160
6 Equilibrium Structures from Spectroscopy
Rovibrational spectroscopy is considered to be the best method to determine
accurate equilibrium structures, but it requires an extremely thorough analysis of the
spectra to avoid contamination of the moments of inertia by resonances. Such an
analysis requires time and expertise, and one is never sure that all resonances have
been correctly taken into account. For this reason, this method is limited to small
molecules.
The semiexperimental method combined with the mixed regression is probably
the fastest and easiest method to determine accurate structures of medium-sized
molecules.
Estimating the accuracy of a structure is difficult. This is discussed in Chap. 9
and, more particularly, Sect. 9.11.
6.13 Appendices
6.13.1 Kraitchman’s Equations for an Asymmetric Top
Molecule
For the treatment of the general asymmetric rotor, it is convenient to use the planar
moment tensor P which is a 3 × 3 matrix. For the parent molecule in its principal
axis system, P is diagonal and its elements are
P a = P aa =
1
2
(−I a + I b + I c ) =
m i a
2
i
P ab =
m i a i b i = 0
The other elements are obtained by cyclic permutation of a, b, c. Using the
definition of the center of mass
x
i = x i −
m i x i
m i
with x = a, b, c
one sees that the elements of the P
tensor of the substituted molecule with respect
of the principal axis system of the parent molecule are
P
aa = P a + μa
2
P
ab = μab
The eigenvalues of P
give the planar principal moments P
x (x = a, b, c), which
are known experimental values
6 Equilibrium Structures from Spectroscopy
Rovibrational spectroscopy is considered to be the best method to determine
accurate equilibrium structures, but it requires an extremely thorough analysis of the
spectra to avoid contamination of the moments of inertia by resonances. Such an
analysis requires time and expertise, and one is never sure that all resonances have
been correctly taken into account. For this reason, this method is limited to small
molecules.
The semiexperimental method combined with the mixed regression is probably
the fastest and easiest method to determine accurate structures of medium-sized
molecules.
Estimating the accuracy of a structure is difficult. This is discussed in Chap. 9
and, more particularly, Sect. 9.11.
6.13 Appendices
6.13.1 Kraitchman’s Equations for an Asymmetric Top
Molecule
For the treatment of the general asymmetric rotor, it is convenient to use the planar
moment tensor P which is a 3 × 3 matrix. For the parent molecule in its principal
axis system, P is diagonal and its elements are
P a = P aa =
1
2
(−I a + I b + I c ) =
m i a
2
i
P ab =
m i a i b i = 0
The other elements are obtained by cyclic permutation of a, b, c. Using the
definition of the center of mass
x
i = x i −
m i x i
m i
with x = a, b, c
one sees that the elements of the P
tensor of the substituted molecule with respect
of the principal axis system of the parent molecule are
P
aa = P a + μa
2
P
ab = μab
The eigenvalues of P
give the planar principal moments P
x (x = a, b, c), which
are known experimental values