7.7um is ca. 1300 cm-1 which is in the standard region of IR spectroscopy. There is a lot going on in this spectral region of the methane spectrum, but from figure 1 in this publication you should be able to get the absorption coefficient for the exact rovibrational band that you need:

Article Optical Methods of Methane Detection

Jürgen Weippert Thank you for the share. However, I find some contradictory value in another paper: https://opg.optica.org/oe/fulltext.cfm?uri=oe-24-20-23109&id=350423.

Here they have used 174 (L/mol.cm). Dont know which one to use. Moreover in the HITRAN database, it is a bit confusing to locate the value.

I haven't done the recalculation math between the two, but one of the references is with a ppm concentration and one mol/l, also one is epsilon and one is alpha, of which one is commonly with respect to a decadic and one with respect to a natural logarithm, so Itrans=I0*10-epsilon*c*d=I0*e-alpha*c*d. When considering these aspects, do they still contradict each other?

seems like I found the correct absorption coefficient (1/cm) at standard atmospheric conditions.

https://raw.githubusercontent.com/radis/radis-examples/master/hitran_spectra/out/5%20-%20CH4%20infrared%20spectrum.png

Careful, there are natural and decadic logarithmic coefficients, as I mentioned in my post above. Which one is this and what qualifies it as "correct" for you?