Staggering

Another way to overcome the step-size restriction fc < is to use multiple-time-stepping methods [4] or implicit methods [17, 18, 12, 3). In this paper, we examine the latter possibility. But for large molecular systems, fully implieit methods are very expensive. For that reason, we foeus on the general class of scmi-implicit methods depicted in Fig. 1 [12]. In this scheme. Step 3 of the nth time step ean be combined with Step 1 of the (n - - l)st time step. This then is a staggered two-step splitting method. We refer to [12] for further justification. 

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. 

Figure 4-11 The Potential Energy Form for Ethane. The midpoint of the range of oj is m =0° and the end points are 180°. The end points and the minima are identical by molecular symmetry and correspond to the stable staggered form.

Figure 4-14 Excess Steiic Energy of the Methyl-Metliyl Coiiforiiiatiori Relative to tlie Metliyl-Hydiogeri Coriforiiia-tion. The Staggered Forms arc Ignored for Simplicity.

In the staggered conformation each C—H bond of one carbon bisects an H—C—H angle of the other carbon... 

FIGURE 3 2 Some commonly used draw mgs of the staggered 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... 

Rotation around carbon-carbon bonds is one of the fastest processes m chemistry Among the ways that we can describe the rate of a process is by its half life which is the length of time it takes for one half of the molecules to react It takes less than 10 s for half of the molecules m a sample of ethane to go from one staggered conformation to another at 25°C... 

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... 

Staggered arrangement of bonds in chair conformation of cyclohexane... 

It IS no accident that sections of our chair cyclohexane drawings resemble saw horse projections of staggered conformations of alkanes The same spatial relationships seen m alkanes carry over to substituents on a six membered ring In the structure... 

Torsional strain destabilization that results when adjacent atoms are not staggered... 

Section 3 1 The most stable conformation of ethane is the staggered conformation It IS approximately 12 kJ/mol (3 kcal/mol) more stable than the eclipsed, which IS the least stable conformation... 

Staggered conformation of ethane (most stable conformation)... 

The difference m energy between the staggered and eclipsed forms is due almost entirely to the torsional strain m the eclipsed conformation At any instant almost all the molecules of ethane reside m the staggered con formation... 

Section 3 2 The two staggered conformations of butane are not equivalent The anti conformation is more stable than the gauche... 

Section 3 3 Higher alkanes adopt a zigzag conformation of the carbon chain m which all the bonds are staggered... 

Like hydrogen peroxide the inorganic substances hydrazine (H2NNH2) and hydroxylamine (H2NOH) possess conformational mobility Wnte stmctural representations or build molecular models of two different staggered conformations of (a) hydrazine and (b) hydroxylamine... 

One of the staggered conformations of 2 methylbutane in Problem 3 17b is more stable than the other Which one is more stable" Why" ... 

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