The existing bibliographies on collision-induced absorption (CIA) list more than 800 original papers published in the 45 years of history of the field. Furthermore, a number of review articles focusing on one aspect of CIA or another are listed, along with compilations of lectures given at summer schools, advanced research seminars or scientific conferences. A monograph which attempts to review the experimental and theoretical foundations of CIA, however, cannot be found in these carefully compiled listings.

Yet the field is of great significance and continues to attract numerous specialists from various disciplines. CIA is a basic science dealing with the interaction of supermolecular systems with light. It has important applications, for example in the atmospheric sciences. CIA exists in all molecular fluids and mixtures. It is ubiquitous in dense, neutral matter and is especially striking in matter composed of infrared-inactive molecules. As a science, CIA has long since acquired a state of maturity. Not only do we have a wealth of experimental observations and data for virtually all common gases and liquids, but rigorous theory based on first principles exists and explains nearly all experimental results in considerable detail. Ab initio calculations of most aspects of CIA are possible which show a high degree of consistency with observation, especially in the low-density limit.

In this Chapter, we will briefly look at a number of topics related to collision-induced absorption of infrared radiation in gases. Specifically, in Section 7.1, we consider collision-induced spectra involving electronic transitions in one or more of the interacting molecules. In Section 7.2, we focus on collision-induced light scattering, which is related to collision-induced absorption in the same way that Raman and infrared spectra of ordinary molecules are related. The collision-induced Raman process arises from the fact that the polarizability of interacting atoms/molecules differs from the sum of polarizabilities of the non-interacting species. Closely related to the collision-induced Raman and infrared spectroscopies are the second (and higher) virial coefficients of the dielectric properties of gases, which provide independent measurements of the collision-induced dipole moments, Section 7.3. Finally, we look at the astrophysical and other applications of collision-induced absorption in Sections 7.4 and 7.5.

Collision-induced electronic spectra

Collision-induced electronic spectra have many features in common with rovibrotranslational induced absorption. In this Section, we take a look at the electronic spectra. We start with a historical note on the famous forbidden oxygen absorption bands in the infrared, visible and ultraviolet. We proceed with a brief study of the common features, as well as of the differences, of electronic and rovibrotranslational induced absorption.

In this Appendix we attempt to briefly review developments since the early 1990ies in the field of collision-induced absorption in gases. Many of the new contributions were announced, and numerous references to current literature were given in the proceedings of periodic conferences and special workshops. We mention especially the Proceedings of the biennial International Conferences on Spectral Line Shapes and the annual Symposia on Molecular Spectroscopy. New work in collision-induced absorption in gases has been reviewed in the Proceedings of a NATO Advanced Study Institute, a NATO Advanced Research Workshops, and in a recent monograph Molecular Complexes in Earth's, Planetary, Cometary, and Interstellar Atmospheres. A multi-authored volume, a significantly augmented treatment of bremsstrahlung, is also of interest here, for example when electrically charged particles exist in dense, largely neutral and hot environments, e.g., in shock waves, in the atmospheres of “cool” white dwarf stars, in sonoluminescence studies, etc.

Binary Interaction-Induced Dipoles.Ab initio quantum chemical calculations of interaction-induced dipole surfaces are known for some time (Section 4.4, pp. 159 ff.) Such calculations were recently extended for the H2—He and H2—H2 systems, to account more closely for the dependencies of such data on the rotovibrational states of the H2 molecules.

The theory of collision-induced absorption developed by van Kranendonk and coworkers and other authors has emphasized spectral moments (sum formulae) of low order. These are given in closed form by relatively simple expressions which are readily evaluated. Moments can also be obtained from spectroscopic measurements by integrations over the profile so that theory and measurement may be compared. A high degree of understanding of the observations could thus be achieved at a fundamental level. Moments characterize spectral profiles in important ways. The zeroth and first moments, for example, represent in essence total intensity and mean width, the most striking parameters of a spectral profile.

While spectral moments permit significant comparisons between measurements and theory, it is clear that some information is lost if a spectroscopic measurement is reduced to just one or two numbers. Furthermore, for the determination of experimental moments, substantial extrapolations of the measured spectra to low and high frequencies are usually necessary which introduce some uncertainty, even if large parts of the spectra are known accurately. For these reasons, line shape computations are indispensible for detailed analyses of measured spectra, especially where the complete absorption spectra cannot be measured. Moreover, one might expect that the line shape of the induced spectra, with its ‘differential’ features like logarithmic slopes and curvatures and the dimer structures, depend to a greater degree on the details of the intermolecular interactions than the spectral moments.

In this chapter we summarize some background information concerning molecular collisions, dipoles and radiation, spectroscopy, and statistical mechanics that will be needed later. This Chapter should be skipped in a first reading. It is hoped that a reader who comes back to this Chapter later with specific questions will find the answers here — or, at least, some useful reference for further study.

Intermolecular potentials

The ideal gas law, Eq. 1.1 with B = C = … = 0, may be derived with the assumption of non-interacting ‘point particles’. While in the case of rarefied gases at high temperatures this assumption is successful in that it predicts the relationship between pressure, density and temperature of a gas in close agreement with actual measurement, it was clear that important features of gaseous matter, such as condensation, the incompressibility of liquids and solids, etc., could not be modeled on that basis. As early as in 1857, Clausius argued convincingly that intermolecular forces must be repulsive at short range and attractive at long range. When in 1873 van der Waals developed his famous equation of state, a significant improvement over the ideal gas law, he assumed a repulsion like that of hard spheres at near range, and attraction at a more distant range.

Our general understanding of molecular collisions and energy transfer rests mainly upon classical mechanics. Except for particular quantum mechanical processes, such as transitions between different electronic states, and quantum mechanical features like resonances or interferences classical mechanics is a very useful tool for the study of molecular encounters (Porter and Raff 1976; Pattengill 1979; Truhlar and Muckerman 1979; Schatz 1983; Raff and Thompson 1985; Levine and Bernstein 1987:ch.4). This holds true for photodissociation as well (Goursaud, Sizun, and Fiquet-Fayard 1976; Heller 1978a; Brown and Heller 1981; Schinke 1986c; Goldfield, Houston, and Ezra 1986; Schinke 1988b; Guo and Murrell 1988a,b).

Classical mechanics is the limit of quantum mechanics as the de Broglie wavelength λB = 2πħ/(2mE)½ becomes small. The total energy released as translational and internal energy in UV photodissociation often exceeds 1 eV and therefore λB is of the order of 0.1 Å or shorter. On the other hand, the range of the potential is typically much larger so that the quantum mechanical wavefunction performs many oscillations over the entire interaction region (see Figures 2.3 and 3.2, for example). Furthermore, in many cases the fragments are produced with high internal excitation (Figure 3.3) which additionally favors a classical description.

The classical picture of photodissociation closely resembles the timedependent view. The electronic transition from the ground to the excited electronic state is assumed to take place instantaneously so that the internal coordinates and corresponding momenta of the parent molecule remain unchanged during the excitation step (vertical transition).

Rotational excitation of photofragments is a wide field with many subtleties. In the foregoing chapters we have considered exclusively the scalar properties of rotational excitation, i.e., the distributions of final rotational states of the products and the forces that control them. For this purpose, it was sufficient to study the case that the total angular momentum of the entire molecular system is zero, J = 0. This restriction drastically facilitated the theoretical formulation and allowed us to concentrate on the main effects without being intimidated by complicated angular momentum coupling. In Section 11.1 we will extend the theory of rotational excitation to general total angular momentum states J ≠ 0. Our aim is the investigation of final rotational product states following the photodissociation of single rotational states of the parent molecule (Section 11.3). Before doing so, however, we discuss in Section 11.2 the distribution of the various electronic fine-structure states (Λ-doublet states) if the fragment possesses a nonzero electronic angular momentum which couples with the angular momentum of the nuclear motion. Important examples are OH and NO.

The vector of the electromagnetic field defines a well specified direction in the laboratory frame relative to which all other vectors relevant in photodissociation can be measured. This includes the transition dipole moment, μ, the recoil velocity of the fragments, v, and the angular momentum vector of the products, j. Vector correlations in photodissociation contain a wealth of information about the symmetry of the excited electronic state as well as the dynamics of the fragmentation. Section 11.4 gives a short introduction.

Dissociation via a single excited electronic state is the exception rather than the rule. The remarkable success with which all experimental results for the dissociation of H2O, for example, have been reproduced by rigorous calculations without any adjustable parameter rests mainly upon the fact that only one electronic state is involved (Engel et al. 1992). Many other photodissociation processes, however, proceed via two or even more electronic states with the possibility of transitions from one state to another. Figure 15.1 illustrates a common situation: the photon excites the molecule from the electronic ground state (index 0) to a dipole-allowed upper state (index 1) which further out in the exit channel interacts with a second electronic state (index 2). The latter may be dipole-forbidden and therefore not directly accessible by the photon. The corresponding diabatic potentials V1 and V2 cross at some internuclear distance Rc. In the proximity of this point the coupling between the two electronic states, which was ignored throughout all of the preceding chapters, can be large with the consequence that a transition from state 1 to state 2 and/or vice versa becomes possible (radiationless transition, electronic quenching). Electronic transitions manifest the break-down of the Born-Oppenheimer approximation, i.e., the motion of the electrons and the heavy particles can no longer be adiabatically separated.

Let us imagine a wavepacket starting in the Franck-Condon region on potential V1 When it reaches the crossing region it splits under the influence of the coupling into two parts.

In indirect photodissociation a potential barrier or some other dynamical constraint hinders immediate dissociation of the complex that the light pulse has created in the excited electronic state. Figure 7.1 shows a typical one-dimensional example. The barrier may be due to an avoided crossing with another electronic state. The potential energy surface (PES) of the S1 state of CH3ONO (Figure 1.11) is a typical two-dimensional example. Depending on the efficiency of internal energy redistribution between the various degrees of freedom the lifetime of the complex may range from a few to several thousand internal vibrational periods, in contrast to direct processes where the fragmentation finishes in less than one internal period. Because of the long lifetime, the final state distributions of the photofragments no longer reflect the initial coordinate distribution of the parent molecule in the ground electronic state like they do in direct dissociation. The coupling between the various modes in the complex gradually erases the memory of the initial state before the molecule finally breaks apart.

The main characteristics of indirect dissociation are resonances in the time-independent picture and recurrences in the time-dependent approach. Resonances and recurrences are the two sides of one coin; they reveal the same dynamical information but provide different explanations and points of view. To begin this chapter we discuss in Section 7.1, on a qualitative level, indirect photodissociation of a one-dimensional system. A more quantitative analysis follows in Section 7.2. The time dependent and the time-independent views of indirect photodissociation are outlined and illustrated in Sections 7.3 and 7.4, respectively, with emphasis on vibrational excitation of the NO moiety in the photodissociation of CH3ONO(S1).

So far we have consistently assumed — with only very few exceptions — that the photodissociation starts from the lowest vibrational state of the parent molecule. The corresponding bound-state wavefunction is typically a narrow multi-dimensional Gaussian-like function centered at the equilibrium configuration in the electronic ground state. This wavefunction defines the starting zone for the motion of the time-dependent wavepacket or the swarm of classical trajectories on the excited-state potential energy surface (PES). If the dissociation proceeds in a direct way, the forces near the Franck-Condon region determine to a large extent the fate of the wavepacket and ultimately the energy and state dependence of the dissociation cross sections. Since the initial wavefunction for a normal, chemically bound molecule such as H2O has a typical width of the order of 0.1−0.2 Å, the evolving wavepacket explores only a relatively small portion of the dissociative PES (see Figures 3.2, 9.8, and 9.9 for example).

By starting the photodissociation from an excited vibrational level one can access a significantly wider range of the upper-state PES (see Figure 13.1) and to some extent manipulate and steer the reaction path. One example has already been discussed in Section 10.1: dissociation of excited bending states of H2O through the à state probes a much wider angular region of the corresponding PES than dissociation of the lowest bending state. The influence of the increased anisotropy for smaller HOH angles clearly shows up in the final rotational state distribution of the OH product (see Figure 10.5).

Theoretically, the calculation of photodissociation cross sections for excited vibrational states proceeds in exactly the same way as for the dissociation of the lowest level.

Photodissociation can be roughly classified as either direct or indirect dissociation. In a direct process the parent molecule dissociates immediately after the photon has promoted it to the upper electronic state. No barrier or other dynamical constraint hinders the fragmentation and the “lifetime” of the excited complex is very short, less than a vibrational period within the complex. For comparison, the period of an internal vibration typically ranges from 30 to 50 fs. The photodissociation of CH3ONO via the S2 state is a typical example; the corresponding potential energy surface (PES) is depicted in the upper part of Figure 1.11. A trajectory or a quantum mechanical wavepacket launched on the S2-state PES immediately leads to dissociation into products CH3O and NO.

In indirect photofragmentation, on the other hand, a potential barrier or some other dynamical force hinders direct fragmentation of the excited complex and the lifetime amounts to at least several internal vibrational periods. The photodissociation of CH3ONO via the S1 state is a representative example. The middle part of Figure 1.11 shows the corresponding PES. Before CH3ONO(S1) breaks apart it first performs several vibrations within the shallow well before a sufficient amount of energy is transferred from the N-0 vibrational bond to the O-N dissociation mode, which is necessary to surpass the small barrier.

Direct dissociation is the topic of this chapter while indirect photofragmentation will be discussed in the following chapter. Both categories are investigated with the same computational tools, namely the exact solution of the time-independent or the time-dependent Schrodinger equation. The underlying physics, however, differs drastically and requires different interpretation models.

Photodissociation of small polyatomic molecules is an ideal field for investigating molecular dynamics at a high level of precision. The last decade has seen an explosion of many new experimental methods which permit the study of bond fission on the basis of single quantum states. Experiments with three lasers — one to prepare the parent molecule in a particular vibrational-rotational state in the electronic ground state, one to excite the molecule into the continuum, and finally a third laser to probe the products — are quite usual today. State-specific chemistry finally has become reality. The understanding of such highly resolved measurements demands theoretical descriptions which go far beyond simple models.

Although the theory of photodissociation has not yet reached the level of sophistication of experiment, major advances have been made in recent years by many research groups. This concerns the calculation of accurate multi-dimensional potential energy surfaces for excited electronic states and the dynamical treatment of the nuclear motion on these surfaces. The exact quantum mechanical modelling of the dissociation of a triatomic molecule is nowadays practicable without severe technical problems. Moreover, simple but nevertheless realistic models have been developed and compared against exact calculations which are very useful for understanding the interrelation between the potential and the nuclear dynamics on one hand and the experimental observables on the other hand.

The aim of this book is to provide an overview of the theoretical methods for treating photodissociation processes in small polyatomic molecules and the achievements in merging ab initio calculations and detailed experiments. It is primarily written for graduate students starting research in molecular physics.

In the preceding fifteen chapters of this monograph we have described how one can infer information about the dissociation process and ultimately about the multi-dimensional potential energy surface(s) (PES) in the excited electronic state(s) from the observables which one measures in “conventional” experiments, namely the absorption spectrum, the emission spectrum of the transient molecule, and the various final state distributions of the fragments. By “conventional” we mean those experiments in which the molecule is irradiated by a long, more or less monochromatic laser pulse. The last open question, which we will address here, concerns the true time dependence of the molecular system as it evolves from the Franck-Condon region, through the transition state, into the possible fragment channels and how this motion can be made transparent in the laboratory.

The lifetime of the complex in the excited electronic state is either in the range of 10−15−10−13 seconds for direct dissociation respectively 10−12 seconds or longer for indirect fragmentation. In contrast, conventional experiments are performed with pulse lengths of the photolysis laser of the order of 10−9 seconds. Thus, no matter how refined such experiments are — full preparation of the initial state and complete resolution of the fragment states — they are inherently unable to resolve the real time dependence of the breakup process. They need accompanying theoretical studies (classical trajectories or quantum mechanical wavepackets) in order to disentangle the interaction among the various degrees of freedom and to disclose the evolution of the system.†