the dependence of the Kerr constant on electric properties of a molecule is significantly simplified and the polarizability anisotropy can be directly determined
from the Kerr constant.
The experimental methods for polarizability determination based on the Stark
effect use the displacements and splitting of rotational energy levels of small
molecules under the influence of an external electric field [11–14]. The usual
accuracy of these methods is in the range of 3–10 %.
Finally, let us mention the experimental methods that use other physical effects
to measure molecular polarizability. These methods use the birefringence effects
[15] in any magnetic field (Cotton–Mouton effect) and flow (dynamic optical effect
of Maxwell), the acoustic birefringence effect, absorption spectra induced by the
electric field [16] and so on. It should be noted that last group of methods have the
greater errors compared to the methods discussed above.
The feature of the all considered experimental methods is that they allow us to
define the values of the molecular polarizability only at the equilibrium position of
molecular nuclei. To obtain the dependencies of molecular polarizabilities on the
mutual location of nuclei in a molecule, the Raman effect can be used The line
intensities of Raman spectra depend on the values of polarizability derivatives with
respect to the nuclei displacements. The first works to define the polarizability
derivatives of molecules have appeared immediately after the creation of the theory
of Raman light scattering (Placzek theory of polarizability) [17]. However, the
experimental technique of “pre-laser” period could not obtain the high-quality
results. Some experimental results of this period are summarized in [18]. Currently,
these data have only a historical interest. Now, laser technologies allow to increase
the measurement accuracy and, as a result, significantly improve and revise the
“pre-laser” data. Nevertheless, up to day the experimental data on the polarizability
derivatives of molecules are fragmentary and do not give the impression of systematic studies of the polarizability of molecules as a function of the nuclei coordinates, even for diatomic molecules [19–39].
Note also, that U. Hohm has recently compiled the static mean dipole-dipole
polarizability evaluated from gas phase measurements for 174 molecules [40].
4.1 Interaction-induced Polarizability Theory
4.1.1 Ab Initio Calculation Features
The polarizability is the second derivative of the interaction energy by the external
field F
0
a . The calculation formulas can be also obtained using the finite-difference
method like for the dipole moment. As a result, for example, the 3-point finite
difference approximation (with errors of order ðF
0
a Þ
2 ) gives
52
4 Interaction-induced Polarizability
from the Kerr constant.
The experimental methods for polarizability determination based on the Stark
effect use the displacements and splitting of rotational energy levels of small
molecules under the influence of an external electric field [11–14]. The usual
accuracy of these methods is in the range of 3–10 %.
Finally, let us mention the experimental methods that use other physical effects
to measure molecular polarizability. These methods use the birefringence effects
[15] in any magnetic field (Cotton–Mouton effect) and flow (dynamic optical effect
of Maxwell), the acoustic birefringence effect, absorption spectra induced by the
electric field [16] and so on. It should be noted that last group of methods have the
greater errors compared to the methods discussed above.
The feature of the all considered experimental methods is that they allow us to
define the values of the molecular polarizability only at the equilibrium position of
molecular nuclei. To obtain the dependencies of molecular polarizabilities on the
mutual location of nuclei in a molecule, the Raman effect can be used The line
intensities of Raman spectra depend on the values of polarizability derivatives with
respect to the nuclei displacements. The first works to define the polarizability
derivatives of molecules have appeared immediately after the creation of the theory
of Raman light scattering (Placzek theory of polarizability) [17]. However, the
experimental technique of “pre-laser” period could not obtain the high-quality
results. Some experimental results of this period are summarized in [18]. Currently,
these data have only a historical interest. Now, laser technologies allow to increase
the measurement accuracy and, as a result, significantly improve and revise the
“pre-laser” data. Nevertheless, up to day the experimental data on the polarizability
derivatives of molecules are fragmentary and do not give the impression of systematic studies of the polarizability of molecules as a function of the nuclei coordinates, even for diatomic molecules [19–39].
Note also, that U. Hohm has recently compiled the static mean dipole-dipole
polarizability evaluated from gas phase measurements for 174 molecules [40].
4.1 Interaction-induced Polarizability Theory
4.1.1 Ab Initio Calculation Features
The polarizability is the second derivative of the interaction energy by the external
field F
0
a . The calculation formulas can be also obtained using the finite-difference
method like for the dipole moment. As a result, for example, the 3-point finite
difference approximation (with errors of order ðF
0
a Þ
2 ) gives
52
4 Interaction-induced Polarizability