9.11 Accuracy of the Structural Parameters
261
Example 14 Another interesting illustration is phenylacetylene, C 6 H 5 C≡CH
(Rudolph et al. 2013). Its structure is defined by 13 independent parameters and
its semiexperimental structure was fitted with different weighting methods, with the
help of three different force fields, and using the rotational constants of 39 isotopologues including many deuterated ones. In this particular case, differently deuterated isotopologues are useful because their rovibrational contribution is significantly
different mitigating the effect of systematic errors. Furthermore, the great number of
data (104 degrees of freedom) gives us some confidence in the reliability of the standard deviations of the fit. Finally, these semiexperimental structures were compared to
a very accurate ab initio Born–Oppenheimer structure. The results given in Table 9.11
are fully compatible. This example gives an idea of the accuracy that can be achieved
for the semiexperimental equilibrium structure of a medium-sized molecule.
References
Albritton DL, Schmeltekopf AL, Zare RN (1976) An introduction to the least-squares fitting of
spectroscopic data. In: Rao KN (ed) Molecular spectroscopy: modern research, vol 2, Academic
Press, New York, pp 1–67
Albritton DL, Schmeltekopf AL, Zare RN (1977) A method for merging the results of separate
least-squares fits and testing for systematic errors. J Mol Spectrosc 67:132–156
Bartell LS, Romanesko DJ, Wong TC (1975) Augmented analyses: method of predicate observations. In: Sim GA, Sutton LE (eds) Chemical society specialist periodical report n° 20: molecular
structure by diffraction methods, vol 3. The Chemical Society, London, pp 72–79
Belsley DA (1991) Conditioning diagnostics. Collinearity and weak data in regression. Wiley, New
York
Bizzocchi L, Degli Esposti C, Botschwina P (2004) Millimeter-wave spectroscopy of rare
isotopomers of HC 5 N and DC 5 N: determination of a mixed experimental–theoretical equilibrium
structure for cyanobutadiyne. J Mol Spectrosc 225:145–151
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2005) Rotation
spectrum and infrared fundamental bands of 123 SbD 3 . Determination of molecular geometry and
ab initio calculations of spectroscopic parameters. Mol Phys 103:557–577
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2006) Rotation
spectrum and high resolution infrared spectra of the fundamental bands of 121 SbD 3 . Determination of the ground state and equilibrium structures. Ab initio calculations of the spectroscopic
parameters. J Mol Struct 780–781:98–110
Demaison J (2011) The method of least-squares. In: Demaison J, Boggs JE, Császár AG (eds)
Equilibrium molecular structures. CRC Press, Boca Raton, pp 29–52
Demaison J, Wlodarczak G, Rudolph HD (1997) Determination of reliable structures from rotational
constants. In: Hargittai M, Hargittai I (eds) Advances in molecular structure research, vol 3. JAI
Press, Greenwich
Demaison J, Margulès L, Rudolph HD (2010) Accurate determination of an equilibrium structure
in the presence of a small coordinate: the case of dimethylsulfide. J Mol Struct 978:229–233
Dréan P, Demaison J, Poteau L, Denis J-M (1996) Rotational spectrum and structure of HCP. J Mol
Spectrosc 176:139–145
Dréan P, Paplewski M, Demaison J, Breidung J, Thiel W, Beckers H, Bürger H (1996b) Millimeterwave spectra, ab initio calculations, and structure of fluorophosphane and chlorophosphane.
Inorg Chem 35:7671–7678
261
Example 14 Another interesting illustration is phenylacetylene, C 6 H 5 C≡CH
(Rudolph et al. 2013). Its structure is defined by 13 independent parameters and
its semiexperimental structure was fitted with different weighting methods, with the
help of three different force fields, and using the rotational constants of 39 isotopologues including many deuterated ones. In this particular case, differently deuterated isotopologues are useful because their rovibrational contribution is significantly
different mitigating the effect of systematic errors. Furthermore, the great number of
data (104 degrees of freedom) gives us some confidence in the reliability of the standard deviations of the fit. Finally, these semiexperimental structures were compared to
a very accurate ab initio Born–Oppenheimer structure. The results given in Table 9.11
are fully compatible. This example gives an idea of the accuracy that can be achieved
for the semiexperimental equilibrium structure of a medium-sized molecule.
References
Albritton DL, Schmeltekopf AL, Zare RN (1976) An introduction to the least-squares fitting of
spectroscopic data. In: Rao KN (ed) Molecular spectroscopy: modern research, vol 2, Academic
Press, New York, pp 1–67
Albritton DL, Schmeltekopf AL, Zare RN (1977) A method for merging the results of separate
least-squares fits and testing for systematic errors. J Mol Spectrosc 67:132–156
Bartell LS, Romanesko DJ, Wong TC (1975) Augmented analyses: method of predicate observations. In: Sim GA, Sutton LE (eds) Chemical society specialist periodical report n° 20: molecular
structure by diffraction methods, vol 3. The Chemical Society, London, pp 72–79
Belsley DA (1991) Conditioning diagnostics. Collinearity and weak data in regression. Wiley, New
York
Bizzocchi L, Degli Esposti C, Botschwina P (2004) Millimeter-wave spectroscopy of rare
isotopomers of HC 5 N and DC 5 N: determination of a mixed experimental–theoretical equilibrium
structure for cyanobutadiyne. J Mol Spectrosc 225:145–151
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2005) Rotation
spectrum and infrared fundamental bands of 123 SbD 3 . Determination of molecular geometry and
ab initio calculations of spectroscopic parameters. Mol Phys 103:557–577
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2006) Rotation
spectrum and high resolution infrared spectra of the fundamental bands of 121 SbD 3 . Determination of the ground state and equilibrium structures. Ab initio calculations of the spectroscopic
parameters. J Mol Struct 780–781:98–110
Demaison J (2011) The method of least-squares. In: Demaison J, Boggs JE, Császár AG (eds)
Equilibrium molecular structures. CRC Press, Boca Raton, pp 29–52
Demaison J, Wlodarczak G, Rudolph HD (1997) Determination of reliable structures from rotational
constants. In: Hargittai M, Hargittai I (eds) Advances in molecular structure research, vol 3. JAI
Press, Greenwich
Demaison J, Margulès L, Rudolph HD (2010) Accurate determination of an equilibrium structure
in the presence of a small coordinate: the case of dimethylsulfide. J Mol Struct 978:229–233
Dréan P, Demaison J, Poteau L, Denis J-M (1996) Rotational spectrum and structure of HCP. J Mol
Spectrosc 176:139–145
Dréan P, Paplewski M, Demaison J, Breidung J, Thiel W, Beckers H, Bürger H (1996b) Millimeterwave spectra, ab initio calculations, and structure of fluorophosphane and chlorophosphane.
Inorg Chem 35:7671–7678