Fluctuating dipole moments

Neumann, M. Dipole moment fluctuation formulas in computer simvilations of polar systems. Mol. Phys. 50 (1983) 841-858. 

This equation gives the mean-square value of the voltage appearing across the terminals of a capadtor filled with a dielectric of zero-frequency relative permittivity, s in terms of Co, the capacitance without a dielectric, and the absolute temperature, T. This noise voltage is caused by the thermally induced dipole-moment fluctuations which are themselves inextricably bound up with the dissipative processes. That this is so is indicated by the fact that equation (42) applied to aJ,to) leads to the relation... 

With local information given by INM analysis in mind, we next see the character of rotational relaxation in liquid water. The most familiar way to see this, not only for numerical simulations [76-78] but for laboratory experiments, is to measure dielectric relaxation, by means of which total or individual dipole moments can be probed [79,80]. Figure 10 gives power spectra of the total dipole moment fluctuation of liquid water, together with the case of water cluster, (H20)io8- The spectral profile for liquid water is nearly fitted to the Lorentzian, which is consistent with a direct calculation of the correlation function of rotational motions. The exponential decaying behavior of dielectric relaxation was actually verified in laboratory experiments [79,80]. On the other hand, the profile for water cluster deviates from the Lorentzian function. As stated in Section III, the dynamics of finite systems may be more difficult to be understood. 

Figure 10. The power spectrum density of the total dipole moment fluctuation of liquid water (solid line) and water cluster (H2O)108 (dashed line). The simulation of liquid water was performed for 216 water molecules under the periodic boundary condition.

M. Neumann, Mol. Phys., 50, 841 (1983). Dipole Moment Fluctuation Formulas in Computer Simulations of Polar Systems. 

The basic molecular parameters employed are btnid dipole mmnents. The remaining parameters are derivatives of bphysical significance of bond dipoles and their contrUmdon to die dipole moment fluctuations determinir die intensities of vibradmial transitions. 

The electric field of a molecule however is not static but fluctuates rapidly Although on average the centers of positive and negative charge of an alkane nearly coincide at any instant they may not and molecule A can be considered to have a temporary dipole moment... 

Infrared activity of vibrations is readily deduced. The symmetric stretching vibration has no associated dipole moment change during the vibration and is, therefore, infrared inactive. The asymmetric stretching vibration has an associated dipole moment which fluctuates with the frequency of the vibration. The vibration is, therefore, infrared active. 

FIGURE 5.5 The rapid fluctuations in the electron distribution in two neighboring molecules result in two instantaneous electric dipole moments that attract each other. The fluctuations flicker into different positions, but each new arrangement in one molecule induces an arrangement in the other that results in mutual attraction. 

The rapidly varying electric held of the incident electromagnetic radiation can, therefore, cause a rapid fluctuation in the dipole moment of the molecule. The magnitude of this oscillation depends on the polarisability of the molecule but is generally small. 

Any periodic distortion that causes polarization of a molecule can also cause interaction with the electric field component of radiation. An example is the asymmetric stretching vibration of the CO2 molecule, that creates a fluctuating dipole moment as shown below. 

The induced dipole moment in a given direction fluctuates at double the rotational frequency of the molecule as shown schematically below. The upper diagram shows the electric field in phase with a rotating polar molecule. 

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