158
6 Equilibrium Structures from Spectroscopy
quadrupole tensor, the order of magnitude of the difference being about 1° (Kisiel
1998).
6.10 Accuracy of Equilibrium Structures
Assuming that the errors are random, it is possible to use the law of propagation
of errors to estimate the accuracy of an equilibrium structure. In many cases, this
method concludes that the structure is highly accurate. Unfortunately, systematic
errors are dominant. The first approximation to discuss is the Born–Oppenheimer
approximation. Although it is a good approximation, it limits the accuracy of the
structure. In the particular case of diatomic molecules, Sect. 3.11 and Table 3.8, it
has been shown that it is not justified to determine the equilibrium structure with a
precision much higher than about 0.01 pm (one standard deviation) when the breakdown of the Born–Oppenheimer approximation is neglected. This conclusion also
applies to polyatomic molecules because the effect of the breakdown is visible too,
for instance for CO 2 (Teffo and Ogilvie 1993) and perhaps for HC≡CH (Tamassia
et al. 2016) and SbH 3 (see Sect. 9.11). To date, there are no theoretical expressions
that allow the derivation of bond lengths and correction parameters for polyatomic
molecules, but we may extrapolate and conclude that the best reliable accuracy that
can be obtained cannot be much better about 0.01 pm.
The second source of errors is the way the rotation–vibration interaction constants
(α-constants) are obtained. When they are determined experimentally, they are quite
often sensitive to anharmonic resonances and/or Coriolis interactions, see Sect. 6.6.
On the other hand, when they are derived from an ab initio force field, the error is
almost constant and does not effect much the structure (see the example of the semiexperimental structure of 1,1-difluoroethene in Sect. 6.7 and Table 6.9). However, it
has been observed that the level of ab initio calculation should be high enough in
order to avoid random fluctuations.
Finally, the accuracy—or neglect—of higher-order rotation–vibration interaction
constants [γ -constants, see (6.1)], the electronic correction, and the centrifugal distortion correction may also affect the accuracy. A typical example is SO 2 , which has
been studied in great detail in Sect. 6.6. There is no difficulty to take into account the
electronic (Sect. 4.10) and the centrifugal distortion (Sect. 4.8.2) corrections. On the
other hand, taking into account the γ -constants is a big problem because they have
to be determined experimentally and it was done for only a few small polyatomic
molecules (mainly triatomic). It is indeed a tedious task requiring the study of many
overtone and combination levels. Fortunately, it is only for light molecules that the
γ -constants has a significant contribution.
The accuracy is further discussed in Sect. 9.11 from the statistical point of view.
6 Equilibrium Structures from Spectroscopy
quadrupole tensor, the order of magnitude of the difference being about 1° (Kisiel
1998).
6.10 Accuracy of Equilibrium Structures
Assuming that the errors are random, it is possible to use the law of propagation
of errors to estimate the accuracy of an equilibrium structure. In many cases, this
method concludes that the structure is highly accurate. Unfortunately, systematic
errors are dominant. The first approximation to discuss is the Born–Oppenheimer
approximation. Although it is a good approximation, it limits the accuracy of the
structure. In the particular case of diatomic molecules, Sect. 3.11 and Table 3.8, it
has been shown that it is not justified to determine the equilibrium structure with a
precision much higher than about 0.01 pm (one standard deviation) when the breakdown of the Born–Oppenheimer approximation is neglected. This conclusion also
applies to polyatomic molecules because the effect of the breakdown is visible too,
for instance for CO 2 (Teffo and Ogilvie 1993) and perhaps for HC≡CH (Tamassia
et al. 2016) and SbH 3 (see Sect. 9.11). To date, there are no theoretical expressions
that allow the derivation of bond lengths and correction parameters for polyatomic
molecules, but we may extrapolate and conclude that the best reliable accuracy that
can be obtained cannot be much better about 0.01 pm.
The second source of errors is the way the rotation–vibration interaction constants
(α-constants) are obtained. When they are determined experimentally, they are quite
often sensitive to anharmonic resonances and/or Coriolis interactions, see Sect. 6.6.
On the other hand, when they are derived from an ab initio force field, the error is
almost constant and does not effect much the structure (see the example of the semiexperimental structure of 1,1-difluoroethene in Sect. 6.7 and Table 6.9). However, it
has been observed that the level of ab initio calculation should be high enough in
order to avoid random fluctuations.
Finally, the accuracy—or neglect—of higher-order rotation–vibration interaction
constants [γ -constants, see (6.1)], the electronic correction, and the centrifugal distortion correction may also affect the accuracy. A typical example is SO 2 , which has
been studied in great detail in Sect. 6.6. There is no difficulty to take into account the
electronic (Sect. 4.10) and the centrifugal distortion (Sect. 4.8.2) corrections. On the
other hand, taking into account the γ -constants is a big problem because they have
to be determined experimentally and it was done for only a few small polyatomic
molecules (mainly triatomic). It is indeed a tedious task requiring the study of many
overtone and combination levels. Fortunately, it is only for light molecules that the
γ -constants has a significant contribution.
The accuracy is further discussed in Sect. 9.11 from the statistical point of view.