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Journal of Radio Electronics Online scientific journal · eISSN 1684-1719
2019, № 10 · RADIO WAVE PROPAGATION

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

S.V. Titov1, K.D. Kazarinov1, A.S. Titov2,3, I.P. Kalmykov4,5

1 Fryazino Branch of Kotelnikov IRE RAS, Friazino, Russia
2 Московский физико-технический институт (ГУ), Moskovskaia oblact, Russia
3 Moscow Institute of Physics and Technology (State University), Dolgoprudnyy, Russia
4 Университет Перпиньяна, Perpinian, France
5 Université de Perpignan, Via Domitia, France
Full text (PDF) DOI: 10.30898/1684-1719.2019.10.6 UDC 535.36+337.9 EDN EVXLPH

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.

  • уравнение Ланжевена
  • симметричный волчок
  • автокорреляционная функция квадрупольного момента
  • непреводимый сферический тензорный оператор
  • тензора поляризуемости молекулы
  • Langevin equation
  • symmetrical top molecule
  • autocorrelation function of quadrupole moment
  • irreducible spherical tensor operator
  • polarizability tensor
Аннотация (на русском)

Автокорреляционная функция квадрупольного момента молекулы типа симметричного волчка: метод векторного уравнения Ланжевена

Уравнение Ланжевена для вектора дипольного момента молекулы типа симметричного волчка, полученное в работе J. Mol. Liquids. 1991, 49, 79 используется для вывода автокорреляционной функции (АКФ) квадрупольного момента молекул этого типа. При этом результаты для шарового и линейного волчков получаются как частные случаи. Метод вывода основан на использовании непреводимых сферических тензорных операторов и является более простым и наглядным по сравнению с ранее использованными методами.

For citation

Titov S.V., Kazarinov K.D., Titov A.S., Kalmykov I.P. Quadrupole autocorrelation function of the symmetric top molecule: Langevin vector equation approach // Journal of Radio Electronics. – 2019. – No. 10. https://doi.org/10.30898/1684-1719.2019.10.6

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