Radius cavity

Tlie molecular volume Vm can in turn be obtained by dividing the molecular weight by density or from refractivity measurements is Avogadro s number. The cavity radius (... 

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. 

Exercise 2.1. Evaluate the ground-state potential surface for the CH3OCH3—> CH3 + CH30- reaction using the reaction field model, with a cavity radius a = R/2 + 1.5. 

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... 

From Eqs. (6.1) and (6.4) one can find the limiting values of the cavity radius of active sizes on the heated surface... 

Figure 6.4 shows the relation between the heat flux and the wall superheat at the ONB position obtained by Hino and Ueda (1975) in the range of the largest cavity radius r x = 0.22—0.34 pm. Experimental points show that the wall superheat at the ONB position was practically independent of the mass flux and the inlet subcooling. The lines shown in this figure represent the values of Sato and Matsumura (1964), and Bergles and Rohsenow (1964). The wall superheats reported by Hino and Ueda (1975) were much greater than those predicted by Eq. (6.9). 

Equation (2-14) provides a way to calculate the liquid temperature in equilibrium with the ready-to-grow bubble if the saturation pressure or temperature, the value of B, and the cavity radius are known (Shai, 1967). Several modified versions of nucleation criteria have since been advanced. An example is the model proposed by Lorenta et al. (1974), which takes into account both the geometric shape of the cavity and the wettability of the surface (in terms of contact angle < >). Consider an idealized conical cavity with apex angle ip, and a liquid with a flat front penetrating into it (Fig. 2.3a). Assume that once the vapor is trapped in by the liquid front, the interface readjusts to form a cap with radius of curvature rn. Conservation of vapor... 

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. 

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. 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02< 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

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... 

We begin with a comparison of the various DO models to each other. Based on a parametric procedure that takes account of the molecular volume encompassed by the 0.001 a.u. electron density envelope, Wong et al. [297] suggested that an appropriate spherical cavity radius is 3.8 A. Szafran et al. [157]... 

Young et al. [195] have provided a calculation in which they compared expanding the multipole series up to /= 6 in a spherical cavity of 3.8 A. These results may be compared directly to those of Wong et al. [297] at the identical level of theon asis set in order to assess the effect of including higher moments. In each case, the differential solvation free energy increases by about 40%. This illustrates nicely the relationship between cavity radius and model... 

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