Temperature Dependence of the Mean Dipole Moment

The mean value of the electric dipole moment of a molecule in an external electric field % directed along the Z axis of laboratory system of coordinates (LSC), if the intermolecular interaction and the quantization of the rotational degrees of freedom are neglected, is given by the relation 

Molecular Systems in Twofold Degenerate Electronic States of Dipolar Type 

The twofold degeneracy of dipolar type can be realized, for instance, in molecules with D3h symmetry. Consider first the a(T) dependence in the absence of vibronic interaction. In this case 

Taking into account the linear vibronic coupling in the Hamiltonian of the system (the linear E (x) e problem), we have 

Here 4 and p are the vectors of dimensionless coordinates and impulses, respectively, o .is the frequency of the harmonic vibrations active in the Jahn-Teller effect a is the vibronic constant related to the usual F (Ber- 

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Another conclusion is that the temperature dependence of the mean dipole moment for vibronic systems has a complicated form essentially dependent on several parameters of the system (the effective electronic de and nuclear d dipole moments and the vibronic constant a or the values of the dipole moments in the adiabatic potential minima configurations d and the tunneling splitting magnitude, etc.). Therefore the measurement... 

The analysis of the preceding results leads to several important conclusions about the electric properties of vibronic systems. First, in accordance with the results obtained in the preceding, nonpolar molecules may have both types of behavior of the mean dipole moment—that for rigid dipole molecules and that for nondipolar ones. Only in the cases of limit values of temperatures or vibronic coupling constants can they be related to either the former or the latter. This statement can be illustrated by the case of a molecule with two dipolar-type minima [Eq. (19)]. Consider the two limit cases A kT. In the former case the function a(T) transforms into the classical linear dependence on 11 kT inherent to rigid dipole molecules. In the limit case of low temperatures, a(T) is reduced to a constant value equal to the static polarizability of molecules that have no proper dipole moment. 

The system of coupled equations [Eqs (63), (64), and (66)], along with the recurrence formula for a/ (119) and Eq. (62) for /p, constitute the model describing the temperature and geometry dependence of the mean-square dipole moment of the droplet (p ). Furthermore, by inserting the calculated values of die mean square dipole moment into Eq. (49), we can obtain the equation ... 

The permanent dipole moment /tt of a polar molecule is determined in Exp. 29 from measurements of the dielectric constant of a solution containing such molecules as solute. In the present experiment, the permanent dipole moment of a gas molecule is determined. The orientation polarization can be separated from the distortion polarization by means of measurements at more than one temperature, making use of the fact that the former is temperature dependent while the latter is not. An alternative method, which is recommended for this experiment, is to obtain the orientation polarization by subtracting from the molar polarization the distortion polarization as determined separately from the refractive index of the gas, which is determined by means of a laser interferometer. Thus the molar polarization needs to be determined at only one temperature. 

A RIS model with neighbor dependence is used to calculate mean-square dipole moments and their temperature coefficients for PDMS chains over a wide range of molecular weight. Chain conformational energies required in the calculations are obtained from a previous analysis of the random-coil dimensions of PDMS chains in the limit of large x (S 116). 

Dielectric constants are determined for pure liquid dimethylsiloxane oligomers. Mean-square dipole moments, calculated from the Onsager equation, are in good agreement with predicted values based on the RIS model (S 117) with neighbor dependence and chain conformational energies obtained in an independent analysis of the random-coil dimensions of such chains. In addition, the observed temperature coefficients of are in qualitative agreement with calculated results. 

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