Dear Khoi Quang Nguyen,

As you might know that:

For a single wavelength, E = h c / Lambda

The differential form is: deltaE = - h c / Lambda2 delta Lambda

To obtain E as eV units you should divide the value of E by the elementary charge (1.602 E-19) .

This is why we should convert nm to eV. Generally the energy of orbitals is expressed in eV.

I think that both units should be indicated as in the attachment named ex1.

Hoping this will be helpful,

Rafik

Thanks Rafik

so if we don't convert nm to eV units in fitting PL spectra. Is it correct or incorrect?

Dear Khoi Quang Nguyen,

It is still correct. An example is the second attachment in your question.

Rafik

Hi,

Dr. Peter Kapusta is correct. Please follow his response. 

Dr. Kapusta,

Can you extend your answer? I always change between nm and eV with the expresion λ(nm) = 1240/eV. What can I do for a correct change?

Thanks a lot for your answer

Hi 

I request every one, to kindly explain the reason for devoting the answers, so that we can also learn new, forgotten and unknown facts. Please do not just use devote as an option to express your disagreement. We can have a fruitful debate on this topic.

Cannot thank.

mr Das

A question then to you: why would one want to describe a spectrum with a single Gaussian function. Does the questioner mean a single emission line and for what compound in what example?

For instance the Lorentz line-shape has a theoretical background and information on the lifetime of the luminescent level.

Dear all!

Almost all of you are wrong. You are giving wrong answer to the question. I just repeat my answer from here:

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

"

First I would say that fitting Gaussian to absorption spectra where independent parameter is the wavelength is a mistake (actually not just Gaussian, but also Lorentian). If you want to make a Gaussian fitting you should do it on frequency (energy) scale. (Same is true for making derivatives.) Consequently a Gaussian peak on the wavelength scale is not symmetric, it is very much asymmetric, having longer tail in the longer wavelegth side. That is why UV peaks have a long tail to the visible region. So ALWAYS fit functions on a frequency scale!

Second, as a first try I would fit Lorentzian function. A single transition always has a Lorentzian shape. Gaussian arises if many single transitions are convoluted. It happens very often but single transitions are not so rare. Even if you have a complex spectrum it is worth first to fit with the sum of several Lorentzians.

Using derivative does not mean that you have eliminated the baseline problem. Baseline is eliminated by deriving the function ONLY if it is a linear baseline (in this case it will add a constant baseline only to the derivative spectrum). If the baseline comes from the tail of other peaks, making derivative spectrum would not solve your problem.

If all these problems are solved then I agree with all answers above. You should fit a polynomial baseline together with the Gaussian. However you should be very careful. If the baseline fitting result in a polynomial where maxima and minima exist, you can easily add false peaks to your evaluation (with both positive and negative amplitude) As a rule baseline should always be a MONOTONIC function, therefore polynomial fitting is acceptable if it results a monotonic fit. It is very useful if the fitting program lets you investigate the individual functions fit."

I have to add that frequency scale (cm-1 or Hz) and energy scale (eV or whatever unit you use) are the same in this respect.

Csaba Bagyinka

Could you give some reference about the comments on Gaussian and Lorentian fitting? Why a single transition usually shows as a Lorentian peak?

Thanks.

@ Yongchao Jia:

You can find in any physics book where they explain the frequency of the spring vibration that resonance frequency has a Lorentz distribution depending on the frequency of the force (forced vibration). This is the simplest case and many transitions can be described with this simple case. In my practice, the Lorentz function can describe absorption peaks in many-many cases. I have experience mostly in IR and Raman spectroscopy, but UV-Vis absorption very frequently can also be fitted with Lorentians (on the energy scale of course).

Lorentzian shape for IR-vis-UV only applies for atoms, very small molecules and larger gas-molecules at very low temperatures in which a transition is not overlapped by often a host of close lying other associated with a change in rotational number

In case of larger molecules the shape is not Gaussian but an overlap of a host of Lorentzian lines into bands that may not even be completely resolved

Harry ten Brink I agree, nevertheless vibrations of small, but well separated parts of molecules (i.e C-H or C-H2) can also be resolved, even in proteins and lipids (i.e. you can group different types in the protein matrix). I agree also, that they can overlap, but in many cases you can resolve them, of course the number of resolved peaks depends on the noise and how close they are.

Csaba Bagyinka

I agree that vibrational bands can be resolved but the band width is much larger than that of the "natural line broadening" due to the lifetime of the excited state

This corresponds to a FWHM of 10-3 cm-1 for vibronic transitions etc

I liked the following presentation best as illustration

in section 2 Types of line broadening

https://cefrc.princeton.edu/sites/cefrc/files/Files/2013%20Lecture%20Notes/Hanson/pLecture6.pdf

Harry ten Brink

That is true, Natural line broadening is small.

Csaba Bagyinka Harry ten Brink

Thanks.

Dear Khoi,

let me answer in two steps:

1) First, why conversion to energy scale is necessary. A PMT or any modern luminescence detector typically does photon counting. If light of a given intensity impinges on a detector, this corresponds to a power per unit area. From classical electrodynamics, it follows that there is an radiant energy flux impinging on a detector. Thus, the number of photons can be elucidated by dividing this particular overall energy by the single photon energy.

The monochromators in spectrometers almost all work wavelength-dispersively. Moreover, users tend to feel more familiar with wavelengths. Therefore, the raw spectral data is immediately presented as wavelength-dependent data. Given the detection principle of a e.g. PMT, however, it does not really help much, because you only obtain the physically relevant data by proper conversion to an energy scale. It then depends a bit on what you want to extract. Sometimes, it is still accessible from the wavelength-dispersive data.

2) Usage of Gaussian fitting functions: My predecessors are right about using a Lorentzian if natural line broadening is the only relevant mechanism. In that case, any resonance is indeed described by a Lorentzian.

In a solid or thin film (as I could see from the publications), however, vibrational broadening or even inhomogeneous broadening due to slightly different crystallographic environment takes place. While vibrational broadening is, strictly speaking, connected to a Poissonian shape, both the number of progressions, but also inhomogeneous broadening finally lead to the validity of the central theorem of statistics, namely, that a Gaussian shape evolves. From the data, you can get at least limited amount of information. But it almost impossible to observe a Lorentzian shape in a solid if there are multiple emitters. Only in the limit of single-emitting sources such as in carefully prepared quantum dot samples, a Lorentzian could be indeed observed. That is very unusual in solid samples, however.

I hope that answer helps you a bit out.

All the best,

Markus

Csaba Bagyinka

Could you please explain when we would need to normalize a spectrum and when to fit the spectrum with a polynomial as a baseline to our gaussian function?

Darsh Khandelwal

I think I have explained the baseline fitting in my first answer. If you need a more specific answer please ask more specifically.

Regarding the normalization, I have never said anything about it. Actually, I do not understand why the normalization might be useful when fitting a function. So I cannot explain the need for normalization.

BTW the "normalization" - for me - is not a well-defined phrase. What do you mean by that? Equalize the highest amplitudes? Make the area below the function the same? Neither makes sense to me. "Normalization" should be done by an independent parameter, like concentration, path length, etc.