produced surprises. One example is
the discovery of a single, sharp resonance peak in vibrational-
excitation cross sections for several polar and nonpolar molecules just
above the excitation thresholds. Several models have been suggested,
invoking virtual states and other mechanisms, but the issue remains
unsettled.
MOLECULAR DYNAMICS
Chemical reactions involve complex many-body interactions. Be-
cause the quantity of information required to characterize all the
particles in a reaction is enormous, the practical and intellectual goals
of obtaining a clear picture appear formidable. By combining super-
sonic molecular beams with laser schemes for detecting the reaction
products, however, the problem can become tractable. For instance,
state-specific reactive scattering studies are now capable of distinguish-
ing complicated reactive interactions according to the classes of forces
and the stages of temporal evolution. It is possible to distinguish the
signatures of energy being released while the reagents approach and
while the reactive products separate. Similarly, it is now recognized
that the branching ratios for different reaction products can depend
critically on the orientations of the electron orbitals. In many cases,
highly detailed studies of complex molecular phenomena have led to
simple physical explanations and to new points of view.
OCR for page 100
100 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
State-to-State Chemistry
Chemical reactions are usually described by listing the initial and
final products, though this actually gives little insight into how the
reaction occurs. The complete enumeration of all the quantum num-
bers of the system, initial and final, would provide a far more thorough
description, one that could allow a rigorous confrontation of theory
with experiment. This has now been accomplished for the most
elementary type of molecular encounter: collisions in which energy is
transferred to a molecule from an atom or another molecule. If all the
important quantum numbers are measured these are called state-to-
state collisions. The study of state-to-state collisions in the past decade
constitutes an important advance in basic molecular physics. The
results have already provided new insights into molecular dynamics,
and they are expected to be valuable in applications involving energy
transfer in gases.
Experiments on state-to-state collisions have been made possible by
two advances. The first is high-intensity supersonic molecular beams.
These beams have an extremely narrow velocity distribution, and they
can achieve very low internal temperatures rotational temperatures
of a few kelvins are typical. (See Figure 5.2.) As a result, the molecular
states have a much smaller thermal spread in quantum numbers than
otherwise possible. The second advance is the tunable dye laser. These
lasers make it possible to resolve completely the quantum states of the
collision products. The lasers can also serve as precise velocity
analyzers by utilizing the Doppler shift, and they can be used to
prepare the system in high vibrational states by optical pumping.
State-to-state collisions of HD with He provide one example of the
power of the technique. Differential cross sections for transitions from
individual initial rotational state to each final state have now been
measured with high resolution. Furthermore, the cross sections have
been calculated using a full quantum-dynamical formulation and a
potential surface generated from first principles. Comparison of exper-
iment and theory pointed to the need for some corrections to the
potential surface, but with these, theory and experiment agreed even to
minute details of the quantum diffractionlike oscillations in the data.
Similar studies have been carried out with other simple systems.
Rotational state-to-state collisions represent the most elementary
form of energy transfer in molecular systems. Such energy-transfer
processes play critical roles in the dynamics of supersonic expansions,
gas lasers, atmospheric physics, and planetary atmospheres and in
OCR for page 101
MOLECULAR PHYSICS 101
FIGURE 5.2 Molecular-Beam Scattering. Molecular beams, originally created to study
the proper ties of isolated atoms and molecules, are now extensively used to study
interactions between molecular species and the dynamics of chemical reactions. This
molecular-beam scattering apparatus is designed for studying collisions in systems such
as helium and molecular nitrogen. It uses supersonic atomic or molecular beams to
provide intense streams of neutral particles that have only a small spread in their speeds.
Particles in two separate beams collide under highly controlled conditions, and the speed
and direction of the scattered particles are measured with high resolution. The experi-
ments provide detailed information on how energy is transferred between atoms and
molecules, for instance, how much of the energy goes into translational motion and how
much goes into rotation. Experiments such as these guide the development of the theory
of energy transfer and provide an important step toward understanding the precise steps
that occur in a chemical reaction. The information is also useful for understanding the
drag on airplanes and spacecraft. Early molecular-beam experiments were of the
table-top variety, but, as the picture indicates, the apparatus now can be large and
elaborate. (Courtesy of the Max-Planck-Institute for Fluid Dynamics, Gottingen, Federal
Republic of Germany.)
OCR for page 102
102 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
many other problems. Enormous numbers of cross sections may be
required to understand a typical problem. State-to-state experiments
frequently generate huge arrays of data 100 cross sections for a single
system are not unusual and the sheer volume can be overwhelming,
obscuring the confrontation with theory and complicating attempts to
model molecular energy transfer in specific situations. Fortunately, in
the course of studying state-to-state collisions in systems like Na2-Xe
and LiH-He, a universal type of behavior was discovered. By combin-
ing ideas of angular momentum addition and topology, a general
explanation for this behavior has been found. Out of this has emerged
a model that provides simple classification of the data, realistic
extrapolation and interpolation of the measurements, and accurate
analytical forms. One of the surprises from state-to-state research is
that the empirical rules previously used to estimate energy transfer
rates were misleading and could have led to potentially serious errors
in applications.
Radiative Collisions
Beginning in 1972, a series of papers in a Soviet journal suggested
that intense radiation could affect inelastic atom-atom collisions. The
effect was demonstrated 5 years later in the United States in a study of
collisions between excited strontium and ground-state calcium in the
presence of intense radiation from a dye laser. Without the laser light
the collisions were elastic; with it, a large energy exchange occurred:
the excitation was transferred from the calcium to the strontium. The
surprise is that the laser light was resonant with neither strontium nor
calcium atomic transitions. The light was resonant with molecular
levels of the strontium-calcium system as they evolved during the
collision. The experiment can be viewed as the spectroscopy of a
chemical reaction in progress an event never before witnessed. It is
now recognized that radiative collisions bear on large classes of basic
molecular phenomena and that they also have the potential for useful
applications in chemical processing.
Radiative collisions provide a new and flexible probe for studying a
chemical reaction in progress. One can describe the collision in terms
of the radiative excitation of an atom whose energy levels are tuned
into resonance with the laser light by the changing perturbation of a
second atomic species. Alternatively, one can describe the two collid-
ing atoms as a single molecular entity whose energy levels come into
resonance with the laser radiation.
OCR for page 103
MOLECULAR PHYSICS 103
Radiative collision can occur even if the radiation is not in resonance
between two discrete atomic or molecular levels; the radiation can be
in resonance with continuum levels. Radiative electron-atom scattering
and collisional ionization are two examples. In the first, the energy
spectra of electrons scattered on argon atoms in the presence of a
pulsed carbon dioxide laser exhibit peaks corresponding to both
absorption and stimulated emission. Electrons that have changed their
kinetic energy by as many as 11 carbon dioxide photons have been
detected.
Chemical reactions can occur during a radiative collision. Xenon and
molecular chlorine have been observed to react to form XeC1 in the
presence of laser light, though no reaction occurs otherwise. Thus,
radiative collisions have the potential of leading to new forms of
photochemistry. In particular, one can envisage triggering the release
of a great deal of stored chemical energy with a relatively weak light
pulse. The process can occur very rapidly, perhaps rapidly enough to
be useful in a very-short-wavelength laser.
New Ways to Understand the Dynamics of Chemical Reactions
Chemical reactions usually generate products in states of internal
excitation; the products then give off heat, emit radiation, or go on to
react further. The relative rates at which these internal product states
are formed are important for applications ranging from research into
new chemical species to industrial processes and the creation of
chemical lasers. In the last decade, much has been learned about the
dynamics of chemical reactions in the gas phase. (See Figure 5.3.)
The dynamics of a chemical reaction is controlled by the potential
energy surfaces that describe the interaction between the reacting
particles. These interactions determine the motion, whether or not the
reaction occurs, and the detailed path from the initial states of the
reactants to the final states of the products. In many cases the potential
energy surfaces can be obtained by the techniques of modern quantum
chemistry. Once the surfaces have been calculated, the rates of
reaction and the detailed dynamics must be predicted. A variety of new
theoretical approaches are available, almost all relying heavily on
computers. We describe here three of these. In order of increasing
difficulty, and increasing detail and accuracy, they are variational
transition-state theory, quasi-classical trajectory calculations, and ap-
proximate quantum scattering calculations.
OCR for page 104
104 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
0.40
0.22
q2 o.o5
-0.13
4
5
^ 6
A, 7
o
8
cn
-
11
4~N
1 1 1 1 1 1 1 1 1 1
__ at/ q-~=
-0.30
~0.35 -0.17 0.0 0.17 0.35 -0.75-0.50-0.25 0 0.25 Q50 0.75
ql q1
°: ~ ~ ~
Man
~n=10
12 , . 1 . ~
04 8 12 16
B (10 teslo)
-
44C
46
48
520
540
20 0
0.75
0.50
q2 0.25
o
~ 0.25
-0.50
~!
I ~ I ~ 1 1 1
-0.75-0.50-0.25 0 0.25 Q50 0.75
.
1000 2000 3000 4a)) 5000 6000
FIELD (V/cm)
FIGURE 5.3 Classical and Quantum Chaos. The transition between orderly and
chaotic motion is important in wide classes of classical systems. Similar behavior is
beginning to be recognized in quantum systems. The upper left drawing is a plot of
position against speed for a simple nonlinear system; the motion is orderly. If the system
is slightly perturbed, however, the motion abruptly becomes disorderly, as shown in the
upper right-hand drawing. Analogous behavior appears to be displayed by atomic
systems. The lower left drawing shows energy levels of a highly excited hydrogen atom
in a strong magnetic field. The energy levels appear to evolve in a simple and orderly
fashion. The lower right-hand drawing shows energy levels for a highly excited sodium
atom~ssentially a perturbed hydrogen atom in an electric field. The levels look
orderly at low field, but as the field is increased they abruptly become disorderly.
Order-disorder transitions appear to play important roles in molecular systems for
instance, the localization of energy of a highly excited polyatomic molecule in a single
vibrational mode and in optical systems such as optically bistable devices. (Courtesy of
the Joint Institute for Laboratory Astrophysics.)
Variational Transition-State Theory
The transition-state theory of chemical reactions has been in exist-
ence for many years, but in the last decade the formal basis of the
theory has been re-examined and the theory has been reformulated to
yield much more accurate results. The variational transition-state
theory requires finding the set of atom configurations that most
effectively divides reactants from products. Using classical mechanics,
OCR for page 105
MOLECULAR PHYSICS 105
the reaction rate is calculated by determining the rate at which systems
can cross this dividing surface.
Quasi-classical Trajectory Calculations
The method of quasi-classical trajectories employs computers to
trace the dynamics of collisions between a large set of reactants. The
calculations determine which states will react and what the distribution
of energy will be in the products. This approach, which provides an
excellent semiquantitative guide, is now widely used. The method has
recently been extended to electronically nonadiabatic collisions, colli-
sions in laser fields, and a number of other processes. This approach
will undoubtedly be used extensively in the next decade to predict
reactivity and selectivity of relatively simple chemical reactions.
Approximate Quantum-Scattering Calculations
The dynamics of chemically reacting systems can, in principle, be
predicted precisely by using accurate potential energy surfaces and
quantum scattering theory. The calculations are extraordinarily dif-
ficult for larger systems, but a number of approximations have been
developed that greatly simplify the problem yet preserve the accuracy.
"Sudden approximations" permit mapping a set of simple collinear
quantum reactive scattering calculations onto three-dimensional space
to yield approximations to the true scattering cross sections. Collinear
quantum calculations have been used to correct results from classical
transition-state theories and to investigate the role of resonances in
reactive scattering.
Recently the approximate quantum calculations revealed a new type
of molecular state, a true bound state of some triatomic systems but
with binding occurring only because of the vibrational motion. The
molecule FHF appears to be a prime candidate for exhibiting such
states. The study of this phenomenon, and of other quantum effects in
reactive scattering, will undoubtedly lead to better control of chemical
reactions and, one hopes, the eventual development of systems in
which the various state-to-state reactions can be selectively activated.
Resonances in a Simple Reaction Complex
Some time ago chemical physicists developed techniques for calcu-
lating cross sections for simple chemical reactions such as H2 + F >
HE + H. The results contained an unexpected conclusion: for systems
OCR for page 106
106 A TOMIC, MOLECULAR, AND OPTICA ~ PHYSICS
constrained to move along a line the reaction probability changes
abruptly as the initial translational energy is varied. It was discovered
that this behavior is due to the formation, at certain energies, of
long-lived dynamic resonances in which the colliding reagents remain
close together for several vibrational periods. The resonances arise
from a temporary trapping of the energy of the system in the internal
degrees of freedom. Such resonances occur elsewhere in physics, in
nuclear reactions, and in electron-molecule collisions, for instance, but
they had never been observed for chemical reactions.
The resonances were discovered in recent experiments using crossed
molecular beams for the reaction H2 + F > HF + H. The theoretical
studies reveal that the resonances are sensitive probes of the potential
energy surfaces in the region where the atoms are close to each other.
The agreement between theory and experiment illustrates the increas-
ing predictive power of dynamical chemical theory.
Bond Breaking and "Half-Collisions"
The breaking of a molecular bond is an essential step for most
chemical reactions, but until recently the process could not be wit-
nessed directly. Now, however, the structure and molecular motion
during dissociation can be observed. Because the latter half of many
chemical reactions involves a dissociative state whose products fly
apart, the photofragmentation process has come to be known as a
"half-collision." Laser light is used to break selectively the bonds in
simple molecules. The speed and angular distribution of the molecular
fragments can be measured directly or found indirectly from the
spectrum of the dissociating molecule. From this it is possible to
determine details of the dissociative state and whether dissociation
occurs quickly or slowly. Molecular-bond-breaking processes as short
as 1o-~4 S have been studied.
Not only is the laser useful as a scalpel to break bonds, it is a
versatile tool for interrogating the fragments of the bond-breaking
process. Detailed information on the states of the fragments can be
obtained by re-exciting the molecules or atoms and observing fluores-
cence from particular excited states. Because the laser light is naturally
polarized, specific orientations of the molecular fragments can be
obtained as well. Thus it is possible to "photograph" the structure of
the highly excited molecule as it is on the verge of breaking up, to
measure the forces experienced by the fragments as the bond is
broken, and to study the photofragment states that result. This is
invaluable for understanding, and possibly for influencing, the way that
OCR for page 107
MOLECULAR PHYSICS 107
reactions distribute the energy released among the product molecule
electronic, vibrational, rotational, and translational motions.
In addition to their contribution to our basic understanding of
chemical reactions, molecular photofragmentation techniques have
played key roles in applications such as the study of photochemical
smog formation and the development of new lasers. Photodissociation
measurements provide much needed information on the kinds and
concentrations of reactive radical species that are created in the
atmosphere by sunlight and the reactions that form harmful pollutants
or deteriorate the ozone layer. Molecular photofragmentation lasers
were one of the first of the chemical lasers. The art has advanced to the
point that it is now possible to activate molecular gas lasers by direct
irradiation with sunlight. Solar-pumped lasers may become practical
for space-based communications.
Reactions at Very Low Temperatures
Traditional thinking about ion-molecule reaction at very low temper-
atures suggests that their behavior should be simple and predictable:
either the rate coefficient at temperatures below 300 K should be as
predicted by simple orbiting theory or there must be an energy barrier
that makes the rate completely negligible at temperatures of less than
about 100 K. Recent studies indicate that surprises are in store. One
new technique utilizes Penning traps in which the ions can be cooled to
below 10 K and held for many hours while reacting with cold gas at low
densities. A study of NH3+ + H2 ~ NH4+ + H at 300 K and above
indicated a substantial energy barrier for this process. It had been
assumed that this process was totally negligible at the 10-20 K
temperatures of dense clouds in the interstellar medium. However, the
trapped-ion studies at temperatures of 10-20 K, coupled with other
studies at 80-300 K, have shown that as the temperature is decreased
the rate coefficient goes through a minimum and then starts rising very
steeply. This process is important at the temperatures of the interstellar
medium. It is believed that a complex is formed at low temperatures
that lives long enough to permit quantum-mechanical tunneling through
the centrifugal barrier.
SOME NOVEL MOLECULAR SPECIES
A large variety of novel molecular species and molecules in unusual
classes of states have emerged from the laboratories of molecular
physicists within the past few years. In addition to the species
OCR for page 108
108 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
discussed in the first section of this chapter, the list includes positive
and negative ions, neutral and ionic clusters, metal atom dimers, van
der Waals molecules, free radicals and other highly reactive species,
unstable isomers, metastable molecules, and polyatomic molecules in
selected highly excited rotation-vibration levels. From this list we
chose two for discussion: molecular ions and van der Waals molecules.
Molecular Ions
Molecular ions play key roles in the chemistry of solutions, in
atmospheric chemistry, in the interstellar medium, in plasmas, and in
flames. Until recently the experimental study of ions in the gas phase
was extremely difficult because ions could not be prepared at high
concentration or in isolation from other molecular species. The only
practical way to study molecular ions was in the solid state- in
crystals. Now, however, the spectroscopy of free positive ions is
nourishing. A technique called laser magnetic resonance has opened
the way to the study of a host of ions and free radicals, including a
number that are of astronomical interest. Another method employs
laser spectroscopy in an ac discharge. Owing to the Doppler effect, the
alternating electric field shifts the transition frequency of the ions in
and out of the narrow laser resonance, allowing the signal to be
separated from the intense background the'. is due to the abundant
molecules. Virtually any stable neutral particle with one extra proton
can be created, and the method works with numerous other molecular
ions and radicals. A third method employs a pulsed supersonic
molecular beam. The ions are formed in a plasma and then cooled and
isolated in the beam's expansion region. As the supersonic beam
expands, the temperature drops rapidly, cooling the rotational and
vibrational modes. This reduces the number of states occupied, vastly
simplifying the spectrum. Rotational temperatures as low as a few
degrees are routinely achieved. The cold gas can condense into
well-defined cluster-ion species. It is actually possible to watch how a
vibrational frequency of a free molecular ion evolves as the ion joins
increasingly large clusters of inert gas atoms, finally reaching the limit
where it is essentially isolated in a rare-gas matrix. (Clusters are
discussed further in Chapter 7 in the sections on Condensed-Matter
Physics and Materials Science and on Surface Science.)
In addition to optical spectroscopy, positive molecular ions have
recently been studied by other approaches. For example, ultraprecise
infrared spectroscopy of the elementary ions H2+ and HD+ has been
OCR for page 109
MOLECULAR PHYSICS 1 O9
carried out using light from an accurately known fixed-frequency laser.
The light is tuned into resonance by varying the speed of the ion beam.
Van der Waals Molecules
Within the past decade the study of weakly bound molecules has
emerged as a new tool for understanding the principles of chemical
structure. These molecules are composed of stable molecules, or inert
atoms, which are held together not by the covalent or ionic forces that
normally hold molecules together, nor by hydrogen bonding, but by the
weak van der Waals force.
The list of van der Waals molecules that have been studied include
species such as argon attached to a variety of atoms and tightly bound
molecules, dimers such as hydrogen, (H212, or hydrofluoric acid,
(HF)2, and such unlikely chemicals as HF-C1F. In fact, essentially any
simple combination of atoms and molecules can now be studied.
The structure of a van der Waals molecule is often unexpected. For
instance, one would expect argon to attach itself to the middle of C1F
simply because that would put it closest to most neighbors, forming a
T-shaped molecule. It does not- the molecule is linear, with the argon
attached to the chlorine. Because hydrogen bonding is relatively
strong, one would expect HE to bond to FC1 with hydrogen shared
between two partners, for instance FH-FC1. It does not the structure
is HF-FC1. The benzene dimer, by contrast, is much simpler than one
might expect. The planes of the ring are perpendicular, forming a T.
The conformation is the same as the crystalline solid.
Van der Waals molecules provide new opportunities to study how
molecular pairs interact and the configurations that they assume. The
significance of the work lies in this: Chemical structure remains a
fundamentally unsolved problem. There is no way to predict the
geometric conformation of molecules from general principles, and
there is no perturbation theory for chemical bonding every species
behaves like a new system. By providing an opportunity to test
approximate theories on a large class of relatively simple systems, van
der Waals molecules provide an advance toward understanding molec-
ular structure in all of its manifestations, including the liquid and solid
states, and toward understanding chemical reactions.
Representative terms from entire chapter:
chemical reactions
