1,3—Butadiene, approximate calculation

The NBMO coefficients can be used in approximate calculations of a-electron energies by a method developed by Dewar and by Longuet-Higgins. Consider a conjugated hydrocarbon (RS)with an even number of carbons and a tt-electron system that might be considered to be the result of joining up two odd AH radica (R and S) by one or more a bonds. The a-electron system of butadiene would be the result of linking up the a systems of allyl and methyl, while benzene would result from pentadienyl and methyl or two allyls. 

Once these approximations have been made, HMO theory becomes very simple. Using 1,3-butadiene, 1, as an example, we can work through an HMO calculation in order to outline the process involved. Firstly, we assign numbers to the carbon atoms, as shown in Figure 7-19. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

Relationship of absorption positions and intensity to structures. While quantum mechanical calculations permit prediction of the correct number and approximate positions of absorption bands, they are imprecise. For this reason, electronic spectroscopy also relies upon a combination of empirical rules and atlases of spectra that can be used for comparison purposes.74 76 The following may help to orient the student. The position of an absorption band shifts bathochromically (to longer wavelength, lower energy) when the number of conjugated double bonds increases. Thus, butadiene absorbs at 46,100 cm 1 (217 nm) vs the 61,500 cm 1 of ethylene. As the number of double bonds increases further, the bathochro-mic shifts become progressively smaller (but remain more nearly constant in terms of wavelength than wave number). For lycopene (Fig. 23-10) with 11... 

The SHMO orbitals of pyrrole, pyridine, and pyridinium are shown in Figure 11.6. The HOMO of pyrrole is the same as that of butadiene. Thus pyrrole is more reactive than benzene toward electrophilic attack. Attack, leading to substitution, occurs mainly at the 2- and 5-positions where the electron density of the HOMO is concentrated. In the case of pyridine (Figure 11.6b), the HOMO is not the n orbital, but the nonbonded MO, wn, which would be situated at approximately a - 0.5 //. Thus, it is not pyridine but pyridinium (Figure 11.6c) which undergoes electrophilic attack and substitution. The reactivity is much less than that of benzene, although this could not be deduced directly from the SHMO calculation. Neither does the calculation suggest the reason that electrophilic substitution occurs mainly at the 3- and 5-positions, since the n HOMO is... 

Thus qmin as well as the average q are proportional to p for a constant value of 8. If in the case of spherical aggregates 1.2 qmin, which is always smaller than 1, becomes smaller than 0.5, the two-block polymers tend to avoid this strong deformation of the butadiene sequences by forming cylindrical aggregates. Both particle shapes are observed in cases when qmin is calculated to be approximately 0.5 to 0.7 both for spheres and cylinders. 

An estimate of the volume of solvent added to the hydrocarbon mixture was obtained by calculating the difference in the liquid level before and after gas addition, which is approximately equal to the volume of gas dissolved in the liquid phase. This value is added to the volume above the liquid interface to obtain the total solvent volume added to the system. The ratio of ethylene/ammonia solvent mixture added to the volume of butadiene/butene solution was approximately 5 1. 

In Figure 5 are plotted the fraction of unconverted 1-butene, (1-X), and the butadiene and MA yields, respectively. The only information on the actual behaviour of the reactor exists in the measured value of the MA yield. Without any parameter fitting the model is seen to give a yield value that is close to the measured one. The calculation shows that a maximum of the MA yield is obtained at a height of 7 cm above the bottom plate whereas 2 metres of bed height were necessary on the pilot scale to obtain approximately the same yield. This strong influence of the scale on the performance of the reactor is typical for fluidized bed reactors (22). The model calculations show that this influence is due to changes in fluid bed hydrodynamics in the course of the scale-up. 

Platinum complexes, 161 Polarographic studies, 153, 154 of 2-aminothiazoles, 29 of 2-anilinothiazoles, 30 of 2-azothiazoles, 107, 108 Polyacrylonitrile, 105, 163, 164, 167 Polyamines, 156-168 Polycaprolactam, 156-168 Polyesters, 163, 165, 166, 167 Polyhalogenothiazole. reactivity of, 408-409 Polymers, e-caprolactam, butadiene, 438 Polymorphism, of sulfathiazole, 116 Positive colored image, 440 Postemergence activity, 134 Potassium salts, of acetamido thiazoles, 90 Potentiometric measurements, and amido-imido equilibrium, 116 and amino-imino equilibrium, 21 P.P.P. approximation, charge diagrams calculations by, 17... 

In contrast to the great number of calculations concerning the all-carbon Diels-Alder reaction [39], there are only a few theoretical studies on the hetero Diels-Alder reaction [41,42,45 - 53 ]. The general mechanism of the Diels-Alder reaction is still in discussion however, in most cases a concerted reaction is assumed,but there is also evidence for a two-step path. The ab initio calculations carried out for the butadiene/ethene system by Houk, Ortega, Bernardi und Gajewski gave a symmetrical transition structure only using the semiempirical AM1/CI method (half electron approximation) an unsymmetrical diradicaloid intermediate was found [40]. 

Figure 1. Electron correlation in butadiene as a function of the strength of an electric field applied along the longitudinal (x) axis relative to the correlation energy at zero field strength. The top two curves are nearly coincident, showing the similarity between CCSD and the approximate form ACCSD (see Table I). The bottom two curves are also nearly coincident. They correspond to MP2 calculations done without correlating the carbon li orbitals and with the inclusion of correlation from these core orbitals. All the other correlation treatments were done without including core correlation effects. The middle curve is the Brueckner orbital ACCD curve.

Some analysts, such as US EPA (2002) for the analysis of 1,3-butadiene carcinogenicity examined in more detail below, assumed a distribution shape (normal in that case, with a standard deviation calculated from the estimated MLE and confidence limits of the qi estimates). However, as will be shown below, such assumptions are approximate at best even in favorable cases. Zeise et al. (1991) demonstrated a procedure to generate the required distribution by tracing the likelihood profile of the linear term ( i) for a linearized multistage fit to dichotomous tumor data. This used a modified version (Zeise and Salmon 1991) of the MSTAGE program developed by Crouch (1985). More recently. Crouch (2006) developed a similar program that provides the likelihood distribution for estimates of qi when... 

Using a model like that in Section 2.1.2.3, the extra conjugation for this kind of Z-substituted allyl anion will mix v 3 of the pentadienyl anion with ip2 of butadiene (Fig. 4.5). This also suggests that the terminus, the y carbon, ought to be the more nucleophilic site. Clearly this is not borne out in practice, but measurements of the total electron population agree with this result. The excess n charge, calculated from the 13C-NMR chemical shifts of the lithium dienolate 4.75, show that the charge on C-2, the a carbon, is approximately twice that at C-4.328 The simple version of Hilckel theory is inadequate for this problem. 

All ab initio and solvation model calculations were carried out with the Gaussian 98 program [24], by using a 16-node SP IBM RS/6000 supercomputer [74], The discrete, continuum, and discrete-continuum solvation models are used to approximate the effect of solvent on the butadiene and acrolein Diels-Alder reaction. The... 

---