Using rotation constants to define molecular structures

6 Using rotation constants to define molecular structures 

The primary use of a measured rotation constant is for the calculation of the corresponding moment of inertia, which depends of the structure of the molecule (Eq. 7.1). 

Other symmetrical molecules, such as CS2 and SiH4, also only have one stmctural parameter, and this can be determined from the rotation constant for a single isotopic species, as for a diatomic. Even so, it is necessary to collect sufficient experimental information to correct Bq to Bg, in order to define rg. 

For more complicated molecules these problems are worse. We can extend Eq. 7.11 to cover any number of vibrations by writing 

Non-linear molecules have more rotation constants than hnear ones, and more information is in principle available for each isotopic species, though some of it may uot be easy to obtain. The discrepancies between Bq and Be types of information are important, and we may have to make an inordinate nmnber of measurements in order to calculate a few rehable structural parameters. Cousider, for example, CCXTl2, [13] for which three rotation constants (A, B and C) have been determined experimentally for the ground vibrational state and for the first excited states of aU six vibrations, a total of 21 experimental determinations. From these, the equilibrium rotation constants A., B and Ce can be found. But after aU this effort, these data contain only two independent pieces of information, as 7c = /a + /b for planar body this is indeed found to be so for the equihbrium moments of inertia, though not for those derived from the rotation constants of any of the vibrational states (ground or excited). We thus have iusufficieut data to define the structure, as this requires three parameters (the C=0 and C Tl distances, and an angle). 

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