Electric properties of van der Waals complex when using ab initio calculations
should be, if possible, corrected for the BSSE and BSIE similar to the interaction
energy. The BSSE could reach up to 10 % for the dipole moments in the range of
the van der Waals wells for the case of a medium sized basis set, like aug-cc-pVTZ
(see Fig. 3.1, for example). However, for the systems with multireference character
the BSSE correction is not used when a size-inconsistent method is employed.
3.2.1 Dipole Moments of Small Complexes
Dipole moments of atom-atomic complexes are now studied very well. These
complexes are the simplest van der Waals complexes and, as a result, they have
been studied first of all and fully enough (see, for instance [14–21]). Particular
analytical forms of dipole moments for atom-atomic complexes can be easily
obtained from the general expressions of Sect. 3.1 with a given accuracy using the
symmetry properties (Appendix B) of interacting atoms. In particular, Eq. (3.1.9)
gives for two interacted atoms (when at least one of them has nonzero quadruple
moment) the asymptotic behavior as R
−4 . And when these atoms are in the state
s (spherical symmetry) the leading term (*R
−7 ) is caused only by the second
dispersion term in (3.1.10). It should be noted that these dependences can be
effectively used to construct the dipole moment function of diatomic molecules for
large interatomic distances [22, 23].
The dipole moments of the atom-diatomic complexes X 2 -Y, in contrast to the
atom-atomic ones, depend also on the angle θ between the axis of diatomic
molecule and the axis passing through the atom Y and the molecule X 2 (Fig. 3.2a).
Note that if the nonrigidity of the diatomic molecule X 2 is taken into account, then
the additional dependence of dipole moment of the complex on r appears. So, in
general we have a surface of the dipole moment for such complex. Nevertheless,
these van der Waals complexes are relatively simple yet and they are studied
intensively up to now because of their importance (see, for instance, [24–30]).
X 2 -Y complex. The r dependence can be easily obtained for X 2 -Y complexes
(where Y is an atom of noble gas in the ground state) in (3.1.9) if only the leading
quadrupole-induced dipole interaction is taken into account. In this case, the
equilibrium distances (R e ) of the complexes are comparable with the size of X 2
molecules. As a result, the modelling of a molecule in the form of a point, for which
the interacting molecules are considered as not having the size, can not be applied
and should be modified to take the size of a molecule into account. For this purpose,
each molecule of a complex is considered as two effective point atoms without any
interactions between them. The position of these atoms coincides with those of the
nuclei of the molecule. The tensor of the total quadrupole moment of the effective
atoms is the same as that of the molecule. For the diatomic homonuclear molecule
the quadrupole moments of the effective atoms are equal to each other. Thus, the
dipole moment of the complex is a function of intra- and intermolecular separations
and relative orientation of the complex components. As a result, in the framework
24
3 Interaction-induced Dipole Moment
should be, if possible, corrected for the BSSE and BSIE similar to the interaction
energy. The BSSE could reach up to 10 % for the dipole moments in the range of
the van der Waals wells for the case of a medium sized basis set, like aug-cc-pVTZ
(see Fig. 3.1, for example). However, for the systems with multireference character
the BSSE correction is not used when a size-inconsistent method is employed.
3.2.1 Dipole Moments of Small Complexes
Dipole moments of atom-atomic complexes are now studied very well. These
complexes are the simplest van der Waals complexes and, as a result, they have
been studied first of all and fully enough (see, for instance [14–21]). Particular
analytical forms of dipole moments for atom-atomic complexes can be easily
obtained from the general expressions of Sect. 3.1 with a given accuracy using the
symmetry properties (Appendix B) of interacting atoms. In particular, Eq. (3.1.9)
gives for two interacted atoms (when at least one of them has nonzero quadruple
moment) the asymptotic behavior as R
−4 . And when these atoms are in the state
s (spherical symmetry) the leading term (*R
−7 ) is caused only by the second
dispersion term in (3.1.10). It should be noted that these dependences can be
effectively used to construct the dipole moment function of diatomic molecules for
large interatomic distances [22, 23].
The dipole moments of the atom-diatomic complexes X 2 -Y, in contrast to the
atom-atomic ones, depend also on the angle θ between the axis of diatomic
molecule and the axis passing through the atom Y and the molecule X 2 (Fig. 3.2a).
Note that if the nonrigidity of the diatomic molecule X 2 is taken into account, then
the additional dependence of dipole moment of the complex on r appears. So, in
general we have a surface of the dipole moment for such complex. Nevertheless,
these van der Waals complexes are relatively simple yet and they are studied
intensively up to now because of their importance (see, for instance, [24–30]).
X 2 -Y complex. The r dependence can be easily obtained for X 2 -Y complexes
(where Y is an atom of noble gas in the ground state) in (3.1.9) if only the leading
quadrupole-induced dipole interaction is taken into account. In this case, the
equilibrium distances (R e ) of the complexes are comparable with the size of X 2
molecules. As a result, the modelling of a molecule in the form of a point, for which
the interacting molecules are considered as not having the size, can not be applied
and should be modified to take the size of a molecule into account. For this purpose,
each molecule of a complex is considered as two effective point atoms without any
interactions between them. The position of these atoms coincides with those of the
nuclei of the molecule. The tensor of the total quadrupole moment of the effective
atoms is the same as that of the molecule. For the diatomic homonuclear molecule
the quadrupole moments of the effective atoms are equal to each other. Thus, the
dipole moment of the complex is a function of intra- and intermolecular separations
and relative orientation of the complex components. As a result, in the framework
24
3 Interaction-induced Dipole Moment