Very interesting discussion and proposals to solve for calculating the absorbance of a single layer of MoS2 .

The absorbance is important to optically characterize the materials. The absorbance is the absorbed fraction of the incident light with a specific wavelength on a material with a given thickness. It is required for optical filters and for photodetectors and solar cells.

The dependence on the incident light wave length stems from the energy band structure of the material such that it is dependent on the probability of transferring of an electron from the valence band to the conduction band by the incident photons. Specifically it depends on the absorption coefficient as a function of the wavelength.

The key point for the solution is to calculate the energy band structure of the two dimensional material and from it you can get the absorption coefficient as a function of lambda. Then you can calculate the absorbance. As you have here a single layer the absorption coefficient will be equal to the absorbance.

You might benefit from the thesis given in the link: https://digitalcommons.mtu.edu/cgi/viewcontent.cgi?article=1049&context=etds

I am quite sure that quantum mechanics will allow you to deduce a formula for the absoption of a substance deending on the wavelength. The problem is: this is really difficult.So have fun with finding a solution and prepare a nice place for the Nobel medal in case you do find it.

However, it might be easier to use measured spectra (as precise as possible) and come up with an "empirical formula" that describes the spectrum well enough for the purpose. This may be guided in part by theory as well, maybe even more by "classical" electromagnetic theory than by quantum theory.

Hi Samir Mandal

As Jochen Wilhelm said quantum mechanics is the clue. Lathought Everything is already done, and you will not get a nobel price. :p

First lets define what its absorbance:

When a visible or UV photon is absorbed by a chemical compound, an electron from an orbital is promoted to an unoccupied orbital. Generally, an electron from the first vibrational (v=0) singlet spin multiplicity (S) electronic ground state (S0) is excited to an electronic excited state, most commonly the first electronic state (S1). The probability of such a transition proportional to the square overlap of the vibrational wavefunctions of the states involved in the transition.

Experimentally, the efficiency of light absorption at a wavelength by an absorbing species is characterized by the absorbance (A) and transmittance (T) with the absorbance that follow the Beer-Lambert law:

A( λ )=e( λ )*L*C

Where (A) is absorbance, (e) epsilon or molar extinction coefficient , (L) the optical path and (C) the concentration of the sample.

The molar absorption coefficient quantify the ability of a molecule to absorb light in a given medium. In the classical theory, molecular absorption of light can be described by considering the molecule as an oscillating dipole and then a quantity called oscillator strength is related to the integral of the absorption band as follows:

f=(4*me*e0 / NA*ce^2)*B

where me is the mass of an electron, e0 the vacuum permittivity, NA Avogadro’s constant, ce the elementary charge and B the molar natural absorption coefficient integrated over the whole band in units of frequency. (sorry I cannot write integrals in the answer but you can check on goolge)

In theoretical chemistry the transition moment is defined to characterize the transition between an initial state and a final state. The transition moment represents the transient dipole resulting from the displacement of charges during the transition. The oscillator strength (classical approach) and transition moment (quantum chemistry) are linked through Einstein coefficient.

For relation between oscillator strenght and eisntein coefficients check wikipedia page for Einstein coefficient last section.

I will advise to check check on google more about oscillator strenght and absortion. And questions like this:

https://www.researchgate.net/post/How_can_I_calculate_oscillator_strength_from_excitation_energy

As Jochen Wilhelm said is not an easy task what you want to do. And I will recommend using some computational chemistry software like Gaussian would be much easy than writing thing that are alredy done.

For more theoretical stuff, please check books such as P. W. Atkins, Physical Chemistry, 5th edition, Oxford University Press,Oxford, 1994.

Cheers

Lucas

I think only considering the atoms' and molecules' internal orbitals and considering the molecules as independent oscillating dipoles can only be correct for vapor state.

In solid state materials such as MoS2, the issue is more complicated. Since atoms and molecules are much more close to each other in a bulk semiconductor material, countless orbitals of countless atoms have interactions with each other.

According to Pauli exclusion principle, each electron in such a system should have it's own unique energy state. These interactions result in forming the material's `band structure` that models countless energy states which constitute an almost consistent specific range of energy states (called energy bands) and some energy gaps with no energy state in other specific ranges. For being a photon absorbed by an electron, not only it is needed to find an unoccupied energy level with some energy equal to summation of the energy of the electron and photon in the destination energy level, there should be some point in the material's band structure with the excited electron's momentum value (equivalent with 'wavenumber' in quantum mechanics) in the destination energy level. Every semiconductor material has it's own `density of states' function that determines these energy states' density. 'Fermi-Dirac' distribution function determines the probability of being each energy state occupied if that energy state exists according to the material's Density of states function. Integral of the multiplication of these two functions determines the number of electrons in each specific energy range.

All in all, I recommend you make a quick wikipedia search about 'band structure', 'density of states function` and 'Fermi-Dirac' distribution for finding the formula that you need for MoS2. At least you may find the structure of the formula in this way. If you found the structure you can apply 'least square' based 'system identification' methods by python on your experimental data for reaching to final result.

And about your main and first question, "why?": I'm not sure why you asked this question but simply one important reason is exactly about your research field, spectroscopy. This absorbance vs wavelength diagram is unique for each material and when we want to know what materials exist in something, we can plot this diagram and understand what it is made of by comparing it with the figures of known materials. In Photonics, this diagram is necessary in almost every project. For example when you are designing a solar cell, you should make sure that your device absorbs as much spectra of sunlight as possible and you need to know how much does each material absorb in each wavelength.

Best regards.

Very interesting discussion and proposals to solve for calculating the absorbance of a single layer of MoS2 .

The absorbance is important to optically characterize the materials. The absorbance is the absorbed fraction of the incident light with a specific wavelength on a material with a given thickness. It is required for optical filters and for photodetectors and solar cells.

The dependence on the incident light wave length stems from the energy band structure of the material such that it is dependent on the probability of transferring of an electron from the valence band to the conduction band by the incident photons. Specifically it depends on the absorption coefficient as a function of the wavelength.

The key point for the solution is to calculate the energy band structure of the two dimensional material and from it you can get the absorption coefficient as a function of lambda. Then you can calculate the absorbance. As you have here a single layer the absorption coefficient will be equal to the absorbance.

You might benefit from the thesis given in the link: https://digitalcommons.mtu.edu/cgi/viewcontent.cgi?article=1049&context=etds

thank you sir Abdelhalim Zekry

This is great. All the information is valuable. Note the absorbance spectra of different species may be obtained in the vapor phase. An interesting point for the vapor phase is the molecules are typically not close to each other and thus little molecule-molecule interaction. Your opportunity is a molecule or more appropriately a tessellation of like molecules across a surface of one or more solid materials.

The molecular spectrum of a molecule isolated in a box will be the result of the electrons' distribution across the entire molecule (as long as it does not touch the box). When that same molecule is laid down on a surface, the molecules 'box' is extended to the layer to which it is coating and adjacent coating molecules. If we start with a pure silicon substrate, electrons of the coating molecule will have some interaction with the substrate. The molecule will have different energy properties due to the coating's electrons interacting with the substrate material. Similarly, the substrate electrons will interact with the coating. If we use as a substrate, a layered silicate with the planar surface perpendicular to the coated surface, there will be a different electronic structural environment for the coating than if the silicate is oriented with the planar surface as the interface.

If we know the spectrum of the coating in the vapor phase, and compare that with the spectrum of the coating on different substrates, there will be differences due to these interactions.

Each bond in the coating molecule will contribute to the molecular spectrum. Each bond in the molecule can be mapped to a specific line in the spectrum or range of the spectrum. This mapping has been performed for a large number of molecules in the vapor phase and liquid phase.

With the molecule applied to a substrate, there will be some difference in the spectrum of the adherent molecule when compared to the isolated molecule. The isolated and coated spectra may be compared to indicate which bonds are affected and how much they are affected. There will also be effects on adjacent coating molecules.

It is interesting the interactions are with electrons. That is, the interactions are electronic. Let's imagine a substrate that has nano wires which each being independently electrically charged. Let's take a spectral snap shot with the nano wires not energized. Then, oppositely charge each wire to a low level. How does the spectrum change? Increase the voltage and see how the spectrum change. Continue for a wide range of voltages. How does the spectra change with voltage? Does the change saturate at some voltage. What happens when the voltage is reversed?

Now, apply the coating when there is a uniform electric field with some particular orientation to the nano wires and repeat the experiment.

Continue the exercise with different angels between the nano wires and the applied uniform electric field. How do the spectra change with the different orientations?

This might also be performed by applying an optical image on the substrate when the substrate is being applied. For example, a laser may be used to project a nano grid of light.

Consider what other conditions you could vary to study the effects on the spectra. Such a consideration may be altering the pure silicon with different dopants, different percentages, along with different voltages.

I am sure you could come up with more appropriate changes by looking at why your surface is being coated. Focusing in on the application may provide more valuable conditions to study.