Abstract

The spectrum of CO2 in the photographic infrared has been studied with absorbing paths up to 5500 m. Thirteen absorption bands were found of which eleven have been analyzed in detail. One of these is due to C13O2. From the band origins of the C12O2 bands improved values for some of the anharmonic constants of the molecule have been derived.

The study of the rotational structure of the photographic infrared CO2 bands has yielded considerably improved values for the rotational constants. The new values are B000=0.39020 cm−1, α1=+0.00109, α2=−0.00073, α3=+0.00307 cm−1. From these the following equilibrium values of rotational constant, moment of inertia, and internuclear distance are obtained:

Be=0.39155cm-1,         Ie=71.468×10-40gmcm2,         re=1.16005×10-8cm.

By taking account of the effect of Fermi resonance, excellent agreement of the observed B[v] values with those calculated from the αi and Be is obtained.

The l-type doubling in the states 0110, 1113, and 0313 has been determined. The agreement of the splitting constants q with those obtained from theory is satisfactory.

© 1953 Optical Society of America

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References

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  1. W. S. Adams and T. Dunham, Publ. Astron. Soc. Pacific 44, 243 (1932).
    [CrossRef]
  2. A. Adel and V. M. Slipher, Phys. Rev. 46, 240 (1934).
  3. G. Herzberg and L. Herzberg, J. Chem. Phys. 18, 1551 (1950).
    [CrossRef]
  4. G. Herzberg, in G. P. Kuiper’s The Atmospheres of the Earth and Planets (University of Chicago Press, Chicago, 1949), first edition, p. 346; (1952), second edition, p. 406. See also a preliminary note on the photographic infrared spectrum by G. Herzberg and H. Verleger, Phys. Rev. 48, 706 (1935).
    [CrossRef]
  5. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945).
  6. H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
    [CrossRef]
  7. G. Herzberg (unpublished): see Astron. J. 52, 147 (1947).
  8. G. Herzberg, reference 5, p. 274.
  9. R. C. Herman, Astrophys. J. 107, 386 (1948).
    [CrossRef]
  10. R. S. Mulliken, J. Phys. Chem. 41, 159 (1937).
    [CrossRef]
  11. Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
    [CrossRef]
  12. Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
    [CrossRef]
  13. W. S. Benedict and E. K. Plyler, J. Research Natl. Bur. Standards 46, 246 (1951).
    [CrossRef]
  14. A. H. Nielsen and Y. T. Yao, Phys. Rev. 68, 173 (1945).
    [CrossRef]
  15. This is also shown by the appreciable scatter of the B″ values obtained by Goldberg et al. for different bands without the use of combination differences.
  16. J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).
    [CrossRef]
  17. A. Adel and D. M. Dennison, Phys. Rev. 44, 99 (1933).
    [CrossRef]
  18. G. Herzberg, Revs. Modern Phys. 14, 219 (1942).
    [CrossRef]
  19. For a more detailed explanation see Fig. 111, p. 389 of ref. (5) and the accompanying discussion.
  20. P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).
    [CrossRef]
  21. J. de Heer and H. H. Nielsen, J. Chem. Phys. 20, 101 (1952).
    [CrossRef]

1952 (2)

Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

J. de Heer and H. H. Nielsen, J. Chem. Phys. 20, 101 (1952).
[CrossRef]

1951 (2)

W. S. Benedict and E. K. Plyler, J. Research Natl. Bur. Standards 46, 246 (1951).
[CrossRef]

J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).
[CrossRef]

1950 (1)

G. Herzberg and L. Herzberg, J. Chem. Phys. 18, 1551 (1950).
[CrossRef]

1949 (1)

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

1948 (2)

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[CrossRef]

R. C. Herman, Astrophys. J. 107, 386 (1948).
[CrossRef]

1945 (1)

A. H. Nielsen and Y. T. Yao, Phys. Rev. 68, 173 (1945).
[CrossRef]

1942 (1)

G. Herzberg, Revs. Modern Phys. 14, 219 (1942).
[CrossRef]

1937 (1)

R. S. Mulliken, J. Phys. Chem. 41, 159 (1937).
[CrossRef]

1934 (1)

A. Adel and V. M. Slipher, Phys. Rev. 46, 240 (1934).

1933 (1)

A. Adel and D. M. Dennison, Phys. Rev. 44, 99 (1933).
[CrossRef]

1932 (2)

P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).
[CrossRef]

W. S. Adams and T. Dunham, Publ. Astron. Soc. Pacific 44, 243 (1932).
[CrossRef]

Adams, W. S.

W. S. Adams and T. Dunham, Publ. Astron. Soc. Pacific 44, 243 (1932).
[CrossRef]

Adel, A.

A. Adel and V. M. Slipher, Phys. Rev. 46, 240 (1934).

A. Adel and D. M. Dennison, Phys. Rev. 44, 99 (1933).
[CrossRef]

Barker, E. F.

P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).
[CrossRef]

Benedict,

Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

Benedict, W. S.

W. S. Benedict and E. K. Plyler, J. Research Natl. Bur. Standards 46, 246 (1951).
[CrossRef]

Bernstein, H. J.

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[CrossRef]

Cohen, E. R.

J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).
[CrossRef]

de Heer, J.

J. de Heer and H. H. Nielsen, J. Chem. Phys. 20, 101 (1952).
[CrossRef]

Dennison, D. M.

A. Adel and D. M. Dennison, Phys. Rev. 44, 99 (1933).
[CrossRef]

DuMond, J. W. M.

J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).
[CrossRef]

Dunham, T.

W. S. Adams and T. Dunham, Publ. Astron. Soc. Pacific 44, 243 (1932).
[CrossRef]

Goldberg,

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

Herman, R. C.

R. C. Herman, Astrophys. J. 107, 386 (1948).
[CrossRef]

Herzberg, G.

G. Herzberg and L. Herzberg, J. Chem. Phys. 18, 1551 (1950).
[CrossRef]

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[CrossRef]

G. Herzberg, Revs. Modern Phys. 14, 219 (1942).
[CrossRef]

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945).

G. Herzberg (unpublished): see Astron. J. 52, 147 (1947).

G. Herzberg, reference 5, p. 274.

G. Herzberg, in G. P. Kuiper’s The Atmospheres of the Earth and Planets (University of Chicago Press, Chicago, 1949), first edition, p. 346; (1952), second edition, p. 406. See also a preliminary note on the photographic infrared spectrum by G. Herzberg and H. Verleger, Phys. Rev. 48, 706 (1935).
[CrossRef]

Herzberg, L.

G. Herzberg and L. Herzberg, J. Chem. Phys. 18, 1551 (1950).
[CrossRef]

Kuiper, G. P.

G. Herzberg, in G. P. Kuiper’s The Atmospheres of the Earth and Planets (University of Chicago Press, Chicago, 1949), first edition, p. 346; (1952), second edition, p. 406. See also a preliminary note on the photographic infrared spectrum by G. Herzberg and H. Verleger, Phys. Rev. 48, 706 (1935).
[CrossRef]

Martin, P. E.

P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).
[CrossRef]

McMath,

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

Mohler,

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

Mulliken, R. S.

R. S. Mulliken, J. Phys. Chem. 41, 159 (1937).
[CrossRef]

Nielsen, A. H.

A. H. Nielsen and Y. T. Yao, Phys. Rev. 68, 173 (1945).
[CrossRef]

Nielsen, H. H.

J. de Heer and H. H. Nielsen, J. Chem. Phys. 20, 101 (1952).
[CrossRef]

Pierce,

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

Plyler, E. K.

W. S. Benedict and E. K. Plyler, J. Research Natl. Bur. Standards 46, 246 (1951).
[CrossRef]

Slipher, V. M.

A. Adel and V. M. Slipher, Phys. Rev. 46, 240 (1934).

Strong,

Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

Taylor,

Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

Yao, Y. T.

A. H. Nielsen and Y. T. Yao, Phys. Rev. 68, 173 (1945).
[CrossRef]

Astrophys. J. (1)

R. C. Herman, Astrophys. J. 107, 386 (1948).
[CrossRef]

J. Chem. Phys. (4)

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30 (1948).
[CrossRef]

G. Herzberg and L. Herzberg, J. Chem. Phys. 18, 1551 (1950).
[CrossRef]

Taylor, Benedict, and Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

J. de Heer and H. H. Nielsen, J. Chem. Phys. 20, 101 (1952).
[CrossRef]

J. Phys. Chem. (1)

R. S. Mulliken, J. Phys. Chem. 41, 159 (1937).
[CrossRef]

J. Research Natl. Bur. Standards (1)

W. S. Benedict and E. K. Plyler, J. Research Natl. Bur. Standards 46, 246 (1951).
[CrossRef]

Phys. Rev. (6)

A. H. Nielsen and Y. T. Yao, Phys. Rev. 68, 173 (1945).
[CrossRef]

Goldberg, Mohler, McMath, and Pierce, Phys. Rev. 76, 1848 (1949).
[CrossRef]

J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).
[CrossRef]

A. Adel and D. M. Dennison, Phys. Rev. 44, 99 (1933).
[CrossRef]

A. Adel and V. M. Slipher, Phys. Rev. 46, 240 (1934).

P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).
[CrossRef]

Publ. Astron. Soc. Pacific (1)

W. S. Adams and T. Dunham, Publ. Astron. Soc. Pacific 44, 243 (1932).
[CrossRef]

Revs. Modern Phys. (1)

G. Herzberg, Revs. Modern Phys. 14, 219 (1942).
[CrossRef]

Other (6)

For a more detailed explanation see Fig. 111, p. 389 of ref. (5) and the accompanying discussion.

This is also shown by the appreciable scatter of the B″ values obtained by Goldberg et al. for different bands without the use of combination differences.

G. Herzberg, in G. P. Kuiper’s The Atmospheres of the Earth and Planets (University of Chicago Press, Chicago, 1949), first edition, p. 346; (1952), second edition, p. 406. See also a preliminary note on the photographic infrared spectrum by G. Herzberg and H. Verleger, Phys. Rev. 48, 706 (1935).
[CrossRef]

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945).

G. Herzberg (unpublished): see Astron. J. 52, 147 (1947).

G. Herzberg, reference 5, p. 274.

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Figures (3)

Fig. 1
Fig. 1

CO2 bands near 12 000A obtained with an absorbing path of 530 m at 1 atmos (1st order, 21-ft grating). (a) The bands ν1+3ν3 and ν1+ν2+3ν3ν2. (b) Bands 2ν2+3ν3 and 3ν2+3ν3ν2. Lines of main bands are marked below, those of “hot” bands above each strip. The staggering in the “hot” bands is exaggerated in the leading lines.

Fig. 2
Fig. 2

Vibrational energy levels of the CO2 molecule. Only ∑+ and Π levels are shown. Several Δ, Φ, ⋯ levels have been found by Taylor, Benedict, and Strong (see reference 11). They all have v3=0 and are close to the levels 100, 110, 200, 210, and 300 shown in the figure. Observed levels are shown by heavy full lines, predicted levels by broken lines. Observed transitions are indicated by light vertical lines. The bands ν2+2ν3 and 3ν2+2ν3 shown in the third column have been found under low dispersion in unpublished work of Herzberg and Kuiper (see reference 4).

Fig. 3
Fig. 3

Deviations of the lines in the band ν1+ν2+ν3 from those calculated with the constants of Table VI. On the abscissa m is plotted which is J+1 for the R branch and −J for the P branch.

Tables (7)

Tables Icon

Table I Band heads (λh, νh), band origins (ν0), and assignments of CO2 bands observed in the photographic infrared.

Tables Icon

Table II Wave numbers of the lines in the CO2 bands (νvac, cm−1).a

Tables Icon

Table III Wave numbers of the lines in the C13O2 band (νvac, cm−1).a

Tables Icon

Table IV Vibrational constants of CO2.

Tables Icon

Table V Combination differences Δ2F(J) for the ground state (00°0) of CO2.

Tables Icon

Table VI Rotational constants Bv of CO2.

Tables Icon

Table VII l-type doubling constants for CO2.

Equations (16)

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B e = 0.3915 5 cm - 1 ,             I e = 71.46 8 × 10 - 40 gm cm 2 ,             r e = 1.1600 5 × 10 - 8 cm .
Σ g + Σ u + ,             Σ g + Π u ,             Σ u + Π g ,             Π u Π g .
G 0 ( v 1 , v 2 , v 3 ) = ω 1 0 v 1 + ω 2 0 v 2 + ω 3 0 v 3 + x 11 v 1 2 + x 22 v 2 2 + x 33 v 3 2 + x 12 v 1 v 2 + x 13 v 1 v 3 + x 23 v 2 v 3 + g 22 l 2 2 + ,
B 000 = 0.3902 0 cm - 1 ,             D 000 = 0.12 × 10 - 6 cm - 1 .
B 010 ( c ) = 0.3912 3 cm - 1 ,             B 010 ( d ) = 0.3905 8 cm - 1 .
R ( J ) + P ( J ) = 2 ν 0 + ( 2 B - 4 D ) + 2 ( B - B - 6 D ) J ( J + 1 ) - 2 ( D - D ) J 2 ( J + 1 ) 2 .
B v 1 v 2 v 3 = B e - α 1 ( v 1 + 1 2 ) - α 2 ( v 2 + 1 ) - α 3 ( v 3 + 1 2 ) ,
B e = h 8 π 2 c I e = h 16 π 2 c m O r e 2 .
α 1 = + 0.00109 ,             α 2 = - 0.00073 ,             α 3 = + 0.00307 cm - 1 .
B e = 0.3915 5 cm - 1 .
I e = 71.46 8 × 10 - 40 gm cm 2 , r e = 1.1600 5 × 10 - 8 cm ,
I 0 = 71.71 5 × 10 - 40 gm cm 2 , r 0 = 1.1620 5 × 10 - 8 cm .
B n = a 2 B n 0 + b 2 B i 0 , B i = b 2 B n 0 + a 2 B i 0 ,
B i = a i i 2 B i 0 + a i j 2 B j 0 + a i k 2 B k 0 , B j = a j i 2 B i 0 + a j j 2 B j 0 + a j k 2 B k 0 , B k = a k i 2 B i 0 + a k j 2 B j 0 + a k k 2 B k 0 ,
B 000 ( C 13 O 2 ) = 0.3903 7 cm - 1 .
Δ ν = q J ( J + 1 ) ,