154
6 Equilibrium Structures from Spectroscopy
ε = I 0 − I e has an inverse proportionality with the vibrational frequencies and, as
the complexes have several low-frequency intermolecular vibrations, the rovibration
correction is much larger than for semirigid molecules. For the same reason, it is
difficult to calculate the rovibrational correction accurately from an ab initio cubic
force field. A typical example is H 2 O· · · HF (Demaison and Liévin 2008). The rovibration correction is 2.4% and 3.1% of the corresponding moments of inertia I b and
I c , respectively, whereas for a semirigid molecule with similar rotational constants,
the rovibrational corrections would be an order of magnitude smaller; see Table 6.2.
For this reason, as expected, the empirical effective structure is rather far from the
equilibrium structure: r 0 (F· · · O) = 267.6(3) pm and β 0 = 143.2(4)° to be compared
with r e (F· · · O) = 264.9 pm and β e = 132.7° (β is the angle between the F–O
direction and the bisecting line of the HOH angle).
To try to obtain structures close to the equilibrium ones, Kisiel (2003) tested the
applicability of the mass-dependent method (r m ) and obtained encouraging results.
Unfortunately, as explained in Sect. 6.5, this method often gives unreliable results
because of the large number of parameters to be determined. However, it can be
significantly improved by the use of predicates; see Sects. 6.5 and 9.7.
6.9.4 Distance Between the Monomers, Pseudo-Diatomic
Approximation
It is possible to calculate the intermolecular structural parameters using a formula
that expresses the moments of inertia of the complex in terms of intermolecular
coordinates and the known moments of inertia of the free monomers, assuming that
their structure is not significantly affected by the complex formation (Leopold 2012).
As an example, consider a complex formed from a linear molecule 1 and a symmetric
top 2; see Fig. 6.3. r CM is the distance between the center of masses of the monomers
and the angles θ 1 and θ 2 describe their large-amplitude motion in the symmetry
plane. For a prolate top, the vibrationally averaged moments of inertia I bb and I cc
can be written
I bb = I cc = μ D
r
2
CM
+ I
(1)
bb
1 +
cos
2
θ 1
Fig. 6.3 A complex formed from a linear molecule and a symmetric top
6 Equilibrium Structures from Spectroscopy
ε = I 0 − I e has an inverse proportionality with the vibrational frequencies and, as
the complexes have several low-frequency intermolecular vibrations, the rovibration
correction is much larger than for semirigid molecules. For the same reason, it is
difficult to calculate the rovibrational correction accurately from an ab initio cubic
force field. A typical example is H 2 O· · · HF (Demaison and Liévin 2008). The rovibration correction is 2.4% and 3.1% of the corresponding moments of inertia I b and
I c , respectively, whereas for a semirigid molecule with similar rotational constants,
the rovibrational corrections would be an order of magnitude smaller; see Table 6.2.
For this reason, as expected, the empirical effective structure is rather far from the
equilibrium structure: r 0 (F· · · O) = 267.6(3) pm and β 0 = 143.2(4)° to be compared
with r e (F· · · O) = 264.9 pm and β e = 132.7° (β is the angle between the F–O
direction and the bisecting line of the HOH angle).
To try to obtain structures close to the equilibrium ones, Kisiel (2003) tested the
applicability of the mass-dependent method (r m ) and obtained encouraging results.
Unfortunately, as explained in Sect. 6.5, this method often gives unreliable results
because of the large number of parameters to be determined. However, it can be
significantly improved by the use of predicates; see Sects. 6.5 and 9.7.
6.9.4 Distance Between the Monomers, Pseudo-Diatomic
Approximation
It is possible to calculate the intermolecular structural parameters using a formula
that expresses the moments of inertia of the complex in terms of intermolecular
coordinates and the known moments of inertia of the free monomers, assuming that
their structure is not significantly affected by the complex formation (Leopold 2012).
As an example, consider a complex formed from a linear molecule 1 and a symmetric
top 2; see Fig. 6.3. r CM is the distance between the center of masses of the monomers
and the angles θ 1 and θ 2 describe their large-amplitude motion in the symmetry
plane. For a prolate top, the vibrationally averaged moments of inertia I bb and I cc
can be written
I bb = I cc = μ D
r
2
CM
+ I
(1)
bb
1 +
cos
2
θ 1
Fig. 6.3 A complex formed from a linear molecule and a symmetric top