# What's the meaning of absorbance in the absorption spectrum calculated by the GW-BSE method?

• Q1: As shown in the previous figure, what's the physical meaning of absorbance (y-axis) in the absorption spectrum calculated with the GW-BSE method?

• Q2: Here the absorbance for the absorption onset $$X_1$$ and $$X_2$$ is so low, is it meaningful to talk about it? Or what's the physical difference between $$X_1/X_2$$ and $$X_3$$?

• Maybe it's worth writing out the name of whatever GW-BSE is? I've never heard of it and I'm at least pretty familiar with absorbance spectroscopies. Sep 7 '20 at 19:18
• @jheindel GW-BSE is well-known by enough people. You can now click on the gw-bse tag for more information. Sine you are familiar with absorbance, perhaps you can elaborate on my answer below. I really would have liked to be able to go into much more detail about absorbance but it's been almost 10 years since I worked in a field that used that term. It would be nice to get more answers/question anyway. Sep 7 '20 at 19:28
• @NikeDattani Fair enough. I've just been reading about it since I posted that comment. I can see that it is definitely well known. It seems to have had more use in condensed matter and seems to have origins in high-energy physics. But the way it's used for molecular systems (which is what I'm familiar with) seems very similar to TDDFT, but I need to read a lot more about the theory to understand it. It seems quite interesting to me as a perturbative correction beginning from DFT actually. Sep 7 '20 at 19:36
• @jheindel It's true that GW-BSE will be more known by condensed-matter people but there's also the GW100 community which is getting quite big: they've all applied GW to the same dataset of 100 molecules (mainly diatomics, small polyatomics, and some neucleic acids like guanine and cystine). Here is one of the many papers on GW for molecules: pubs.acs.org/doi/abs/10.1021/acs.jctc.5b00453. Would you be able to write an answer complementary to mine, that explains absorbance in the way you understand it? It would be appreciated! Sep 7 '20 at 19:41
• But actually I think a part of the answer is that it is always physically meaningful to talk about the bound states of any system. It is not even that uncommon that optically dark states, ones which have zero absorbance (often under the dipole approximation) due to symmetries of the system, can couple with optically active states and hence still appear in a spectrum, albeit with diminished intensity. So, in some cases the absorbance of a state being small tells you about the electronic character of that state. Sep 7 '20 at 19:43

The term absorbance does not have anything directly related to the GW approximation or the Bethe-Salpeter equation (BSE). The "absorbance" is a property of a material, while GW and BSE are just methods of calculating things. It's similar to saying that the conductivity of a material has to do with how much a material allows the flow of electrons, but nothing directly related to "DFT" which is just a method that can be used to estimate conductivity.

So what is absorbance? I searched "absorbance" in the paper and it appeared only a few times, and the second instance was their definition of it:

"we plot the optical absorbance by $$A(\omega) = \frac{\omega d}{c}\epsilon_2(\omega)$$, where $$\epsilon_2(\omega)$$ is the calculated imaginary part of the dielectric function and $$d$$ represents the distance between adjacent $$\ce{CrCl_3}$$ layers along the periodic direction of our calculation."

Much more can be said about absorbance in general, but in the specific paper figure in the question, it is exactly defined by the formula in the above quote. The definition with words rather than formulas is given here:

"The absorbance of an object quantifies how much of the incident light is absorbed by it"

The last link I gave says that one of the "measures" of absorbance is the "complex dielectric constant" which leads to this page that defines it as the permitivity of the material divided by the permitivity of a vacuum. In the paper's formula for absorbance, $$\epsilon_2(\omega)$$ is simply the imaginary part of this "complex-valued dielectric constant".

Finally you asked whether or not the two small peaks are meaningful, which I feel can be asked as a separate question. I don't think anyone working on that specific paper or its immediate community knows about Matter Modeling Stack Exchange yet (since we're still so new and small), but at least I can say that those small peaks were significant enough for them to show them in an inset figure.

They also go on for multiple pages talking about $$X_1$$ and $$X_2$$, especially in this part which highlights their importance:

"Importantly, we observe two characteristic excitonic peaks in the optical spectrum at the low energy regime, which are marked as $$X_1$$ and $$X_2$$ at 1.48 and 2.25 eV in Fig. 3(a), respectively. It is worth mentioning that more excitonic states are around $$X_1$$ and $$X_2$$ while most of them are optically dark. In the inset of Fig. 3(a), we also mark the lowest energy dark exciton, $$X_0$$, whose energy is about 20 meV below $$X_1$$ but its dipole oscillator strength is about four orders of magnitude smaller than that of $$X_1$$."