Benzene calculations

Overlap concentration in benzene calculated from the external diameter in benzene. 

For the heats of formation in the G2-1 set, the largest difference between Wl and Wlh theory is 0.3 kcal/molfor Si2 the average difference is less than 0.1 kcal/mol. For some of the systems in the G2-2 set, however, differences are more pronounced, e.g. 0.6 kcal/molfor CF4 and 0.8 kcal/mol for benzene. (Note that the benzene calculation reported as an example application in the original Wl paper [1] is in fact a Wlh calculation the remaining small difference between that reference and the present work is due to the different SCF extrapolations used.) For the G2-1 heats of formation, W2h and W2 are essentially indistinguishable in quality, as could reasonably be expected. 

As an example, let us estimate the diffusivity of benzene in air. According to Table 18.3, the molar volume of benzene calculated from liquid density (89 cm3mol 1) and from the component method by Fuller et al. (90.8 cm3mor1) yield similar results. Incorporating these estimates into Eq. 18-44 yields ... 

A similar treatment of naphthalene17 leads to the value 2.04a, which on equation to the empirical resonance energy 75 kcal/mole fixes a at 37 kcal/mole, in approximate agreement with the result for benzene. Calculations for anthracene and phenanthrene1 lead to 2.95a and 3.02a, respectively, for the resonance energy, giving a = 36 and 35 kcal/mole on comparison with the empirical values. 

Fig. 31. The total differential oscillator strength for benzene calculated without including the structure factor.

FIGURE 9. Energy diagram of Dewar benzene and of hexasila-Dewar benzene calculated at the HF/6-31G level... 

Figure 6. Hess cycle used to relate the Dewar resonance energy of benzene, DRE(b), to the vertical resonance energy, Bq. Vertical resonance energy values for benzene and distorted benzene (calculated in this study111) are shown below the cycle. All energies are given in kcal/mol.

Fig. 3. Distribution of formal charge in the anionic intermediate of the Birch reduction of benzene calculated (a) by the Huckel method, (b) by the Pople method.

Table 17 The 7 - So oscillator strengths in benzene calculated with direct vibronic coupling along e2g modes (i- ). Results are displayed for different basis sets and for the 7r-active space.

The first [] term in the Benzene calculation accounts for the two carbons that are liberated when MA is formed, and the second [] term is for conversion to byproducts, with x/i going to C02 and the other to CO. MA from benzene generates almost four times as much C02 in the reactor than the n-butane route. Additional C02 is generated when unreacted benzene or n-butane and byproduct CO is incinerated in the pollution control equipment from the process. 

An automated vapor pressure method has been used to obtain highly precise values of the partial pressure of benzene as a function of concentration in aqueous solutions of sodium dodecylsulfate (at 15 to 45 C) and 1-hexadecylpyridinium chloride (at 25 to 45 C). Solubilization isotherms and the dependence of benzene activity on the intramicellar composition are inferred from the measurements and related to probable micellar structures and changes in structure accompanying the solubilization of benzene. Calculations are made to determine the efficiency of micellar-enhanced ultrafiltration (MEUF) as a process for purifying water streams contaminated by benzene,... 

Note that the AS p of benzene, calculated in Example 13.4, is within this range. The constancy of ASy p means that and Tb, which vary widely from sub-... 

Shown above is the energy-level diagram for the n orbitals of benzene, calculated on the basis of Hiickel molecular orbital theory. According to this theory, the total energy of the six n electrons of ground-state benzene is given by... 

Here, is the one-electron perturbation Hamiltonian operator. Equation (4.19) has to be solved simultaneously with eqs. (4.20) in a self-consistent fashion by CPDFT. This self-consistent procedure is avoided in SOS-DFPT, where the approximation Fg w Hg is invoked. The spin-spin coupling constants for benzene calculated by Sychrovsky et al. with the B3LYP functional are shown in Table 4.3. A good agreement between the calculated and measured spin-spin coupling constants is obtained for /(C,C), /(C,H), and /(H,H). 

Table 4.3 NMR spin-spin coupling constants for benzene calculated with the B3LYP functional (taken from ref. 45)...

Figure 10.8. Ratio /C12A115 which are elements of the zero-flux matrix of mass transfer coefficients [/c], as a function of the gas-phase Reynolds number. Mass transfer between a gaseous mixture of acetone (l)-benzene (2)-helium (3) and a liquid film containing acetone and benzene. Calculations by Krishna (1982) based on the von Karman turbulent film model and the Chilton-Colburn analogy.

Using the data given below for dilute solutions of nitromethane in benzene, calculate the molar polarization and refraction of the solute in the limit of infinite dilution. Then, estimate the dipole moment of nitromethane on the basis of the Debye model. 

A solution is prepared by condensing 4.00 L of a gas, measured at 27°C and 748 mmHg pressure, into 58.0 g of benzene. Calculate the freezing point of this solution. 

A nonvolatile organic compound Z was used to make up two solutions. Solution A contains 5.00 g of Z dissolved in 100 g of water, and solution B contains 2.31 g of Z dissolved in 100 g of benzene. Solution A has a vapor pressure of 754.5 mmHg at the normal boiling point of water, and solution B has the same vapor pressure at the normal boiling point of benzene. Calculate the molar mass of Z in solutions A and B and account for the difference. 

Table 5.15. Benzene, calculated IR spectrum after discarding IR-inactive or very weak (intensity less than 2 percent of the strongest band) frequencies, ignoring frequencies below 600 cm, correcting frequencies, combining degenerate ftequencies and their intensities, and normalizing intensities. Frequency correction factors [60] HF/3-21G, 0.9085 HF/6-31G, 0.8953 MP2(FC)/6-31G, 0.9434...

Table 1. The CH-stretching vibrational frequencies of benzene calculated at experimental and optimized reference geometries...

The valence and symmetry force constants of benzene calculated using density functional theory were first reported by us [10c,d]. These results are summarized in this section. We discuss the vibrational frequencies (Table 5), isotopic shifts, and absorption intensities (Table 6). Selected force constants in symmetry-coordinate representations are listed and compared to the fields due to the Pulay [10b] et al. as well as OG [10a] in Table 7. 

A detailed account, at the STO-3G level, of conformations, charge distributions and stabilities of 35 monosubstituted benzenes, including 10 of our representative set, has been presented by Hehre et al. (6). Corresponding results for the remaining members (Li, 0", NH, and NHa ) have been obtained more recently (67,10,11). We reproduce here some of the key results for all of the substituents which will be relevant to our subsequent discussion of di- and polysubstituted benzenes. Calculated total energies and dipole moments are listed in Table 1, and Mulliken charges and overlap populations are listed in Table 2. Where more than one conformation is possible, unless otherwise specified, the energy data listed are for the most stable conformation. 

Fig. 4 shows some data for rubber in benzene, calculated by Gee. Below, we return to the influence of the molecular weight, referring now only to the very pronounced temperature influence. For rubber with a mol. weight of 10 the temperature range of solubility is only from about 0 to 25°C at 0°C the solubility becomes practically unmeasurable, at 25°C complete miscibility is reached. 

In an experiment, a drop of dry benzene is put on the surface of pure water. First, the benzene becomes saturated with water, then the water becomes saturated with benzene. Calculate the spreading coefficients in all three stages and from the results describe the course of the physical process. 

Thus the resonance energy of benzene calculated up to third-order is 2.25 (i.e., 113% of the exact value). In Exercise 6.7, the fourth-order energy... 

FIGURE 1.285 IPSDs for (a) MCM-48 and (b) SBA-15 calculated on the basis of the nitrogen adsorption isotherms and the ISDs based on the H NMR spectra of water and water/benzene calculated using the IGT/ MEM-0 method. (With kind permission from Springer Science+Business Media Central Eur. J. Chem., Behaviour of pure water and water mixture with benzene or chloroform adsorbed onto ordered mesoporous silicas, 5, 2007g, 420-454, Gun ko, V.M., Turov, V.V., Turov, A.V. et al., Copyright 2007.)... 

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