Los permisos de salida

In order to validate our simulated spectrum of CO2 we compare our computed results with those listed in the HITRAN 2004 database [1]. According to the HITRAN database the difference between the measured line position and the computed line position is in the order of 0.0001 cm-1 for most of the ro-vibrational lines of the strongest fundamental band of the CO2 in the region of the 4.3 µm [1, 3]. In the same way the computed lines reported by HITRAN present an error around 6% for the same absorption bands [1, 3]. Here we require to evaluate how close are our computed line positions and intensities with those provided by HITRAN in order to be sure that our data have good level of confidence. Firstly, in this section we evaluate the difference between the calculated line positions and those listed in HITRAN. Here we will call to this difference the residual

difference. Secondly, we evaluate the error in the line intensity. Here we just present the

result obtained for the fundamental bands of the three most abundant isotopomers 12

C16O2, 13C16O2 and 16O 12C18O. The residual difference in line position for the fundamental bands 00011←00000 of the 12C16O2 and 13C16O2 isototopomers is in the order of cm-1 for (Fig. 2.2 and 2.3 respectively). The

00000

00011← band of the 16O 12C18O isotopomer has even much lower residual

difference in the order of for (Fig. 2.4). The deviation in the line position is mainly due to precision errors in the constants and since the deviation increases as increase. It can be appreciated with the fundamental band 16O12C18O where the deviation is practically negligible meaning that all the rotational constants for this band are more accurate than is needed for our purposes.

Furthermore, considering that the residual difference in the ro-vibrational line positions for the 00011←00000 band of 12C16O2 is

5

10 1× −

≤ cm-1 for and these ro-vibrational lines have in average a FWMH of 0.14 cm-1; therefore we can say that our model deviates by of a typical ro-vibrational line width for this band when . The deviation is even much lower, in the order of , for the fundamental band of 16O 12C18O. In the next chapter it will be shown that the separation of two rotation lines is of great importance in our project. In average the separation of the ro-vibrational lines of the 12C16O2 fundamental band is around 1.8 cm-1 for the P branch and 1.3 cm-1 for the R branch when . Hence the deviation of the

computed line position is around of the separation between two consecutive ro-vibrational lines.

These deviations are very small and for our application they are negligible. In our particular case in order to simulate our sensor with sufficient accuracy we build a wavenumber axis using an interval of 0.01 cm-1 which is 1/16th of the line width and around 1/160th of the separation of two consecutive ro-vibrational lines. This wavenumber interval is much larger than the residual difference in line position between our computed values and the HITRAN values. It means that using a 0.01 cm-1 interval in the wavenumber axis the evaluated line positions are the same as those given by HITRAN and therefore the residual differences will not affect the final CO2 spectrum. A wavenumber axis with a 0.01 cm-1 interval is good enough to reproduce an accurate CO2 spectrum which can be used to simulate our gas sensors which are based mainly in the separation of the ro-vibrational lines.

The line intensity error (%) of our calculated values and those listed in the HITRAN 2004 for the fundamental bands of of 12C16O2 and 13C16O2 and 16O 12C18O are presented in figures 2.5-2.7. Here it can be seen that the error is around 0.01% for , which is very small. This error is mainly due to precision errors in the rotational constants and in the Herman-Wallis Factors coefficients. However the errors are quite small and this will not introduce a significant error in the simulation of our gas sensor.

According to HITRAN 2004 the total accumulated strength of the fundamental bands of the three most abundant isotopomers 12C16O2, 13C16O2 and 16O12C18O is

at 296K for . In our simulation we are including the fundamental bands of these three isotopomers considering ro- vibrational lines up to and the overall accumulated strength is

. This represents the 99.9996% of the total strength obtained from HITRAN up to . Therefore, if we consider that our model has an error of 0.01% and that just the 99.9996% of the total strength is taken into account we find that our model has an accuracy of around 99.9896 %. Furthermore we need to consider that the HITRAN line intensities have an error of around 6% therefore our computed line intensities have an accuracy of 93.999624% with respect to the real measured intensities [1-3]. This led us to consider that the model presented in the previous section to

calculate the line intensities for CO2 is sufficiently accurate. Finally, in Table 2.5 a comparison between calculated line position and intensities with respect to HITRAN 2004 of some ro-vibrational lines are presented, at 296K the strongest ro-vibrational line is at , here can be observed that the deviations are very small.

Figure 2.4- Residual difference in line position between our calculated positions and HITRAN 2004 for the of 12C16O2.

Figure 2.5- Residual difference in line position between our calculated positions and HITRAN 2004 for the of 13C16O2.

Figure 2.6- Residual difference in line position between our calculated positions and HITRAN 2004 for the of 16O12C18O2.

Figure 2.7- Error in Line intensities between HITRAN 2004 and the computed values 2004 for the of 12C16O2.

.

Figure 2.8- Error in Line intensities between HITRAN 2004 and the computed values 2004 for the of 13C16O2.

Figure 2.9- Error in Line intensities between HITRAN 2004 and the computed values 2004 for the of 16O12C18O2.

Table 2.5- Some calculated line position and intensities versus HITRAN 2004, for the of 12

C16O2.

R Brach P Brach

Calculated HITRAN Calculated HITRAN

Line Position _{2358.727368 2358.727369 2339.372389 2339.37239} 12 Intensity 3.3617x10-18 3.358x10-18 3.0992x10-18 3.096x10-18 Line Position _{2360.109127 2360.109128 2337.658143 2337.658185} 14 Intensity 3.50139x10-18 3.498x10-18 3.2632x10-18 3.260x10-18 Line Position _{2361.466077 2361.466078 2335.91954 2335.919541} 16 Intensity 3.5281x10-18 3.524x10-18 3.3151x10-18 3.312x10-18 Line Position _{2362.798194 2362.798195 2334.156485 2334.156486} 18 Intensity 3.453x10-18 3.449x10-18 3.2652x10-18 3.262x10-18 Line Position _{2364.105453 2364.105455 2332.369045 2332.369047} 20 Intensity 3.29173x10-18 3.288x10-18 3.0992x10-18 3.125x10-18