Abstract

The long tails at low and high frequency in the Rayleigh scattering by gases comprising tetrahedral molecules is attributed to rotational Raman scattering. The rotating part of the collision-induced polarizability is due to the dipole–quadrupole polarizability A and varies as the inverse fourth power of the separation of the two interacting molecules. The rotational section rules are ΔJ = 0, ±1, ±2, ±3, and quantitative agreement is obtained with the observed frequency dependence of the tail in methane. Contributions due to hyperpolarizability are found to be small. A value for the dipole–quadrupole polarizability A of methane is obtained by attributing the excess scattering over that implied by the dipole–induced-dipole model to A.

© 1977 Optical Society of America

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References

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  1. F. Barocchi, J. P. McTague, Phys. Lett. A 53, 488 (1975).
    [CrossRef]
  2. F. Barocchi, M. Zoppi, in Proceedings of the Fifth International Conference on Raman Spectroscopy, E. D. Schmid, J. Brandmüller, W. Kiefer, B. Schrader, H. W. Schrotter, eds. (Schulz Verlag, Freiburg, 1976), p. 386.
  3. D. P. Shelton and G. C. Tabisz, Ref. 2, p. 382.
  4. W. M. Gelbart, Adv. Chem. Phys. 26, 1 (1974).
    [CrossRef]
  5. L. Silberstein, Philos. Mag. 33, 92, 521 (1917).
    [CrossRef]
  6. A. D. Buckingham, R. E. Raab, Proc. Roy. Soc. A 345, 365 (1975).
    [CrossRef]
  7. I. Ozier, K. Fox, J. Chem. Phys. 52, 1416 (1970).
    [CrossRef]
  8. C. G. Gray, Phys J. B 4, 1661 (1971).
    [CrossRef]
  9. A. D. Buckingham, Adv. Chem. Phys. 12, 107 (1967).
    [CrossRef]
  10. P. Lallemand, J. Phys. (Paris) 33, Colloque C1, 259 (1972).
    [CrossRef]
  11. R. C. Watson, R. L. Rowell, J. Chem. Phys. 61, 2666 (1974).
    [CrossRef]
  12. W. Holzer, Y. Le Duff, Phys. Rev. Lett. 32, 205 (1974).
    [CrossRef]
  13. P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
    [CrossRef]
  14. C. G. Gray, J. Chem. Phys. 50, 549 (1969).
    [CrossRef]
  15. G. Birnbaum, E. R. Cohen, J. Chem. Phys. 62, 3807 (1975).
    [CrossRef]
  16. A. D. Buckingham, B. J. Orr, Quart. Rev. Chem. Soc. 21, 195 (1967).
    [CrossRef]
  17. A. D. Buckingham, B. J. Orr, Trans. Faraday Soc. 65, 673(1969).
    [CrossRef]
  18. A. D. Buckingham, J. A. Pople, Trans. Faraday Soc. 51, 1173 (1955).
    [CrossRef]

1976

P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
[CrossRef]

1975

G. Birnbaum, E. R. Cohen, J. Chem. Phys. 62, 3807 (1975).
[CrossRef]

F. Barocchi, J. P. McTague, Phys. Lett. A 53, 488 (1975).
[CrossRef]

A. D. Buckingham, R. E. Raab, Proc. Roy. Soc. A 345, 365 (1975).
[CrossRef]

1974

W. M. Gelbart, Adv. Chem. Phys. 26, 1 (1974).
[CrossRef]

R. C. Watson, R. L. Rowell, J. Chem. Phys. 61, 2666 (1974).
[CrossRef]

W. Holzer, Y. Le Duff, Phys. Rev. Lett. 32, 205 (1974).
[CrossRef]

1972

P. Lallemand, J. Phys. (Paris) 33, Colloque C1, 259 (1972).
[CrossRef]

1971

C. G. Gray, Phys J. B 4, 1661 (1971).
[CrossRef]

1970

I. Ozier, K. Fox, J. Chem. Phys. 52, 1416 (1970).
[CrossRef]

1969

A. D. Buckingham, B. J. Orr, Trans. Faraday Soc. 65, 673(1969).
[CrossRef]

C. G. Gray, J. Chem. Phys. 50, 549 (1969).
[CrossRef]

1967

A. D. Buckingham, B. J. Orr, Quart. Rev. Chem. Soc. 21, 195 (1967).
[CrossRef]

A. D. Buckingham, Adv. Chem. Phys. 12, 107 (1967).
[CrossRef]

1955

A. D. Buckingham, J. A. Pople, Trans. Faraday Soc. 51, 1173 (1955).
[CrossRef]

1917

L. Silberstein, Philos. Mag. 33, 92, 521 (1917).
[CrossRef]

Barocchi, F.

F. Barocchi, J. P. McTague, Phys. Lett. A 53, 488 (1975).
[CrossRef]

F. Barocchi, M. Zoppi, in Proceedings of the Fifth International Conference on Raman Spectroscopy, E. D. Schmid, J. Brandmüller, W. Kiefer, B. Schrader, H. W. Schrotter, eds. (Schulz Verlag, Freiburg, 1976), p. 386.

Birnbaum, G.

G. Birnbaum, E. R. Cohen, J. Chem. Phys. 62, 3807 (1975).
[CrossRef]

Buckingham, A. D.

A. D. Buckingham, R. E. Raab, Proc. Roy. Soc. A 345, 365 (1975).
[CrossRef]

A. D. Buckingham, B. J. Orr, Trans. Faraday Soc. 65, 673(1969).
[CrossRef]

A. D. Buckingham, B. J. Orr, Quart. Rev. Chem. Soc. 21, 195 (1967).
[CrossRef]

A. D. Buckingham, Adv. Chem. Phys. 12, 107 (1967).
[CrossRef]

A. D. Buckingham, J. A. Pople, Trans. Faraday Soc. 51, 1173 (1955).
[CrossRef]

Cohen, E. R.

G. Birnbaum, E. R. Cohen, J. Chem. Phys. 62, 3807 (1975).
[CrossRef]

Fox, K.

I. Ozier, K. Fox, J. Chem. Phys. 52, 1416 (1970).
[CrossRef]

Galatry, L.

P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
[CrossRef]

Gelbart, W. M.

W. M. Gelbart, Adv. Chem. Phys. 26, 1 (1974).
[CrossRef]

Gray, C. G.

C. G. Gray, Phys J. B 4, 1661 (1971).
[CrossRef]

C. G. Gray, J. Chem. Phys. 50, 549 (1969).
[CrossRef]

Holzer, W.

W. Holzer, Y. Le Duff, Phys. Rev. Lett. 32, 205 (1974).
[CrossRef]

Isnard, P.

P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
[CrossRef]

Lallemand, P.

P. Lallemand, J. Phys. (Paris) 33, Colloque C1, 259 (1972).
[CrossRef]

Le Duff, Y.

W. Holzer, Y. Le Duff, Phys. Rev. Lett. 32, 205 (1974).
[CrossRef]

McTague, J. P.

F. Barocchi, J. P. McTague, Phys. Lett. A 53, 488 (1975).
[CrossRef]

Orr, B. J.

A. D. Buckingham, B. J. Orr, Trans. Faraday Soc. 65, 673(1969).
[CrossRef]

A. D. Buckingham, B. J. Orr, Quart. Rev. Chem. Soc. 21, 195 (1967).
[CrossRef]

Ozier, I.

I. Ozier, K. Fox, J. Chem. Phys. 52, 1416 (1970).
[CrossRef]

Pople, J. A.

A. D. Buckingham, J. A. Pople, Trans. Faraday Soc. 51, 1173 (1955).
[CrossRef]

Raab, R. E.

A. D. Buckingham, R. E. Raab, Proc. Roy. Soc. A 345, 365 (1975).
[CrossRef]

Robert, D.

P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
[CrossRef]

Rowell, R. L.

R. C. Watson, R. L. Rowell, J. Chem. Phys. 61, 2666 (1974).
[CrossRef]

Silberstein, L.

L. Silberstein, Philos. Mag. 33, 92, 521 (1917).
[CrossRef]

Watson, R. C.

R. C. Watson, R. L. Rowell, J. Chem. Phys. 61, 2666 (1974).
[CrossRef]

Zoppi, M.

F. Barocchi, M. Zoppi, in Proceedings of the Fifth International Conference on Raman Spectroscopy, E. D. Schmid, J. Brandmüller, W. Kiefer, B. Schrader, H. W. Schrotter, eds. (Schulz Verlag, Freiburg, 1976), p. 386.

Adv. Chem. Phys.

W. M. Gelbart, Adv. Chem. Phys. 26, 1 (1974).
[CrossRef]

A. D. Buckingham, Adv. Chem. Phys. 12, 107 (1967).
[CrossRef]

J. Chem. Phys.

I. Ozier, K. Fox, J. Chem. Phys. 52, 1416 (1970).
[CrossRef]

C. G. Gray, J. Chem. Phys. 50, 549 (1969).
[CrossRef]

G. Birnbaum, E. R. Cohen, J. Chem. Phys. 62, 3807 (1975).
[CrossRef]

R. C. Watson, R. L. Rowell, J. Chem. Phys. 61, 2666 (1974).
[CrossRef]

J. Phys. (Paris)

P. Lallemand, J. Phys. (Paris) 33, Colloque C1, 259 (1972).
[CrossRef]

Mol. Phys.

P. Isnard, D. Robert, L. Galatry, Mol. Phys. 31, 1789 (1976).
[CrossRef]

Philos. Mag.

L. Silberstein, Philos. Mag. 33, 92, 521 (1917).
[CrossRef]

Phys J. B

C. G. Gray, Phys J. B 4, 1661 (1971).
[CrossRef]

Phys. Lett. A

F. Barocchi, J. P. McTague, Phys. Lett. A 53, 488 (1975).
[CrossRef]

Phys. Rev. Lett.

W. Holzer, Y. Le Duff, Phys. Rev. Lett. 32, 205 (1974).
[CrossRef]

Proc. Roy. Soc. A

A. D. Buckingham, R. E. Raab, Proc. Roy. Soc. A 345, 365 (1975).
[CrossRef]

Quart. Rev. Chem. Soc.

A. D. Buckingham, B. J. Orr, Quart. Rev. Chem. Soc. 21, 195 (1967).
[CrossRef]

Trans. Faraday Soc.

A. D. Buckingham, B. J. Orr, Trans. Faraday Soc. 65, 673(1969).
[CrossRef]

A. D. Buckingham, J. A. Pople, Trans. Faraday Soc. 51, 1173 (1955).
[CrossRef]

Other

F. Barocchi, M. Zoppi, in Proceedings of the Fifth International Conference on Raman Spectroscopy, E. D. Schmid, J. Brandmüller, W. Kiefer, B. Schrader, H. W. Schrotter, eds. (Schulz Verlag, Freiburg, 1976), p. 386.

D. P. Shelton and G. C. Tabisz, Ref. 2, p. 382.

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Figures (2)

Fig. 1
Fig. 1

A tetrahedron in an electric field gradient F′xy. Each of the groups at the four corners of the tetrahedron is anisotropically polarizable and contributes to the dipole induced in the z direction by F′xy.

Fig. 2
Fig. 2

The computed Stokes collision-induced Rayleigh scattering spectrum for CH4 at 295 K. The curve •-•-• is the ΔJ = 0 branch, and those represented by ••• are the ΔJ = 1,2,3 branches. The open circles are points on the total spectrum at 20-cm−1 intervals. The profile beyond 200 cm−1 is represented by an exponential function exp(−ω/ω0) with ω0 = 139 cm−1. The DID line is the dipole-induced-dipole contribution estimated using the data in Ref. 1.

Equations (10)

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μ α = μ α ( 0 ) + α α β F β + 1 3 A α β γ F β γ + ,
μ α = μ α ( 1 ) + μ α ( 2 ) = α 1 ( E α + F α ( 1 ) ) + 1 3 A α β γ ( 1 ) F β γ ( 1 ) + α 2 ( E α + F α ( 2 ) ) + 1 3 A α β γ ( 2 ) F β γ ( 2 ) + ,
μ α = α 1 ( E α + T α β μ β ( 2 ) + 1 3 T α β γ θ β γ ( 2 ) + ) 1 3 A α β γ ( 1 ) ( T β γ δ μ δ ( 2 ) + ) + α 2 ( E α + T α β μ β ( 1 ) 1 3 T α β γ θ β γ ( 1 ) + ) + 1 3 A α β γ ( 2 ) ( T β γ δ μ δ ( 1 ) + ) + ,
T α β = ( 4 π 0 ) 1 α β ( R 1 ) = ( 4 π 0 ) 1 ( 3 R α R β R 2 δ α β ) R 5 ,
T α β γ = ( 4 π 0 ) 1 α β γ ( R 1 ) .
α α β = δ μ α / δ E β = ( α 1 + α 2 ) δ α β + 2 α 1 α 2 T α β + 1 3 T α γ δ ( α 1 A β γ δ ( 2 ) α 2 A β γ δ ( 1 ) ) + 1 3 T β γ δ ( α 1 A α γ δ ( 2 ) α 2 A α γ δ ( 1 ) ) + = α β α .
α Z Z 2 = ( α 1 + α 2 ) 2 + 16 5 α 1 2 α 2 2 R 6 ( 4 π 0 ) 2 + 592 105 ( α 1 2 A 2 2 + α 2 2 A 1 2 ) R 8 ( 4 π 0 ) 2 + 95616 4725 A 1 2 A 2 2 R 10 ( 4 π 0 ) 2 + , α X Z 2 = 12 5 α 1 2 α 2 2 R 6 ( 4 π 0 ) 2 + 48 35 ( α 1 2 A 2 2 + α 2 2 A 1 2 ) R 8 ( 4 π 0 ) 2 + 62912 4725 A 1 2 A 2 2 R 10 ( 4 π 0 ) 2 + .
α α β + β α β γ F γ + 1 2 γ α β γ δ F γ F δ + ,
( 4 π 0 ) 2 [ 64 25 ( β 1 2 Ω 2 2 + 6 7 β 1 β 2 Ω 1 Ω 2 + β 2 2 Ω 1 2 ) R 10 + 16 3 ( α 1 + α 2 ) ( γ 1 Ω 2 2 + γ 2 Ω 1 2 ) R 10 ] ; ( 4 π 0 ) 2 [ 48 25 ( β 1 2 Ω 2 2 + 6 7 β 1 β 2 Ω 1 Ω 2 + β 2 2 Ω 1 2 ) R 10 ] .
γ α β γ δ = 1 3 γ ( δ α β δ γ δ + δ α γ δ β δ + δ α δ δ β γ ) .

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