7.11 Accuracy of Structure Determinations …
195
structural differences, etc.). The estimation of these errors is very difficult or even
impossible. Therefore, the total systematic errors are rather underestimated than real.
There are some comprehensive studies revealing the highest accuracy of vibrational
correction calculations to be of a few percent of the correction value itself (see,
for instance, Vogt et al. 2011b). Furthermore, even the less accurate calculations of
vibrational corrections with uncertainties of 10–20% increase the systematic error
(for instance, for the C–C and C–N bond lengths by ≈0.1 pm only).
Comparison of structure data determined by different experimental methods
seems to be the unique way to estimate the real accuracy of the determined structures, as long as they have the same physical meaning. Unfortunately, this way is too
expensive and not always possible to be universal. Several benchmark studies (see,
for instance, Vogt et al. 2013, 2014) demonstrate remarkable agreement between
the semiexperimental equilibrium structures determined by electron diffraction and
microwave spectroscopy and the structures calculated by ab initio methods (see
Table 7.4 and Fig. 7.13 with data for 5-methyl-1H-pyrimidine-2,4-dione (thymine)
as an example).
In the best cases, the accuracy of the r
se
e electron diffraction structure is estimated
to be of a few tenths of pm for the bond lengths and a few tenths of degree for the
bond angles, except for parameters containing hydrogen atom(s).
7.12 Software
There are some computer programs for the processing of experimental data and for
the structural analysis by a least-squares method. The oldest and very remarkable
program package is KCED published by Andersen et al. (1969). Later, Gundersen
et al. (1981) wrote a program for the structural analysis of molecules with largeamplitude motion. The processing of experimental data recorded on image plates
can be carried out by means of the PIMAG program written by Gundersen et al.
(2007). Because the Norwegian scientists kindly also provided the source code of
their programs to the electron diffraction community, there are some new versions of
these programs adapted to the specifics of data processing in different laboratories, for
example KCED version modified by Belyakov et al. (2012), the program PIMAGVIEW coupled with a graphical user interface by Vogt et al. (2011a), and more.
Moreover, there is also some other software used in modern electron diffraction
studies, for example the PLATE program for primary processing of experimental data
(Kochikov et al. 2008), the ed@ed program for the least-squares structural analysis
(Hinchley et al. 2004), the UNEX program package for complete treatment of electron
diffraction data (Vishnevskiy 2019), the software package Symm/Disp/Eldiff/Large
for structural analysis including calculations of vibrational amplitudes, vibrational
corrections to experimental internuclear distances and rovibrational corrections to
ground-state rotational constants (see Kochikov and Tarasov 2003; Kochikov et al.
1999, 2002, etc.). The SHRINK program written by Sipachev (1985, 2000) is more
195
structural differences, etc.). The estimation of these errors is very difficult or even
impossible. Therefore, the total systematic errors are rather underestimated than real.
There are some comprehensive studies revealing the highest accuracy of vibrational
correction calculations to be of a few percent of the correction value itself (see,
for instance, Vogt et al. 2011b). Furthermore, even the less accurate calculations of
vibrational corrections with uncertainties of 10–20% increase the systematic error
(for instance, for the C–C and C–N bond lengths by ≈0.1 pm only).
Comparison of structure data determined by different experimental methods
seems to be the unique way to estimate the real accuracy of the determined structures, as long as they have the same physical meaning. Unfortunately, this way is too
expensive and not always possible to be universal. Several benchmark studies (see,
for instance, Vogt et al. 2013, 2014) demonstrate remarkable agreement between
the semiexperimental equilibrium structures determined by electron diffraction and
microwave spectroscopy and the structures calculated by ab initio methods (see
Table 7.4 and Fig. 7.13 with data for 5-methyl-1H-pyrimidine-2,4-dione (thymine)
as an example).
In the best cases, the accuracy of the r
se
e electron diffraction structure is estimated
to be of a few tenths of pm for the bond lengths and a few tenths of degree for the
bond angles, except for parameters containing hydrogen atom(s).
7.12 Software
There are some computer programs for the processing of experimental data and for
the structural analysis by a least-squares method. The oldest and very remarkable
program package is KCED published by Andersen et al. (1969). Later, Gundersen
et al. (1981) wrote a program for the structural analysis of molecules with largeamplitude motion. The processing of experimental data recorded on image plates
can be carried out by means of the PIMAG program written by Gundersen et al.
(2007). Because the Norwegian scientists kindly also provided the source code of
their programs to the electron diffraction community, there are some new versions of
these programs adapted to the specifics of data processing in different laboratories, for
example KCED version modified by Belyakov et al. (2012), the program PIMAGVIEW coupled with a graphical user interface by Vogt et al. (2011a), and more.
Moreover, there is also some other software used in modern electron diffraction
studies, for example the PLATE program for primary processing of experimental data
(Kochikov et al. 2008), the ed@ed program for the least-squares structural analysis
(Hinchley et al. 2004), the UNEX program package for complete treatment of electron
diffraction data (Vishnevskiy 2019), the software package Symm/Disp/Eldiff/Large
for structural analysis including calculations of vibrational amplitudes, vibrational
corrections to experimental internuclear distances and rovibrational corrections to
ground-state rotational constants (see Kochikov and Tarasov 2003; Kochikov et al.
1999, 2002, etc.). The SHRINK program written by Sipachev (1985, 2000) is more