MOLECULAR SHAPES 145 



ciples, i.e., quantum mechanical theory of these potential barriers. A number of 

 us have played with the problem and I know most of my calculations are still 

 in the file drawer or in the waste basket and I think that is where they belong. 

 We do know a great deal about this subject from the interpretation of experi- 

 mental data; initially, mostly from thermodynamic measurements and then 

 statistical-mechanical interpretations of them, and now more recently from 

 molecular spectroscopy, particularly in the microwave range. We know a great 

 deal about the potential energy effects with respect to internal rotation and it is 

 that information that I will be mentioning this morning. 



I am afraid I will not be able to give due credit at all points to the proper 

 authors, but I would like to mention at this time that Professor Aston and his 

 group at Pennsylvania State University, Professor Yost at the California Insti- 

 tute of Technology, Professor Gwinn on our staff at Berkeley, Professors Wilson 

 and Kistiakowsky at Harvard and others, in addition to many graduate stu- 

 dents who worked with me, have contributed to the sort of information I am 

 going to mention. 



To come down to specific cases, let us consider the parent substance for this 

 problem, namely, ethane, with just a single bond between two carbon atoms 

 and with only hydrogen atoms attached. 



There are two configurations we will consider at length, and these are best 

 visualized by sighting down the line connecting the carbon atoms of ethane. 

 The internal rotation problem is concerned with the orientation of the hydrogen 

 atoms of one CH:i group relative to those of the other CH3 group. If the H atoms 

 are superimposed (sighting down the carbon-carbon bond), the configuration is 

 called "eclipsed." If the H atoms of one end fall just between the atoms at the 

 other end (as viewed down the carbon-carbon bond), the configuration is called 

 ^'staggered." 



Now, we know that this so-called staggered orientation about the single bond 

 is the low energy one. Notice that rotating one methyl group relative to the 

 other restores this low energy configuration after a rotation of either 120° or 

 240°. Hence this low potential energy form corresponds to the angles of zero, 

 120°, 240°, if we plot energy against this rotation angle. The eclipsed configura- 

 tion is about 3 kilocalories higher and corresponds to angles of 60°, 180°, and 

 300° on this plot. 



Connecting these high and low energy points with a smooth curve, we ob- 

 tain a potential energy plot of the energy of the molecule with respect to this 

 angle of rotation. As nearly as we can tell, this curve is well represented by a 

 simple sine curve. Those efjforts which have been made to expand this in Fourier 

 series and find higher terms, show that the higher terms are zero within experi- 

 mental error, so that I am sure there is little error in using just the sine curv^e 

 for this purpose. This is just a starting point. Let me discuss a few other simple 

 modifications of this structure which may represent units that are at least of a 

 type to be of interest in the biologically important substances. 



