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Looking at the Wikipedia page for absorption bands, it seems to me that there's a sizable window - i.e. a local minimum - in the graph for electromagnetic radiation absorption, as per the edited image below.

Water vapor, oxygen, ozone, and methane appear to be entirely transparent to radiation of 4 μm wavelength, carbon dioxide only appears to start absorbing it after that point, and even nitrous oxide has a window there. Moreover, Rayleigh scattering is also minimal there.

On top of that, this Earth Science Stack Exchange answer by Camilo Rada and its source show minimal (sub-0.5%) absorbance of sulfur dioxide at that wavelength.

Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of mid-wavelength infrared) EM radiation.

enter image description here

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    $\begingroup$ Wonder if this may wind up being more of a general chemistry question, as I'd imagine if there is a focused reason, it's to do with specific molecular reasonings? But perhaps someone has some insight here. $\endgroup$ Jun 27, 2022 at 4:09
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    $\begingroup$ Looking at the layout of the different absorption graphs, though, it would seem it's just mainly that there's periodic gaps in H2O, and nothing else happens to be there. But there are very similar sized depressions along the absorptions/scattering profile, wherever water vapor has gaps and there doesn't happen to be another major constituent in that window. $\endgroup$ Jun 27, 2022 at 4:11
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    $\begingroup$ in that single gap is the cause for and explanation of the greenhouse effect,and it show why CO2 concentration is important for our planets temperature. $\endgroup$ Jun 27, 2022 at 4:25
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    $\begingroup$ @trondhansen So, essentially: thermal radiation gets in through that gap, which is transparent to it, soaks into the Earth, and then is radiated away at a wavelength that the atmosphere does absorb? $\endgroup$
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    Jun 27, 2022 at 4:34
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    $\begingroup$ @KEY_ABRADE it works like this:short wave radiation from the sun heats the ground and air and this heat gets radiated out at a longer wavelenght that is at or close to the wavelenght in the gap in your graph,as you can see CO2-methane and nox blocks radiation in different parts of the gap. $\endgroup$ Jun 27, 2022 at 4:50

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There is simply no strong enough absorption of any of the greenhouse gases at this wavelength. However this does not mean that there is none.

Remember that what you are seeing here is the transmission function, and plotted on a linear scale, to add to it. The transmission function per wavelength at a certain atmospheric altitude z is defined as $T = I(z)/I_0 = e^{-\tau(z)}$, where the optical depth $\tau$ is the line-of-sight integral over all species' opacities times densities along a path, i.e. $\tau(z)=\int_z^\infty dz\; \sum_{\rm species} \rho_s(z) \kappa_{s}(z)$, where $\rho(z)$ is the density of a species $s$ at a given altitude, and $\kappa_{s}$.
A quick look at the opacity of water at 1 bar and 300K in logscale (taken from the DACE opacity database) shows that there is just a significant drop in the regular molecular wavebands at this wavelength, and nothing else. Same with the other species.

Opacity function of water at 1 bar and 300K

So the fact that just at 4 micron there seems to be a suspicious drop is because our atmospheric column depth integral over $\rho(z)$ at this wavelength just gives a small, but nonzero value for $\tau(z)$. If the transmission plot were logarithmic, you'd see this nonzero value.

Additionally, to try and make sense of

Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of mid-wavelength infrared) EM radiation.

Just think of molecular opacities being periodic signals in wavelength space. If you stack enough periods, you will always find a minimum somewhere, by superposition. For the few ingredients you mentioned, this minimum just happens to be at 4$\mu$m.

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