4
1 Introduction
is then used to obtain semiexperimental equilibrium structures both by gas-phase
electron diffraction and by spectroscopy or by combined use of these methods.
There are many reviews devoted to structure determination. However, most of the
time, they limit themselves either to a single experimental technique or to ab initio
calculations. There are very few papers where a critical comparison of the experimental and ab initio techniques is made and where the interplay of these methods
is emphasized. Furthermore, although the techniques are described in great detail,
there is no thorough discussion of the accuracy that can be really achieved.
The first question to answer is which accuracy is desirable. There are three reasons
militating in favor of a high accuracy:
• Theoreticians need accurate structures to check their calculations. Although the
accuracy of ab initio calculations varies wildly, it is possible to define a range from
0.3 pm
1 to better than 0.1 pm. For instance, Ruden et al. (2004) computed the
structure of CO and, using higher-order corrections to the usual coupled cluster
method, they obtained 112.84 pm in fair agreement with the experimental value,
r e = 112.8230(1) pm (Authier 1993). It demonstrates that the progress of ab initio
methods remains dependent of experimental results.
• Inspection of the range of a few bond lengths shows that it is rather small. For
instance, it is only 6 pm for the CH and NH bonds. Thus, to compare the structures
of different molecules, an accuracy significantly better than 1 pm is required.
• The energy of a molecule is sensitive to its structure. Molecular mechanics
programs used to calculate the properties of large molecules are parameterized
against a small number of small molecules whose structure is assumed to be accurate. For instance, the distortion of a C–C single bond by 2 pm “costs” 0.6 kJ mol
−1 ;
the distortion of a ∠(CCC) bond angle by 2°, about 0.4 kJ mol
−1 ; and the torsional
distortion of a CCCC chain by 5°, about 0.2 kJ mol
−1 (Hargittai and Levy 1999).
In order to be able to determine the relative energy of a molecule with an acceptable accuracy (a few kJ mol
–1 ), it is necessary to scale the molecular mechanics
programs (Burkert and Allinger 1982) with molecules whose molecular geometry
is very accurately known.
The next step is to see at which condition such an accuracy can be achieved.
For this goal, we will first analyze the approximations, which are made during the
derivation of the molecular Hamiltonian. It will be one of the goals of Chap. 2. It deals
with the concepts of potential energy surfaces and equilibrium molecular structures.
It also describes quantum chemical computations of structures and force fields.
Chapter 3 is devoted to diatomic molecules. As they are much simpler, a more
sophisticated theory may be used and the bond length is determinable with a much
higher accuracy. Furthermore, it is a good introduction to the more complicated case
of polyatomic molecules.
Chapter 4 is a summary of rotational spectroscopy and the determination of rotational constants from experimental spectra, and Chap. 5 is a short introduction to
1 Along the pm unit, the Å unit is also used in this book for practical reason (1 Å = 100 pm).
1 Introduction
is then used to obtain semiexperimental equilibrium structures both by gas-phase
electron diffraction and by spectroscopy or by combined use of these methods.
There are many reviews devoted to structure determination. However, most of the
time, they limit themselves either to a single experimental technique or to ab initio
calculations. There are very few papers where a critical comparison of the experimental and ab initio techniques is made and where the interplay of these methods
is emphasized. Furthermore, although the techniques are described in great detail,
there is no thorough discussion of the accuracy that can be really achieved.
The first question to answer is which accuracy is desirable. There are three reasons
militating in favor of a high accuracy:
• Theoreticians need accurate structures to check their calculations. Although the
accuracy of ab initio calculations varies wildly, it is possible to define a range from
0.3 pm
1 to better than 0.1 pm. For instance, Ruden et al. (2004) computed the
structure of CO and, using higher-order corrections to the usual coupled cluster
method, they obtained 112.84 pm in fair agreement with the experimental value,
r e = 112.8230(1) pm (Authier 1993). It demonstrates that the progress of ab initio
methods remains dependent of experimental results.
• Inspection of the range of a few bond lengths shows that it is rather small. For
instance, it is only 6 pm for the CH and NH bonds. Thus, to compare the structures
of different molecules, an accuracy significantly better than 1 pm is required.
• The energy of a molecule is sensitive to its structure. Molecular mechanics
programs used to calculate the properties of large molecules are parameterized
against a small number of small molecules whose structure is assumed to be accurate. For instance, the distortion of a C–C single bond by 2 pm “costs” 0.6 kJ mol
−1 ;
the distortion of a ∠(CCC) bond angle by 2°, about 0.4 kJ mol
−1 ; and the torsional
distortion of a CCCC chain by 5°, about 0.2 kJ mol
−1 (Hargittai and Levy 1999).
In order to be able to determine the relative energy of a molecule with an acceptable accuracy (a few kJ mol
–1 ), it is necessary to scale the molecular mechanics
programs (Burkert and Allinger 1982) with molecules whose molecular geometry
is very accurately known.
The next step is to see at which condition such an accuracy can be achieved.
For this goal, we will first analyze the approximations, which are made during the
derivation of the molecular Hamiltonian. It will be one of the goals of Chap. 2. It deals
with the concepts of potential energy surfaces and equilibrium molecular structures.
It also describes quantum chemical computations of structures and force fields.
Chapter 3 is devoted to diatomic molecules. As they are much simpler, a more
sophisticated theory may be used and the bond length is determinable with a much
higher accuracy. Furthermore, it is a good introduction to the more complicated case
of polyatomic molecules.
Chapter 4 is a summary of rotational spectroscopy and the determination of rotational constants from experimental spectra, and Chap. 5 is a short introduction to
1 Along the pm unit, the Å unit is also used in this book for practical reason (1 Å = 100 pm).