L. Rosenmann,
J. M. Hartmann,
M. Y. Perrin,
and J. Taine
The authors are with CNRS/ECP Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion, Ecole Centrale des Arts et Manufactures, Grande Voie des Vignes 92295 Chatenay-Malabry CEDEX, France.
L. Rosenmann, J. M. Hartmann, M. Y. Perrin, and J. Taine, "Accurate calculated tabulations of IR and Raman CO2 line broadening by CO2, H2O, N2, O2 in the 300–2400-K temperature range," Appl. Opt. 27, 3902-3907 (1988)
Pressure-broadening coefficients for 12C16O2 lines have been calculated with a recent model derived from the Robert and Bonamy approach which leads to more accurate results than the previouslyused Anderson-Tsao-Curnutte model. Systematic calculations of CO2–CO2, CO2–H2O, CO2–N2, and CO2–O2 broadening coefficients in the 300–2400-K temperature range are presented. The results are suitable for both IR and Raman lines and should be useful for spectra calculations. Tabulations of the broadening coefficients are given together with simple analytical expressions for their rotational quantum number and temperature dependences.
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Comparisons Between the Broadening (in 10−3 cm−1 atm−1) of Various Infrared and Raman CO2 Linesa
H2O-BROADENING
CO2-BROADENING 1
T(K)
INFRARED
RAMAN
INFRARED
RAMAN
Q
P, R
Q
O, S
Q
P, R
Q
O, S
300
116.
1114.
114.
116.
117.
116.
116.
117.
148.
1148.
148.
148.
81.9
82.5
81.9
81.9
135.
1135.
135.
135.
60.7
60.8
60.7
60.7
600
68.2
167.6
67.1
68.2
70.0
69.5
69.0
70.0
84.5
184.4
84.5
84.5
57.9
58.1
57.9
57.8
86.9
186.8
86.9
86.9
41.7
41.9
41.7
41.7
1200
41.0
139.2
40.3
41.0
42.4
42.1
41.7
42.3
48.7
148.6
48.7
48.7
37.5
37.5
37.5
37.4
52.5
152.5
52.5
52.5
31.3
29.1
31.3
31.3
2400
25.9
124.6
25.5
25.9
25.9
26.9
25.5
25.9
29.6
129.5
29.6
29.6
24.2
24.3
24.2
24.3
32.1
132.1
32.1
32.1
22.2
22.2
22.2
22.2
N2-BROADENING
O2-BROADENING
T(K)
INFRARED
RAMAN
INFRARED
RAMAN
Q
P, R
Q
O, S
Q
P, R
Q
O, S
300
92.2
91.5
90.9
92.1
183.4
183.0
82.4
83.3
73.1
73.1
73.1
73.1
161.1
161.1
61.1
61.1
62.7
62.9
62.7
62.6
154.9
154.9
54.9
54.8
600
54.7
54.3
53.8
54.7
150.3
150.0
49.5
50.3
44.0
44.0
44.0
44.0
138.1
138.1
38.1
38.1
41.5
41.5
41.5
41.5
135.8
135.8
35.8
35.8
1200
32.6
32.4
32.1
32.6
130.2
130.0
29.7
30.2
28.3
28.3
28.3
28.3
124.7
124.7
24.7
24.7
27.0
27.0
27.0
27.0
123.5
123.5
23.5
23.5
2400
20.0
19.8
19.7
20.0
118.5
118.4
18.3
18.5
19.0
19.0
19.0
19.0
116.9
116.9
16.9
16.9
17.9
17.9
17.9
17.9
116.0
116.0
16.0
16.0
Successive values are for J = 3,43,83 (Q, P lines); J = 2,42,82 (R, S lines); J = 4, 44, 84 (lines), where J is the rotational quantum number of the lower level of the transition.
Table II
Broadening and Temperature Coefficients γ|m| (300 K) (in 10−3 cm−1 atm−1) and N|m| [see Eq.(1)] of CO2 Lines Broadened by CO2, H2O, N2, and O2
LINE |m|
CO2–CO2
CO2–H2O
CO2–N2
CO2–CO2
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
1
119.9
0.723
117.7
0.726
95.0
0.737
85.9
0.721
3
115.8
0.729
113.9
0.754
91.4
0.745
83.0
0.730
5
116.9
0.735
116.7
0.764
91.6
0.747
82.7
0.729
7
117.0
0.731
119.6
0.771
91.4
0.744
82.0
0.723
9
116.1
0.722
123.5
0.782
90.7
0.735
80.8
0.712
11
113.3
0.701
126.5
0.789
89.2
0.722
79.0
0.700
13
111.3
0.689
129.6
0.797
87.2
0.705
76.7
0.682
15
109.2
0.679
132.6
0.802
84.7
0.687
74.1
0.661
17
107.1
0.671
135.6
0.811
82.2
0.669
71.1
0.637
19
106.0
0.670
136.6
0.808
79.6
0.653
68.3
0.617
21
104.9
0.669
136.7
0.800
77.4
0.641
65.9
0.603
23
103.7
0.669
136.7
0.793
75.8
0.635
64.2
0.595
25
102.7
0.669
137.7
0.791
74.6
0.633
63.0
0.595
27
100.8
0.663
140.6
0.802
73.9
0.636
62.5
0.601
29
98.9
0.655
143.5
0.812
73.5
0.642
62.1
0.609
31
97.0
0.646
144.5
0.811
73.2
0.648
61.8
0.615
33
94.8
0.635
144.5
0.804
73.1
0.656
61.6
0.624
35
92.5
0.623
144.5
0.800
73.0
0.661
61.4
0.628
37
90.2
0.609
144.6
0.795
72.9
0.666
61.3
0.633
39
87.8
0.596
145.6
0.795
72.9
0.671
61.2
0.638
41
85.5
0.583
147.6
0.800
72.7
0.674
61.0
0.640
43
83.3
0.570
147.7
0.795
72.5
0.677
60.8
0.642
45
81.2
0.557
146.8
0.785
72.3
0.676
60.6
0.642
47
79.2
0.547
146.9
0.782
72.1
0.678
60.3
0.642
49
77.5
0.537
147.8
0.783
71.9
0.678
60.1
0.643
51
75.7
0.529
148.8
0.784
71.6
0.676
59.9
0.641
53
74.2
0.521
150.8
0.791
71.3
0.677
59.6
0.640
55
72.8
0.515
150.8
0.787
70.9
0.672
59.4
0.640
57
71.4
0.508
150.8
0.784
70.4
0.670
59.1
0.637
59
70.2
0.504
149.9
0.776
70.0
0.666
59.0
0.638
61
69.1
0.500
149.9
0.773
69.5
0.663
58.6
0.635
63
68.0
0.497
148.0
0.761
69.0
0.659
58.3
0.632
65
67.0
0.493
147.0
0.752
68.5
0.655
58.0
0.632
67
66.0
0.492
146.2
0.744
67.9
0.650
57.7
0.630
69
65.1
0.488
145.3
0.736
67.3
0.644
57.3
0.626
71
64.3
0.488
144.4
0.728
66.8
0.639
56.9
0.621
73
63.6
0.487
143.5
0.720
66.1
0.634
56.6
0.619
75
62.9
0.486
141.6
0.709
65.5
0.628
56.2
0.615
77
62.1
0.485
139.7
0.699
64.9
0.622
55.9
0.615
79
61.5
0.486
137.7
0.688
64.2
0.616
55.6
0.610
81
60.9
0.485
136.7
0.683
63.6
0.612
55.2
0.607
83
60.3
0.485
135.7
0.678
62.9
0.606
54.9
0.605
85
59.8
0.485
135.7
0.677
62.3
0.599
54.5
0.600
87
59.3
0.487
135.7
0.677
61.6
0.593
54.1
0.598
89
58.8
0.487
134.7
0.671
60.9
0.588
53.7
0.594
91
58.3
0.487
134.7
0.671
60.3
0.581
53.3
0.591
93
57.7
0.487
133.7
0.666
59.6
0.575
52.9
0.588
95
57.2
0.486
131.7
0.658
58.9
0.568
52.6
0.586
97
56.6
0.486
128.8
0.642
58.3
0.563
52.2
0.583
99
56.0
0.484
127.8
0.639
57.6
0.556
51.9
0.578
101
55.4
0.482
126.7
0.634
56.9
0.550
51.4
0.573
Table III
Parameters γ*|m| (300 K) (in 10−3 cm−1 atm−1) and N*|m| of the Polynomial Correlations[see Eq. (2)]
Broadening coefficients γ*|m| (300 K)
System
a0
a1
a2
CO2-H2O
1.142 10+2
1.266 10+0
−1.163 10−2
CO2-CO2
1.253 10+2
−1.172 10+0
4.660 10−3
CO2-N2
9.169 10+1
−5.323 10−1
2.149 10−3
CO2-O2
80293 10+1
−6.797 10−1
3.982 10−3
Temperature coefficients N*|m|
System
b0
b1
b2
CO2-H2O
7618 10−1
2.354 10−3
−3.785 10−5
CO2-CO2
7.706 10−1
−6.017 10−3
3.078 10−5
CO2-N2
7.146 10−1
−6.306 10−4
−7.544 10−6
CO2-O2
6.947 10−1
−1.798 10−3
8.167 10−6
Table IV
Parameters of the Constant Broadening Coefficient Approximation [see Eq. (4)]
Constant broadening coefficient parameters
System
103(300 K) cm−1 atm−1
(300 K)
α
CO2-H2O
135.
0.750
0.013
CO2-CO2
105.
0.773
0.050
CO2-O2
69.7
0.722
0.017
CO2-N2
80.6
0.736
0.017
Table V
Calculated Broadening Coefficients for High |m| Values (In 10−3 cm−1 atm−1)a
T(K)
CO2-CO2
CO2-H2O
CO2-N2
CO2-O2
300
48.9
110.
49.3
46.3
-
-
-
-
-
-
-
-
600
35.6
77.9
36.8
32.8
29.4
66.2
30.8
2805
-
-
-
-
1200
26.2
51.2
25.7
22.5
23.3
46.4
23.8
21.2
20.5
41.4
21.4
19.5
2400
19.9
32.6
17.4
15.5
17.6
30.9
16.9
15.0
16.2
28.4
16.2
14.5
Successive values are for |m| = 121, 161, 201; —, the corresponding values have not been calculated due to the breakdown of the semiclassical approximation for such high rotational transitions at these temperatures.
Tables (5)
Table I
Comparisons Between the Broadening (in 10−3 cm−1 atm−1) of Various Infrared and Raman CO2 Linesa
H2O-BROADENING
CO2-BROADENING 1
T(K)
INFRARED
RAMAN
INFRARED
RAMAN
Q
P, R
Q
O, S
Q
P, R
Q
O, S
300
116.
1114.
114.
116.
117.
116.
116.
117.
148.
1148.
148.
148.
81.9
82.5
81.9
81.9
135.
1135.
135.
135.
60.7
60.8
60.7
60.7
600
68.2
167.6
67.1
68.2
70.0
69.5
69.0
70.0
84.5
184.4
84.5
84.5
57.9
58.1
57.9
57.8
86.9
186.8
86.9
86.9
41.7
41.9
41.7
41.7
1200
41.0
139.2
40.3
41.0
42.4
42.1
41.7
42.3
48.7
148.6
48.7
48.7
37.5
37.5
37.5
37.4
52.5
152.5
52.5
52.5
31.3
29.1
31.3
31.3
2400
25.9
124.6
25.5
25.9
25.9
26.9
25.5
25.9
29.6
129.5
29.6
29.6
24.2
24.3
24.2
24.3
32.1
132.1
32.1
32.1
22.2
22.2
22.2
22.2
N2-BROADENING
O2-BROADENING
T(K)
INFRARED
RAMAN
INFRARED
RAMAN
Q
P, R
Q
O, S
Q
P, R
Q
O, S
300
92.2
91.5
90.9
92.1
183.4
183.0
82.4
83.3
73.1
73.1
73.1
73.1
161.1
161.1
61.1
61.1
62.7
62.9
62.7
62.6
154.9
154.9
54.9
54.8
600
54.7
54.3
53.8
54.7
150.3
150.0
49.5
50.3
44.0
44.0
44.0
44.0
138.1
138.1
38.1
38.1
41.5
41.5
41.5
41.5
135.8
135.8
35.8
35.8
1200
32.6
32.4
32.1
32.6
130.2
130.0
29.7
30.2
28.3
28.3
28.3
28.3
124.7
124.7
24.7
24.7
27.0
27.0
27.0
27.0
123.5
123.5
23.5
23.5
2400
20.0
19.8
19.7
20.0
118.5
118.4
18.3
18.5
19.0
19.0
19.0
19.0
116.9
116.9
16.9
16.9
17.9
17.9
17.9
17.9
116.0
116.0
16.0
16.0
Successive values are for J = 3,43,83 (Q, P lines); J = 2,42,82 (R, S lines); J = 4, 44, 84 (lines), where J is the rotational quantum number of the lower level of the transition.
Table II
Broadening and Temperature Coefficients γ|m| (300 K) (in 10−3 cm−1 atm−1) and N|m| [see Eq.(1)] of CO2 Lines Broadened by CO2, H2O, N2, and O2
LINE |m|
CO2–CO2
CO2–H2O
CO2–N2
CO2–CO2
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
γ|m| (300K)
N|m|
1
119.9
0.723
117.7
0.726
95.0
0.737
85.9
0.721
3
115.8
0.729
113.9
0.754
91.4
0.745
83.0
0.730
5
116.9
0.735
116.7
0.764
91.6
0.747
82.7
0.729
7
117.0
0.731
119.6
0.771
91.4
0.744
82.0
0.723
9
116.1
0.722
123.5
0.782
90.7
0.735
80.8
0.712
11
113.3
0.701
126.5
0.789
89.2
0.722
79.0
0.700
13
111.3
0.689
129.6
0.797
87.2
0.705
76.7
0.682
15
109.2
0.679
132.6
0.802
84.7
0.687
74.1
0.661
17
107.1
0.671
135.6
0.811
82.2
0.669
71.1
0.637
19
106.0
0.670
136.6
0.808
79.6
0.653
68.3
0.617
21
104.9
0.669
136.7
0.800
77.4
0.641
65.9
0.603
23
103.7
0.669
136.7
0.793
75.8
0.635
64.2
0.595
25
102.7
0.669
137.7
0.791
74.6
0.633
63.0
0.595
27
100.8
0.663
140.6
0.802
73.9
0.636
62.5
0.601
29
98.9
0.655
143.5
0.812
73.5
0.642
62.1
0.609
31
97.0
0.646
144.5
0.811
73.2
0.648
61.8
0.615
33
94.8
0.635
144.5
0.804
73.1
0.656
61.6
0.624
35
92.5
0.623
144.5
0.800
73.0
0.661
61.4
0.628
37
90.2
0.609
144.6
0.795
72.9
0.666
61.3
0.633
39
87.8
0.596
145.6
0.795
72.9
0.671
61.2
0.638
41
85.5
0.583
147.6
0.800
72.7
0.674
61.0
0.640
43
83.3
0.570
147.7
0.795
72.5
0.677
60.8
0.642
45
81.2
0.557
146.8
0.785
72.3
0.676
60.6
0.642
47
79.2
0.547
146.9
0.782
72.1
0.678
60.3
0.642
49
77.5
0.537
147.8
0.783
71.9
0.678
60.1
0.643
51
75.7
0.529
148.8
0.784
71.6
0.676
59.9
0.641
53
74.2
0.521
150.8
0.791
71.3
0.677
59.6
0.640
55
72.8
0.515
150.8
0.787
70.9
0.672
59.4
0.640
57
71.4
0.508
150.8
0.784
70.4
0.670
59.1
0.637
59
70.2
0.504
149.9
0.776
70.0
0.666
59.0
0.638
61
69.1
0.500
149.9
0.773
69.5
0.663
58.6
0.635
63
68.0
0.497
148.0
0.761
69.0
0.659
58.3
0.632
65
67.0
0.493
147.0
0.752
68.5
0.655
58.0
0.632
67
66.0
0.492
146.2
0.744
67.9
0.650
57.7
0.630
69
65.1
0.488
145.3
0.736
67.3
0.644
57.3
0.626
71
64.3
0.488
144.4
0.728
66.8
0.639
56.9
0.621
73
63.6
0.487
143.5
0.720
66.1
0.634
56.6
0.619
75
62.9
0.486
141.6
0.709
65.5
0.628
56.2
0.615
77
62.1
0.485
139.7
0.699
64.9
0.622
55.9
0.615
79
61.5
0.486
137.7
0.688
64.2
0.616
55.6
0.610
81
60.9
0.485
136.7
0.683
63.6
0.612
55.2
0.607
83
60.3
0.485
135.7
0.678
62.9
0.606
54.9
0.605
85
59.8
0.485
135.7
0.677
62.3
0.599
54.5
0.600
87
59.3
0.487
135.7
0.677
61.6
0.593
54.1
0.598
89
58.8
0.487
134.7
0.671
60.9
0.588
53.7
0.594
91
58.3
0.487
134.7
0.671
60.3
0.581
53.3
0.591
93
57.7
0.487
133.7
0.666
59.6
0.575
52.9
0.588
95
57.2
0.486
131.7
0.658
58.9
0.568
52.6
0.586
97
56.6
0.486
128.8
0.642
58.3
0.563
52.2
0.583
99
56.0
0.484
127.8
0.639
57.6
0.556
51.9
0.578
101
55.4
0.482
126.7
0.634
56.9
0.550
51.4
0.573
Table III
Parameters γ*|m| (300 K) (in 10−3 cm−1 atm−1) and N*|m| of the Polynomial Correlations[see Eq. (2)]
Broadening coefficients γ*|m| (300 K)
System
a0
a1
a2
CO2-H2O
1.142 10+2
1.266 10+0
−1.163 10−2
CO2-CO2
1.253 10+2
−1.172 10+0
4.660 10−3
CO2-N2
9.169 10+1
−5.323 10−1
2.149 10−3
CO2-O2
80293 10+1
−6.797 10−1
3.982 10−3
Temperature coefficients N*|m|
System
b0
b1
b2
CO2-H2O
7618 10−1
2.354 10−3
−3.785 10−5
CO2-CO2
7.706 10−1
−6.017 10−3
3.078 10−5
CO2-N2
7.146 10−1
−6.306 10−4
−7.544 10−6
CO2-O2
6.947 10−1
−1.798 10−3
8.167 10−6
Table IV
Parameters of the Constant Broadening Coefficient Approximation [see Eq. (4)]
Constant broadening coefficient parameters
System
103(300 K) cm−1 atm−1
(300 K)
α
CO2-H2O
135.
0.750
0.013
CO2-CO2
105.
0.773
0.050
CO2-O2
69.7
0.722
0.017
CO2-N2
80.6
0.736
0.017
Table V
Calculated Broadening Coefficients for High |m| Values (In 10−3 cm−1 atm−1)a
T(K)
CO2-CO2
CO2-H2O
CO2-N2
CO2-O2
300
48.9
110.
49.3
46.3
-
-
-
-
-
-
-
-
600
35.6
77.9
36.8
32.8
29.4
66.2
30.8
2805
-
-
-
-
1200
26.2
51.2
25.7
22.5
23.3
46.4
23.8
21.2
20.5
41.4
21.4
19.5
2400
19.9
32.6
17.4
15.5
17.6
30.9
16.9
15.0
16.2
28.4
16.2
14.5
Successive values are for |m| = 121, 161, 201; —, the corresponding values have not been calculated due to the breakdown of the semiclassical approximation for such high rotational transitions at these temperatures.