Eclipsing

With these simplifications, and with various values of the as and bs, van Laar (1906-1910) calculated a wide variety of phase diagrams, detennining critical lines, some of which passed continuously from liquid-liquid critical points to liquid-gas critical points. Unfortunately, he could only solve the difficult coupled equations by hand and he restricted his calculations to the geometric mean assumption for a to equation (A2.5.10)). For a variety of reasons, partly due to the eclipse of the van der Waals equation, this extensive work was largely ignored for decades. 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

Example Hthanc is stable in the staggered gauche) con formation. The transition state for rotating a methyl group in ethane has the eclipsed con form at ion, A gcom etry optim i/ation start in g from an eclipsed eon formation yields th e tran sition state. 

A stretch-torsion cross term can be used to model the stretching of a bond that occurs in ai eclipsed conformation. Two possible functional forms are ... 

Gr. helios, the sun). Janssen obtained the first evidence of helium during the solar eclipse of 1868 when he detected a new line in the solar spectrum. Lockyer and Frankland suggested the name helium for the new element. In 1895 Ramsay discovered helium in the uranium mineral clevite while it was independently discovered in cleveite by the Swedish chemists Cleve and Langlet at about the same time. Rutherford and Royds in 1907 demonstrated that alpha particles are helium nuclei. 

Total syntheses of tazettine and 6a-epi-pretazettine have been carried out by application of the Pd-catalyzed cydization of 169, in which a single pentacyclic product 170 was obtained, establishing a preference for an eclipsed orientation of the Pd—C (7-bond and alkene 7r-bond in the key intramolecular insertion step[l40]. 

Ethane is the simplest hydrocarbon that can have distinct conformations Two the stag gered conformation and the eclipsed conformation, deserve special mention and are illustrated with molecular models m Figure 3 1... 

In the eclipsed conformation each C—H bond of one carbon is aligned with a C—H bond of the other carbon... 

FIGURE 3 1 The stag gered and eclipsed confer mations of ethane shown as ball and spoke models left) and as space filling models right)... 

FIGURE 3 3 Some commonly used draw mgs of the eclipsed conformation of ethane... 

Eclipsed bonds are characterized by a torsion angle of 0° When the torsion angle is approximately 60° we say that the spatial relationship is gauche, and when it is 180° we say that it is anti Staggered conformations have only gauche or anti relationships between bonds on adjacent atoms... 

Of the two conformations of ethane the staggered is 12 kJImol (2 9 heal mol) more stable than the eclipsed The staggered conformation is the most stable conformation the eclipsed is the least stable conformation Two main explanations have been offered for the difference in stability between the two conformations One explanation holds that repulsions between bonds on adjacent atoms destabilize the eclipsed conformation The other suggests that better electron delocalization stabilizes the staggered conformation The latter of these two explanations is now believed to be the correct one... 

Conformations m which the torsion angles between adjacent bonds are other than 60° are said to have torsional strain Eclipsed bonds produce the most torsional strain staggered bonds none Because three pairs of eclipsed bonds are responsible for 12 kJ/mol (2 9 kcal/mol) of torsional strain m ethane it is reasonable to assign an energy cost of 4 kJ/mol (1 kcal/mol) to each pair In this chapter we 11 learn of additional sources of strain m molecules which together with torsional strain comprise steric strain... 

At any instant almost all of the molecules are in staggered conformations hardly any are in eclipsed conformations... 

Figure 3 7 illustrates the potential energy relationships among the various confer matrons of butane The staggered conformations are more stable than the eclipsed At any instant almost all the molecules exist m staggered conformations and more are present m the anti conformation than m the gauche The point of maximum potential... 

At Its most basic level separating the total strain of a structure into its components is a qualita tive exercise For example a computer drawn model of the eclipsed conformation of butane using ideal bond angles and bond distances (Figure 3 8) reveals that two pairs of hydrogens are separated by a distance of only 175 pm a value considerably smaller than the sum of their van der Waals radii (2 X 120 pm = 240 pm) Thus this conformation is destabilized not only by the torsional strain associ ated with its eclipsed bonds but also by van der Waals strain... 

FIGURE 3 8 Ball and spoke and space filling models of methyl-methyl eclipsed conformation of butane... 

FIGURE 3 11 Nonplanar ( puckered ) conformation of cydobutane The nonplanar con formation avoids the eclipsing of bonds on adjacent carbons that characterizes the planar con formation... 

Neighboring C—H bonds are eclipsed in any planar cy cloalkane Thus all planar conformations are destabi lized by torsional strain... 

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