Condensed phase, solvent effect

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

In the condensed phase the effect of the environment is of great importance and an interesting review has been provided by Kasha et al. Myers and Birge have derived a simple expression for the effect of solvent on the oscillator strength of a solute, which involves the refractive index of the solvent and another factor depending on the molecular shape and orientation of the transition moment. The theory successfully predicts the effect of solvent polarizability on the oscillator strength of the n n transition of j3-carotene and the n - n transition in pyrazine. 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

As these examples have demonstrated, in particular for fast reactions, chemical kinetics can only be appropriately described if one takes into account dynamic effects, though in practice it may prove extremely difficult to separate and identify different phenomena. It seems that more experiments under systematically controlled variation of solvent enviromnent parameters are needed, in conjunction with numerical simulations that as closely as possible mimic the experimental conditions to improve our understanding of condensed-phase reaction kmetics. The theoretical tools that are available to do so are covered in more depth in other chapters of this encyclopedia and also in comprehensive reviews [6, 118. 119],... 

Wang W, Nelson K A, Xiao L and Coker D F 1994 Molecular dynamics simulation studies of solvent cage effects on photodissociation in condensed phases J. Chem. Phys. 101 9663-71... 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

Magnetic field effects on the reaction kinetics or yields of photochemical reactions in the condensed phase have been studied [20-23]. They have proved powerful for verifying the mechanism of photochemical reactions including triplet states. Previously, we obtained photogenerated triplet biradicals of donor-acceptor linked compounds, and found that the lifetimes of the biradicals were remarkably extended in the presence of magnetic fields up to 1T [24]. It has been reported that Cgo and its derivatives form optically transparent microscopic clusters in mixed solvents [25,26]. The clustering behavior of fullerene (C o) is mainly associated with the strong three-dimensional hydrophobic interactions between the C o units. Photoinduced... 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

The separation of a reactant system (solute) from its environment with the consequent concept of solvent or surrounding medium effect on the electronic properties of a given subsystem of interest as general as the quantum separability theorem can be. With its intrinsic limitations, the approach applies to the description of specific reacting subsystems in their particular active sites as they can be found in condensed phase and in media including the rather specific environments provided by enzymes, catalytic antibodies, zeolites, clusters or the less structured ones found in non-aqueous and mixed solvents [1,3,6,8,11,12,14-30],... 

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