Solvation, definition

On correcting to unit activity Ag (aq), we can obtain E g/Ag - Electron solvation energy is neglected in this definition. 

If classical Coulombic interactions are assumed among point charges for electrostatic interactions between solute and solvent, and the term for the Cl coefficients (C) is omitted, the solvated Eock operator is reduced to Eq. (6). The significance of this definition of the Eock operator from a variational principle is that it enables us to express the analytical first derivative of the free energy with respect to the nuclear coordinate of the solute molecule R ,... 

This chapter has given an overview of the structure and dynamics of lipid and water molecules in membrane systems, viewed with atomic resolution by molecular dynamics simulations of fully hydrated phospholipid bilayers. The calculations have permitted a detailed picture of the solvation of the lipid polar groups to be developed, and this picture has been used to elucidate the molecular origins of the dipole potential. The solvation structure has been discussed in terms of a somewhat arbitrary, but useful, definition of bound and bulk water molecules. 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

The definition of solvent exchange rates has sometimes led to misunderstandings in the literature. In this review kjs 1 (or fc2lsolvent]), sometimes also referred to as keJ s 1, is the rate constant for the exchange of a particular coordinated solvent molecule in the first coordination sphere (for example, solvent molecule number 2, if the solvent molecules are numbered from 1 to n, where n is the coordination number for the solvated metal ion, [MS ]m+). Thus, the equation for solvent exchange may be written ... 

Barone, V. Cossi, M. Tomasi, J. A new definition of cavities for the computation of solvation free energies by the polarizable continuum model. J. Chem. Phys. 1997, 107, 3210-3221. 

In solutions neither H+ nor e can exist in a free state they will be donated only if they are accepted within the solution, e.g., by another acceptor, which may be the solvent and thus cause solvation here the mere solvation of electrons is an exceptional case, but may occur, e.g., in liquid ammonia, where according to Kraus82 the strongly reducing alkali metals dissolve while dissociating into cations M+ and solvated electrons e, which, however, are soon converted into NH2" and H2 gas. Further, from the analogy with acid-base reactions and the definition of... 

Remarkable data on primary hydration shells are obtained in non-aqueous solvents containing a definite amount of water. Thus, nitrobenzene saturated with water contains about 0.2 m H20. Because of much higher dipole moment of water than of nitrobenzene, the ions will be preferentially solvated by water. Under these conditions the following values of hydration numbers were obtained Li+ 6.5, H+ 5.5, Ag+ 4.4, Na+ 3.9, K+ 1.5, Tl+ 1.0, Rb+ 0.8, Cs+0.5, tetraethylammonium ion 0.0, CIO4 0.4, NO3 1.4 and tetraphenylborate anion 0.0 (assumption). 

In Figure 10.19a, no new compound was formed between the solute and solvent. Some solutes can form compounds with their solvents. Such compounds with definite proportions between solutes and solvents are termed solvates. If the solvent is water, the compounds formed are termed hydrates. 

An enormous variety of solvates associated with many different kinds of compounds is reported in the literature. In most cases this aspect of the structure deserved little attention as it had no effect on other properties of the compound under investigation. Suitable examples include a dihydrate of a diphosphabieyclo[3.3.1]nonane derivative 29), benzene and chloroform solvates of crown ether complexes with alkyl-ammonium ions 30 54>, and acetonitrile (Fig. 4) and toluene (Fig. 5) solvates of organo-metallic derivatives of cyclotetraphosphazene 31. In most of these structures the solvent entities are rather loosely held in the lattice (as is reflected in relatively high thermal parameters of the corresponding atoms), and are classified as solvent of crystallization or a space filler 31a). However, if the geometric definition set at the outset is used to describe clathrates as crystalline solids in which guest molecules... 

The identifier HC means that this is the solvation free energy for the case of a hardcore solute with the excluded-volume region established by the inner-shell definition. 

There are basically two semicontinuum models one owing to Copeland, Kestner, andjortner (1970) (CKJ) and another to Fueki, Feng, and Kevan (1970, 1973 Fueki et al, 1971) (FFK). The calculations were designed for eh and eam,but have been extended to other polar media (Fueki et al., 1973 Jou and Dorfman, 1973). In these four or six solvent molecules form the first solvation layer in definite arrangement. Beyond that, the medium is taken as a continuum with two dielectric constants and a value of VQ, the lowest electron energy in the conduction state. 

According to the Arrhenius theory of acids and bases, the acidic species in water is the solvated proton (which we write as H30+). This shows that the acidic species is the cation characteristic of the solvent. In water, the basic species is the anion characteristic of the solvent, OH-. By extending the Arrhenius definitions of acid and base to liquid ammonia, it becomes apparent from Eq. (10.3) that the acidic species is NH4+ and the basic species is Nl I,. It is apparent that any substance that leads to an increase in the concentration of NH4+ is an acid in liquid ammonia. A substance that leads to an increase in concentration of NH2- is a base in liquid ammonia. For other solvents, autoionization (if it occurs) leads to different ions, but in each case presumed ionization leads to a cation and an anion. Generalization of the nature of the acidic and basic species leads to the idea that in a solvent, the cation characteristic of the solvent is the acidic species and the anion characteristic of the solvent is the basic species. This is known as the solvent concept. Neutralization can be considered as the reaction of the cation and anion from the solvent. For example, the cation and anion react to produce unionized solvent ... 

By definition, a molecular transport junction consists of a molecule extended between two macroscopic electrodes. The nature of the molecule, the environment (whether it is solvated or not), the electrode s shape and composition, the temperature, the binding of the molecule to the electrodes, and the applied field are all variables that are relevant to the measurement, which is usually one of differential conductance, defined as the derivative of the current with respect to voltage. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

These definitions are interpreted as follows environment atoms recognize the average weighted states of the ligands each ligand recognizes only the environment atoms and itself with the full scale for estimation of its effective Bom radius. Alternate definitions of the electrostatic solvation energy and the effective Bom radius at the intermediate states are also possible.81... 

When water contains no dissolved solutes, the concentrations of the solvated protons and the hydroxide ions are equal. Accordingly, from our definition of neutral above, we see why pure water should always be neutral, since [H30+(aq)] = [OH (aq)]. 

By considering both the definition of pH in Equation (6.20) and the concentration of the solvated protons from Worked Example 6.1, we see how a sample of super-pure water - which is neutral - has a pH of 7 at 298 K. We now go further and say all neutral solutions have a pH of 7. By corollary, we need to appreciate how an acidic solution always has a pH less than 7. If the pH is exactly 7, then the solution is neutral. 

The article is organized as follows in Section 2, a general discussion concerning the definition of electrostatic potentials in the frame of DFT is presented. In Section 3, the solvation energy is reformulated from a model based on isoelectronic processes at nucleus. The variational formulation of the insertion energy naturally leads to an energy functional, which is expressed in terms of the variation of the electron density with respect to... 

In words, s describes the interaction of the solute charge distribution component p, with the arbitrary solvent orientational polarization mediated by the cavity surface. The arbitrary weights p,, previously defined by (2.11), enter accordingly the definition of the solvent coordinates, and reduce, in the equilibrium solvation regime, to the weights tv,, such that the solvent coordinates are no longer arbitrary, but instead depend on the solute nuclear geometry and assume the form se<> = lor. weq. In equilibrium, the solvent coordinates are correlated to the actual electronic structure of the solute, while out of equilibrium they are not. 

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