Solutes cavity radius

The energetics of this model are shown in Fig. 18. The solute-cavity radius has a minimum energy at a radius ro when the vibrator is in v = 0 and a minimum at a larger radius ro + dr when it is in v = l. When the vibrator is in v = 0, there will be a distribution of cavity sizes at equilibrium due to thermal excitations in the solvent. These different cavities have different vertical transition energies, and the width of the size distribution maps into the width of transitions Aw. 

Where a is the solute cavity radius and e is an average excitation energy for the solute. If the transition dipol moment (P ) of the carotenoid is known, we can calculate the difference in polarizability of the ground(lA ) and the excited state(IB ), i.e a - a. ... 

The volume calculation results in a cavity radius of 3.65. The acetonitrile solution produces only subtle changes in the molecule s structure. The only significant change is a decrease of 0.3-0.4° in the O-C-H bond angle. 

Optimize the two equilibrium structures in solution, using the Onsager SCRF method and the RHF/6-31G(d) model chemistry. You ll of course need to determine the appropriate cavity radius first. 

Here, d is the radius of the cavity around the solute (given in A), the dipole fi is given in A and au, and d is the macroscopic dielectric constant of the solvent. The crucial problem, however, is that the cavity radius is an arbitrary parameter which is not given by the macroscopic model, making the results of eq. (2.18) rather meaningless from a quantitative point of view. A much more quantitative model is provided by the semimicroscopic model described below. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

Catalysis, specific acid, 163 Catalytic triad, 171,173 Cavity radius, of solute, 48-49 Charge-relay mechanism, see Serine proteases, charge-relay mechanism Charging processes, in solutions, 82, 83 Chemical bonding, 1,14 Chemical bonds, see also Valence bond model... 

The exclusion effect of hard-spheres is illustrated in Figure lA., which shows a spherical solute of radius r inside an infinitely deep cylindrical cavity of radius a. Here the exclusion process can be described by straightforward geometrical considerations, namely, solute exclusion from the walls of the cavity. Furthermore, it can be shown thatiQJ... 

Figure 5 shows pn distributions for spherical observation volumes calculated from computer simulations of SPC water. For the range of solute sizes studied, the In pn values are found to be closely parabolic in n. This result would be predicted from the flat default model, as shown in Figure 5 with the corresponding results. The corresponding excess chemical potentials of hydration of those solutes, calculated using Eq. (7), are shown in Figure 6. As expected, /x x increases with increasing cavity radius. The agreement between IT predictions and computer simulation results is excellent over the entire range d < 0.36 nm that is accessible to direct determinations of po from simulation.

FL, and the difference in dipole moments determined from the plot is 2.36 D if the Onsager radius is 0.33 nm [53]. The Onsager cavity radius was obtained from molecular models where the molar volumes were calculated by CAChe WS 5.0 computer program. The simplest method to estimate the cavity radius is to assume a = (3y/47r) 3, where V is the volume of the solute. 

In this second example, we examine simple systems near the water-hexane interface. Specifically, we calculate the difference in the free energy of hydrating a hard-sphere solute of radius a, considered as the reference state, and a model solute consisting of a point dipole p located at the center of a cavity [11]. We derive the formula for A A assuming that the solute is located at a fixed distance z from the interface, and subsequently we examine the dependence of the free energy on z. The geometry of the system is shown in Fig. 2.3. 

For zero cavity radius, eh has a mean radius of charge distribution in the ground state equal to 2.54 A, and E,s = -1.32 eV, which is numerically somewhat less than the experimental heat of solution (1.7 eV). For the excited state, the mean radius of charge distribution is 4.9 A, with hv (see Eq. 6.16) = 1.35 eV Note that hv > —Eu, implying that the 2p(ls) is actually in the continuum. 

Parchment et al. [271] have provided more recent calculations on the 3-hydroxypyrazole equilibrium at the ab initio level. They noted that tautomer 9, which was not considered by Karelson et al. [268], is the lowest-energy tautomer in the gas phase at levels of theory (including AMI) up to MP4/6-31G //HF/3-21G [271], Although 8 is the dominant tautomer observed experimentally in aqueous solution, in the gas phase 8 is predicted to be nearly 9 kcal/mol less stable than 9 at the MP4 level [271], Using a DO model with an unphysically small cavity radius of 2.5 A, Parchment et al. [271] were able to reproduce at the ab initio level the AMI-DO prediction of Karelson et al. [268], namely that 8 is the most stable tautomer in aqueous solution. With this cavity, though, 8 is predicted to be better solvated than 9 by -22.2 kcal/mol [271], This result is inconsistent with molecular dynamics simulations with explicit aqueous solvation [271], and with PCM and SCME calculations with more reasonable cavities [271] these predict that 8 is only about 3 kcal/mol better solvated than 9. In summary, the most complete models used by Parchment et al. do not lead to agreement with experiment... 

Several details with respect to implementation of Equations [22] and [23] deserve further discussion. Whereas the approximation of the solute residing in a spherical cavity is clearly of limited utility, since most molecules are not approximately spherical in shape, there is also the issue of the choice of the cavity radius, a. Obvious approaches include (1) recognizing that the spherical cavity approximation is arbitrary and thus treating a as a free parameter to be chosen by empirical rules, and (2) choosing a so that the cavity encompasses either the solvent-accessible van der Waals surface of the solute or the same volume. Wong et al. have advocated a quantum mechanical approach like the last method wherein the van der Waals surface is replaced by an isodensity surface. Because g depends on the third power of a, the calculations are quite sensitive to the radius choice, and some nonphysical results have been reported in the literature when insufficient care was taken in assigning a value to a. Implementations that replace the cavity sphere with an ellipsoid have also appeared. 

It does not appear that any attempt has been made to couple this BKO model to a means by which to calculate the CDS components of solvation, and this limits the model s accuracy, especially for solvents like water, where the CDS terms are not expected to be trivial. For water as solvent, studies have appeared that surround the solute with some small to moderate number of explicit solvent molecules, with the resulting supermolecule treated as interacting with the surrounding continuum. 23,230 Although such a treatment has the virtue of probably making the calculation less sensitive to the now-large cavity radius, it suffers from the usual explicit-solvent drawbacks of the size of the system, the complexity of the hypersurface, and the need for statistical sampling. 

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