7.14 Conclusion
199
7.14 Conclusion
The thermal-average structures (r g and r a ) being depending from the temperature of
experiment cannot be directly used to benchmark structural data from other methods.
The equilibrium structure can be derived from electron diffraction data taking into
account vibrational corrections to the thermal-average internuclear distances. The
use of harmonic vibrational corrections calculated in rectilinear coordinates, which
are overestimated for the bonded internuclear distances and underestimated for the
non-bonded distances, leads to strong deformation of the refined structure (r h0 , r
h
e or
r α ). On the contrary, the r h1 structure derived with harmonic vibrational corrections
taking into account nonlinear kinematic effects is characterized by overestimated
bonded distances.
Anharmonic vibrational corrections being noticeably larger than the estimated
experimental errors have to be taken into account for the precise determination of
molecular structure (semiexperimental equilibrium structure, r
se
e ). These corrections
can be estimated with appropriate accuracy using an anharmonic force field from
high-level quantum-chemical computations.
The anharmonic approximation (static model) is good enough also for the study
of non-rigid molecules if the large-amplitude motion has harmonic character. Otherwise, the method of pseudo-conformers based on adiabatic separation of smallamplitude vibrations and large-amplitude motion(s) should be used for an accurate
structure determination.
The accuracy of semiexperimental equilibrium structure derived from electron
diffraction data can reach a few tenths of pm for the bond lengths and a few tenths
of degree for the bond angles.
References
Andersen B, Seip HM, Strand TG, Stølevik R (1969) Computer programs for the structure determination of gaseous molecules from electron diffraction data. Acta Chem Scand
23:3224–3234
Bartell LS (1955) Effects of anharmonicity of vibration on the diffraction of electrons by free
molecules. J Chem Phys 23:1219–1222
Bartell LS (1963) Calculation of mean atomic positions in vibrating polyatomic molecules. J Chem
Phys 38:1827–1833
Bartell LS (1988) Status of electron scattering theory with respect to accuracy in structure analysis.
In: Hargittai I, Hargittai M (eds) Stereochemical applications of gas-phase electron diffraction.
Part A. The electron diffraction technique. VCH Publishers Inc, New York, pp 55–84
Bastiansen O, Hassel O, Risberg E (1955) The Oslo electron diffraction units for gas work. Acta
Chem Scand 9:232–238
Bastiansen O, Kveseth K, Møllendal H (1979) Structure of molecules with large amplitude motion
as determined from electron-diffraction studies in the gas phase. Top Curr Chem 81:99–172
Belyakov AV, Baskakov AA, Berger RJF, Mitzel NW, Oberhammer H, Arnason I, Wallevik SÒ
(2012) Molecular structure and conformational preferences of gaseous 1-iodo-1-silacyclohexane.
J Mol Struct 1012:126–130
199
7.14 Conclusion
The thermal-average structures (r g and r a ) being depending from the temperature of
experiment cannot be directly used to benchmark structural data from other methods.
The equilibrium structure can be derived from electron diffraction data taking into
account vibrational corrections to the thermal-average internuclear distances. The
use of harmonic vibrational corrections calculated in rectilinear coordinates, which
are overestimated for the bonded internuclear distances and underestimated for the
non-bonded distances, leads to strong deformation of the refined structure (r h0 , r
h
e or
r α ). On the contrary, the r h1 structure derived with harmonic vibrational corrections
taking into account nonlinear kinematic effects is characterized by overestimated
bonded distances.
Anharmonic vibrational corrections being noticeably larger than the estimated
experimental errors have to be taken into account for the precise determination of
molecular structure (semiexperimental equilibrium structure, r
se
e ). These corrections
can be estimated with appropriate accuracy using an anharmonic force field from
high-level quantum-chemical computations.
The anharmonic approximation (static model) is good enough also for the study
of non-rigid molecules if the large-amplitude motion has harmonic character. Otherwise, the method of pseudo-conformers based on adiabatic separation of smallamplitude vibrations and large-amplitude motion(s) should be used for an accurate
structure determination.
The accuracy of semiexperimental equilibrium structure derived from electron
diffraction data can reach a few tenths of pm for the bond lengths and a few tenths
of degree for the bond angles.
References
Andersen B, Seip HM, Strand TG, Stølevik R (1969) Computer programs for the structure determination of gaseous molecules from electron diffraction data. Acta Chem Scand
23:3224–3234
Bartell LS (1955) Effects of anharmonicity of vibration on the diffraction of electrons by free
molecules. J Chem Phys 23:1219–1222
Bartell LS (1963) Calculation of mean atomic positions in vibrating polyatomic molecules. J Chem
Phys 38:1827–1833
Bartell LS (1988) Status of electron scattering theory with respect to accuracy in structure analysis.
In: Hargittai I, Hargittai M (eds) Stereochemical applications of gas-phase electron diffraction.
Part A. The electron diffraction technique. VCH Publishers Inc, New York, pp 55–84
Bastiansen O, Hassel O, Risberg E (1955) The Oslo electron diffraction units for gas work. Acta
Chem Scand 9:232–238
Bastiansen O, Kveseth K, Møllendal H (1979) Structure of molecules with large amplitude motion
as determined from electron-diffraction studies in the gas phase. Top Curr Chem 81:99–172
Belyakov AV, Baskakov AA, Berger RJF, Mitzel NW, Oberhammer H, Arnason I, Wallevik SÒ
(2012) Molecular structure and conformational preferences of gaseous 1-iodo-1-silacyclohexane.
J Mol Struct 1012:126–130