Computational methods Cyclohexane

In superacid catalyzed reactions of hydroxyquinolines and isoquinolines, dicationic superelectrophiles were proposed as intermediates in their reactions (see Table 4).35d In order to explain differences in relative reactivities between the isomeric superelectrophiles, the energies of the lowest unoccupied molecular orbitals Ultimo ), the square of the coefficients (c2) at the reactive carbon atoms, and the NBO charges (q) on CH groups were determined by MNDO and DFT computational methods. For example, 8-hydroxyquinoline (85) is found to be more reactive than 6-hydroxyquinoline (87) in the superacid catalyzed reactions with benzene and cyclohexane (eqs 47 -8). 

While various computational methods disagree on the magnitude of the relative roles of steilcs and hyperconjugation, the 0.9kcal/mol penalty for the gauche conformations is a useful conformational observation that can be transferred to larger systems. For example, such interactions in chair cyclohexane moieties illushate why adamantane and related diamondoid compounds are not completely free of strain. 

In the following main program equations (2.61-2.64) are solved using the Broyden method. The distribution coefficients are computed from equations (2.58 - 2.60) written for C = 3 components. The starting values used are very simple, for the extract phase we start from poor Furfural and for the raffinate phase from the original n-Heptane - Cyclohexane mixture. Negative mole numbers and mole fractions are not allowed. 

Chandler and co-workers successfully used stochastic dynamics in their studies of -alkanes and cyclohexane isomerization in solution. The method used is based on the BGK theory. The assumption is that the primary form of interaction between the solvent molecules and the isomerizing system is in the form of hard collisions. These collisions, when they occur, randomize the velocity of one of the isomerizing molecule s atoms. The computational implementation of this is quite simple at random times, based on the collision frequency (which is taken to be proportional to the solvent viscosity), instantaneously change one random atom s velocity to one selected from the Boltzmann distribution at the temperature of interest. Then continue running dynamics until the next collision occurs, at which time another... 

For a further test of the ad hoc substitutions (i) and (ii), Tong et al. [38] prepared three polymer mixtures, each containing four narrow-distribution polystyrenes (Mw X 10 = 11,44.5, 195, 807) at a prescribed weight ratio, allowed each of them to separate into two phases in cyclohexane at various T and , and measured the compositions of the two phases by GPC. They found that the separation factors for the four components computed from the experimental data agreed almost quantitatively with the values calculated by the above method of Einaga et al. This result was significant in that the system contained as many polymer components as four. 

The method reported by Tolliver and McCune for finding the most responsive temperature point was also used for this cyclohexane/w-heptane system. A second computer simulation was run using the same reflux/feed ratio for the separation power base while shifting the D/F (distillate/feed) ratio up. The heavy key impurity concentration in the distillate was... 

In our work, computer-based methods were used to identify the individual contributions to overlapping vibrational bands for spectra (Fig. 7.12a) recorded in mixtures of dimethoxybenzene in cyclohexane. Fig. 7.12b shows that while the position of the higher wavenumber v y (CO) and v gy fCO) bands remains essentially constant, the new pair of v y (CO) and v y (CO) bands shift further to lower wavenumbers as the contribution of the n-stacking increases [50]. This is consistent with either additional n-stacking to form taller stacks [53], or shifts due to random solvent effects in the mixed cyclohexane/arene solvent environment The new pair of v y CO) and bands also broaden more as they shift... 

Oscik and Goworek discuss the calculation of activity coefficients by equations (8) and (9). For systems of molecules of the same size the two methods should be equivalent. The authors have analysed the experimental data of Lu and Lama for the adsorption from benzene+cyclohexane mixtures by silica gel. The graphically presented results indicate that the curves derived from equation (8) and (9) deviate considerably from one another. However, since no details are given of the values assumed for the molar areas it is not possible to identify the origin of these discrepancies, which because of the close similarity of the sizes of the molecules concerned, are unexpected. Madan has used equation (9) to calculate the activity coefficients of benzene and acetic acid adsorbed from their mixtures by tin oxide gel 0 — 160 m g ). The results look surprising and consideration of the behaviour of ln(Y2/yT) shows that the two sets of activity coefficients are thermodynamically inconsistent, presumably as a result of a computational error. 

Figure 10.3 Room temperature (295 K) So Si absorption spectrum of rraws-stilbene computed using harmonic approximation by time-independent (upper panel [7]) and time-dependent (lower panel [63]) methods. Both computational results are compared with the experimental absorption spectmm measured at 295 K in cyclohexane by Mathies and co-workers [77]. (From J. Tatchen and E. Pollack, J. Chem. Phys. 2008, 128, 164303. Copyright 2008. Reprinted with permission of the American Institute of Physics.)...

The calculation of TCF in multicomponent systems has been done only for spherical cavities with the formalism developed by Lebowitz et al. Methods IV and V can in principle be extended for TCF calculation for nonspherical cavities in multicomponent systems. An artificial binary system (benzene-water) was selected here to illustrate the computational methodology. In practice, these two solvents mix very little, and their mixture can be of little interest, but they are quite different in their chemical nature and this makes such a system interesting. The method is by no means limited to certain mixtures and is universally applicable to any mixture if the molecular and physical parameters of the pure components are known (hard sphere diameter, number density, thermal expansion coefficient, dielectric constant). Figure 9 displays TCF calculated as a function of solvent mole fractions for a spherical cavity of cyclohexane size created in a hypothetical water-benzene mixture. Gc (Figure 9) increases with the increase of water mole fraction, but there is little difference between pure benzene and a mixture containing around 50% water as far as solvation of cyclohexane is concerned. 

A significant difference of 4.4 1.0 kJ mol (that is, a 21% relative differenee) is found between the enthalpies measured in CCU and in cyclohexane. It appears that the diiodine affinities measured in alkanes must not be mixed with those measured in CCI4, as was unfortunately done in the Drago EC analysis of Lewis affinity. Moreover, the experimental value to be compared with the diiodine affinity of DMSO computed in vacuo by quantum chemical methods is the value measured in cyclohexane. Taking into account the solvent effect of cyclohexane, a good calculated value should be at least —25.3 ( 0.8) kJ mor. ... 

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