Butadiene bond orders

A common way of representing the situation schematically is indicated in (XXIII) for butadiene. Bond orders are indicated on the bonds and free valences by arrows. It is clear that butadiene has a good deal more residual bonding capacity on its terminal atoms, and this is consistent with the fact that free radical attack on butadiene occurs predominantly on the end atoms. Other examples of correlation between free valence and rate of free radical addition have been reported. A plot of rate data for methyl... 

The total it electron energy is the sum of occupied orbital energies multiplied by two if. as is usually the ease, the orbital is doubly occupied. The charge densities and free valency indices were treated in separate sections above. The bond order output should be read as a lower triangular serni matrix. The bond order semi matrix for the butadiene output is shown in Fig. 7-7. 

The full bond order matrix is a symmetric tridiagonal matrix (Chapter 2). It is symmetric because the bond order Cji Y Na,ack is the same as tiie bond order Na,i, a,j. Elements off the tridiagonal (-.4472 in the butadiene example) are artifacts of the minimization atid should be disi egarded. The full bond order matrix for butadietie is... 

It is often of interest to compare the 7r-electron densities in bonds rather than on atoms. Although cross terms above were assumed to vanish because of the HMO zero-overlap assumption, they are actually not zero, especially not between a.o. s on nearest neighbours. The coefficients of the cross terms can hence be interpreted as a measure of overlap in the bonds. On this basis bond order is defined as pim = Yljnjcijcmj- For the 1-2 bond in butadiene pl2 = 2chc2i + 2c2iC22 = 0.88 = P34. p23 = 0.40. These values showthat the delocalized bond contributes more strongly to bind the end pairs than the central pair and gives a simple explanation of the experimental fact that the end bonds are shorter than the central bond. 

Molecular-orbital bond orders are 1.930 for the C-l.C-2 bond, 1.859 for the C-3.C-6 bond and 1.363 for the C-2.C-3 bond.34 Comparing these values with those for butadiene (p. 31), we see that the C-l,C-2 bond contains more and the C-3.C-6 bond less double-bond character than the double bonds in butadiene. The resonance picture supports this conclusion, since each C-l.C-2 bond is double in three of the five canonical forms, while the... 

The decrease in bonding order arising from delocalization of multiple bonds in conjugated systems results in a shielding of the central carbon atoms. This can be clearly seen by comparison of the pairs 1-butene/1,3-butadiene and ris-3-octene/ri.s-ris-3,5-octadiene ... 

Comparison of the calculated C—C bond distances (MP2) of 105 [C(1)=C(2) 1.357, C(2)—C(3) 1.439, C(3)=C(4) 1.371, C(l)—C(7) 1.497 A] with trans-butadiene [C(1)=C(2) 1.341,C(2)—C(3) 1.461 A]244 shows that a considerable degree of bond equalization is present in 105. Cremer and Kraka suggest that this is the consequence of homo-conjugative electron delocalization238. This conclusion was confirmed by these authors from the values of the calculated bond orders and -character indices. These results are contrary to predictions obtained at lower, less reliable levels of theory239-243. 

Pyrolytic fragmentations of other suitable precursors also lead to dimethylsilanone (97). For example, 6-oxa-3-silabicyclo[3.1.0]hexane 96 is reported to be split into 97 and 1,3-butadiene upon pyrolysis104. Other possible routes to 97 consist in the pyrolysis of (allyloxy)dimethylsilane (99)105 or Diels-Alder adduct 98104. Matrix-isolated 97 gives its trimer hexamethylcyclotrisiloxane when the matrix is warmed up to 35-40 K. The SiO stretching vibration of 97 was found at 1210 cm-1. This frequency fits the calculated force constant and bond order and has to be considered as evidence for significant double bonding in 97104. Octamethylcyclotetrasiloxane, allyl(allyloxy)dimethylsilane and 2,2,6-trimethyl-2-silapyrane failed as precursors for 97 and only the SiO molecule (cf Section V.B) and CH3 radicals were found on the matrix holder105. 

This reasoning was used by the author in 1961 to rationalize the ubiquitous photochemical cyclization of butadienes to cyclobutenes here it was noted that the excited state has a high 1,4-bond order. The same reasoning was applied 6,12) to understanding the key step of cyclohexadienone rearrangements (vide infra). Still another example is the decreased central bond order in the excited state of stilbene which, as Daudel has noted 13), is in accord with photochemical cis-trans interconversion. 

As expected, the C-4—C-5 bond orders found for these derivatives of the 1,3-dithiolium system are even higher. Contrary to the theoretical expectations, however, Mayer and Gebhardt124 have recently found that halogens do not add to these compounds, and both isotrithione and isodithione are stable towards butadiene or furan under conditions in which vinylene carbonate readily enters into Diels-Alder reactions 176 under drastic conditions, isodithione gives an adduct with cyclopentadiene, but the structure of this adduct is not yet known. 

Figure 10. Schematic illustration of a tendency of each benzene fragment in naphthalene to retain its aromaticity by producing cis 1,3-butadiene partial localization in its twin-ring as described by the resonance structures (7a) and (7b) yielding the resulting predominant canonical structure (7c). This intuitive argument is supported by the (HF/6-31G ) bond distances and the corresponding 7r-bond orders given within parentheses.

The diene ligands transform to the cisoid form because of the thermodynamic stability of the complex. Because the bond distances of Cj—and C2—Cy in the butadiene ligand are 1.45 and 1.46 A, respectively, the double bond character between C2—C3 and the bond order alternation is still insignificant [43]. This may be due to the strong K-acidity of three carbonyl ligands which reduces n-back donation from iron to the butadiene ligand. (Cyclohexadiene)tricarbonyliron complexes are also noteworthy. Fe(l,3-cyclo-hexadiene)(CO)3 was prepared by the reaction of 1,3-cyclohexadiene with Fe(CO)5 [44] (eq (13)) and more stable Fe(l,4-cyclohexadiene)(CO)3 was also prepared [45]. 

Charge distributions and bond orders of the cation and anion of 2//-benz[crf]azulene, on the other hand, are dissimilar. The seven-membered ring of the cation is delocalized, containing most of the positive charge, while that of the anion 87 is localized and the negative charge resides mainly in the delocalized indenyl moiety. A delocalized indolizine part with a localized butadiene bridge in the isoelectronic cycl-... 

Fig. 4-10 Total bond-orders of carbon-carbon and carbon-hydrogen bonds in butadiene.

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