# Calculation of the Absorption Cross Sections of Some Molecules from GEISA Database at the Wavelengths of Isotopically Different CO2 Lasers

Authors: Asylkhan Rakhymzhan; Alexey Chichinin
Journal: ISRN Analytical Chemistry
 (2013)

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## Abstract

A calculation of the absorption cross section of some molecules (NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O) at the wavelengths transmitted by a CO2 laser filled with different isotopes (12C16O2, 13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O) is presented. The spectroscopical parameters for the molecules from GEISA database have been used. Hence the selection of the molecules was substantially based on the availability of the parameters in the database. The results of the calculations may be used in designing the differential absorption technique for remote monitoring of these molecules. The pressure and temperature dependence of the cross sections are described by KT and KP coefficients; these coefficients were calculated for the largest absorption cross sections for each molecule. The absorption cross sections of CH3OH and HCOOH at low pressures for all these CO2 lasers are also presented. These calculations are provided for design of new CO2-laser-pumped far-infrared lasers.


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## Body

## 1. Introduction

In this paper we report molecular absorption cross sectionsσ(M) at CO2-laser emission frequencies for several selected gases of atmospheric relevance (M = NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O). This information may be useful mainly in the differential absorption (Light Detection and Ranging) LIDAR technique for remote measurement of the gas species [1–8] and also may be used to monitor the CO2 content in fuel combustion products [9], remote sensing of gases in human breath [10], or multiphoton dissociation processes or to measure water vapor concentration and wind speed vector in the plume of volcano [11, 12]. Note that the LIDAR technique sometimes is used for remote sensing of some exotic gases, like, for example, chemical warfare [13].In some cases (CH3OH and HCOOH) it also may be used in designing optically pumped FIR (far infrared=THz) lasers where CO2 laser is used as a source of a pump radiation [14]. Also, the absorption of CO2-laser radiation by a cell with a mixture of some of these gases is used in our lab for quick check and assignment of the CO2-laser lines.The focus of the present study is to predict absorption cross section in pure air at wavelengths of seven isotopic CO2 lasers: 12C16O2 (normal), 13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O, which we hereafter denote as 26-, 36-, 28-, 46-, 48-, 38-, and 268-lasers.In the clear atmosphere, absorption at 9–11μm is due primarily to water vapor and carbon dioxide. Since the fraction of CO2 in the atmosphere is about 3.8 × 10−4 and σ(CO2)~10−22 cm2, the resonant absorption of 50% of the 26-laser radiation by atmospheric molecules occurs at the distance about 7 km. This distance may be not large enough for typical LIDAR applications, like monitoring of air pollution over the large town or early detection of small forest fires [15, 16]. Also, the fluctuations of the CO2 concentration in the atmosphere decrease strongly the accuracy of the LIDAR based on the 26-laser. Hence the first advantage of latter six CO2 lasers over conventional 26-laser is low attenuation from atmospheric CO2, which may extend strongly the detection distance and/or the accuracy of the LIDAR. Moreover, these isotopically substituted CO2 lasers may be used to detect the concentration of CO2 in the atmosphere or, more simply, to monitor the CO2 content in fuel combustion products [9].Another advantage is another set of wavelengths; sometimes it makes it possible to detect molecules, unavailable for conventional 26-laser LIDAR.It is important to note that the use of CO2 lasers for LIDAR remote sensing offers some advantages over that of the more current LIDAR experiments being conducted using the fundamental absorption transitions of hydrocarbons near 3 to 4 μm and CW Quantum Cascade Lasers, in that the absorption values near 10 μm are not too high and not too low for remote sensing at ranges of a few hundred meters, and the output power of the CO2 laser is high offering good detection ranges.Note that commercially available CO2 lasers often may be filled with different isotopic gases (e.g., PL3 series from Edinburgh Photonics). Also, CO2 lasers make up to 108 shots without changing of the gas mixture (e.g., InfraLight series of CO2 lasers); hence there is no large difference, which isotopic modification of CO2 gas to use.This work was greatly facilitated by usage of GEISA spectroscopical database [17], and only the molecules from the database were involved in calculations. We have not included several gases (N2H4, C6H6, C2Cl4, C2HCl3, C2H3Cl, C2H5SH, C2H4Cl2, CF2Cl2, and CFCl3) which may be detected by CO2 lasers [18], since no information is available on their absorption cross sections in the GEISA and HITRAN databases.There were a lot of experimental measurements of the absorption coefficients at 26-laser frequencies. The most popular molecules are SF6 [19–21], C2H4 [22–24], and NH3 [22–26], and the list of references here is very large. A lot of σ(M) for more complicated molecules are also reported in the literature, for example, for acetonitrile, benzene, cyclohexane, 1,2-dichloroethane, ethyl acetate, freon-12, freon-113, furan, isopropanol, methyl chloroform, methyl ethyl ketone, t-butanol, vinyl chloride, and iodopropane [27]; seven hydrazine fuel gases [28]; hydrazine, unsymmetrical dimethylhydrazine, and monomethylhydrazine [29]; C2H4, C2H3Cl3, C2HCl3, and Freon-113 [3]; and triacetone triperoxide [8].However, much less information is available regardingσ(M) of CO2 lasers other than 26-laser. For example, we know the measurements of σ(H2O) at 26-, 36-, and 46-laser wavelengths [30], σ(ClO2) at 28-laser wavelengths [31], σ(NH3) at a 36-laser [32]. Also, the photoacoustic spectroscopy has been used to determine σ(M) for M = NH3, CCl2F2, CHClF2, CFCl3, and CClF3 at 36-laser wavelengths [33].To the best of our knowledge, the FIR lasers normally are pumped by 26-lasers or, much rarely, by 36-laser [34–37]; the other CO2 lasers are used very rarely [38, 39]. Note that while 26-laser has about 100 laser lines, using different isotopic CO2 lasers gives up to 1000 lines; hence the amount of different FIR-lasers pumped by CO2 lasers should increase accordingly.With this in mind, we performed the calculation which hopefully provides the information of the quality comparable with that of the experimental studies. We hope that it will stimulate using isotopically different CO2 lasers for different applications.


## 2. Results

Assuming Lorentzian line shapes, we calculated the absorption cross sectionsσ(M) at all possible CO2-laser frequencies. Tables 1, 2, and 3 show σ(M) for 26-, 36-, and 28-lasers, respectively, for CO2-laser lines between P(40) and R(40), excluding the range P(6)–R(6). Atmospheric pressure P0=1 bar and temperature T0=296 K are assumed everywhere, and the self-broadening is neglected (i.e., [M]≪[air]). The following expressions were used:
(1)σ(M)=∑i‍Si(T)πΔνi(P,T)Δνi2(P,T)+(ν-νi-δiP)2,Si(T)=Si0(T0T)Lexp(-EikT+EikT0),Δνi(P,T)=Δνi0(PP0)(T0T)mi,
where the index i labels all transitions in molecule M, Si(T) is intensity of the ith spectral line, Si0=Si(T0), Δνi(P,T) is Lorentzian width, Δνi0=Δνi(P0,T0), νi is the absorption maximum frequency of the ith spectral line, δi is the pressure shift of the line transition, Ei is the energy of the lower state for ith transition, L=1 for linear molecules like CO2 and L=3/2 for nonlinear molecules, P and T are air pressure and temperature, respectively, and k is Boltzmann constant.Table 1
Absorption cross sections of12C16O2-lasers radiation (for all the units are  10−20) cm2, but for H2O, the units are 10−23 cm2).
Line
00°1 → 10°0, 10.4μma
00°1 → 02°0, 9.4μmb
ν, cm−1
CO2
NH3
C2H4
CH3OH
O3
PH3
HNO3
SF6
H2O
ν, cm−1
CO2
NH3
C2H4
CH3OH
HCOOH
O3
PH3
H2O
P(40)
924.97398
0.0019
3.73
2.12
0.006
0.003
0.262
2.91
1.38
3.2576
1027.38217
0.0030
7.67
2.58
15.9
1.01
21.7
0.316
0.0753
P(38)
927.00832
0.0025
16.5
7.86
0.006
0.003
0.075
1.95
1.68
0.0065
1029.44209
0.0038
0.656
3.45
12.8
1.26
32.6
0.446
1.1490
P(36)
929.01744
0.0030
32.9
4.66
0.006
0.004
0.053
1.31
2.10
0.4532
1031.47743
0.0048
2.18
1.68
28.5
1.47
27.1
15.5
0.0072
P(34)
931.00143
0.0039
55.2
5.91
0.007
0.004
0.028
0.892
2.69
0.0023
1033.48800
0.0059
13.5
7.19
103
3.00
13.3
2.08
0.0056
P(32)
932.96042
0.0046
57.6
4.42
0.007
0.004
0.105
0.627
3.57
0.0092
1035.47362
0.0070
0.930
2.36
8.62
1.06
19.8
0.318
0.0027
P(30)
934.89450
0.0054
3.33
6.12
0.007
0.005
0.375
0.476
5.03
0.0041
1037.43411
0.0083
0.234
4.97
6.20
1.10
22.8
1.76
0.0103
P(28)
936.80375
0.0065
1.06
4.95
0.008
0.005
1.34
0.402
8.01
0.0035
1039.36931
0.0096
0.198
0.77
4.30
1.43
32.7
1.80
0.0583
P(26)
938.68826
0.0072
1.02
7.86
0.008
0.006
0.225
0.268
16.1
0.2236
1041.27907
0.0109
0.391
0.81
15.8
1.01
21.5
7.94
0.0163
P(24)
940.54810
0.0079
0.364
8.62
0.009
0.007
0.036
0.204
42.5
0.0205
1043.16324
0.0121
0.915
1.26
15.0
1.64
2.71
5.99
0.0134
P(22)
942.38334
0.0086
0.245
5.38
0.009
0.008
0.037
0.159
119
0.0049
1045.02167
0.0134
1.62
3.04
25.3
3.28
7.20
16.2
0.0122
P(20)
944.19403
0.0094
0.347
7.63
0.010
0.009
5.45
0.131
262
0.0106
1046.85423
0.0138
13.2
1.54
14.8
2.10
16.9
4.44
0.0045
P(18)
945.98023
0.0095
0.395
13.8
0.010
0.010
5.72
0.104
349
0.0150
1048.66081
0.0142
1.06
2.88
29.3
1.64
23.3
6.28
0.0148
P(16)
947.74198
0.0094
2.30
21.4
0.011
0.015
0.134
0.079
862
0.1346
1050.44128
0.0142
0.702
0.69
29.7
1.85
32.8
0.88
0.0202
P(14)
949.47931
0.0092
1.84
133
0.011
0.013
0.030
0.060
412
0.0261
1052.19555
0.0137
1.40
0.47
48.6
2.06
47.4
8.53
0.0030
P(12)
951.19226
0.0085
2.57
17.3
0.012
0.026
0.079
0.046
354
0.0054
1053.92350
0.0128
3.70
0.47
24.8
2.43
44.0
4.62
0.0022
P(10)
952.88085
0.0075
0.675
13.0
0.013
0.022
0.045
0.037
67.9
0.0038
1055.62507
0.0118
1.08
1.28
30.8
3.70
23.0
3.14
0.0040
P(8)
954.54509
0.0063
1.01
5.83
0.014
0.030
4.30
0.032
22.3
0.0431
1057.30016
0.0096
0.208
2.94
26.5
3.14
49.2
2.10
0.0048
P(6)
956.18498
0.0049
2.86
7.96
0.015
0.043
3.78
0.027
12.2
0.0093
1058.94871
0.0073
0.377
1.18
39.0
4.65
34.4
3.42
0.0804
R(6)
966.25036
0.0057
124
7.99
0.030
0.088
0.284
0.011
2.07
0.0159
1069.01409
0.0086
0.541
1.24
11.5
10.6
2.93
1.48
0.0317
R(8)
967.70723
0.0071
102
3.68
0.037
0.128
0.255
0.010
1.76
0.0088
1070.46231
0.0108
7.04
1.33
11.1
13.3
1.76
1.71
0.0978
R(10)
969.13955
0.0083
2.62
5.26
0.059
0.150
0.099
0.010
1.53
0.0068
1071.88377
0.0125
0.972
1.47
9.16
16.6
0.871
9.28
0.0344
R(12)
970.54724
0.0092
1.09
7.58
0.679
0.160
0.127
0.009
1.34
0.3381
1073.27848
0.0139
1.12
0.391
7.25
16.6
0.749
4.55
0.1450
R(14)
971.93026
0.0097
27.6
6.51
1.44
0.215
0.844
0.009
1.18
0.0225
1074.64649
0.0149
2.37
0.257
5.15
23.0
0.616
3.91
0.0539
R(16)
973.28852
0.0099
0.485
3.76
1.60
0.286
0.234
0.009
1.06
0.1583
1075.98782
0.0153
52.1
1.12
4.39
27.0
0.470
2.07
3.2810
R(18)
974.62194
0.0098
0.270
2.39
0.81
0.397
0.834
0.008
0.953
0.0270
1077.30252
0.0152
0.450
2.17
4.28
29.5
0.351
4.00
0.0822
R(20)
975.93044
0.0095
0.193
4.70
3.33
0.429
0.868
0.008
0.864
3.3148
1078.59064
0.0147
0.226
0.520
2.23
33.8
0.408
1.15
0.0213
R(22)
977.21392
0.0089
0.152
12.7
1.78
0.377
0.574
0.008
0.789
0.0128
1079.85226
0.0139
0.225
0.289
2.01
35.1
0.494
1.60
0.0118
R(24)
978.47229
0.0081
0.126
19.3
2.09
0.491
0.846
0.008
0.725
0.0044
1081.08743
0.0134
0.274
0.689
0.718
47.8
0.820
3.53
0.0127
R(26)
979.70542
0.0073
0.109
8.84
3.68
0.520
0.618
0.007
0.669
0.0028
1082.29624
0.0116
0.511
0.276
0.622
35.5
0.446
0.55
0.0829
R(28)
980.91321
0.0063
0.098
10.3
1.32
0.639
3.51
0.007
0.620
0.0054
1083.47878
0.0102
1.90
0.101
0.394
59.4
0.443
0.36
0.0587
R(30)
982.09553
0.0054
0.092
1.47
4.58
0.674
4.60
0.007
0.578
0.0123
1084.63514
0.0089
303
0.671
0.687
57.1
0.359
0.73
0.6919
R(32)
983.25225
0.0046
0.089
3.91
2.91
1.65
8.01
0.007
0.540
0.0046
1085.76544
0.0077
2.35
0.183
0.068
47.1
0.351
5.23
0.0261
R(34)
984.38323
0.0037
0.090
2.39
8.29
0.823
4.43
0.006
0.507
0.0246
1086.86979
0.0062
0.945
0.134
0.053
59.6
0.304
1.35
0.0098
R(36)
985.48831
0.0030
0.097
10.7
3.93
1.05
5.83
0.006
0.478
0.0036
1087.94831
0.0051
0.403
1.39
0.046
54.1
0.533
5.94
0.3016
R(38)
986.56735
0.0024
0.116
14.7
9.68
1.21
2.94
0.006
0.451
0.0104
1089.00112
0.0041
1.73
0.109
0.041
69.9
0.299
0.53
0.0072
R(40)
987.62018
0.0019
0.574
18.8
5.04
1.42
2.12
0.006
0.427
0.1652
1090.02837
0.0036
0.672
0.252
0.038
65.5
0.507
3.16
0.0054
aCross sections for HCOOH are omitted; σ(HCOOH) <10−21 cm2.
bCross sections for HNO3 and SF6 are omitted; σ(HNO3) <3×10−23 cm2; and  σ(SF6) <1.1×10−21 cm2.Table 2
Absorption cross sections of13C16O2-lasers radiation (for all the units are  10−20 cm2, but for H2O, the units are 10−23 cm2).
Line
00°1→ 10°0, 11 μma
00°1→ 02°0, 10 μmb
ν, cm−1
CO2
NH3
C2H4
PH3
HNO3
SF6
H2O
ν, cm−1
CO2
NH3
C2H4
CH3OH
HCOOH
O3
PH3
SF6
H2O
P(40)
878.43359
0.00003
0.056
3.55
0.823
69.6
0.142
1.6272
980.80503
0.00190
0.099
6.85
1.32
0.051
0.603
1.32
0.625
0.0045
P(38)
880.37051
0.00005
0.055
2.93
0.413
26.7
0.150
0.0211
982.91254
0.00026
0.089
5.95
1.57
0.052
0.736
0.887
0.551
0.0054
P(36)
882.28741
0.00006
0.074
4.07
0.029
33.3
0.159
0.0222
984.99314
0.00015
0.093
4.92
2.11
0.053
0.764
2.58
0.490
0.0044
P(34)
884.18435
0.00005
0.111
2.59
0.026
37.1
0.169
0.1661
987.04662
0.00013
0.139
11.5
2.53
0.085
1.04
2.84
0.440
0.0455
P(32)
886.06142
0.00006
0.327
5.11
0.037
32.9
0.179
0.0348
989.07282
0.00010
0.251
1.61
2.88
0.099
1.82
19.1
0.398
0.0089
P(30)
887.91867
0.00009
58.5
5.77
0.026
38.5
0.190
0.0968
991.07153
0.00008
1.56
3.09
3.49
0.086
1.48
2.31
0.362
0.0085
P(28)
889.75616
0.00008
0.515
6.16
0.228
48.6
0.203
0.0461
993.04260
0.00008
10.1
2.16
4.57
0.110
3.81
7.59
0.331
0.0022
P(26)
891.57394
0.00009
4.53
2.93
0.312
40.8
0.216
0.0541
994.98585
0.00011
0.354
5.15
6.55
0.124
3.16
0.908
0.304
0.0037
P(24)
893.37207
0.00010
0.640
1.91
0.405
35.3
0.231
0.0037
996.90115
0.00008
0.143
22.1
8.66
0.128
5.04
0.736
0.280
0.0016
P(22)
895.15057
0.00013
0.157
3.09
0.389
50.6
0.247
0.0057
998.78832
0.00009
0.100
3.94
14.8
0.282
3.44
0.068
0.260
0.0028
P(20)
896.90948
0.00016
0.087
7.85
0.017
33.7
0.265
0.0036
1000.64726
0.00009
0.095
8.23
23.4
0.204
6.96
3.15
0.242
0.0364
P(18)
898.64883
0.00015
0.072
2.55
0.016
33.4
0.284
0.0017
1002.47781
0.00008
0.185
3.63
27.0
0.281
6.64
0.166
0.226
0.0033
P(16)
900.36865
0.00027
0.406
3.49
0.447
30.2
0.305
0.0018
1004.27987
0.00008
0.197
7.15
27.8
0.253
10.2
2.92
0.212
0.0282
P(14)
902.06895
0.00015
0.109
8.26
0.596
24.1
0.329
0.0037
1006.05332
0.00008
1.14
11.4
28.3
0.291
12.4
0.259
0.199
0.0020
P(12)
903.74974
0.00012
0.134
2.11
0.490
21.3
0.354
0.0039
1007.79807
0.00021
19.3
6.77
26.1
0.386
10.7
0.204
0.188
0.0054
P(10)
905.41104
0.00014
0.253
5.76
0.075
26.4
0.383
0.0183
1009.51402
0.00007
0.699
6.54
18.4
0.392
17.5
0.340
0.177
0.0105
P(8)
907.05284
0.00009
1.17
1.43
1.347
22.1
0.415
0.0379
1011.20110
0.00006
58.0
5.34
23.2
0.423
8.58
2.23
0.168
0.0639
P(6)
908.67515
0.00011
6.65
18.5
0.034
19.4
0.451
0.6599
1012.85922
0.00005
7.21
2.47
19.8
0.597
10.1
0.099
0.159
0.0031
R(6)
918.74396
0.00080
5.33
4.27
0.182
9.07
0.830
0.0581
1022.92804
0.00016
0.425
2.44
10.8
0.648
29.2
0.563
0.120
0.0169
R(8)
920.21948
0.00014
1.01
2.49
0.027
8.22
0.924
0.0159
1024.36774
0.00009
0.315
4.54
18.3
0.693
30.6
9.46
0.115
2.0415
R(10)
921.67529
0.00020
3.94
6.48
0.047
5.97
1.04
0.1895
1025.77827
0.00013
0.688
2.01
12.1
0.804
18.5
1.61
0.111
0.0241
R(12)
923.11133
0.00034
2.35
7.93
3.736
4.15
1.17
0.0353
1027.15966
0.00036
40.1
11.1
14.1
1.01
27.3
1.05
0.107
0.0417
R(14)
924.52755
0.00019
2.12
5.52
4.968
3.16
1.32
0.0856
1028.51193
0.00014
0.657
1.92
10.9
1.29
39.6
0.293
0.103
0.2480
R(16)
925.92391
0.00016
11.1
5.39
1.391
2.50
1.51
0.0223
1029.83513
0.00022
1.22
2.59
11.6
1.32
24.4
4.35
0.100
0.1042
R(18)
927.30032
0.00028
119
2.81
0.166
1.83
1.73
0.0060
1031.12930
0.00029
1.45
2.17
25.2
1.59
23.8
1.31
0.097
0.0084
R(20)
928.65672
0.00028
48.6
3.72
0.033
1.40
2.01
0.0151
1032.39450
0.00021
9.72
3.79
52.2
1.71
34.6
3.37
0.094
0.0245
R(22)
929.99305
0.00017
61.6
7.50
0.159
1.04
2.36
0.0048
1033.63081
0.00118
8.69
2.87
98.2
2.29
16.0
1.48
0.091
0.0048
R(24)
931.30921
0.00031
92.2
6.99
0.026
0.858
2.80
0.0020
1034.83829
0.00032
3.15
0.822
11.3
1.10
41.4
0.571
0.089
0.0033
R(26)
932.60512
0.00033
29.0
3.83
0.064
0.699
3.38
0.0037
1036.01703
0.00023
0.522
1.90
9.385
1.32
22.8
0.586
0.087
0.0031
R(28)
933.88070
0.00035
12.9
4.32
4.787
0.519
4.16
0.0018
1037.16713
0.00063
0.259
4.61
6.56
1.01
18.4
1.12
0.084
0.0056
R(30)
935.13584
0.00054
3.89
2.31
0.778
0.407
5.29
0.0093
1038.28870
0.00019
0.187
2.46
8.77
1.29
23.7
7.02
0.082
0.5229
R(32)
936.37044
0.00028
1.83
4.27
0.305
0.356
7.09
0.0076
1039.38184
0.00934
0.201
0.755
4.29
1.35
32.5
1.70
0.080
0.0622
R(34)
937.58440
0.00029
4.36
7.51
0.100
0.345
10.3
0.0092
1040.44668
0.00036
0.206
1.79
9.24
0.92
28.3
1.31
0.079
0.3301
R(36)
938.77760
0.00287
0.711
8.95
0.122
0.297
16.7
0.0647
1041.48333
0.00122
0.258
1.50
11.7
1.61
21.1
5.00
0.077
0.0152
R(38)
939.94992
0.00021
0.290
8.38
0.020
0.239
30.3
0.0094
1042.49195
0.00045
0.276
1.33
7.18
2.44
3.34
0.876
0.075
0.9977
R(40)
941.10124
0.00023
0.352
9.78
0.020
0.181
58.7
0.3694
1043.47268
0.00068
0.450
1.45
19.0
1.81
2.85
1.22
0.074
0.0074
aCross sections for CH3OH, HCOOH, and O3 are omitted; σ(CH3OH) <10-22 cm2; σ(HCOOH) <5×10-23 cm2, and σ(O3) <9×10-23 cm2.
bCross sections for HNO3 are omitted; σ(HNO3) <7×10-23 cm2.Table 3
Absorption cross sections of12C18O2-lasers radiation (for all the units are  10−20 cm2, but for H2O, the units are 10−23 cm2).
Line
00°1→ 10°0, 10.5 μma
00°1→ 02°0, 9 μmb
ν, cm−1
CO2
NH3
C2H4
CH3OH
O3
PH3
HNO3
SF6
H2O
ν, cm−1
CO2
NH3
C2H4
CH3OH
HCOOH
O3
PH3
H2O
P(40)
933.98651
0.00023
7.92
3.30
0.007
0.004
1.81
0.553
4.24
0.0019
1052.26317
0.00763
1.41
0.495
45.8
2.24
59.2
4.32
0.0027
P(38)
935.88894
0.00013
14.9
2.92
0.008
0.005
0.217
0.388
6.27
0.0070
1054.01438
0.00542
5.55
0.354
24.1
3.24
39.3
2.96
0.0021
P(36)
937.76432
0.00014
2.43
5.59
0.008
0.006
0.143
0.279
11.0
0.0056
1055.74733
0.00352
0.755
0.775
26.8
3.49
35.0
4.43
0.0047
P(34)
939.61272
0.00022
0.586
8.01
0.008
0.006
0.023
0.224
25.3
0.0054
1057.46193
0.00235
0.194
2.37
33.8
4.15
29.9
2.79
0.0052
P(32)
941.43421
0.00020
0.313
7.15
0.009
0.007
0.021
0.170
70.9
0.0357
1059.15808
0.00168
0.187
1.61
27.5
5.50
26.6
17.3
0.3398
P(30)
943.22886
0.00020
0.291
8.33
0.009
0.009
0.094
0.121
180
0.0044
1060.83568
0.00090
0.178
0.436
28.0
4.57
21.4
0.785
0.0601
P(28)
944.99673
0.00019
0.341
10.0
0.010
0.013
4.10
0.100
319
0.2328
1062.49464
0.00040
0.277
0.547
28.3
6.06
36.7
3.25
0.0111
P(26)
946.73787
0.00039
0.435
16.5
0.010
0.014
0.139
0.075
418
0.1333
1064.13489
0.00024
1.01
0.686
18.2
6.45
9.19
4.82
0.0116
P(24)
948.45233
0.00022
8.59
31.7
0.011
0.014
0.052
0.059
473
0.9095
1065.75632
0.00046
48.1
0.731
21.7
8.65
15.0
0.723
0.1324
P(22)
950.14015
0.00022
0.772
51.2
0.012
0.019
0.021
0.049
476
0.0190
1067.35888
0.00124
1.32
0.523
15.3
12.3
4.85
2.05
0.0094
P(20)
951.80137
0.00023
44.0
14.6
0.013
0.017
0.025
0.040
215
0.0042
1068.94248
0.00500
0.576
1.42
12.4
9.70
3.14
0.949
0.0393
P(18)
953.43603
0.00022
0.402
7.47
0.013
0.025
0.112
0.035
42.0
0.0048
1070.50705
0.00822
11.1
1.42
10.4
13.1
1.71
2.21
0.0788
P(16)
955.04415
0.00022
0.905
11.7
0.014
0.026
0.990
0.030
18.1
0.1436
1072.05253
0.00232
1.15
3.79
10.1
19.7
0.596
2.09
0.0436
P(14)
956.62576
0.00022
0.909
7.80
0.015
0.041
0.246
0.027
10.8
0.0051
1073.57887
0.00101
1.55
0.617
6.17
17.0
0.388
4.11
0.0368
P(12)
958.18087
0.00019
2.76
6.31
0.017
0.040
0.142
0.018
7.31
0.0033
1075.08599
0.00063
9.99
0.250
6.53
21.7
0.890
8.62
0.0940
P(10)
959.70950
0.00015
6.090
7.24
0.018
0.040
0.063
0.016
5.34
0.1043
1076.57386
0.00053
1.62
0.316
3.47
25.7
0.382
1.33
0.6481
P(8)
961.21166
0.00006
10.7
3.56
0.020
0.058
0.087
0.017
4.10
0.0092
1078.04242
0.00056
0.262
0.227
2.65
30.2
0.337
1.21
0.0334
P(6)
962.68734
0.00009
16.0
4.63
0.022
0.077
0.053
0.013
3.27
0.0161
1079.49163
0.00077
0.541
0.973
1.73
37.8
0.352
0.538
0.0132
R(6)
971.63344
0.00066
5.32
2.18
1.60
0.305
0.376
0.009
1.22
0.0693
1088.43774
0.00069
0.500
0.118
0.044
68.5
0.474
0.460
0.0092
R(8)
972.91019
0.00046
0.671
3.69
1.18
0.315
0.889
0.009
1.09
0.0253
1089.74096
0.00046
1.71
0.748
0.039
62.8
0.349
0.461
0.0069
R(10)
974.16030
0.00035
0.315
2.27
1.42
0.257
4.12
0.009
0.98
0.13597
1091.02466
0.00256
0.494
0.345
0.035
64.7
0.341
2.60
0.0203
R(12)
975.38372
0.00029
0.219
10.3
1.86
0.223
0.855
0.008
0.89
0.06139
1092.28884
0.00039
0.682
0.061
0.032
58.1
0.239
1.75
0.0056
R(14)
976.58041
0.00028
0.170
6.73
1.12
0.322
0.935
0.008
0.82
0.04755
1093.53351
0.00028
3.06
0.670
0.029
60.9
0.245
0.184
0.0064
R(16)
977.75031
0.00028
0.139
7.77
3.71
0.344
2.88
0.008
0.76
0.00860
1094.75869
0.00068
1.64
0.654
0.027
49.7
0.546
0.205
0.0159
R(18)
978.89336
0.00031
0.119
18.3
1.15
0.669
1.80
0.007
0.70
0.00365
1095.96438
0.00008
3.93
0.080
0.025
55.0
0.259
1.73
0.0256
R(20)
980.00950
0.00043
0.106
2.27
4.07
0.569
0.884
0.007
0.65
0.00286
1097.15060
0.00006
0.610
0.200
0.024
41.3
0.306
0.702
0.0127
R(22)
981.09866
0.00082
0.097
3.50
1.43
0.766
2.86
0.007
0.61
0.00823
1098.31739
0.00005
0.336
0.538
0.022
38.0
0.284
0.640
0.0109
R(24)
982.16077
0.00287
0.091
1.83
5.35
0.581
2.51
0.007
0.57
0.00986
1099.46477
0.00005
0.219
0.076
0.021
28.0
0.343
0.308
0.0319
R(26)
983.19575
0.00273
0.089
3.92
2.40
1.03
7.74
0.007
0.54
0.00442
1100.59277
0.00006
0.245
0.181
0.020
20.5
0.211
0.424
0.1863
R(28)
984.20351
0.00052
0.090
2.43
5.30
1.04
1.77
0.007
0.51
0.13352
1101.70143
0.00005
0.528
0.367
0.019
15.1
0.338
0.309
0.2239
R(30)
985.18397
0.00020
0.094
2.22
3.01
0.648
1.70
0.006
0.48
0.00385
1102.79079
0.00001
3.34
0.058
0.018
12.9
0.112
0.245
0.0393
R(32)
986.13704
0.00011
0.106
17.3
7.81
2.00
1.62
0.006
0.46
0.00541
1103.86091
0.00001
8.85
0.690
0.017
26.7
0.403
1.41
0.0131
R(34)
987.06260
0.00012
0.140
11.4
2.51
1.08
2.61
0.006
0.44
0.04930
1104.91182
0.00001
0.871
0.113
0.017
228
0.231
0.298
0.0123
R(36)
987.96056
0.00011
0.339
27.6
6.97
1.49
3.63
0.006
0.42
0.02590
1105.94358
0.00001
0.313
0.366
0.016
102
0.177
0.267
0.0115
R(38)
988.83081
0.00020
0.309
3.26
4.97
2.32
10.2
0.006
0.40
0.11022
1106.95625
0.00001
0.248
0.099
0.015
36.9
0.154
1.43
0.0145
R(40)
989.67323
0.00093
0.315
6.78
5.73
1.26
9.46
0.006
0.38
0.00456
1107.94989
0.00000
3.61
0.181
0.015
26.3
0.293
0.682
0.0275
aCross sections for HCOOH are omitted; σ(HCOOH) <9×10-22 cm2.
bCross sections for HNO3 and SF6 are omitted; σ(HNO3) <7×10-23 cm2 and σ(SF6) <6×10-22 cm2.The parametersνi, Si0, Δνi0, mi, δi, and Ei are taken from GEISA database for each transition of each M molecule. Note that the pressure shifts δi are given in the database only for CH3CN and NO2 molecules. All of them are rather small (≈10−3 cm−1/atm), and they change only the third digit in calculated absorption cross sections. We hope that there is the same situation with all other molecules; hence we present the cross sections with three-digit accuracy; the last digit may be wrong due to the pressure shifts. All CO2-laser frequencies were taken from Freed et al. [40].In Table4 we present the “best” laser transitions for each isotopic variation of CO2 laser and for each molecule M. The pressure and temperature dependence of the cross sections are described by KT and KP coefficients as KT=dlnσ/dlnT, KP=dlnσ/dlnT, and the coefficients have been calculated from (1) and presented in Table 4 also.Table 4
For each CO2 laser and for each molecule M, the laser transitions with the largest absorption by selected molecules are presented. The cross sections σ(M) (in 10−20 cm2 units) and  KT  and  KP  coefficients are shown.
Laser
M
Transition
ν, cm−1
σ(M)a
K
T
K
P
26
NH3
10R(30)
1084.63514
303
0.38
-
0.83
C2H4
11P(14)
949.47931
133
0.16
-
0.13
O3
10P(14)
1052.19555
47.4
-
0.62
0.08
10P(8)
1057.30016
49.2*
-
0.02
-
0.12
NO2
11P(48)
916.58177
0.143
3.11
-
0.36
PH3
10P(22)
1045.02167
16.2
-
0.19
-
0.46
HNO3
11P(44)
920.82912
6.89
1.90
-
0.02
SF6
11P(16)
947.74198
862
-
0.02
-
0.58
CH3OH
10P(34)
1033.48800
103
0.44
-
0.05
HCOOH
10R(28)
1083.47878
59.4
0.37
-
0.22
OCS
10P(32)
1035.47362
1.68
-
0.13
-
0.14
CH3CN
10R(16)
1075.98782
1.82
1.38
-
0.30
SO2
10R(26)
1082.29624
0.430
2.26
-
0.31
SO2
10R(40)
1090.02837
0.595*
1.54
0.15
H2O
11R(20)
975.93044
0.00331
6.47
-
0.85
36
NH3
11R(18)
927.30032
119
0.57
-
0.87
C2H4
10P(24)
996.90115
22.1
-
0.14
-
0.44
CO2
10R(32)
1039.38184
0.009
7.45
-
0.93
O3
10R(24)
1034.83829
41.4
-
0.02
-
0.42
NO2
11P(38)
880.37051
0.461
1.43
-
0.25
PH3
10P(32)
989.07282
19.1
0.92
-
0.21
HNO3
11P(22)
895.15057
50.6
0.36
-
0.01
11P(40)
878.43359
69.6*
0.26
0.05
SF6
11R(42)
942.23141
110
0.87
0.14
11R(44)
943.34030
189*
0.38
0.02
CH3OH
10R(22)
1033.63081
98.2
0.45
-
0.07
HCOOH
10R(38)
1042.49195
2.44
1.22
-
0.23
OCS
10R(36)
1041.48333
2.08
-
0.14
-
0.50
CH3CN
10R(10)
1025.77827
2.86
0.23
0.01
C2H6
11P(48)
870.48389
0.493
0.85
0.06
H2O
9R(8)
1024.36774
0.00204
6.41
0.65
28
NH3
11P(20)
951.80137
44.0
-
0.89
-
0.88
11P(42)
932.05695
67.9*
-
0.37
-
0.27
C2H4
11P(22)
950.14015
51.2
0.49
0.04
CO2
10P(18)
1070.50705
0.008
5.22
-
0.50
10P(44)
1048.70641
0.010*
6.19
-
0.42
O3
10P(40)
1052.26317
59.2*
-
0.38
-
0.38
10P(36)
1055.74733
35.0
-
0.10
0.04
NO2
11P(42)
932.05695
0.021*
2.86
-
0.54
11P(34)
939.61272
0.013
3.56
-
0.55
PH3
10P(32)
1059.15808
17.3
0.58
-
0.87
HNO3
11P(34)
939.61272
0.224
2.39
0.20
11P(42)
932.05695
0.756*
2.57
0.03
SF6
11P(22)
950.14015
476
-
0.33
-
0.21
CH3OH
10P(40)
1052.26317
45.8
0.42
-
0.22
HCOOH
10R(34)
1104.91182
228
-
0.56
-
0.26
OCS
10P(28)
1062.49464
2.06
0.54
-
0.58
CH3CN
10P(32)
1059.15808
3.74
-
0.26
-
0.30
SO2
10R(36)
1105.94358
1.73
0.80
-
0.12
H2O
11P(24)
948.45233
0.000910
4.62
0.79
46
NH3
9P(18)
967.44673
151
-
0.95
-
0.13
C2H4
9P(36)
949.82361
75.5
0.55
-
0.07
CO2
9P(38)
947.72257
0.009
6.83
-
0.85
O3
9R(38)
1007.32003
14.4
1.51
-
0.20
NO2
10R(18)
880.14964
0.617
1.99
-
0.45
PH3
9R(12)
992.16155
20.1
-
0.75
0.42
HNO3
10R(16)
878.74397
116
0.00
-
0.16
SF6
9P(38)
947.72257
860
-
0.01
-
0.57
CH3OH
9R(36)
1006.33091
31.1
0.96
-
0.19
HCOOH
9R(40)
1008.28028
0.572
0.85
-
0.04
OCS
10R(14)
877.32170
2.41
1.16
-
0.59
CH3CN
9R(16)
994.82189
0.839
1.88
-
0.47
C2H6
10P(4)
862.98995
0.666
0.98
-
0.18
H2O
11R(16)
878.74397
0.000532
4.97
0.77
38
NH3
10R(10)
1034.18567
86.9
-
0.39
-
0.22
C2H4
11R(34)
949.30088
121
0.14
-
0.19
CO2
10R(32)
1046.81398
0.011
6.41
-
0.50
O3
10R(14)
1036.67254
33.4
-
0.20
-
0.28
10R(8)
1032.91023
38.3*
-
0.22
-
0.39
10R(40)
1050.77747
50.5*
-
0.62
-
0.15
NO2
11P(16)
916.81456
0.134
2.86
-
0.36
PH3
10R(22)
1041.39099
11.3
-
0.29
-
0.65
10R(6)
1031.61345
13.9*
-
0.57
-
0.29
HNO3
11P(38)
898.25437
35.3
0.43
-
0.07
11P(40)
896.42949
53.4*
-
0.16
-
0.03
SF6
11R(30)
947.29249
641
-
0.06
-
0.16
CH3OH
10R(10)
1034.18567
66.3
0.16
-
0.04
10R(8)
1032.91023
81.5*
0.79
-
0.02
HCOOH
10R(24)
1042.51764
2.50
1.22
-
0.28
10R(40)
1050.77747
4.01*
1.15
-
0.25
OCS
10R(12)
1035.43977
1.98
0.08
-
0.52
CH3CN
10R(34)
1047.83586
3.57
-
0.10
-
0.62
SO2
10R(46)
1053.53509
0.024
4.78
0.00
H2O
11R(32)
948.30848
0.00577
5.06
-
0.34
48
NH3
9P(20)
967.55794
79.2
-
1.48
0.56
C2H4
9P(40)
950.27719
38.0
0.31
0.19
CO2
9P(18)
969.16198
0.008
6.48
-
0.83
O3
9R(32)
1002.18855
11.4
2.01
-
0.15
9R(40)
1006.00000
11.8*
1.68
-
0.22
NO2
10P(12)
880.59011
0.159
1.00
0.08
PH3
9R(14)
992.26858
21.3
-
0.08
-
0.29
HNO3
10P(14)
879.08844
90.0
-
0.53
-
0.08
SF6
9P(40)
950.27719
476
-
0.23
-
0.23
9P(42)
948.42788
484*
-
0.68
0.20
CH3OH
9R(36)
1004.13958
28.9
1.23
-
0.25
HCOOH
9R(34)
1003.17544
0.365
1.63
-
0.06
OCS
10P(30)
866.40889
6.03
-
0.43
-
0.39
CH3CN
10R(28)
907.29104
0.559
-
0.06
-
0.24
C2H6
10P(36)
861.34626
0.777
0.46
-
0.02
H2O
11P(24)
871.30294
0.00549
4.02
-
0.29
268
NH3
10P(32)
1046.35094
264
-
0.52
-
0.64
C2H4
11P(21)
949.43752
149
0.23
-
0.30
CO2
10R(11)
1081.07931
0.013
7.17
-
0.95
O3
10P(27)
1050.83825
56.6
-
0.54
-
0.26
NO2
11P(37)
934.69411
0.067
3.71
0.03
PH3
11R(36)
988.95058
19.8
1.33
-
0.21
11R(42)
991.76694
38.6*
-
1.11
0.02
HNO3
11P(50)
921.46702
6.33
2.00
-
0.04
SF6
11P(23)
947.68595
851
0.00
-
0.55
CH3OH
10P(46)
1033.08142
95.5
0.73
-
0.08
HCOOH
10R(24)
1089.24975
77.9
-
0.33
-
0.13
OCS
10P(16)
1060.23019
2.20
0.14
-
0.60
CH3CN
10P(24)
1053.46560
2.92
-
0.12
-
0.55
SO2
10R(36)
1095.95040
1.03
1.38
-
0.22
H2O
9R(16)
1084.33484
0.00439
5.37
0.21
aAsterisk marks the cases where the σ(M) is large, but the CO2 laser line is marginal. The values below 8×10-23 cm2 are omitted.It is not easy task to point out the “best” CO2-laser line for detection of molecule M. Normally the “best” CO2-laser line should lie in the ranges R(10)–R(40), P(10)–P(40) and has the largest absorption by M molecules; if the largest σ(M) values occur outside these ranges, we mark it by asterisk shown in the table also. However, if the largest σ(M) values occur at marginal lines of CO2 laser and are much larger than all other cross sections, we present this marginal line only.


## 3. Discussion

Some of our results are compared with the experimental literature data in Table5. As one can see from the table, the present results agree favorably with the experimental data of Patty et al. [24] and Persson et al. [22], who have determined σ, KP, and KT coefficients for 26-laser absorption by NH3, O3, and C2H4 molecules.Table 5
Comparison of our calculation results with the experimental literature data for the strongest transitions in NH3, C2H4, and O3 molecules at  12C16O2 laser frequencies.
M
Laser line
ν, cm−1
σ(M), 10−20 cm2
K
T
K
P
[24]
[22]
a
[22]
a
[22]
a
NH3
9R(16)
1075.98782
51.6
c
52.1
c
0.70
c
-
0.29
11R(8)
967.70723
88.9
92.6
102
-
1.07
-
0.98
-
0.30
-
0.33
11R(14)
971.93026
2.56b
30.2
27.6
-
0.62
-
0.96
-
0.59
-
0.61
11P(32)
932.96042
60.9
c
57.6
c
0.03
c
-
0.44
11P(34)
931.00143
50.3
c
55.2
c
-
0.87
c
0.60
9R(30)
1084.63514
c
c
303
c
0.38
c
-
0.83
9P(20)
1046.85423
8.77
12.1
13.2
-
1.50
-
1.62
0.96
0.92
C2H4
11P(14)
949.47931
118.4
145.1
133
-
0.54
0.16
0.03
-
0.13
11P(16)
947.74198
c
23.9
21.4
-
0.46
-
0.55
-
0.02
0.01
11R(24)
978.47229
20.5
20.9
19.3
-
0.83
-
0.49
-
0.06
-
0.02
11P(12)
951.19226
c
19.7
17.3
-
0.01
-
0.46
0.30
0.42
O3
9P(14)
1052.19555
51.6
c
47.4
c
-
0.62
c
0.08
9P(12)
1053.92350
49.5
c
44.0
c
-
0.38
c
-
0.22
9P(8)
1057.30016
51.6
c
49.2
c
-
0.02
c
-
0.12
aThis work.
bProbably, misprint.
cNo data.Note that only in several cases our M molecules are important as “standard” air pollutant (NH3, C2H4, PH3, and O3) and in other cases our M molecules may happen in the air only near special industrial objects. As one can see from Tables 1–4, 26-laser is a good choice for all these four gases.There are several advantages of the other CO2 lasers: monitoring of HNO3, NO2, C2H6, and CO2 molecules requires 46-/48-/36-, 36-, 36-/46-/48-, and 38-/268-lasers, respectively, instead of 26-laser.We included in Table4 several molecules with low cross sections (OCS, CH3CN, C2H6, SO2, and NO2). Although CO2 laser is not the best choice to detect these molecules, these data may be useful in special cases, for example, when CO2 LIDAR is used to monitor the leakage of these gases from industrial areas.Surely, the data in all our tables are only starting points in discussion about applicability of particular CO2-laser transitions for remote sensing under atmospheric conditions, because at many wavenumbers, the absorption by H2O may be much stronger than absorption by the gases of interest. Hence one always should find the tradeoff between the absorption of H2O and the absorption of these gases.For example, the “best” line for NH3 detection by 26-laser in Table 4 is 10R(30) with σ(NH3) = 303 × 10−20 cm2. However, at this wavelength, the ratio σ(NH3)/σ(H2O) is only 4.4 × 105. If we choose another 26-laser line for NH3 detection, P(34) (931.0014 cm−1) with σ(NH3) = 55.2 × 10−20 cm2 and σ(H2O) = 0.0023 × 10−23 cm2, the ratio will be much higher: σ(NH3)/σ(H2O) = 2.4 × 107. Hence, this another 26-laser line is better for NH3 detection, although the value σ(NH3) is lower.Therefore, we included H2O in our calculations; see the results in Tables 1, 2, and 3. Our σ(H2O) data in the tables should help to choose the “best” pairs of CO2-laser lines (absorbing and nonabsorbing) for remote sensing of the gases of interest. Note that the pair of CO2-laser wavenumbers may originate from two isotopically different CO2 lasers; therefore the possibility to use many isotopic variations of CO2 laser simplifies strongly the choice of such pairs.


## 4. Application to FIR Lasers

There are several important benchmark molecules which are normally used in CO2-laser-pumped FIR lasers: CH3OH, CH2F2, HCOOH, 15NH3, CD3OD, CD3 OH, CD3Cl, 13CD3I, and 13CH3F. The absorption of CO2 radiation by these molecules results in FIR-laser emission. Table 6 lists our σ(M) values for CH3OH and HCOOH at low pressures, where the shapes of spectral lines of these molecules are given by Doppler effect. As one can see, there are a lot of interesting possibilities to obtain new strong sources of FIR radiation. One of them may be 9R(19) line of 268-laser, which has very large σ(HCOOH) value.Table 6
The largest absorption cross sections (in 10−20 cm2 units) of CH3OH and HCCOH at low pressure and T = 296 K. The Doppler shape of spectral lines is assumed.
M
Laser
Line
ν, cm−1
σ(M)a
CH3OH
26
10P(34)
1033.48800
126
36
10P(16)
1004.27987
67.2
28
10P(22)
1067.35888
93.0
38
10R(8)
1032.91023
200*
38
10R(40)
1050.77747
193*
38
10P(36)
998.62350
113
46
9R(46)
1010.98950
44.7*
46
9R(28)
1002.08279
19.4
48
9R(40)
1006.00000
146*
48
9R(24)
998.01156
107
268
10P(27)
1050.83825
368
HCOOH
26
10R(18)
1077.30252
186
26
10R(28)
1083.47878
189
26
10R(40)
1090.02837
976*
36
10R(28)
1037.16713
9.59
28
10P(8)
1078.04242
327
28
10R(34)
1104.91182
285
38
10R(44)
1052.63615
19.3
46
9R(26)
1000.94716
2.64
48
9R(30)
1001.17880
2.74
268
10R(19)
1086.22023
118
aAsterisk marks the cases where the σ(M) is large, but the CO2-laser line is marginal.Although there is no direct relation between intensities of CO2 absorption and FIR emission, it is clear that using 1000 CO2-laser lines instead of 100–200 should increase strongly the amount of strong FIR-laser transitions.


## 5. Conclusion

The absorption cross sections andKT and KP parameters of some molecules (NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O) at CO2 laser frequencies (12C16O2,13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O) have been calculated with the use of spectroscopical parameters from GEISA database. The present results are in reasonable agreement with other experimental measurements for NH3, O3, and C2H4. The results of the calculations may be used in designing the differential absorption technique for remote monitoring of these molecules.



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*Source: 592971-2013-11-26.xml*