Subject: Summary: UV/vis visualisation

From: Andreas Goeller <[email-masked]>
Date: Fri, 24 Mar 2000 10:45:20 +0100

Dear all,

here's the summary of my question about simulating UV/vis spectra:

________________________________________________________________________
*The original question:
*from semiempirical calculations I get transition energies (say, in
*wavenumbers, lam) and oscillator strengths (osc), i.e. a line spectrum.
*The osc are proportional to the surface below one extinction curve. I
*can model this curve approximately by using a Gauss curve f(x), and by
*summation over all curves (g(x)) I get something comparable to an
*experimental spectrum. The function is
*
*g(x)= sum_i(osc_i*(fx_i))
*f(x)= 1/(sigma*sqrt(2*pi))*exp(-0.5*((x-x0)/sigma)**2)
*
*Can anybody give me a hint about reasonable choices for sigma, the
*standard deviation? The smaller sigma, the steeper the curve. 
*
_________________________________________________________________________

There seems to be no quantitative relationship one can use. There are
empirical factors that work. 

_________________________________________________________________________
From:"Paul N. Day MLPJ CON" <[email-masked]>

It seems like with the normalization coefficient you have put
on f(x), you will always get f(x)=1.  I think you want to model
the absorption spectrum with a gaussian such as

epsilon=epsilon(max)*exp(-0.5*((x-x0)/sigma)**2)

where epsilon(max) is the extinction coeficient at the line maximum
with frequency x0.  Then when you integrate this over x and multiply
by the appropriate constant (4.33e-9 in customary units), you will get 
the oscillator strength.
sigma is related to the linewidth at half-max, gamma, by

sigma = 0.5*gamma/sqrt(2*ln2)

It seems like the usual practice is to choose an arbitrary value for
the line-width based on experiment.  In a paper by Albota, et al
(Science 281, 1653(1998)), for the calculations they use 0.1 eV for 
the linewidth.  The linewidth is related to the decay rate of the
state and is affected by temperature, solvent, etc.  I do not know
of a rigorous theoretical method for getting the linewidth, but I
would be interested in hearing about any that you hear about.

Thanks,
Paul
_________________________________________________________________________
From: Demetrio Antonio da Silva Filho - doutorado <[email-masked]>

I do the same as you to fit the UV-Vis peaks that we get from QC
calculations ( I have a fortran CODE do to that and I can send the code
to
you if you want).
The value of sigma depends on the resolution of the article that you
have
to compare your results. I have an article which the experimental
resolution was 10nm. So I use the same!
Hope it helps!
Demetrio Filho
_________________________________________________________________________
From: Sérgio Emanuel Galembeck <[email-masked]>

    Some years ago I simulate some spectra of organic substances using a
Gaussian, and I considered sigma an empirical parameter that are ajusted
in
order to reproduce experimental spectra.
    There some softwares that calculate a Gaussian using absorption and
oscillator stenghts, as
synspec.

_________________________________________________________________________
From: Scott McMillan <[email-masked]>

I've looked into this issue.  I also use Gaussians for each individual 
excitation.  In my case, I looked at the half-width of Gaussians fit to
the 
experimental spectrum and used something similar to that.  I found that
a 
half-width between 500 and 1000 cm-1 works well.  If you have
experimental 
spectra, you could also trying fitting the half-widths although you
could have 
a lot of fitting parameters.  I don't know of a way to determine the
width of 
the Gaussians a priori.  Please send me a summary of the responses to
your 
question. Thanks.

_________________________________________________________________________
From: Stefan Grimme <[email-masked]>

to my expierience, the band width at 1/e height is about
0.3-0.5 eV for larger molecules if measured in solution.

I mailed back to Demetrio:

>it would be nice if I could have your source for reasons of comparison.
>What exactly do you mean with sigma=10nm. The std. dev. or the line
>width?

and got the answer:

______________________________________________________________________________
10nm is my  dd, and it's your  (sigma)^2

To run the the code, after compilation, you should have an archive
called fort.1 with the energy in one column and the dipole oscilator
strenght in the other. The archive fort.2, that will be created after
running
the program, will contains the spectrum with gaussians.
Hope it helps!
Demetrio FIlho

f(x)= 1/(sigma*sqrt(2*pi))*exp(-0.5*((x-x0)/sigma)**2)

Here is the code!

        implicit real*8(a-h,o-z)
        dimension energy(600),weight(600)
c       energy(i) e' a energia da transicao em eV ou comprimento de onda
c               em nanometros
c       weight(i) e' a forca de oscilador
c       dd e' a largura da gaussiana em eV ou nanometros
c       nn the number of transitions to be read
        read(1,*)nn,dd
       READ(1,*)( energy(I),weight(i),i=1,NN)
       eini=energy(1)-100.d0
        emax=energy(nn)+100.d0
       de=1.d0
       e=eini
       pi=3.1415927d0
       den=dsqrt(2.d0*pi)*dd
        dd=dd*dd
       npoint=(emax-eini)/de
       do i=1,npoint
       f=0.d0
         do j=1,nn
        w=weight(j)
        ene=energy(j)
         if(dabs(e-ene).le.500.d0) f=f+w*exp(-0.5*(e-ene)**2/dd)
         enddo
       f=f/den
       write(2,*)e,f
       e=e+de
       enddo
        stop
        end

-- 
                                Andreas Goeller

---------------------------------------------------------------
   Dr. Andreas Goeller       Institut fuer Physikalische Chemie
                               Friedrich-Schiller-Universitaet
                                       Lessingstr. 10
phone: +49(0)-3641-948352               D-07743 Jena
  fax: +49(0)-3641-948302 (secretary)     Germany
email: [email-masked]
http://www.uni-jena.de/chemie/photo/goeller/goeller.html
---------------------------------------------------------------
   Dr. Andreas Goeller   ehemals Computer Chemie Centrum

email: [email-masked]
http://www.organik.uni-erlangen.de/clark/goeller/goeller.html
---------------------------------------------------------------