Information on orientational relaxation may be obtained by a wide range of techniques. Dielectric relaxation and magnetic resonance, neutron and light scattering, infrared spectroscopy and fluorescence depolarization are widely used. These different experimental probes of the phenomenon characterize it in different ways. The advantage of spectroscopic investigations is that they give information on relaxation times as well as on the corresponding correlation functions and their spectra. In particular, by combining the information in an absorption spectrum with that obtained from Raman scattering, one can determine the two lowest correlation functions of a molecule's axis position. A complete description of orientational relaxation is given by the infinite set of these functions.

The orientation of linear rotators in space is defined by a single vector directed along a molecular axis. The orientation of this vector and the angular momentum may be specified within the limits set by the uncertainty relation. In a rarefied gas angular momentum is well conserved at least during the free path. In a dense liquid it is a molecule's orientation that is kept fixed to a first approximation. Since collisions in dense gas and liquid change the direction and rate of rotation too often, the rotation turns into a process of small random walks of the molecular axis. Consequently, reorientation of molecules in a liquid may be considered as diffusion of the symmetry axis in angular space, as was first done by Debye.

It was demonstrated in Chapter 6 that impact theory is able to describe qualitatively the main features of the drastic transformations of gas-phase spectra into liquid ones for the case of a linear molecule. The corresponding NMR projection of spectral collapse is also reproduced qualitatively. Does this reflect any pronounced physical mechanism of molecular dynamics? In particular, can molecular rotation in dense media be thought of as free during short time intervals, interrupted by much shorter collisions?

It seems that an affirmative answer is hardly possible on the contemporary level of our general understanding of condensed matter physics. On the other hand, it is necessary to find a reason for numerous successful expansions of impact theory outside its applicability limits.

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the ‘continuation’ of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation–vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation.

As is seen from relations (2.5)–(2.8), isotropic scattering is independent of orientational relaxation. Since the isotropic component of the polarization tensor is invariant to a molecule's reorientation, the corresponding correlation function K0 describes purely vibrational relaxation. This invariance does not mean however that vibrational relaxation is completely insensitive to angular momentum relaxation. Interaction between vibrations and a molecule's rotation determines the rotational structure of the isotropic scattering spectra observed in highly rarefied gases. The heavier the molecule, the smaller is the constant αe of the Q-branch rotational structure. In fact this thin structure is easily resolved only in hydrogen and deuterium. The isotropic Raman spectrum of most other gases is usually unresolved even at rather low pressure and when describing its shape at higher densities one may consider J a classical (continuous) variable.

Within the framework of the impact theory J(t) is a purely discontinuous Markovian process. The same is valid for the corresponding frequency, or ‘rotational component’, which changes its position in the spectrum after each collision. This phenomenon, known as spectral diffusion or rotational frequency exchange, is accompanied by adiabatic dephasing of the vibrational transition caused by these same collisions. Both processes contribute to observed spectral transformation with increasing collision frequency, however they have opposite effects. While frequency exchange leads to collisional narrowing, dephasing results in the spectrum-broadening. If dephasing is weak and the collision frequency is small, the tendency for the spectrum to narrow prevails.

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.