Quantum solvation

How would solvation proceed if the solvated particle is an electron rather than essentially classical ion or dipole  

Experimentally, electrons can be injected into and dissolve in molecular liquids. In liquid ammonia solvated electrons form blue, relatively stable, solutions. In water, solvated electrons can be created by photoionizing solute anions or even neat water. These electrons eventually disappear by recombining with the parent species, but live long enough as distinct species with a typical absorption peak near 7000 A. Provided that the injection and subsequent probing are done with ultrafast time resolution, it is possible to follow the solvation process of the electron via its evolving spectrum. 

This fascinating subject has attracted much experimental and theoretical effort for the past two decades, but a conclusive word may still lie ahead. We will not 

In addition to the intrinsic interest of quantum solvation phenomena, the process of electron solvation offers another example of a localized quantum process taking place in an otherwise essentially classical environment. We have encountered a similar situation in the vibrational relaxation of high-frequency diatomic molecules 

A polaron is an electron attached to, and moving with, the polarization induced by it in a polar environment. This concept is used mostly in solid state physics the liquid analog is the solvated electron. 

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Modified Zusman Equation for Quantum Solvation Dynamics and Rate Processes... 

Modified Zusmati Equation for Quantum Solvation Dynamics and Rate Processes 323 Here, s is the reduced system Liouvillian ... 

Lehnig R, Slenczka A. (2004) Quantum solvation of phthalocyanine in superfluid helium droplets. J. Chem. Phys. 120 5064-5066. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

In either case, the structure of the solvation shell has to be calculated by otiier methods supplied or introduced ad hoc by some fiirther model assumptions, while charge distributions of the solute and within solvent molecules are obtained from quantum chemistry. 

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

Blake N P and Metiu H 1995 Efficient adsorption line shape calculations for an electron coupled to many quantum degrees of freedom, applications to an electron solvated in dry sodalites and halo-sodalites J. Chem. Phys. 103 4455... 

The GB equation is suitable for the description of solvent effects in molecular mechanics and dynamics [16], as well as in quantum mechanical calculations (17,18]. An excellent review of implicit solvation models, with more than 900 references, is given by Cramer and Truhlar [19]. 

Cramer C J and Truhlar D G 1995. Continuum Solvation Models Classical and Quantum Mechanical Implementations. In Lipkowitz K B and D B Boyd (Editors) Reviews in Computational Chemistry Volume 6. New York, VCH Publishers, pp. 1-72. 

The Poisson equation has been used for both molecular mechanics and quantum mechanical descriptions of solvation. It can be solved directly using numerical differential equation methods, such as the finite element or finite difference methods, but these calculations can be CPU-intensive. A more efficient quantum mechanical formulation is referred to as a self-consistent reaction field calculation (SCRF) as described below. 

From the experimental results and theoretical approaches we learn that even the simplest interface investigated in electrochemistry is still a very complicated system. To describe the structure of this interface we have to tackle several difficulties. It is a many-component system. Between the components there are different kinds of interactions. Some of them have a long range while others are short ranged but very strong. In addition, if the solution side can be treated by using classical statistical mechanics the description of the metal side requires the use of quantum methods. The main feature of the experimental quantities, e.g., differential capacitance, is their nonlinear dependence on the polarization of the electrode. There are such sophisticated phenomena as ionic solvation and electrostriction invoked in the attempts of interpretation of this nonlinear behavior [2]. 

Methods for evaluating the effect of a solvent may broadly be divided into two types those describing the individual solvent molecules, as discussed in Section 16.1, and those which treat the solvent as a continuous medium. Combinations are also possible, for example by explicitly considering the first solvation sphere and treating the rest by a continuum model. Each of these may be subdivided according to whether they use a classical or quantum mechanical description. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

Prediction of tautomeric equilibria by a quantum mechanical continuum model of solvation Tautomerism of thiophenes... 

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