Correlation functions collision-induced

In previous simulation studies of collision induce effects in rare gases, y=0 and only the first term in (56b) contributes to AA2 [92]. The first and second rank collision induced correlation functions, (57) and (60), are notoriously difficult to calculate they involve four point correlation functions, (i induced by j correlated with k induced by Z and the simulation runs in [90, 91, 92] are for tens of thousands of timesteps). 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

Spectroscopic techniques have been applied most successfully to the study of individual atoms and molecules in the traditional spectroscopies. The same techniques can also be applied to investigate intermolecular interactions. Obviously, if the individual molecules of the gas are infrared inactive, induced spectra may be studied most readily, without interference from allowed spectra. While conventional spectroscopy generally emphasizes the measurement of frequency and energy levels, collision-induced spectroscopy aims mainly for the measurement of intensity and line shape to provide information on intermolecular interactions (multipole moments, range of exchange forces), intermolecular dynamics (time correlation functions), and optical bulk properties. 

It was recently shown that a formal density expansion of space-time correlation functions of quantum mechanical many-body systems is possible in very general terms [297]. The formalism may be applied to collision-induced absorption to obtain the virial expansions of the dipole... 

Long-time behavior of correlation functions. The dipoles induced in successive collisions are correlated as Fig. 3.4 on p. 70 suggests. As a consequence, the dipole autocorrelation function has a negative tail of a duration comparable to the mean time between collisions, Fig. 5.3. Furthermore, the area under the negative tail is of similar order of magnitude as the area under the positive (or intracollisional) part of C(r). If the neg-... 

Constant acceleration approximation. An approximation introduced to the time-dependent intermolecular correlation function G, which was commonly referred to as the constant acceleration approximation (CAA), was used to compute the line shapes of collision-induced absorption spectra of rare gas mixtures, but the computed profiles were found to be unsatisfactory [286], It does not give the correct first spectral moment. 

M. Moraldi, Virial expansion of correlation functions for collision-induced spectroscopies, in Spectral Line Shapes 6, L. Frommhold and J. W. Keto, eds., American Institute of Physics 1990. 

An explanation was offered by van Kranendonk many years after the experimental discovery. Van Kranendonk argued that anticorrelations exist between the dipoles induced in subsequent collisions [404], Fig. 3.4. If one assumed that the induced dipole function is proportional to the intermolecular force - an assumption that is certainly correct for the directions of the isotropic dipole component and the force, and it was then thought, perhaps even for the dipole strength - an interference is to be expected. The force pulses on individual molecules are correlated in... 

It is suggested that the two electronic states fa and l °f noninteracting partners provide a good basis set to be used for constructing orthonormal adiabatic electronic functions fa and fa. At R — oo the functions fa and fa adiabatically correlate with fa and fa, so that the nonadiabatic transition probability calculated for a particular trajectory R(f) refers to the collision-induced transition between the two states of the partners. 

First, there are terms of the form <5S(12)[z —0L (12 z)] 5S(12)>o. From its definition in (9.12), we see that 55(12) is the deviation of the reactive operator from its velocity average. The correlation function above characterizes the time evolution (Laplace transformed) of these fluctuations. If the chemical reaction is slow, we expect that perturbations of the velocity distribution induced by the reaction will be small hence such contributions may be safely neglected in this limit. This argument may be made more formal using limiting procedures analogous to those described in Section V. In principle, one may also use this term to introduce a modification to in S(/- 2) due to velocity relaxation effects. This will lead to some effective reactive collision frequency in place of k p. 

This review contains an account of the models which have been used in the simulation of realistic molecular fluids. Methods for including the long-range dipole-dipole interaction and for calculating correlation functions and spectra are discussed. We review simulated dynamic properties with relation to experiment and describe the calculation of allowed and collision-induced infrared and light scattering spectra. 

The anisotropic ( -2) light scattering spectrum is slightly more complicated. The underlying correlation function contains a purely collective orientational part, a collision induced part, and a cross term. 

In studying the intense laser interactions with the CS2 molecules, and observing the behaviour of the orientational distribution and pair correlation functions [g(S)J through the time-evolution of the optical field-induced anisotropy, we are emphasizing external field-induced phenomena rather than interaction-induced or collision-induced events. 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

In this collision model (i) the velocity distribution function is assumed to be unperturbed by ax. field (ii) the employed induced distribution F in GT and in VIG was termed the correlation-orientation distribution, since in the work by Gross [37] the case g = 1 was originally considered. Here the term Gross collision model is ascribed to an arbitrary g-value, which is involved in Eq. (30). 

Both these mechanisms follow one projectile-electron encounter, and hence their cross sections are proportional to the square of the projectile charge, q They are both induced by the electron-electron interaction (or correlation) in the case of SO, correlation happens in the initial wave function, while the TS-1 mechanism proceeds via the electron-electron interaction during (or after) the collision. They can therefore not be described in the independent electron approximation. 

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