Mode coupling theories description

Li et al. subsequently developed a schematic mode coupling theory description of the short-time as well as long-time dynamics of mesogens in the isotropic phase near the I-N transition [91]. Their treatment started with a very general form [92] for the kinetic equation of the autocorrelation function (j)2(t) of the anisotropy of polarizability... 

The friction coefficient of a large B particle with radius ct in a fluid with viscosity r is well known and is given by the Stokes law, Q, = 67tT CT for stick boundary conditions or ( = 4jit ct for slip boundary conditions. For smaller particles, kinetic and mode coupling theories, as well as considerations based on microscopic boundary layers, show that the friction coefficient can be written approximately in terms of microscopic and hydrodynamic contributions as ( 1 = (,(H 1 + (,/( 1. The physical basis of this form can be understood as follows for a B particle with radius ct a hydrodynamic description of the solvent should... 

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

The only currently existing theory for the glass transition is the mode coupling theory (MCT) (see, e.g. [95, 96, 106]). MCT is an approach based on a rather microscopic description of the dynamics of density fluctuations and correlations among them. Although the theory was only formulated originally for simple (monatomic) fluids, it is believed to be of much wider applicability. In this review we will only briefly summarize the main basis and predictions of this theory, focusing on those that can be directly checked by NSE measurements. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

These are, of course, just the standard arguments used to motivate the mode coupling theories, which have proved useful in the description of critical phenomena and the asymptotic decay of correlation functions. ... 

The aromaticity of benzene is linked, in spin-coupled theory, to the particular mode of coupling of the electron spins, and so it seems reasonable to suppose that the orbital descriptions of Dih cyclobutadiene and of benzene could be fairly similar, but for these to be associated with very different modes of spin coupling. To a first approximation, this indeed turns out to be the case. With benzene-like orbitals ordered a,b,c,d around the ring, the symmetry requirements of an overall Bu state are such that the electron spins associated with each diagonal (ale and bid) must be strictly triplet coupled. These two triplet subsystems combine to a net singlet. A characteristic feature of antiaromatic situations in spin-coupled theory is the presence of such triplet-coupled pairs of electrons. 

We initially believed [23] that a similar mode of description carries over to 03, but we now realise that this system is somewhat more complicated than we had first supposed. Calculations for the four out-of-plane n electron, whether using spin-coupled theory or at the CASSCF level, reveal that there exist two solutions that are remarkably close in energy. The one that lies lowest, provided we optimize properly the description of the inactive electrons, corresponds to a singlet diradical whereas the other corresponds to a hypercoordinate central atom [24]. It is clear that neither description carries much conviction on its own, and that we must consider expanding the active space. 

The kinetic theory of condensed-phase chemical reactions is a direct outgrowth of kinetic theory and mode coupling descriptions of dense, simple fluids, which have been developed primarily in the past 10 years. This work in turn relies on an older body of literature, but we shall, when possible, draw parallels with the more recent interpretations of liquid-state dynamics. At present there are a variety of techniques available for constructing kinetic equations that are useful for describing dense, simple, nonreacting liquids. These range from approaches based on the dynamic hierarchy ... 

The specific examples chosen in this section, to illustrate the dynamics in condensed phases for the variety of system-specific situations outlined above, correspond to long-wavelength and low-frequency phenomena. In such cases, conservation laws and broken symmetry play important roles in the dynamics, and a macroscopic hydrodynamic description is either adequate or is amenable to an appropriate generalization. There are other examples where short-wavelength and/or high-frequency behaviour is evident. If this is the case, one would require a more microscopic description. For fluid systems which are the focus of this section, such descriptions may involve a kinetic theory of dense fluids or generalized hydrodynamics which may be linear or may involve nonlinear mode coupling. Such microscopic descriptions are not considered in this section. 

Vibronic-coupling theory has been a well established area of research since many years. The basic elements of the theory are the concept of dia-batic electronic states, the normal-mode description of vibrational motion, and the application of symmetry selection rules to derive appropriate model Hamiltonians. The applications of vibronic-coupling theory cover the full range of molecular spectroscopy, including, in particular, optical absorption and emission and photoelectron spectroscopy. Typical spectroscopic phenomena associated with vibronic interactions are the appearance of nominally forbidden electronic bands, the excitation of nontotally symmetric modes, or unusual and complex vibronic fine structures of electronic spectra. A fairly comprehensive and up-to-date exposition of vibronic-coupling theory is provided by the monograph of Bersuker and Polinger. ... 

For radical-radical reactions, the full mode coupling and anharmonicity effects for the relative and overall rotational motions must be explicitly accounted for. We have derived a direct variable reaction coordinate transition state theory approach that appears to 3deld accurate rate coefficients for a number of alkyl radical reactions.This approach is analogous to that embodied in Eq. (4.10) for the long-range transition state, but includes variational optimizations of the form of the reaction coordinate and does not make the large orbital moment of inertia assumption. A detailed description of this approach was provided in some of our recent articles. 

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