Proposal for changes in DoniachModel

[JulioAzcarate]

Hi!

I would like to suggest some changes to DoniachModel.
The math expression actually used in lmfit is the same showed in CasaXPS, which is an approximation only valid for low-asymmetric peaks. That math expression lacks the factor "Gamma(1-alpha)" present in the original lineshape (eq. 18 in Doniach, S.; Sunjic, M. Many-Electron Singularity in X-Ray Photoemission and X-Ray Line Spectra from Metals. Journal of Physics C: Solid State Physics 1970, 3 (2), 285–291. https://doi.org/10.1088/0022-3719/3/2/010.) Here, Gamma is the Gamma function

Also, I would like to suggest the use of parameters names than the original paper:

lmfit	Doniach-Sunjic paper
sigma	gamma (core-hole lifetime)
gamma	alpha (singularity index, or asymmetry)

Do you think these changes could be implemented in the next version of lmfit?

My best regards

[newville]

@JulioAzcarate that seems reasonable to me - I'm not an XPS expert, but happy to try to support that better. Would you be willing to make a Pull Request?

If our sigma is really meant to be "core hole lifetime", should that be a variable parameter or something that is looked up and used as a constant? I guess another way to ask that is: are instrumental or other broadenings also Lorentzian?

[JulioAzcarate]

@newville Thank you so much for your answer and for considering it !!!.

In XPS there is instrumental broadening. Then, the Lorentzian or Doniach-Sinjic (DS) function must be convolved with a gaussian function. Sometimes, the core-hole lifetime (Lorentzian width) and asymmetry are knowledge and must be set as constant during the fitting and just the Gaussian width is varied. In the case of Lorentzian-Gaussian convolution, one just uses a Voigt profile. However, in the case of DS profile, one must convolve the DoniachModel with a GaussianModel and the use of sigma parameter name in both functions could be confusing. For that reason, I propose changes in the names ... just to be more "scholarship".

If you considered improving the DoniachModel may be a good idea to use the convolved form DS-Gaussian (eq 7 and 8 in (1) Joyce, J. J.; Del Giudice, M.; Weaver, J. H. Quantitative Analysis of Synchrotron Radiation Photoemission Core Level Data. Journal of Electron Spectroscopy and Related Phenomena 1989, 49 (1), 31–45. https://doi.org/10.1016/0368-2048(89)80035-0.).
For example, in IgorPro they implemented a function dsgn as the result of the DS-Gaussian convolution for the integration of eq 8 in Joyce's paper by Simpson's rule. Maybe a similar strategy could be done in lmfit. Then, the DS-Gaussian profile will have the following parameters:

Parameters	meaning
center	center or position of the peak
amplitude	amplitude or height of the peak
gamma	Lorentzian width
alpha	asymmetry
sigma	Gaussian width

Do you think it would be better to make a Pull Request proposing the DoniachModel as the DS-Gaussian convolution?

My best regards

[newville]

Hi Julio,

On Fri, Feb 12, 2021 at 7:02 AM JulioAzcarate ***@***.***> wrote: @newville <https://github.com/newville> Thank you so much for your answer and for considering it !!!. In XPS there is instrumental broadening. Then, the Lorentzian or Doniach-Sinjic (DS) function must be convolved with a gaussian function. Sometimes, the core-hole lifetime (Lorentzian width) and asymmetry are knowledge and must be set as constant during the fitting and just the Gaussian width is varied. In the case of Lorentzian-Gaussian convolution, one just uses a Voigt profile.

Right, that would match my experience with other X-ray measurements. I don't think we want to get too domain-specific here, but have that Lorentzian width be a constant makes sense while the Gaussian portion may be more necessary to vary in a fit.

However, in the case of DS profile, one must convolve the DoniachModel with a GaussianModel and the use of sigma parameter name in both functions could be confusing. For that reason, I propose changes in the names ... just to be more "*scholarship*".

When we picked the parameter names for the different peak-like models we tried to use consistent names so that it would be easier to swap models. For a lineshape/model class like DS that really does seem to be domain-specific (or so widely in one domain that it dominates the others), I think it would be OK to migrate the parameter names to match those most commonly used in the literature. That transition could cause some trouble, but maybe a deprecation cycle or a new function model name would be appropriate.

If you considered improving the DoniachModel may be a good idea to use the convolved form DS-Gaussian (eq 7 and 8 in (1) Joyce, J. J.; Del Giudice, M.; Weaver, J. H. Quantitative Analysis of Synchrotron Radiation Photoemission Core Level Data. *Journal of Electron Spectroscopy and Related Phenomena* *1989*, 49 (1), 31–45. https://doi.org/10.1016/0368-2048(89)80035-0.). For example, in IgorPro they implemented a function dsgn as the result of the DS-Gaussian convolution for the integration of eq 8 in Joyce's paper by Simpson's rule. Maybe a similar strategy could be done in lmfit. Then, the DS-Gaussian profile will have the following parameters:

Sure, I think it would be fine to have a Model that convolved DS with a Gaussian.

Parameters means center center or position of the peak amplitude amplitude or height of the peak gamma Lorentzian width alpha asymmetry sigma Gaussian width Do you think it would be better to make a Pull Request proposing the DoniachModel as the DS-Gaussian convolution?

Yes, I think that is all OK. That is, I guess that "convolved with a Gaussian" is more general (well, "sigma -> Inf" would effectively be "not convolved"). If others have suggestions or opinions on how to handle the transition, please chime in.

…

--Matt