Modern Spectroscopy

5.4 STRUCTURE DETERMINATION FROM ROTATIONAL CONSTANTS 133
Figure 5.19 The r s structure of aniline
dealing with equilibrium, rather than zero-point, structure is apparent. Determination of A e
and B e for 2 H 2CO, for which equilibrium structure is identical to that of 1 H 2CO, would allow
a complete structure determination, three structural parameters being found from four
rotational constants.
However, even for a small molecule such as H 2CO, determination of the rotational
constants in the v ¼ 1 levels of all the vibrations presents considerable difficulties. In larger
molecules it may be possible to determine only A 0 , B 0 and C 0. In such cases the simplest
way to determine the structure is to ignore the differences from A e, B e and C e and make
sufficient isotopic substitutions to give a complete, but approximate, structure, called the r 0
structure.
An improvement on the r 0 structure is the substitution structure, or r s structure. This is
obtained using the so-called Kraitchman equations, which give the coordinates of an atom,
which has been isotopically substituted, in relation to the principal inertial axes of the
molecule before substitution. The substitution structure is also approximate but is nearer to
the equilibrium structure than is the zero-point structure.
One of the largest molecules for which an r s structure has been obtained is aniline, shown
in Figure 5.19. The benzene ring shows small deviations from a regular hexagon in the
angles but no meaningful deviations in the bond lengths. As might be expected, by
comparison with the pyramidal NH 3 molecule, the plane of the NH 2 group is not coplanar
with the rest of the molecule.
Worked example 5.2
XY r s(XY)=A˚ XYZ (ff XYZ) s=deg
NH1 1.001 0.01 H1NH7 113.1 2
C1N 1.402 0.002 C6C1C2 119.4 0.2
C1C2 1.397 0.003 C1C2C3 120.1 0.2
C2C3 1.394 0.004 H2C2C3 120.1 0.2
C3C4 1.396 0.002 C2C3C4 120.7 0.1
C2H2 1.082 0.004 H3C3C2 119.4 0.1
C3H3 1.083 0.002 C3C4C5 118.9 0.1
C4H4 1.080 0.002
Note: out-of-plane angle of NH2 is 37.5 2
Question.
(a) From the value for B 0 of 1.923 604 0.000 027 cm 71 , obtained from the rotational Raman
spectrum of 14 N 15 N, calculate the bond length r 0.
(b) Why does it differ from r 0 for 14 N 2?