Calculation of the Absorption Cross Sections of Some Molecules from GEISA Database at the Wavelengths of Isotopically Different CO 2 Lasers

A calculation of the absorption cross section of some molecules (NH 3 , C 2 H 4 , CO 2 , O 3 , NO 2 , PH 3 , HNO 3 , SF 6 , CH 3 OH, HCOOH, OCS, CH 3 CN, C 2 H 6 , SO 2 , and H 2 O) at the wavelengths transmitted by a CO 2 laser filled with different isotopes (CO 2 , CO 2 , CO 2 , CO 2 , CO 2 , CO 2 , and COO) 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 K T and K P coefficients; these coefficients were calculated for the largest absorption cross sections for each molecule. The absorption cross sections of CH 3 OH and HCOOH at low pressures for all these CO 2 lasers are also presented. These calculations are provided for design of new CO 2 laser-pumped far-infrared lasers.


Introduction
In this paper we report molecular absorption cross sections (M) at CO 2 -laser emission frequencies for several selected gases of atmospheric relevance (M = NH 3 , C 2 H 4 , CO 2 , O 3 , NO 2 , PH 3 , HNO 3 , SF 6 , CH 3 OH, HCOOH, OCS, CH 3 CN, C 2 H 6 , SO 2 , and H 2 O).This information may be useful mainly in the differential absorption (Light Detection and Ranging) LIDAR technique for remote measurement of the gas species [1][2][3][4][5][6][7][8] and also may be used to monitor the CO 2 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 (CH 3 OH and HCOOH) it also may be used in designing optically pumped FIR (far infrared=THz) lasers where CO 2 laser is used as a source of a pump radiation [14].Also, the absorption of CO 2 -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 CO 2 -laser lines.
The focus of the present study is to predict absorption cross section in pure air at wavelengths of seven isotopic CO 2 lasers: 12 C 16 O 2 (normal), 13  In the clear atmosphere, absorption at 9-11 m is due primarily to water vapor and carbon dioxide.Since the fraction of CO 2 in the atmosphere is about 3.8 × 10 −4 and (CO 2 )∼ 10 −22 cm 2 , 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 CO 2 concentration in the atmosphere decrease strongly the accuracy of the LIDAR based on the 26-laser.Hence the first advantage of latter six

Results
Assuming Lorentzian line shapes, we calculated the absorption cross sections (M) at all possible CO 2 -laser frequencies.Tables 1, 2, and 3 show (M) for 26-, 36-, and 28-lasers, respectively, for CO 2 -laser lines between P (40) and R (40), excluding the range P(6)-R (6).Atmospheric pressure  0 = 1 bar and temperature  0 = 296 K are assumed everywhere, and the self-broadening is neglected (i.e., [M]≪[air]).The following expressions were used: where the index  labels all transitions in molecule M,   () is intensity of the th spectral line,  0 =   ( 0 ), Δ]  (, ) is Lorentzian width, Δ] 0 = Δ]  ( 0 ,  0 ), ]  is the absorption maximum frequency of the th spectral line,   is the pressure shift of the line transition,   is the energy of the lower state for th transition,  = 1 for linear molecules like CO 2 and  = 3/2 for nonlinear molecules,  and  are air pressure and temperature, respectively, and  is Boltzmann constant.
The parameters ]  ,  0 , Δ] 0 ,   ,   , and   are taken from GEISA database for each transition of each M molecule.Note that the pressure shifts   are given in the database only for CH 3 CN and NO 2 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 CO 2 -laser frequencies were taken from Freed et al. [40].
In Table 4 we present the "best" laser transitions for each isotopic variation of CO 2 laser and for each molecule M. The pressure and temperature dependence of the cross sections are described by   and   coefficients as   =  ln / ln ,   =  ln / ln , and the coefficients have been calculated from (1) and presented in Table 4 also.
It is not easy task to point out the "best" CO 2 -laser line for detection of molecule M. Normally the "best" CO 2 -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 (M) values occur outside these ranges, we mark it by asterisk shown in the table also.However, if the largest (M) values occur at marginal lines of CO 2 laser and are much larger than all other cross sections, we present this marginal line only.). Line

Discussion
Some of our results are compared with the experimental literature data in  these data may be useful in special cases, for example, when CO 2 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 CO 2 -laser transitions for remote sensing under atmospheric conditions, because at many wavenumbers, the absorption by H 2 O may be much stronger than absorption by the gases of interest.Hence one always should find the tradeoff between the absorption of H 2 O and the absorption of these gases.
Therefore, we included H 2 O in our calculations; see the results in Tables 1, 2, and 3. Our (H 2 O) data in the tables should help to choose the "best" pairs of CO 2 -laser lines (absorbing and nonabsorbing) for remote sensing of the gases of interest.Note that the pair of CO 2 -laser wavenumbers may originate from two isotopically different CO 2 lasers; therefore the possibility to use many isotopic variations of CO 2 laser simplifies strongly the choice of such pairs.

Application to FIR Lasers
There are several important benchmark molecules which are normally used in CO 2 -laser-pumped FIR lasers: CH 3 OH, CH 2 F 2 , HCOOH, 15 NH 3 , CD 3 OD, CD 3 OH, CD 3 Cl, 13 CD 3 I, and 13 CH 3 F.The absorption of CO 2 radiation by these molecules results in FIR-laser emission.Table 6 lists our (M) values for CH 3 OH 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 (HCOOH) value.
Although there is no direct relation between intensities of CO 2 absorption and FIR emission, it is clear that using 1000 CO 2 -laser lines instead of 100-200 should increase strongly the amount of strong FIR-laser transitions.

Table 4 :
For each CO 2 laser and for each molecule M, the laser transitions with the largest absorption by selected molecules are presented.The cross sections (M) (in 10 −20 cm 2 units) and   and   coefficients are shown.

Table 4 :
Continued.Asterisk marks the cases where the (M) is large, but the CO 2 laser line is marginal.The values below 8 × 10 −23 cm 2 are omitted. a

Table 5 :
Comparison of our calculation results with the experimental literature data for the strongest transitions in NH 3 , C 2 H 4 , and O 3 molecules at 12 C 16 O 2 laser frequencies.
a This work.b Probably, misprint.c No data.

Table 5 .
[22]ne 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 ,   , and   coefficients for 26-laser absorption by NH 3 , O 3 , and C 2 H 4 molecules.Note that only in several cases our M molecules are important as "standard" air pollutant (NH 3 , C 2 H 4 , PH 3 , and O 3 ) and in other cases our M molecules may happen in the air only near special industrial objects.As one can see from Tables1-4, 26-laser is a good choice for all these four gases.There are several advantages of the other CO 2 lasers: monitoring of HNO 3 , NO 2 , C 2 H 6 , and CO 2 molecules requires 46-/48-/36-, 36-, 36-/46-/48-, and 38-/268-lasers, respectively, instead of 26-laser.We included in Table4several molecules with low cross sections (OCS, CH 3 CN, C 2 H 6 , SO 2 , and NO 2 ).Although CO 2 laser is not the best choice to detect these molecules,

Table 6 :
The largest absorption cross sections (in 10 −20 cm 2 units) of CH 3 OH and HCCOH at low pressure and  = 296 K.The Doppler shape of spectral lines is assumed.
a Asterisk marks the cases where the (M) is large, but the CO 2 -laser line is marginal.