Debye's theory, considered in Chapter 2, applies only to dense media, whereas spectroscopic investigations of orientational relaxation are possible for both gas and liquid. These data provide a clear presentation of the transformation of spectra during condensation of the medium (see Fig. 0.1 and Fig. 0.2). In order to describe this phenomenon, at least qualitatively, one should employ impact theory. The first reason for this is that it is able to describe correctly the shape of static spectra, corresponding to free rotation, and their impact broadening at low pressures. The second (and main) reason is that impact theory can reproduce spectral collapse and subsequent pressure narrowing while proceeding to the Debye limit.

The above capabilities of impact theory are illustrated in preceding chapters by consideration of the isotropic scattering spectrum, which consists of one Q-branch. The peculiarity of the present problem is that in the spectrum of orientational relaxation there are always several branches, and, generally speaking, one cannot consider their transformation independently. The very first attempt to build a quasi-classical impact theory of rotational structure drew one's attention to this fact as being of principal importance. It made the theory similar to the quantum theory of unresolved atomic spectra, whose Stark or Zeeman components interfere with each other during collisions. Interference of the same nature takes place between rotational branches of vibrational spectra, described classically. Increase of collisional frequency causes spectral collapse, but very rarely does an atomic spectrum narrow afterwards.

The quasi-classical theory of spectral shape is justified for sufficiently high pressures, when the rotational structure is not resolved. For isotropic Raman spectra the corresponding criterion is given by inequality (3.2). At lower pressures the well-resolved rotational components are related to the quantum number j of quantized angular momentum. At very low pressure each of the components may be considered separately and its broadening is qualitatively the same as of any other isolated line in molecular or atomic spectroscopy.

At the beginning, line shape theory concentrated on calculation of the width and shift of an isolated line broadened by collisions considered as instantaneous. This approach, known as ‘impact theory’, which originated with the pioneering work of Lorentz and Weisskopf, was initially purely adiabatic. The assumed adiabaticity of collisions excluded in principle any interference between spectral lines in the frame of impact theory. The situation changed with enhanced study of Stark multiplets of atoms in plasmas. The Stark sublevels were so weakly split in a weak electrical field of ions that a condition similar to (1.7) was met (ΔEτc ≪ 1) and a non-adiabatic generalization of impact theory became necessary. Transitions between Stark sublevels as an effective mechanism of their broadening were first taken into account by Kolb. Subsequently nonadiabatic theory was employed to describe overlapping Stark multiplets. It was mentioned that a qualitatively new feature arises when collisions are non-adiabatic: collisionally induced interference between components of the Stark structure causes spectral collapse.

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After ‘unfreezing’, rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions. In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational ‘sites’ libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic.

Line-shape analysis of the absorption or scattering spectra supplies us with normalized contours Gℓ(ω) which are the spectra of orientational correlation functions Kℓ = 〈Pℓ; [u(t)·u(0)]〉. The full set of averaged Legendre polynomials unambiguously defines the orientational relaxation of a linear or spherical rotator whose molecular axis is directed along the unit vector u(t). Unfortunately, only the lowest few Kℓ are available from spectroscopic investigation. The infrared (IR) rotovibrational spectroscopy of polar molecules gives us G1(ω – ωυ) which is composed of some rotational branches around vibrational frequency ωυ.

Spectroscopy is concerned with the interaction of light with matter. This monograph deals with collision-induced absorption of radiation in gases, especially in the infrared region of the spectrum. Contrary to the more familiar molecular spectroscopy which has been treated in a number of well-known volumes, this monograph focuses on the supermolecular spectra observable in dense gases; it is the first monograph on the subject.

For the present purpose, it is useful to distinguish molecular from supermolecular spectra. In ordinary spectroscopy, the dipole moments responsible for absorption and emission are those of individual atoms and molecules. Ordinary (or allowed) spectra are caused by intra-atomic and intra molecular dynamics. Collisions may shift and broaden the observable lines, but in ordinary spectroscopy collisional interactions are generally not thought of as a source of spectral intensity. In other words, the integrated intensities of ordinary spectral lines are basically given by the square of the dipole transition matrix elements of individual molecules, regardless of intermolecular interactions that might or might not take place. Supermolecular spectra, on the other hand, arise from interaction-induced dipole moments, that is dipole moments which do not exist in the individual (i.e., non-interacting) molecules. Interaction-induced dipole moments may arise, for example, by polarization of the collisional partner in the electric multipole field surrounding a molecule, or by intermolecular exchange and dispersion forces, which cause a temporary rearrangement of electronic charge for the duration of the interaction.

In Chapter 5 the absorption spectra of complexes of interacting atoms were considered. If some or all of the interacting members of a complex are molecular, additional degrees of freedom exist and may be excited in the presence of radiation. As a result, besides the translational profiles discussed in Chapter 5, new spectral bands appear at the rotovibrational transition frequencies of the molecules involved, and at sums and differences of such frequencies – even if the non-interacting molecules are infrared inactive. The theory of absorption by small complexes involving molecules is considered in the present Chapter.

We will be concerned with the spectral bands in the microwave and infrared regions. The translational and the purely rotational bands appear both at low frequencies and form in general one composite band, especially at the higher temperatures where individual lines tend to overlap (‘rototranslational band’). Moreover, various rotovibrational bands in the near infrared will be considered, such as the fundamental and the overtone bands. Even high overtone bands in the visible are of interest, e.g., of H2. We have seen in Chapter 3 that induced spectra of the kind are readily discernible in gases whose (non-interacting) molecules are infrared inactive, but evidence exists that suggests the presence of induced absorption in the allowed molecular bands as well. Induced absorption involving electronic transitions will be briefly considered in Chapter 7.

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.