198
7 Molecular Structures from Gas-Phase Electron Diffraction
such as r g , r a , and r s , are thermal-average or have no clear physical meaning. Unfortunately, there are not many equilibrium structures r e , although they are necessary
to benchmark the structure data obtained by different methods and, thus, to estimate real accuracy of structure determinations. Particularly for the large molecules,
the semiexperimental structures are often derived taking into account only kinematic and harmonic vibrational effects (r h1 structures) due to great efforts to calculate the anharmonic force fields. Many such examples can be found in the recently
published monograph by Vogt and Vogt (2019). The r h1 bond lengths are overestimated in comparison with the r
se
e values due to the neglect of anharmonic vibrational
corrections r 3 (see Sect. 7.8). Due to the power of modern computers, it became
possible to calculate the cubic force fields at an appropriate level of theory even for
large molecules. In these cases, the semiexperimental equilibrium bond lengths can
be estimated from the published r h1 values as follows: r
se
e = r h1 − r 3 . As an
example, the r
se
e bond lengths of bis(acetylacetonato)magnesium are derived from
the published r h1 values (Zhakharov et al. 2004) by taking into account the anharmonic vibrational corrections of up to 2.1 pm (for the Mg–O term). The results are
presented in Table 7.5 together with a computed structure of CCSD(T)_ae/CVQZ
quality. The equilibrium bond lengths r
se
e being close to computed values r
BO
e seem
to be noticeably more accurate than the published r h1 values.
Table 7.5 Equilibrium structure of bis(acetylacetonato)magnesium (bond lengths r and
anharmonic vibrational corrections r 3 in pm, and bond angles ∠ in °; see Fig. 7.14 for molecular
model)
Parameter
r h1
a
r 3 b
r se
e
c
r BO
e
d
r(Mg–O)
196.6(4)
2.1
194.5(4)
193.5 0
r(O–C)
127.9(3)
0.6
127.3(3)
127.0 2
r(C–C (ring))
140.8(3)
0.8
140.0(3)
140.3 7
r(C–C(methyl))
153.4(4)
1.6
151.8(4)
150.4 4
r(C(methyl)–H)
109.9(4)
1.7
108.1(4)
108.8 0
∠(O–Mg–O)
93.3(4)
93.2 2
∠(C–C–C (ring))
125.4(12)
124.9 9
∠(C–C–O (ring))
124.8 0
∠(O–C–C(methyl))
116.2(5)
116.1 1
a Zhakharov et al. (2004)
b Anharmonic vibrational corrections calculated according to algorithm by Sipachev (2000) from
the cubic force field computed at the B3LYP/VTZ level of theory
c Semiexperimental equilibrium structure estimated from the published by Zhakharov et al. (2004)
r h1 structure taking into account anharmonic vibrational effects
d The r BO
e structure of CCSD(T)_ae/CVQZ quality was estimated as r BO
e = r e (CCSD(T)/VTZ) +
[r e (MP2/VQZ) − r e (MP2/VTZ)] + [r e (MP2_ae/CVTZ) − r e (MP2/CVTZ)]; for significance of
this structure, see Sects. 2.10 and 2.11
7 Molecular Structures from Gas-Phase Electron Diffraction
such as r g , r a , and r s , are thermal-average or have no clear physical meaning. Unfortunately, there are not many equilibrium structures r e , although they are necessary
to benchmark the structure data obtained by different methods and, thus, to estimate real accuracy of structure determinations. Particularly for the large molecules,
the semiexperimental structures are often derived taking into account only kinematic and harmonic vibrational effects (r h1 structures) due to great efforts to calculate the anharmonic force fields. Many such examples can be found in the recently
published monograph by Vogt and Vogt (2019). The r h1 bond lengths are overestimated in comparison with the r
se
e values due to the neglect of anharmonic vibrational
corrections r 3 (see Sect. 7.8). Due to the power of modern computers, it became
possible to calculate the cubic force fields at an appropriate level of theory even for
large molecules. In these cases, the semiexperimental equilibrium bond lengths can
be estimated from the published r h1 values as follows: r
se
e = r h1 − r 3 . As an
example, the r
se
e bond lengths of bis(acetylacetonato)magnesium are derived from
the published r h1 values (Zhakharov et al. 2004) by taking into account the anharmonic vibrational corrections of up to 2.1 pm (for the Mg–O term). The results are
presented in Table 7.5 together with a computed structure of CCSD(T)_ae/CVQZ
quality. The equilibrium bond lengths r
se
e being close to computed values r
BO
e seem
to be noticeably more accurate than the published r h1 values.
Table 7.5 Equilibrium structure of bis(acetylacetonato)magnesium (bond lengths r and
anharmonic vibrational corrections r 3 in pm, and bond angles ∠ in °; see Fig. 7.14 for molecular
model)
Parameter
r h1
a
r 3 b
r se
e
c
r BO
e
d
r(Mg–O)
196.6(4)
2.1
194.5(4)
193.5 0
r(O–C)
127.9(3)
0.6
127.3(3)
127.0 2
r(C–C (ring))
140.8(3)
0.8
140.0(3)
140.3 7
r(C–C(methyl))
153.4(4)
1.6
151.8(4)
150.4 4
r(C(methyl)–H)
109.9(4)
1.7
108.1(4)
108.8 0
∠(O–Mg–O)
93.3(4)
93.2 2
∠(C–C–C (ring))
125.4(12)
124.9 9
∠(C–C–O (ring))
124.8 0
∠(O–C–C(methyl))
116.2(5)
116.1 1
a Zhakharov et al. (2004)
b Anharmonic vibrational corrections calculated according to algorithm by Sipachev (2000) from
the cubic force field computed at the B3LYP/VTZ level of theory
c Semiexperimental equilibrium structure estimated from the published by Zhakharov et al. (2004)
r h1 structure taking into account anharmonic vibrational effects
d The r BO
e structure of CCSD(T)_ae/CVQZ quality was estimated as r BO
e = r e (CCSD(T)/VTZ) +
[r e (MP2/VQZ) − r e (MP2/VTZ)] + [r e (MP2_ae/CVTZ) − r e (MP2/CVTZ)]; for significance of
this structure, see Sects. 2.10 and 2.11