"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 10, 2019

contents of issue      DOI  10.30898/1684-1719.2019.10.6     full text in Russian (pdf)  

UDC 535.36+337.9

Quadrupole autocorrelation function of the symmetric top molecule: Langevin vector equation approach

S. V. Titov 1, K. D. Kazarinov 1, A. S. Titov 2, Yu. P. Kalmykov 3

1 Fryazino Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Vvedenskii sq. 1, Fryazino, Moscow reg 141120, Russia

2 Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudnyy, Moscow Region, 141701, Russia

3 Université de Perpignan Via Domitia, 52 av.Paul Alduy 66860 Perpignan Cedex 9, France

 

The paper is received on October 9, 2019

 

Abstract. Analysis of Rayleigh or Raman scattering usually involves the autocorrelation functions (ACF) of the quadrupole moments of molecules, which are also essential for probing the rotational dynamics of molecular liquids, because they are a signature of the rotational motion existing in dense gases or liquids, which varies from strongly hindered to almost free rotation. Thus, the Langevin equation for the dipole moment vector of a symmetric top molecule obtained in J. Mol. Liquids. 1991, 49, 79 is used to derive the ACF of the quadrupole moment for a classical system of freely rotating symmetrical top molecules. This idealized picture (free rotation) is widely used, e.g. in liquids composed of molecules with large moments of inertia and weak intermolecular interaction, where the description of the rotational motion as purely inertial is accurate at least at short time intervals. Free rotation between strong collisions is also assumed in models of extended rotational diffusion, where the orientational ACFs of molecules in such models may be represented as the corresponding ACFs of a free rotator combined with additional parameters characterizing the collision process. Thus, analysis of free rotation provides a basis for the study of the dynamics of molecules and scattering spectra of liquids in the context of extended diffusion. The relevant equation of motion is solved analytically and the averages over a canonical ensemble are calculated by quadratures. The results for ACFs of spherical and linear molecules are obtained as special cases. The calculations do not involve any approximation. The method hinges on the irreducible spherical tensor operators and is more transparent than those used hitherto.

Key words: Langevin equation, symmetrical top molecule, autocorrelation function of quadrupole moment, irreducible spherical tensor operator, polarizability tensor.

References

1.            Gaiduk V.I., Kalmykov Yu.P. Dielectric relaxation and molecular motion in polar fluids: dynamic and kinetic approaches. J. Mol. Liquids. 1987. Vol. 34. No. 1-3. pp. 1-222. DOI: : https://doi.org/10.1016/0167-7322(87)80047-8

2.            Mc Clung R.E.D. On the extended rotational diffusion models for molecular orientation in fluids. Adv. Mol. Relaxation and Interaction Processes. 1977. Vol. 10. pp. 83-171. DOIhttps://doi.org/10.1016/0378-4487(77)80001-0

3.            Morita A., Calderwood J.H., Walker S. Free rotational models for far-infrared absorptions of linear and symmetrical-top molecules dissolved in inert solvents. J. Phys. D: Appl. Phys. 1976. Vol. 9, pp. 2485-2498.

DOI: https://doi.org/10.1088/0022-3727/9/17/009

4.            Coffey W.T., Evans M.W., Grigolini P. Molecular Diffusion and Spectra. N.Y.: Wiley. 1984. 215 p.

5.            Coffey W.T., Kalmykov Yu.P. The Langevin equation for the dipole vector of symmetric top molecules. J. Mol. Liquids. 1991. Vol. 49. pp. 79-85.

DOI: https://doi.org/10.1016/0167-7322(91)80066-D

6.            Kalmykov Yu.P., Titov S.V., Coffey W.T., Zarifakis M. Langevin equation for the dipole vector of an accidental symmetric top molecule. J. Mol. Liquids. 2019. Vol. 289. pp. 111123 (5 pages). DOI: https://doi.org/10.1016/j.molliq.2019.111123

7.            Landau L.D., Lifshitz E.M. Mechanics, 3rd edition. London. Pergamon Press. 1976. 170 p.

8.            Elyashevich M.A. Atomnaya i molekulyarnaya spektroskopiya [Atomic and molecular spectroscopy]. 2-nd ed.  oscow, URSS Publ., 2001. 896 p. (In Russian)

9.            Zare R.N. Angular Momentum. Understanding Spatial Aspects in Chemistry and Physics. N. Y. John Wiley and Sons. 1988. 368 p.

10.       St.Pierre A.G., Steel W.A. Time Correlations and Conditional Distribution Functions for Classical Ensembles of Free Rotors. Phys. Rev. 1969. Vol. 184. No. 1. pp. 172-186. DOI: https://doi.org/10.1103/PhysRev.184.172

11.       Varshalovich D.A., Moskalev A.N., Khersonskii V.K. Quantum Theory of Angular Momentum. Singapore. World Scientific. 1998. 514 p.

 

 

For citation:

S.V.Titov, K.D.Kazarinov, A.S.Titov, Yu.P.Kalmykov. Quadrupole autocorrelation function of the symmetric top molecule: Langevin vector equation approach. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No. 10. Available at http://jre.cplire.ru/jre/oct19/6/text.pdf

DOI  10.30898/1684-1719.2019.10.6