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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

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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

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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

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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.

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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.

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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

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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. OH. 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

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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

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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 modeselectronic, 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

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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

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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

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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.

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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

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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.)

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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.

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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.

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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,

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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

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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

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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

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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

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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.