Subject: Summary: Calculated Spectra and Oscillator Strength Questions

From: Mike Peleah <[email-masked]>
Date: Wed, 19 Sep 2001 08:59:12 +0300

::: Calculated Spectra and Oscillator Strength Questions Summary ::::::::::::

    (as of 19-Sep-2001)

:: Original questions :::::::::::::::::::::::::::::::::::::::::::::::::::::::
> I  have  one  (may  be  dummy  question)  on  calculated UV/Vis spectra.
> I use ArgsuLab 2.0.0. for calculation of spectra. As a result I get smth
> like that > (see below). Here are my questions:
> *  How  could  I  compare  Oscillator  Strength  data  with  lg  e values
>    from experiment?
> *  Where  could  I  find  description of length, velocity and Hansen
>    Oscilator Strength?
> * Could anybody point me references on TDA and RPA excited state analysis?
> [...ArgusLab output skipped...]
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:: Summary ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
* No direct comparison between osc. str. and lg e values could be made. This
  is treated as a rough guide--large numbers indicate intense peaks.
* Length, velocity and Hansen oscilator strength are described in John
  McKelvey's messge below.
* Excelent source of information is Q-Chem reference manual
  <http://www.q-chem.com/tech/guides/guide2_0.pdf> which covers CIS, RPA,
  TDDFT and approximate (TDA) TDDFT
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:: Original answers :::::::::::::::::::::::::::::::::::::::::::::::::::::::::
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From:    [email-masked] <[email-masked]>
Date:    Saturday, September 08, 2001, 9:59:43 AM
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Mike ,

Good questions; empirical answers.

After 20+ years of running Zindo on dyes I can only tell you that computed
oscillater strengths [f] of ~1 or larger tend to correlate with log(e)'s of 4-5.
It is necessary to calibrate the f's against log(e)'s or e's themselves.

The length OS is computed simply using the transition density with the already
available dipole moment matrix elements over basis set.  This is very cheap and
easy.

Sum(i,j) TD(i,j)<Xi|x,y,z|Xj>.  TD is computed using the MO's and the CI
coefficients for configurations.  F is proportionsl the this quantity**2*
Excitation energy.

The velocity form is TD*<Xi|grad(x),..|Xj>.  Fis proportional to this squared *
the inverse of the transition energy.  This is more complicated, but still not
expensive.

The Hansen [I think] is proportional to the product of the two above [before
sqaring], and the transition energy cancels out.  For large systems the Hansen
result often lies between the two from which it is derived.  The velocity form is
probably the most reliable, but again, do some plotting against experiment...

Hope this helps..

There is a discussion comparing the length and velocity forms in the QM book by
Eyring, Waletr, and Kimball.  For a complete basis set and a complete CI, i.e. an
exact calculation, the two forms are supposed to give exactly the same result.
But being in INDO space, etc....  Calibrate.

Regards

John McKelvey

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From:    Geoff Hutchison <[email-masked]>
Date:    Wednesday, August 22, 2001, 5:29:28 AM
.............................................................................

>*  How  could  I  compare  Oscillator  Strength  data  with  lg  e values
> from experiment?
Don't. In a very approximate sense, osc. str. is roughly proportional
to the intensity of the peaks. Even for very accurate electronic
structure methods, this is treated as a rough guide--large numbers
indicate intense peaks, etc.

>* Could anybody point me references on TDA and RPA excited state analysis?

TDA is roughly the same as CIS as far as ab-initio methods go.
Basically it would be RPA, but you only treat single excitations
rather than both excitations and de-excitations as you do in RPA.

How detailed a reference are you looking for? Do you want
descriptions of the equations-of-motion and the derivations, or do
you want a reference manual?

.............................................................................
From:    elewars <[email-masked]>
Date:    Friday, August 17, 2001, 8:34:20 PM
.............................................................................
To compare oscillator strength with exp, do calculations on some compounds for
which you have exp epsilon values, and cf. the calc and exp values.

EL

.............................................................................
From:    [email-masked] <[email-masked]>
Date:    Friday, August 17, 2001, 10:45:49 AM
.............................................................................

Mike,

Some partial answers:

The mapping of theory onto experiment in the semi-empirical world, like in
ARGUS [basically Zerner's INDO/S], depends in a significant part on SE
theory giving results "that make sense," i.e., getting large oscillator
strengths about where one finds large extinction coefficients, etc. It is
hard to hope/expect more.  The basis set is limited, the CI usually much
too small, and the methods are calibrated to behave in a certain molecular
size space. [ I know of one code, Roos' MOLCAS-5, that nails things so well,
including vibronic effects, that it is shocking, but it is ab initio.... ]

Oscillator strengths come basically in two "pure" flavors, and also in a
mixed flavor.

Dipole:     f = constant*hv*<GS|R|ES>**2
Velocity   f = constant*1/hv*<GS|Grad|ES>**2

Mixed      f = constant *<GS|R|ES>*<GS|Grad|ES>..

I 've seen fairly good results from TDDFT;  from SE RPA the results can be
_quite_ dependent on parameterization, but can't provide any references.
I hope you will post the results of your query.

Regards,

John McKelvey

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From:    Geoff Hutchison <[email-masked]>
Date:    Wednesday, August 22, 2001, 6:15:12 PM
.............................................................................

> Reference  manual  would  be  OK, but I am not sure if I could find it
> here in Moldova. Of cource if reference manual available from Internet
> it would be great. Also, I  would like to have a reference on original
> articles of this methods or review of this methods.

I'd probably recommend part of the Q-Chem reference manual:
<http://www.q-chem.com/tech/guides/guide2_0.pdf> which covers CIS, RPA,
TDDFT and approximate (TDA) TDDFT. It includes references as needed. See
chapter 6 (p. 135-162).

-Geoff

.............................................................................
From:    Stefan Grimme <[email-masked]>
Date:    Tuesday, March 14, 2000, 1:24:25 PM
.............................................................................
Dear Mike,

a rough estimate is

epsilon(l/mol cm-1)=f*2.5x10^8/delta

with delta the band half-width in cm-1 (e.g. 5000).

Stefan

___________________________________________
       Prof. Dr. Stefan Grimme
    Organisch-Chemisches Institut
     (Abt. Theoretische Chemie)
  Westfaelische Wilhelms-Universitaet
         Corrensstrasse 40
         D-48149 Muenster
     Tel (+49)-251-83 36512/33241
     Fax (+49)-251-83 36515
     Email:[email-masked]
___________________________________________

.............................................................................
From:    Deepak Singh <[email-masked]>
Date:    Tuesday, March 14, 2000, 12:07:21 AM
.............................................................................
Oscillator strengths are traditionally always in the same dimensionless
units, so a value of 1 would indicate a high transition probability and
one as low as yours would argue against a transition.  Unfortunately with
CIS you cannot look at forbidden transitions.

Regards

Deepak

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From:    [email-masked] <[email-masked]>
Date:    Monday, March 13, 2000, 6:47:36 PM
.............................................................................

Mike,

First, in general, the calculated oscillator strengths, are about the only
fingerprint one has to identify in the calculation what might correspond to
experiment...  That's probably what you are doing.  The oscilator strength
calculated corresponds in name to the extinction coefficient multiplied by
the band width at half-height, in 1/cm space, times a constant...i.e. the
area under the absorbtion band.  If all 1/2 heights are assumed to be the
same then there may be a rather reasonable comparicon, as you are concerned
about.

With log(E) ~ 4, it is usually safe to use "f" to identify what corresponds
to experimental bands.  I diod this for ~20 years at Kodak, and it ~always
worked...

John McKelvey

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