150
6 Equilibrium Structures from Spectroscopy
It is preferable to exploit the advantages of the mixed regression method, which
combines, as input, the moments of inertia of the non-deuterated isotopologues and
the ab initio internal coordinates of the hydrogen atoms; see for instance Vogt et al.
(2014).
The semiexperimental method used in conjunction with the mixed estimation
method (see Sect. 9.7), contrary to the purely experimental one, may be used to
determine an accurate structure for medium-sized molecules, as for instance proline
(C 5 H 9 NO 2 17 atoms, 45 independent structural parameters) (Vogt et al. 2017) or
fructose (C 6 H 12 O 6 , 24 atoms, 66 degrees of freedom) (Vogt et al. 2016). This method
is now routinely used for molecules containing only second-period or third-period
elements, but it has also been used with success on molecules with fourth-period
atoms such as bromine, as, for instance, on bromofluoromethane, CH 2 BrF (Puzzarini
et al. 2007). The method can also be used for molecules with an atom as heavy as
Sb [for instance stibine, (Canè et al. 2005)] or even
209 Bi (Jerzembeck et al. 2004).
Further examples are discussed in Chap. 9.
6.8 Extrapolation Method (Kummli et al. 2006, 2010)
There is still another way to obtain an accurate structure by extrapolating the
computed ab initio rotational constants to infinite basis set size. The ab initio equilibrium values of the rotational constants of the parent species X e (X = A, B, C) are first
calculated. For this goal, the ab initio structure is optimized with the coupled cluster
method with single and double excitations and a perturbative treatment of connected
triples [CCSD(T)] with the correlation-consistent polarized weighted core-covalence
n-uple-zeta (cc-pwCVnZ) basis set (n = T, Q), all electrons being correlated (AE), see
Chap. 2. To these X e (T) and X e (Q) values, the rovibrational correction X 0 = X o – X e
is added giving X 0 (T) and X 0 (Q) under the assumption that this rovibrational correction is almost constant, which is generally a good assumption. Then, the rotational
constants X 0 (T) and X 0 (Q) are extrapolated as a function of the computed structural
parameters r e (T) and r e (Q). The intersection of the line with the experimental X 0 of
the parent species gives the extrapolated r e .
As an example, using the data from Craig et al. (2015), the equilibrium structure of
the heavy-atom skeleton of trans-hexatriene was redetermined by different methods
and is given in Table 6.11. The agreement between the different methods is about
0.1 pm for the bond lengths and 0.1° for the angles.
6 Equilibrium Structures from Spectroscopy
It is preferable to exploit the advantages of the mixed regression method, which
combines, as input, the moments of inertia of the non-deuterated isotopologues and
the ab initio internal coordinates of the hydrogen atoms; see for instance Vogt et al.
(2014).
The semiexperimental method used in conjunction with the mixed estimation
method (see Sect. 9.7), contrary to the purely experimental one, may be used to
determine an accurate structure for medium-sized molecules, as for instance proline
(C 5 H 9 NO 2 17 atoms, 45 independent structural parameters) (Vogt et al. 2017) or
fructose (C 6 H 12 O 6 , 24 atoms, 66 degrees of freedom) (Vogt et al. 2016). This method
is now routinely used for molecules containing only second-period or third-period
elements, but it has also been used with success on molecules with fourth-period
atoms such as bromine, as, for instance, on bromofluoromethane, CH 2 BrF (Puzzarini
et al. 2007). The method can also be used for molecules with an atom as heavy as
Sb [for instance stibine, (Canè et al. 2005)] or even
209 Bi (Jerzembeck et al. 2004).
Further examples are discussed in Chap. 9.
6.8 Extrapolation Method (Kummli et al. 2006, 2010)
There is still another way to obtain an accurate structure by extrapolating the
computed ab initio rotational constants to infinite basis set size. The ab initio equilibrium values of the rotational constants of the parent species X e (X = A, B, C) are first
calculated. For this goal, the ab initio structure is optimized with the coupled cluster
method with single and double excitations and a perturbative treatment of connected
triples [CCSD(T)] with the correlation-consistent polarized weighted core-covalence
n-uple-zeta (cc-pwCVnZ) basis set (n = T, Q), all electrons being correlated (AE), see
Chap. 2. To these X e (T) and X e (Q) values, the rovibrational correction X 0 = X o – X e
is added giving X 0 (T) and X 0 (Q) under the assumption that this rovibrational correction is almost constant, which is generally a good assumption. Then, the rotational
constants X 0 (T) and X 0 (Q) are extrapolated as a function of the computed structural
parameters r e (T) and r e (Q). The intersection of the line with the experimental X 0 of
the parent species gives the extrapolated r e .
As an example, using the data from Craig et al. (2015), the equilibrium structure of
the heavy-atom skeleton of trans-hexatriene was redetermined by different methods
and is given in Table 6.11. The agreement between the different methods is about
0.1 pm for the bond lengths and 0.1° for the angles.