How does an uncharged non-polar molecule that has a quadrupole moment (such as carbon dioxide) behave in an electric field? I know that in a homogeneous electric field, ions travel while dipoles orient along the field (rotate) and non-polar molecules are not affected.
What kind of electrical field, if any, would exert a force on a molecule with a quadrupole moment?
Answer
Different moments of a charge distribution couple to different components of the external electric field. In the case of the quadrupole moment, the coupling is to the gradient of the electric field (EFG). Such an interaction is for instance relevant in NMR of quadrupolar nuclei, NQR (not to be confused with naked quad run, according to the wikipedia - o tempora, o mores) and Mössbauer spectroscopy, although those techniques consider the nuclear quadrupole moment.
In the case of atoms and molecules without permanent electric monopoles or dipoles, EFG interactions with permanent quadrupoles are the leading field-multipole interaction energy term (ignoring dispersion terms, ie induced dipole-induced dipole). In some cases such interactions can be of particular importance, for instance in aromatic compounds (see Kocman et al. cited below).
The quadrupole moment has been measured in $\ce{CO_2}$, see eg Chetty cited below, which includes experimental methods.
References
Electric quadrupole moment of graphene and its effect on intermolecular interactions M. Kocman, M. Pykal and P. Jurecka Physical Chemistry Chemical Physics Vol. 16, 2014
N. Chetty and V.W. Couling Measurement of the electric quadrupole moments of CO2 and OCS Molecular Physics Vol. 109 (5), 2011, 655–666
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