Chapter 6
Equilibrium Structures
from Spectroscopy
Abstract The determination of the geometry of a molecule from its rotational
constants is reviewed in detail. First, the different empirical methods are critically examined. Then, the different ways to determine an equilibrium structure
are described. A particular emphasis is put on the semiexperimental method that
combines ground-state experimental rotational constants and computed ab initio
rovibrational corrections. The accuracy of the different methods is discussed.
6.1 Introduction
As shown in Chaps. 3 and 4, the structural information is contained in the equilibrium
moments of inertia that are reciprocals of the equilibrium rotational constants. Spectroscopic methods are extremely accurate and permit obtaining rotational constants
with eight or more significant digits and, in most cases, a theory exists that allows
one to fit the spectra to within the uncertainties of the most accurate observations.
One might think that the equilibrium structure of a molecule can be obtained with a
precision comparable to that of the rotational constants. However, there are two difficulties: (i) even in its ground vibrational state, a molecule undergoes zero-point vibrational motions that induce vibration–rotation interactions making the extraction of an
accurate equilibrium structure from experimental rotational constants a difficult task;
(ii) a molecule has at most three different rotational constants (two for a symmetric
molecule and only one for a linear molecule) and the number of independent structural
parameters is often much larger, unless the molecule has the formula XY n and sufficiently high symmetry, as for the linear molecules XY 2 (e.g., CO 2 ) or the asymmetric
molecules XY 2 (e.g., SO 2 ). However, based on the Born–Oppenheimer approximation (see Sect. 2.3), the equilibrium structure is isotopically invariant and additional
information may be supplied by the rotational constants of isotopologues. In theory,
rotational constants of isotopologues solve the problem. However, in practice, it is
not easy because there are experimental as well as computational difficulties.
Sections 6.2 and 6.3 explain how to obtain equilibrium rotational constants (see
also Chap. 4). The next Sects. 6.4 and 6.5, describe the different ways to determine
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_6
127
Equilibrium Structures
from Spectroscopy
Abstract The determination of the geometry of a molecule from its rotational
constants is reviewed in detail. First, the different empirical methods are critically examined. Then, the different ways to determine an equilibrium structure
are described. A particular emphasis is put on the semiexperimental method that
combines ground-state experimental rotational constants and computed ab initio
rovibrational corrections. The accuracy of the different methods is discussed.
6.1 Introduction
As shown in Chaps. 3 and 4, the structural information is contained in the equilibrium
moments of inertia that are reciprocals of the equilibrium rotational constants. Spectroscopic methods are extremely accurate and permit obtaining rotational constants
with eight or more significant digits and, in most cases, a theory exists that allows
one to fit the spectra to within the uncertainties of the most accurate observations.
One might think that the equilibrium structure of a molecule can be obtained with a
precision comparable to that of the rotational constants. However, there are two difficulties: (i) even in its ground vibrational state, a molecule undergoes zero-point vibrational motions that induce vibration–rotation interactions making the extraction of an
accurate equilibrium structure from experimental rotational constants a difficult task;
(ii) a molecule has at most three different rotational constants (two for a symmetric
molecule and only one for a linear molecule) and the number of independent structural
parameters is often much larger, unless the molecule has the formula XY n and sufficiently high symmetry, as for the linear molecules XY 2 (e.g., CO 2 ) or the asymmetric
molecules XY 2 (e.g., SO 2 ). However, based on the Born–Oppenheimer approximation (see Sect. 2.3), the equilibrium structure is isotopically invariant and additional
information may be supplied by the rotational constants of isotopologues. In theory,
rotational constants of isotopologues solve the problem. However, in practice, it is
not easy because there are experimental as well as computational difficulties.
Sections 6.2 and 6.3 explain how to obtain equilibrium rotational constants (see
also Chap. 4). The next Sects. 6.4 and 6.5, describe the different ways to determine
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_6
127