Phase Calculation

Figure 3 presents results for acetic acid(1)-water(2) at 1 atm. In this case deviations from ideality are important for the vapor phase as well as the liquid phase. For the vapor phase, calculations are based on the chemical theory of vapor-phase imperfections, as discussed in Chapter 3. Calculated results are in good agreement with similar calculations reported by Lemlich et al. (1957). ... 

Most of the envisioned practical applications for nonlinear optical materials would require solid materials. Unfortunately, only gas-phase calculations have been developed to a reliable level. Most often, the relationship between gas-phase and condensed-phase behavior for a particular class of compounds is determined experimentally. Theoretical calculations for the gas phase are then scaled accordingly. 

Ab initio, gas phase calculations found two minima and one maximum for the reaction coordinate, leading to an exothermic formation of the tetrahedral complex. Oneminimum is an ion-dipole... 

Be sure to remind students that these frequencies are gas phase data and arc thus not the same as the more-faniiliar solution spectra (we will treat solvated systems in Chapter 9). Even so, such gas phase calculations make excellent discovery-based exercises, For example, students may be asked to explain the substituent effects observed tising basic chemistry knowledge. 

We ran an SCRF single point energy calculation for gauche dichloroethane conformers in cyclohexane (e=2.0), using the Onsager model at the Hartree-Fock and MP2 levels of theory (flfl=3.65) and using the IPCM model at the B3LYP level. The 6-31+G(d) basis set was used for all jobs. We also ran gas phase calculations for both conformations at the same model chemistries, and an IPCM calculation for the trans conformation (SCRF=Dipole calculations are not necessary for the trans conformation since it has no dipole moment). 

The predicted energies in solution are generally given in the same location within the Gaussian output as for gas phase calculations, with the following variations ... 

Alternative pathways a and b, gas-phase calculations and [in brackets[ simulation of the MeCn solution (cf. Scheme 15 and Table IV). 

Figure 2 shows the conversions obtained with the three series studied, as a function of the mechanical mixtures composition, one hour after the beginning of the reaction and at the steady-state. Each series presents a maximum of activity, but at a different composition. SA6 series has a maximum between R , values of 50 and 75, whereas SA12 series has a maximum around = 50, and SA60 series near R , = 75. The dashed lines on the figures represent the sum of the individual contributions of the pure phases, calculated according to Equation 3. A very important synergetic effect is observed in all series, i.e., the activity of the mixtures is... 

Figure 3 shows the amount of Bronsted sites, as measured by the surface of the characteristic IR peak at 1540 cm after outgassing at 523 K, as a function of the composition of the mechanical mixtures. The dashed lines represent the addition of the contribution of the pure phases, calculated as in Equation 3. An enhancement of the amount of Bronsted sites on the mixtures, when compared to the theoretical values, is observed. This effect is not very clear in SA6 series, but it is more evident in SA12 and SA60 series. The reproducibility of the experiments has been checked the variation between different wafers of the same sample was always inferior to 10%. 

Figure 3. The phase lag produced by the Gouy phase, calculated using the analytic model described in the text for 0)3 + 3t0i excitation, with two additional coi photons in one of the channels. The calculations are performed for various ratios of the molecular beam radius d to the Rayleigh range zr.

The decanter vessel is sized on the basis that the velocity of the continuous phase must be less than settling velocity of the droplets of the dispersed phase. Plug flow is assumed, and the velocity of the continuous phase calculated using the area of the interface ... 

Although the tautomeric ratios of the 4 species have not been measured directly, it is known that in aqueous solution the keto-N2H form dominates, while the keto-NlH form is only detectable in non-polar solvents. An analysis of experimental data concluded that in aqueous solution the stability (lowest free energy) is in the order keto-N2H > imino-N2H > enol-NlH > keto-NIH. In the gas phase, calculations predict that the keto-N2H form is the least stable. While solvation is found to favour this species, which is the most polar, this stabilisation is not enough to reverse the order of stability. It is thus clearly predicted that the keto-NIH tautomer is the most stable in... 

Assuming ideal mixing for both gas and liquid phases, calculate ... 

Table 11.1 lists the resulting low-temperature phases calculated for this set of compounds. Where experimental data are available (marked with a star) the predicted structures are those observed at low temperatures. Inverse denotes a perovskite structure in which a large divalent ion is 12-coordinate and a smaller univalent ion 6-coordinate. Unit cell dimensions are predicted to within 1% of the measured values. 

Both reactions are carried out in nonpolar solvents which should not only accentuate polar interactions, but should also make gas phase calculations relevant to these solution processes. 

Gas phase calculations on the CS state of 22 also predict a large change in the cavity size, from 10 A in the ground state, to only about 6 A in the CS state, and that this change is mainly caused by out-of-plane bending of both DC V and DMAn groups.1381 Similar geometric distortions are predicted for other U-shaped dyads in their CS states. 

Finally, one has to concede that gas-phase calculations are not the ideal way to model a reaction taking place on a catalyst surface. Computational chemistry developments in this area have been continuing but they are a long way from providing completely realistic models. For example, the overall kinetics for dehydrocyclizations are likely to be rate-limited by the binding of the alkane substrate to catalytically active sites. 

Figure 4.24. Near-neighbour diagrams for binary phases calculated according to Pearson (1972) for a few structural types. The lines calculated for the different interatomic contacts are shown. The numbers of contacts X-Y, Y-X, X-X, etc. are indicated. The experimental values determined for the various compounds are contained, for each structure type, within the hatched fields, (a) XY3 compounds belonging to the cP4-AuCu3 structural type (b) XY2 Taves phases of the cF24-Cu2Mg type (c) XY compounds of the cF8-ZnS structural type. Notice the importance of the high coordination contacts in the more metallic phases, whereas in the ZnS-type compounds the role of the chemical bond factor is clearly relevant.

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