The total solvent effect

With the Leffler-Grunwald delta operator symbolism we define 5,AG =AG ,(x2)-AG ,( 2=0) which, applied to eqs. [5.5.20] and [5.5.21], gives our final result  

The quantity 5 can be read the solvent effect on the solution free energy. Because of eq. [5.5.1], S AG is proportional to the relative solubility, log[(x3 / (x ], that 

It will be no surprise that the first use of eq. [5.5.23] was to describe the equilibrium solubility of solid nonelectrolytes in mixed aqueous-organic solvents. Equilibrium solubility in mol L, C3, is converted to mole fraction, X3, with eq. [5.5.24], where p is the saturated solution density, w is the wt/wt percentage of organic cosolvent, and Mj, M2, M3 are the molecular weights of water, cosolvent, and solute.  

Clearly eq. [5.5.24] possesses the functional flexibility to describe the data. (In some systems a 1 -step (2-state) equation is adequate. To transform eq. [5.5.24] to a 1-step version, set K2 = 0 and let / = Yj - Yi ) The next step is to examine the parameter values for their possible physical significance. It seems plausible that K, and Kj should be larger than tmity, but not very large, on the basis that the solutes are organic and so are the cosolvents, but the cosolvents are water-miscible so they are in some degree water-like. In fact, we find that nearly all Ki and Kj values fall between 1 and 15. Likewise the gA values seem, in the main, to be physically reasonable. Earlier estimates of g (reviewed in ref. ) put it in the range of 0.35-0.5. A itself can be estimated as the solvent-accessible surface area of the solute, and many of the gA values found were consistent with such estimates, though some were considerably smaller than expected. Since gA arises in the theory as a hydrophobicity parameter, it seemed possible that A in the equation represents only the nonpolar surface area of the 

Areas in molecule standard deviations in parentheses. The cosolvent was methanol. 

The quantity 6, AG , can be read the solvent effect on the solution free energy. Because of eq. [5.5.1], d AG is proportional to the relative solubility, log[(xj / (Xj that is, the logarithm of the solubility in the mixed solvent of composition Xj relative to the solubility in pine water. The subtraction that yields eq. [5.5.23], a workable equation with just three unknown parameters (gA, Kj, and K2), has also prevented us from dealing with absolute solubilities. 

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The contributions of solvent effects on the activation free enthalpies of the reactions under study are reported in Tables 4 and 5 where also a comparison can be done among the different procedures. These effects are given by the differences between the solvent effects on the TSs and those on the reactants. The total solvent effect (TOT for reactants and TOT for the activation free enthalpy) consists of two contributions, labelled CDS(CDS for "cavitation+dispersion+structural" and ENP(ENP ) for "electronic+nuclear+polarisation" in the AMSOL procedure, CDR(CDR ) for "cavitation+dispersion+repulsion" and ELEC(ELEC for "electrostatic" in the Tomasi procedure. 

The results presented in Table 1.14 shows that including only specific H-bonding effects (i.e. considering gas-phase clusters) means to take into account only a part of the total solvent effect while the complete description is reproduced by adding long-range effects (here represented by the external continuum). 

To quantify further the various contributions to these calculated effects, the data in Tables I and II are presented. In Table I, the value of the penalty function (C) is given at points during the various rotations. Since the total solvent effect is typically an order of magnitude larger than the values of C in Table I, it is seen that C is serving only as a penalty function , and not disturbing the calculated solvent effect. 

In Table II, the various contributions to the total solvent effect are listed, at angles corresponding to the predicted minimum energy points. These data also indicate the small role that the penalty function plays in the solvent effect. In addition, it is seen... 

Great attention has been paid to the problem of solvent effect on spectral, chemical and reactivity data [16]. Kamlet considered the total solvent effect to be composed of three independent contributions solvent polarity (n ), acidity (a) and basicity (P) for hydrogen bond acceptor (HBA) solvents. These contributions are gathered in one equation as follows ... 

We might, therefore, use these values of AT(46) to provide an estimate of substituent effects on the values of K(Al), whilst using the data in Tables 21 and 22 to deduce substituent effects on the values of k1 and on the overall rate coefficient, k°2bs. At the same time, it is convenient also to refer to Table 24, p. 164, which contains data on the related brominolysis of tetraalkyltins in the non-polar solvent carbon tetrachloride. The total substituent effects may be broken down into three sections. 

This extension of the PCM is described in detail in [26], Here, it is sufficient to say that such an extension is an application of a nonequilibrium scheme within a QM perturbative linear response (PCM-LR) approach. The total electronic coupling, Kotai, is obtained as a sum of two terms, the direct (or Coulombic-exchange) coupling, implicitly modified by the medium (Vs), and the contribution involving the explicit solvent effect (T xpiicit) ... 

The distribution coefficient Kj (Equation 2) is defined as the volume fraction of pores, in a stationary phase, which is effectively permeated by a solute of a given size. V0 is the interstitial volume of the porous medium, measured by the elution volume of a high molar mass solute that is totally excluded from the matrix pores. Ve is the elution volume of the product of interest. Vs represents the total solvent volume within the pores, available for small solutes. 

In order to distinguish between ionic HBs and LBHBs, it is essential to first define the LBHB proposal in a way that reflects the energetics of the system and can be used to determine the actual catalytic contribution associated with this proposal. At present, the best way to define the LBHB proposal is to use the VB representation. This representation can be treated in a simplified two-state version of the three-state model of Coulson and Danielsson,110,111 augmented by the EVB solvent effect.22 Here we consider as an example the [X H — Y , X — II Y ] system, but the same considerations will be applicable to the [X — I I B X — II fi] system. At any rate, in the two-state VB representation we can describe the total wave function by ... 

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