Isotropic collision induced light scattering spectra from gaseous SF<sub>6</sub>

(1)

Isotropic collision induced light scattering spectra from gaseous SF 6

J.-L. Godet, F. Rachet, Y. Le Duff, K. Nowicka, and T. Bancewicz

Citation: The Journal of Chemical Physics 116, 5337 (2002); doi: 10.1063/1.1463421 View online: http://dx.doi.org/10.1063/1.1463421

View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/116/13?ver=pdfcov Published by the AIP Publishing

Articles you may be interested in

Simulations of light induced processes in water based on ab initio path integrals molecular dynamics. II.

Photoionization

J. Chem. Phys. 135, 154302 (2011); 10.1063/1.3649943

Isotropic and anisotropic collision-induced light scattering by gaseous sulfur hexafluoride at the frequency region of the ν 1 vibrational Raman line

J. Chem. Phys. 118, 11009 (2003); 10.1063/1.1575733

Dipole, dipole–quadrupole, and dipole–octopole polarizability of adamantane, C 10 H 16 , from refractive index measurements, depolarized collision-induced light scattering, conventional ab initio and density functional theory calculations

J. Chem. Phys. 115, 7957 (2001); 10.1063/1.1410392

Contributions of multipolar polarizabilities to the anisotropic and isotropic light scattering induced by molecular interactions in gaseous CF 4

AIP Conf. Proc. 386, 519 (1997); 10.1063/1.51803

Collision induced light scattering in metal vapors: The mercury spectra AIP Conf. Proc. 386, 453 (1997); 10.1063/1.51800

Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 193.52.40.1 On: Tue, 03 May 2016

(2)

Isotropic collision induced light scattering spectra from gaseous SF

₆

J.-L. Godet, F. Rachet, and Y. Le Duff

Laboratoire des Proprie´te´s Optiques des Mate´riaux et Applications, Universite´ d’Angers, 2 boulevard Lavoisier, 49045 Angers, France

K. Nowicka and T. Bancewicz

Nonlinear Optics Division, Institute of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan´, Poland

共Received 15 November 2001; accepted 31 January 2002兲

The experimental binary isotropic collision-induced light scattering spectrum of the gaseous sulfur hexafluoride is measured in absolute units in the 30– 210 cm^⫺¹ frequency range. The contribution of dipole–multipole mechanisms is computed in a semi-classical way. From comparison with experiment, the independent component E of the dipole–octopole polarizability tensor is estimated.

The study of collision induced light scattering 共CILS兲 intensities has been demonstrated to be a useful method to investigate collision induced polarizabilities in gaseous samples.^{1– 4}In the case of molecules, it has been shown that multipolar polarizabilities contribute to CILS intensities.^{5– 8} In particular, for SF₆, dipole–octopole polarizability has been derived from the measurement of CILS anisotropic spectra.^9,10 One of the difficulties for this evaluation comes from the weakness of the multipolar induced intensities. In- deed, most of the collision induced anisotropic intensities of the light scattered by gaseous SF₆ comes from translational effects including dipole-induced dipole 共DID兲and electron- overlap interactions. The rototranslational intensities due to dipole–octopole polarizability represent only a small part of the integrated anisotropic CILS intensities. In this work, we have measured, for the first time, the isotropic CILS intensities for the Rayleigh band of gaseous SF₆ at room temperature. For isotropic scattering, contributions from DID translational effects are relatively small contrary to anisotropic spectra and this yields favorable spectroscopic conditions to study rototranslational effects from isotropic spectra. Experi- mental data have been compared to theoretical rototransla- tional intensities calculated using ab initio polarizability val- ues and two intermolecular potentials.

The theory considers a pair of molecules, A and B, sepa- rated by a distance R_AB. General form for the excess interaction-induced irreducible spherical multipole pair polarizability tensor 共linear in the interaction tensor T_N) have been derived by us elsewhere.¹¹Here we are interested in the trace value of this interaction-induced polarizability. The isotropic component ⌬A₀₀ of the excess polarizability reads

共PAIR兲共1兲⌬A₀₀⫽ 2 ) _j

兺

A, j_Bl_A, l_B 共⫺1兲^l^B^⫹¹

冉

^共^2l^A^兲²^!^共^N^2l^B^兲^!

冊

^1/2

⫻X_j

Aj_BN

再

^l^j^A^B ^l^j^B^A ^N¹

冎

⫻关T_N共R_AB兲丢共A_j

A (1 l_A)

丢A_j

B (1 l_B)

兲N兴00, 共1兲 where兵^{. . .}其^and^丢 stand for the 6- j Wigner symbol and the

irreducible tensor product, respectively. Moreover A_j

i (1,l_i)

is the irreducible j_ith-rank spherical tensor of dipole-l_ith rank multipole polarizability tensor of molecule i, Xa b . . . f

⫽关(2a⫹1)(2b⫹1) . . . (2 f⫹1)兴^1/2 and N⫽l_A⫹l_B. First we consider the dipole-induced dipole共DID兲light scattering mechanism. In the dipolar approximation when l_A⫽l_B⫽1 the octahedral symmetry SF₆ molecules are optically isotro- pic: j_A⫽j_B⫽0; A₀₀⁽¹¹⁾⫽⫺)␣^{. From Eq.}共1兲we note imme- diately that in this case the triangular condition is violated and the first order DID isotropic 共trace兲 part⁽¹⁾⌬A₀₀ of the excess interaction-induced polarizability vanishes. From the closed-form for all-orders DID formula,

(PAIR)⌬A₀₀⫽⫺) 4␣³

R_AB⁶ ⫺␣^RAB

3 ⫺2␣² ^共²^兲

we note that the leading term of_(PAIR)⌬A₀₀is R_AB^⫺⁶. Let us consider the influence of intrinsic multipolar po- larizabilities of individual molecules on the excess trace polarizability. Due to octahedral 共centrosymmetric兲 shape of SF₆ molecules their dipole–quadrupole polarizability, tensor A vanishes. Then the first multipolar polarizability of SF₆ is of the dipole–octopole origin. Due to the symmetry in the main axes reference frame, there is only one independent Cartesian component (E_z,z,zz⫽E) of the dipole–octopole po- larizability tensor E. We apply Eq.共1兲to a pair of octahedral molecules. With l_A⫽1, l_B⫽3; j_A⫽0, j_B⫽4 together with l_A⫽3, l_B⫽1; j_A⫽4, j_B⫽0 the isotropic first-order pair po- larizability due to the ␣^T4E induction operator is of the form

(PAIR)(1)⌬A₀₀⫽⫺2

冑

³⁰^关^(A)^␣兵^T⁴^(AB)^丢^(B)^A⁴^(1,3)^其⁰

⫹(B)␣兵^T4

(AB)丢(A)A₄^(1,3)其⁰兴. 共3兲 With l_A⫽3, l_B⫽3; j_A⫽4, j_B⫽4 the excess isotropic pair polarizability due to the E T₆E induction operator becomes:

(PAIR)⌬A₀₀⫽

冑

¹³³⁵

36 兵^T6

(AB)丢关(A)A₄^(1,3)丢(B)A₄^(1,3)兴(6)其0. 共4兲

5337

(3)

When considering radiation scattered by low density gaseous systems we usually are justified in assuming that the molecules of the scattering volume are correlated radially but uncorrelated orientationally.^5,6,12–14 Using pair polarizabilities of Eqs.共3兲and共4兲we get

具(PAIR)⌬A₀共0兲䉺(PAIR)⌬A₀共t兲典⫽²²⁴9 ␣²^E²^R4共t兲S₄共t兲共5兲 and

具(PAIR)⌬A₀共0兲䉺(PAIR)⌬A₀共t兲典^⫽⁵⁵³^E⁴共R₄共t兲兲²S₆共t兲, 共6兲 where rotational functions R_j(t) and translational functions S_N(t) have been defined previously.^8,12

Our experimental setup has been described previously.¹⁵ We used a 15 Watt argon-ion laser linearly polarized operat- ing at 2 watt on the 514.5 nm line for excitation. The gaseous sample was contained in a four windows cell and its pressure was changed from 1 to about 21 bar. Sulfur hexafluoride was purchased from Praxair company with a purity of 99.995%.

Densities were calculated from PVT data of Ref. 16. The light scattered at 90 degrees was detected through a conventional Raman spectrometer using a low noise photomultiplier associated to a photon counter. Two types of scattering in- tensities, I_储(␯^{) and I}_⬜⁽␯), were recorded with the laser po- larization parallel and perpendicular to the scattering plane, respectively. These intensities take into account a correction related to the value of the aperture of the scattered light collection angle.¹⁷ For each frequency shift ␯ studied, we have measured scattering intensities at several densities and used a power series expansion in density to obtain the binary intensities I_储⬘⁽␯^{) and I}_⬜⬘⁽␯) scattered by the pairs of mol- ecules. Then, the binary isotropic scattering intensity I_iso(␯⁾ was deduced from

I_iso共␯兲⫽I_⬜⬘共␯兲⫺⁷6I_储⬘共␯兲. 共7兲 According to Eq. 共7兲 the weak isotropic intensity I_iso(␯^{) is} derived from a difference of two already weak signals which have to be measured and calibrated independently. Generally this procedure results in large uncertainties for the isotropic spectral intensities.

As shown previously,¹¹ the CILS isotropic intensities from a pair of molecules are generated by the trace component of the interaction induced polarizability tensor of molecular pair.¹¹We may observe that this polarizability tensor influences also the behavior of the depolarization ratio

␩⁽␯⁾⫽I_储⬘⁽␯^)/I_⬜⬘⁽␯). In Fig. 1, we show the experimental binary spectral depolarization ratio up to frequency shift equal to 110 cm^⫺¹. The dispersion of the experimental data grows for the highest frequencies partly due to weak Raman bands present at these frequencies as well as the weakness of the CILS intensities. Several frequency regions may be considered in Fig. 1. At low frequencies, lower than 30 cm^⫺¹, the depolarization ratio is close to 6/7 and the collision induced scattering is depolarized. This frequency region corre- sponds to pairs of molecules with large intermolecular distance and the excess trace of the polarizability tensor is relatively small. At higher frequencies, the depolarization ratio decreases when frequency increases. For these frequen-

cies, contributions to the CILS process come from pairs with smaller intermolecular distance and the excess trace of the polarizability tensor is relatively more important. In Fig. 2 experimental data obtained for the binary isotropic intensities of gaseous SF₆ at room temperature are displayed up to 210 cm^⫺¹. Error bars are given except for few estimated values. For frequencies lower than 30 cm^⫺¹no data are pre-

FIG. 1. Experimental pair depolarization ratio␩⁽␯⁾⫽I储⬘⁽␯^)/I_⬜⬘⁽␯^{) vs fre-} quency shifts␯^{in cm}^⫺¹for the two-body CIS of gaseous SF6at 294.5 K.

FIG. 2. Two-body isotropic scattering spectrum for SF6gas at 294.5 K. The circles共䊊兲indicate our experimental data with error bars; squares共䊐兲are estimated data. Theoretical curves are provided using␣⫽4.549 Å³. For the Zarkova potential given in Ref. 19 and E⫽3.3 Å⁵, the ␣T4E and the E T6E contributions are represented by dashed lines共— - —兲. Solid lines 共——兲correspond to E⫽3.0 Å⁵and the MMSV potential of Ref. 18.

5338 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Godetet al.

(4)

sented since the two quantities in the right side of Eq.共7兲are too close and their difference are not reliable. From 100 to 160 cm^⫺¹ monomolecular Raman bands do not allow to measure accurate collision induced scattering intensities.

Using Eqs. 共5兲 and 共6兲 and a procedure described previously,¹² we have computed theoretical rototranslational contributions due to the dipole–octopole polarizability tensor (␣^T4E, and ET₆E) for two recent intermolecular potentials of SF₆. The first potential proposed by Aziz et al.¹⁸ is a Morse–Morse–spline–van der Waals共MMSV兲function. The second potential calculated by Zarkova¹⁹ takes into account the influence of the vibrational excitation of the globular SF₆ molecule on the temperature-dependent equilibrium distance.

These two potentials predict good viscosity and second virial data.^18,19 We report in Fig. 2 the corresponding theoretical sets of curves for ␣⫽4.549 Å³ 共extrapolated at ␭L

⫽514.5 nm from data given in Ref. 20兲and for values of E which allows theoretical spectrum to fit experimental data in the 30– 85 cm^⫺¹frequency range. These fitted values of E at

␭L⫽514.5 nm are E⫽3.3⫾0.6 Å⁵ and E⫽3.0⫾0.6 Å⁵, for Zarkova and MMSV potentials, respectively. They may be compared to the static SCF value E⫽4.2 Å⁵ recently com- puted ab initio by Maroulis.²¹ The agreement of our fitted values with the one calculated by Maroulis as well as the comparison between theoretical and experimental line shapes point out that the ␣^T4E mechanism may be considered as responsible for most of the spectral intensities in the 30– 85 cm^⫺¹ frequency range. Other contributions exist due to the DID translational mechanism or to short range effects 共like overlap and exchange processes, molecular distortion, and/or spatial charge distribution of the nonpoint-like SF₆ molecule兲. However for the optically isotropic SF₆fluid, the DID contribution to the isotropic spectrum is of the second order (␣^T2␣^T2␣) and very weak: its M₀ moment is about 30 times smaller than that of the␣^T4E contribution. More- over, a large part of the DID integrated intensity is due to bound van der Waals dimers共from 45% up to 70% according to the potential chosen兲. Since dimers contribute only to the very low frequency part of the spectrum (0 – 30 cm^⫺¹), and since the free-dimer DID contribution is purely translational and decreases nearly exponentially, DID may be neglected in the frequency range where experimental data are available (30– 210 cm^⫺¹). On the contrary, short range effects may have a strong influence at high frequencies.²²They may explain, at least partly, the discrepancy between theoretical intensities and experiment beyond 160 cm^⫺¹. The inaccuracy of the potential well shape may also explain the latter discrepancy: it can be noticed in Fig. 2 that the MMSV potential¹⁸provides higher intensities in the 160– 210 cm^⫺¹ frequency region than the one of Zarkova.¹⁹

In Table I, our fitted values of E can be compared to previous evaluations resulting from the study of the depolar- ized collision-induced spectra of SF₆共Ref. 9兲and of SF₆– Xe mixture¹⁰ in the 0 – 70 cm^⫺¹ frequency region. The latter evaluations are two or three times bigger than ours and than the value computed by Maroulis.²¹They result from a comparison between theoretical and experimental depolarized CIS spectra in a frequency region (40– 70 cm^⫺¹) where translational 共mainly first-order DID兲 and rototranslational

(␣^T4E) intensities have the same order of magnitude. Be- cause of the uncertainties on the line shape of the strong translational contribution, this sheds a doubt on the reliability of such a comparison. On the contrary, as it has already been ascertained in the case of the CF₄,¹¹the comparison between theoretical and experimental isotropic CIS spectra is ensured by the predominance of the rototranslational mechanisms in the frequency region where experimental measurements are possible. For the dipole–octopole polarizability E of SF₆共as previously for the dipole–quadrupole polarizability A of CF₄),^11,23this is confirmed by the good agreement between our fitted values and the one computed ab initio by Maroulis.²¹

These results show the importance of isotropic CILS studies for measuring multipolar polarizabilities. The study of the influence of the intermolecular potential on CILS intensities is in progress in our institutes, aiming at an im- provement of the accuracy of the E value.

1G. C. Tabisz, Molecular Spectroscopy (a Specialist Periodical Report), edited by R. F. Barrow, D. A. Long, and J. Sheridan共Chemical Society, London, 1979兲, Vol. 6, pp. 136 –173.

2L. Frommhold, Adv. Chem. Phys. 46, 1共1981兲.

3Phenomena Induced by Intermolecular Interactions, NATO ASI Series, edited by G. Birnbaum共Plenum, New York, 1985兲.

4Collision—and Interaction—Induced Spectroscopy, Vol. 452 of NATO ASI Series C: Mathematical and Physical Sciences, edited by G. C. Tabisz and M. N. Neuman共Kluwer Academic, Dordrecht, 1995兲.

5A. D. Buckingham and G. C. Tabisz, Mol. Phys. 36, 583共1978兲.

6H. Posch, Mol. Phys. 46, 1213共1982兲.

7N. Meinander, J. Chem. Phys. 99, 8654共1993兲.

8T. Bancewicz, Y. Le Duff, and J. L. Godet, in Modern Nonlinear Optics, Part 1, Second Edition, Vol. 119 of Advances in Chemical Physics, edited by M. Evans共Wiley, New York, 2001兲, pp. 267–307.

9S. M. El-Sheikh and G. C. Tabisz, Mol. Phys. 68, 1225共1989兲.

10S. M. El-Sheikh, G. C. Tabisz, and R. T Pack, J. Chem. Phys. 92, 4234 共1990兲.

11A. Elliasmine, J.-L. Godet, Y. Le Duff, and T. Bancewicz, Phys. Rev. 55, 4230共1997兲.

12A. Elliasmine, J.-L. Godet, Y. Le Duff, and T. Bancewicz, Mol. Phys. 90, 147共1997兲.

13D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Kvantovaya Teoria Uglovogo Momenta共Nauka, 1975兲.

14C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids. Vol.1: Fun- damentals共Clarendon, Oxford, 1984兲.

15T. Bancewicz, V. Teboul, and Y. Le Duff, Phys. Rev. A 46, 1349共1992兲.

16P. M. Sigmund, I. H. Silberberg, and J. J. McKetta, J. Chem. Eng. Data 17, 168共1972兲.

TABLE I. Theoretical and experimental fitted values of the independent component E of the dipole–octopole polarizability tensor for the SF6mol- ecule.

Theory E (Å⁵) Reference

Bond model 20 5

Applequist model 9.5 24

SCF ab initio 4.2 21

Experiment E (Å⁵) Potential

SF6depolarized CIS共Ref. 9兲 6.1⫾1.8 28 –7 LJ共Ref. 25兲 8.5⫾2.0 28 –7 LJ共Ref. 26兲 SF6– Xe depolarized CIS共Ref. 10兲 9.13⫾3.00 M3SV共Ref. 10兲 SF6isotropic CIS共this work兲 3.0⫾0.6 MMSV共Ref. 18兲 3.3⫾0.6 Zarkova共Ref. 19兲

(5)

17V. Teboul, J. L. Godet, and Y. Le Duff, Appl. Spectrosc. 46, 476共1992兲.

18R. A. Aziz, M. J. Slaman, W. L. Taylor, and J. J. Hurly, J. Chem. Phys. 94, 1034共1991兲.

19L. Zarkova, Mol. Phys. 88, 489共1996兲.

20H. E. Watson and K. L. Ramaswamy, Proc. R. Soc. London, Ser. A 156, 144共1936兲.

21G. Maroulis, Chem. Phys. Lett. 312, 255共1999兲.

22M. S. Brown, S. K. Wang, and L. Frommhold, Phys. Rev. A 40, 2276 共1989兲.

23G. Maroulis, Chem. Phys. Lett. 259, 654共1996兲.

24M. Neumann, Mol. Phys. 53, 187共1984兲.

25J. C. McCoubrey and N. M. Singh, Trans. Faraday Soc. 55, 1826共1959兲.

26J. G. Powles, J. C. Dore, M. B. Deraman, and E. K. Osae, Mol. Phys. 50, 1089共1983兲.

5340 J. Chem. Phys., Vol. 116, No. 13, 1 April 2002 Godetet al.

Isotropic collision induced light scattering spectra from gaseous SF&lt;sub&gt;6&lt;/sub&gt;

Isotropic collision induced light scattering spectra from gaseous SF 6

Isotropic collision induced light scattering spectra from gaseous SF

兺

冉

冊

再

冎

冑

冑

Isotropic collision induced light scattering spectra from gaseous SF<sub>6</sub>