Linear molecules such as OCS andHCCCl have spectra similar
todiatomicsIn diatomics as well as lineartriatomics, IA = IB; IC =
0 where IA, IBand IC are the three moments ofinertia of molecules
along threeindependent axes of rotation
Just as any translation can bedecomposed into three
independentcomponents along three axes such asx, y and z, any
rotation can bedecomposed into rotations alongthree axes A, B, and
CThe way to choose these axes is tohave the simplest values of IA,
IB andIC
Since triatomics are heavier than theconstituent diatomics,
theirmoments of inertia are larger and thevalues of rotational
constants, B, aresmaller, in the range of 1 cm-1The value of IA or
IB determinedfrom the B value gives the totallength of the
triatomic
To determine the two bond lengthsin the linear triatomic, we
need todetermine the moment of inertia IA'of an isotope of the
triatomicFrom two values of IA and IA' , wecan determine the two
bond lengths
The rotational spectra ofasymmetric molecules for whom IA IB IC
can be quite complicated.For symmetric tops, two momentsof inertia
are equal ie.,
IA = IB IC ; IC 0
In CH3F for example, the mainsymmetry axis is the C F axis.
Weneed two quantum numbers todescribe the rotational motion
withrespect to IA and IC respectively
Let J represent the total angularmomentum of the molecule and
Kthe angular momentum with respectto the C F axis of the
symmetrictop.J takes on integer values and K cannot be greater than
JThe (2J + 1) degeneracy isexpressed through the 2J + 1 valuesthat
K can take
Let J represent the total angularmomentum of the molecule and
Kthe angular momentum with respectto the C F axis of the
symmetrictop.J takes on integer values and K cannot be greater than
JThe (2J + 1) degeneracy isexpressed through the 2J + 1 valuesthat
K can take
There is only one mode of vibration for adiatomic molecule, the
bond stretch.In polyatomic molecules there are severalmodes of
vibration because all the bondlengths and angles may change and
thevibrational spectra are very complex.Nonetheless, we shall see
that infrared andRaman spectroscopy can be used to
obtaininformation about the structure of systemsas large as animal
and plant tissues.
Normal modesA normal mode is an independent,synchronous motion
of atoms orgroups of atoms that may be excitedwithout leading to
the excitation ofany other normal mode. The numberof normal modes
is 3N-6 (fornonlinear molecules) or 3N-5 (linearmolecules).
