.TOURNAL OF MOLECULAR SPECTROSCOPY 36, 73432 (1970)
Structure of the Schumann-Runge Bands from the O-O to the 13-O Band
;\I. ACKERMAN AND 1;. BIAUME
Inslitut d’ACronomie Sputiale de Belgique, 1180 Brussels, Belgium
Spectra of the Schumann-Ilunge bands have been photographed nt high resolution. The 04 band has been measured for the first time. Precise values of the vibrational and rotational constant,s for the 74 to 11-O bands have been determined. Previous results for other bands are confirmed.
A. INTRODUCTION
Absorption spectra of oxygen at room temperature have been photographed by Curry and Herzberg (I), Gauss and Ballard (W), and Brix and Herzberg (3).
Recent st,udies (43) have shown the need for more accurate measurements than those available for some of the bands. The measurements reported here meet this requirement and offer the advantage of having been obtained from the instru- ment used by Brix and Herzberg.
In addition to a list of wave numbers of the observed lines, the deduced molecu- lar constants will be presented and discussed. Information on line widths derived from the spectra are also included.
B. EXPERIMENTAL DETAILS
The S-vacuum spectrograph (3) of the National Research Council of Canada (Ottawa) has been used. The concave grating blazed at an angle of 21%’ and having a radius of 3 meters was ruled with 1200 grooves/mm over an area of 150 X 65 mm.
The absorption tube had a length of 1% cm. Oxygen pressures of 0.4, 1, 3, 10.
“5, 100, and 760 mm Hg were used. The measurements of the O-O and 1-O bands wyrre obtained by filling the absorption cell and the spectrograph with oxygen at a pressure of 1 attn.
The light source was a Lyman discharge tube and all exposures were taken 011 Ilford QZ plates.
The oxygen spectra were obtained in the fourth order of the grating and the measurements were made against silicon lines (/t,7) in the same order and against second order iron lines. The relative wave numbers of sharp and unblended lines are reproducible to about f0.05 cm-‘, whereas the absolute wave numbers
$3
74 ACKERMAN AND BIAUME
may be in error by ho.1 cm-’ since this is the maximum dispersion observed in the determination of standard silicon lines against iron lines. In the case of broad oxygen lines, as in the 4-O band for instance, the accuracy is most probably not better than ~0.4 cm-‘. The accuracy for the other bands can be judged from the evaluated apparent line widths given below.
C. RESULTS
Wave numbers and identifications of the rotational lines measured in the v” = 0 sequence are presented in Table I. The appearance of the same wave number for two or more lines means that these have not been separated on the spectra.
The constants vg , R, and D, were derived from these data by graphical methods (5). To calculate band origins, the following formula was used
R(N) + P(N) - 2((& - B,.)),“N(N + 1)
= 2(vo + B,,) + 2A((& - &)),,N(N + l), (1) where ((B,! - B,.)),, is an approximate difference between the rotational con- stants of the upper and of the lower states and A((B,t - I?,.)),, is the residual
TABLE 1
Wave numbers of the observed lines
O-O Band 1-O Band 2-O Band
v0 =49358.15 cm-l v0 = 50045.68 cm-l y0 = 50710.83 cm-1 N"
1 3 5 7 9 11 13 15 17 19 21 23 25
l- P R T
49355.27 345.83 33 1.33 311.75 287.31 257.72 223.24 183.75 139.32
49360.12 357.10 349.18 336.16 318.11 295.11 267.22 234.13 195.97 154.03
P 50042.90
033.19 018.59 49998.82 973.93 943.95 908.85 868.65 823.28 772.83 717.39
R l- P
50047.49 50708.06
044.48 698.27
036.15 683.36
022.73 663.36
004.25 638.02
49980.6 1 607.44
951.92 571.68
918.01 530.73
879.12 484.54
835.02 433.14
785.67 376.49
731.51 3 14.73
R 50712.57
709.25 700.69 686.85 667.77 643.50 614.00 579.24 539.28 494.20 443.66 388.00 321.57
1
TABLE I (continued)
4-O Band 5-O Band
v,, = 51969.81 cm-l v. = 52561.39 cm-l
N”
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
N”
1
3 5 7 9 11 13 15 17 19 21 23 25 21
3-O Band v, = 51352.26 cm-l
P
51349.72 339.93 324.56 303.96 278.47 247.21 210.73 168.87 121.74 069.41 011.73 50948.52 880.12 806.5 1
l-
R
51353.99 350.20 341.35 326.92 307.40 282.49 252.12 216.63 175.51 129.49 077.50 020.16 50957.81 890.40 818.00
6-O Band Y o = 53122.79 cm-’
P
53119.75 109.86 094.05 072.54 045.22 012.12 52973.36 928.81 878.31 822.55 760.13 693.11 619.77
R 53 124.07
119.75 109.86 094.05 072.54 045.22 012.12 52913.36 928.81 878.3 1
822.55 760.13 693.11 619.77
l-
P
51967.55 957.03 941.81 921.70 894.84 863.03 825.94 783.02 735.19 681.43 622.62
R 5 1970.85
967.55 958.26 942.80 923.14 897.59 865.93 829.75 787.24 740.35 687.20 628.43
TABLE I (continued) 7-O Band v0 = 53656.27 cm-l
P
53653.10 642.81 626.71 604.94 571.24 543.28 503.63 458.10 406.6 1
349.05 285.54 216.38 140.96
R
53657.41 653.10 642.81 626.11 604.30 575.80 541.57 501.63 455.40 403.52 345.48 281.36 211.44 134.93
P
52558.85 548.57 532.89 511.79 484.98 452.92 414.89 371.44 322.12 267.39 206.99 140.96 068.75
-t-
R 52563.01
558.85 549.28 533.82 513.16 486.42 454.49 416.41 373.17 324.25 269.76 209.34 143.55 072.98
8-O Band v0 = 54156.28 cm-1
P
54152.63 143.03 126.62 104.03 075.53 041.07 000.1s 53953.38 900.43 841.55 776.12 704.87 627.25
R 54157.56
152.63 141.73 124.58 101.45 072.13 036.76 53995.18 947.66 893.95 834.31 768.09 695.85 617.78
75
TABLE 1 (continued) 9-O Band Y,, zS4622.17 cm-’
N"
1 3 5 7 9 11 13 15 17 19 21 23
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
p2 p3
54619.31 - -
608.78 54608.78 54608.78
592.14 592.14 592.14
569.17 569.17 569.17
539.89 539.89 539.89
504.3 1 504.31 504.31
462.35 462.62 462.62
414.24 414.39 414.39
359.60 360.22 360.22
298.82 299.41 299.4 1
231.54 232.31 232.31
157.91 158.95 158.95
-I R3
l-
-- %
54623.24 618.03 606.53 588.74 564.56 534.19 497.42 454.46 405.06 349.11 287.14 218.63
TABLE I (continued) 10-O Band Y. = sso50.90 cm-1
R?
54623.24 54623.24
618.03 618.03
606.53 606.53
588.74 588.74
564.56 564.56
534.19 534.19
497.68 497.68
454.76 454.76
405.63 405.63
349.82 349.82
287.90 287.90
219.46 219.46
Pl p2 p3
55048.01 - -
037.46 55037.46 55037.46
020.43 020.43 020.43
54996.89 54996.89 54996.89
966.77 966.77 966.77
930.10 930.10 930.10
886.92 886.92 886.92
837.20 837.57 837.57
780.87 781.53 781.53
718.27 718.92 718.92
648.94 649.70 649.70
572.91 574.10 574.10
490.39 49 1.09 49 1.09
401.03 402.27 402.27
304.99 306.24 306.24
r
Rl R2 R355051.62 55051.62 55051.62
046.27 046.27 046.27
034.23 034.23 034.23
015.60 015.60 015.60
54990.41 54990.41 4990.41
958.82 958.82 958.82
920.45 920.82 920.82
875.58 876.09 876.09
824.29 824.92 824.92
766.67 767.43 767.43
701.82 702.71 702.71
630.84 631.92 631.92
552.83 553.98 553.98
468.11 469.34 469.34
376.81 378.05 378.05
277.73 278.85 278.85
N”
I 3 5 I 9 11 13 15 17 19 21
N”
1 3 5 7 9 11 13 15 17 19
STRUCTURE OF SCHUMAN-RUNGE BANDS
TABLE I (continued) 11-O Band
” D = 55438.90 cm-l
77
PI p2
55435.76 -
425.20 55425.20
407.86 407.86
883.61 883.61
352.6 1 352.6 1
3 14.84 314.84
270.3 1 270.3 1
218.83 219.58
160.43 161.60
095.69 096.74
p3 - 55425.20
407.86 883.61 352.61 314.84 270.3 1 219.58 161.60 096.74
Pl pz p3
-r
RI R2 R3C
55780.72 - - 55784.35 55785.26 55785.26
770. I 8 55770.78 55770.78 778.07 778.60 778.60
752.30 752.71 752.71 764.56 765.11 765.11
727.19 727.73 727.73 743.87 744.51 744.5 1
695.13 695.73 695.73 716.18 717.15 717.15
655.84 656.74 656.74 681.33 682.55 682.55
609.65 610.71 610.71 639.56 640.89 640.89
556.31 557.64 557.64 590.63 592.16 592.16
495.94 497.45 497.45 534.61 536.23 536.23
428.39 430.22 430.22 471.43 473.20 473.20
T- Rl R2 R3
55439.44 55439.44 55439.44
433.74 433.74 433.74
42 1 .OO 421.00 421.00
401.40 40 1.40 401.40
375.22 375.22 375.22
342.15 342.15 342.15
302.35 302.35 302.35
255.43 256.18 256.18
201.71 202.98 202.98
141.44 142.60 142.60
072.41 074.86 074.86
TABLE I (continued) 12-O Band v. = 55784.57 cm-1
1
75 ACKERMAN AND BIAUME
TABLE I (continued) 13-O Band v, = 56085.47 cm1
1 3 S I 9 11 13 1s 17 19
Pl
56080.97 070.13 051.67 025.71 55992.41 951.72 903.69 848.25 785.26
p2 p3
- -
5607 1.38 56071.38
052.91 052.91
027.09 927.09
55993.95 55993.95
953.51 953.51
905.58 905.58
850.30 850.69
787.52 788.15
-r
Rl R2 R356084.37 56085.70 56085.70
077.46 078.69 078.69
063.09 064.39 064.39
041.23 042.78 042.78
012.0s 013.79 013.79
55975.52 55977.36 55977.36
931.52 933.46 934.01
880.13 882.24 882.91
821.24 823.5 1 824.49
754.80 757.16 758.32
between the approximate and the real difference. The residual can be more accurately determined from the plot
[P(N) + R (N) - ~((B,J - B,,,)),,N(N + 1) -2 (~0 + &)I/‘N(N + 1)
= 3A((B,t - B”.)),,, + qo,t - D,.)N(N + l),
ca>
where the D term is taken into account and from which (DOT - D,,() cm be ob- tained. The values of B,,t and D,. determined by Babcock and Herzberg (8) are then introduced into Eqs. (1) and (2) to obtain vo, B,, and D,t . In the bands where the triplet components are resolved the wave numbers of the transitions between the Fz levels for which N = J have been used in the calculations. The band origins and the rotational constants are collected in Table II where, for the sake of completeness and comparison, the data given in previous investiga- tions are included.
Half-widths of lines have been evaluated on microphotometric tracings of t,he photographed spectra. For this purpose, weak neighboring lines were chosen from which the photographic contrast was also determined by means of the theoretical rotational intensity distribution.
The results are presented in Fig. 1.
DISCUSSION
The wave numbers of the O-O band measured for the first time and listed in Table I lead to a value of the band origin in agreement with the early work of Curry and Herzberg (1). This concludes the controversy on the subject (2, 9).
TABLE II Band origins. vibrational quanta and rotational constants of the Schumann-Runge absorption bands - Y. - C 1 : 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 T v, (cm-l) T AG’(v’{-i)(cm-1) T B,, (cm-l) 1 - Prer WC - 0.8 0.8( 0.71 0.7t 0.71 0.7: 0.71 0.65 0.6: 0.61 0.6: 0.F 0.5( 0.5: -
-T- / L
KB(2) wa OC( IO) KB(2) 0.719 0.703 0.671 0.651 0.633 0.593 0.554 0.523 0.492 0.43 1 O(5) 3 (5) Present work 49358.15 50045.68 50710.83 51352.26 51969.81 52561.39 53 122.79 53656.?7 54156.28 54622.17 55050.90 55438.90 55784.57 56085.47
Present work 687.53 665.15 64 1.43 617.55 591 S8 Shl.40 533.48 500.01 465.89 428.73 388.00 345.67 300.90
W(l) BW) 0.813 0.798 0.785 0.770 0.754 0.735 0.719 0.702 0.5625 0.5247 0.4836 0.4399 0.3953 0.347 0.296 0.258 0.207 0.159 1 ‘resen1 work 5.06 6.61 5.10 4.54 3.56 5.71 5.71 b.96 6.71 7.21 9.75 9.3 1 14.16 23.91
OC( 10) 49357.6 50045.65 50710.75 51352.2 5 1969.84 52561.65 53 122.8 536% 8 55784.59 56085.5 1 56340.47 56550.54 56719.50 56852.41 56954.54 57030.18 57082.83 57114.77
688.05 665.1 641.45 617.64 591.81 561.15 534.0 300.92 254.96 210.07 168.96 132.91 102.13 75.64 52.65 31.94
Ml.7 533.6 500.0 466.4 429.2 387.5 346.5 300.1 Fi5.0
> 4.38 13 16.8 21.2 25.7 34.3 45 152 49 76 105
51969.6 5ZXG.6 53 124.3 53658.5 54158.9 54624.4 55053.3 55441.5 55786.9 56087.6 56342.6 5655 1 .O
593.0 561.7 534.2 500.4 465.5 428.9 388.2 345.4 300.7 255.0 208.4
SX60.F 53 122.5 53656. I 54156.1 54622.5 5505 1.7 55439.2 55785.7 56085.8 56340.8 0.?367 0.7183 0.6978 0.6749 0.6508 0.6243
4.5 4.75 5.3 5.9 4.9 9.5
80 ACKERMAN AND BIAUME
4-
f 3-- E z 2- a’
l-l I
0 5 V’ 10 15
FN. 1. Apparent line half-width AV (cm+) versus vihrat,ional quant,um number (23’) of the upper state: (----), the theoretical values given by Murrell and Taylor (I$), normalized at V’ = 4.
The band origins obtained in the present work are in excellent agreement with the other values derived from high resolution spectra (1,3). Now that such data are available for comparison, a systematic and relatively large difference appears with all the values obtained by Knauss and Ballard (2). The discrepancy in- creases from U’ = 4 to higher v’ values and then decreases slightly. Since this variation is slo\v the AG values are much more consistent. This fact gives confi- dence in the accuracy of the differences.
From our data (0 5 v’ 5 12) associated with the values obtained by Brix and Heraberg (3) (13 5 v’ < 20) the following least squares formula
AG,’ = 676.79s - 9.2935 U’ - 2.9221 VI” + 0.088033 v’~,
has been deduced for the vibrational quanta. The differences between all the measured values AG,’ and the calculated AG,’ have been plotted versus v’ in Fig. 2. The purpose of this procedure is only to show the scatter of the measure- ments, However it also reveals a systematic discontinuity at v’ = 5.
To visualize the scatter of the B’ measurements, the least squares formula, B,' = 0.80944 - 6.0191 X lo-‘(u’ + &) - 1.1189 X W3(v + >JJ”
- 1.217 X lo-“(V’ + >s)3, has been calculated from our values (0 5 v’ 5 13) associated with those (14 _<
v’ 5 21) obtained by Brix and Herzberg (3). The differences between all the measurements B,: and the calculated B,' are plotted in Fig. 3.
The half-width measurements presented in Fig. 1 correspond to the line half- width appearing on the spectra and limiting the accuracy of wave number measurements. The variation of this width as a function of the vibrational quan-
STRUCTURE OF SCHUMAN-RUNGE BAN 1 W
QOl
7 E ”
- 0
- ” m
I
‘m E
-0,Ol
I
(8) Ref. (1)
I I I
(+) II (2) +
(8) 11 (3)
+
(a) 11 (5) P
(0) Present work
0 0
0 p 0
0 lx A
0 + +
V + A
m 0 * A A
0
Q I3
0
%8%’
+ A
8 A
+
V A
+ A
0 5 10
V’ 15 20
FIG. 2. Differences between the measured (AG,,,‘) and calculated (AG,‘) values of the vibrational quanta (cm-l) versus v’.
1 I I 1 I ’
(V) Ref. (1)
10 8 (+I II (2)
(A) II (3) (rn) II (10)
BB;
‘; (0) Present work f A
E % A
0
-2 tf
QO 0
I P
I!! 68
‘0 E
a n
@ ,:r
t ,!, A -10 -
I I I I
0 5 10 V’ 15 20
Frc;. 3. Diferences bet,ween the measured (Bm’) and calculated (B,.‘) values of the rot.ational constant R’ (cm-l) versus I/.
turn number may be partly interpreted in terms of predissociation. This is the case for the 40 band where the conclusion of Carroll (II) is supported here.
However, the maximum in the 74 band is partly due to the fact that the P and R components appear superposed on the 6-O band and move away from each
82 ACKERMAN AND BIAUME
other for v’ values larger or smaller than 6. A similar argument applies to the maximum observed at v’ = 11 since there one component of the triplet begins to be more and more separated from the two other ones. In both cases, the separation of adjacent lines is far from complete and the real width is difficult to measure.
Our data do not fully support the theoretical results obtained by ?tlurrell and and Taylor (12). Even if their values represented by the solid curve in Fig. 1 show the same general behavior as the measurements do, a confirmation from another type of experimental measurement seems to be needed.
CONCLUSION
A complete set of accurate experimental values for vibrational and rotational constants obtained from measurements of the Schumann-Runge bands are now available. It appears that information on line width deduced from photographic spectra mainly obtained for purely spectroscopic purposes has to be very care- fully examined before they are used as absorption cross-section data.
We are deeply grateful to Dr. G. Herzberg and his st,aff for their particnlar interest and valuable advice in this work and for providing all the facilities of the Physics Division of the National Research Council of Canada (Ottawa). We express onr thanks to Professor M. Nicolet, for his sustained help and useful suggestions.
RECEIVED: December 21, 1969
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3. P. BILIX AND G. HF,RZBERG, Can. J. Phys. 32, 110 (1954).
4. M. ACI~ERM.\N, F. BIAUME AND M. NICOLF,T, Can. J. Chem. 47, 183-l (1969).
5. M. OGaw.%, Sti. Light (Tokyo) 16, 97 (1966).
6. It. I). HUDSON _&ND V. L. CARTER, J. Opt. Sot. Amer. 58, 1621 (1968).
7. L. J. R.~DZIEMSKI, K. L. ANDRF,~, V. K.~u~M~N, AND U. LITZEN, J. Opt. Sot. Amer. 67, 336 (1967 1.
8. H. I>. B.~ncoc~ AND L. HFXZBERG, Asfropkysical J. 108, 167 (1948).
9. G. H~~RZRERG, “Molecular Spect,ra and Molecular Structllre,” 2nd ed., Vol. 1. Van Nostrand, Princeton, N.J. 1950.
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