Subject: CCL: Summary TD-DFT

From: "Remenyi, Rainer" <[email-masked]>
Date: Thu, 28 Mar 2002 14:39:34 +0100

Hello, 

last week I posted the following question:

Dear all, 

I have got a question about TD-DFT output in G98. What do the numbers
below ?Spin exactly mean and how can one extract an assignment for the
transitions from a TD-DFT calculation in G98. 

Output example from TD-DFT: 

CIS wavefunction symmetry could not be determined.
 Excited State   5:   ?Spin  -?Sym    2.2048 eV  562.34 nm  f=0.0225
     65B -> 75B        0.13525
     68B -> 75B        0.22273
     69B -> 75B       -0.51298
     70B -> 75B        0.17038
     71B -> 75B        0.53289
     72B -> 75B       -0.41843
     73B -> 75B       -0.23022
     74B -> 75B        0.23340     

Here is the summary of the answers, and thanks to the poeple who replied: 

Hello Rainer,

?Spin and ?sym should be the spin and symmetry of the 5th excited state (in
your example). The fact that there are "?" mean that G98 couldn't determine
both ot them. The spin is not difficult to determine from your calculation.
The
reason why you have ?sym, I guess, is because G98 was not able to determine
the
symmetry of all the orbitals: you should have somewhere in your output file
a
list of orbitals with their symmetry. Some of them should be of the form ?A
or
?B...

Now to determine the symmetry of your state you need the symmetries of the
65B
and 75B orbitals. The symmetry of the excited state is simple the inner
product

|65> X |75>. Check the table of multiplication of the symmetry your are
working
with...

Sometimes its much more difficult to determine the symmetry of the excited
state: if you have a transition between degenerated orbitals for example...
But
obviously its not your case.

the numbers (e.g. 0.13525) is just the coefficient of the corresponding
slater
determinant into the total wave function of the excited state. Basically,
it's
roughly equivalent to a CI decomposition.

Hope this help,

Pascal
Dr. Pascal Boulet
Queen Mary, University of London
Centre for Computational Science
Department of Chemistry
Mile End Road
London, E1 4NS
UK
Phone: (+44) (0)20 7882 7759
fax:   (+44) (0)20 7882 7794

Hi Rainer,

Sorry about the late reply but your e-mail bounced.
Dear Rainer:

Output for a TD-DFT calculation for a closed shell species generally 
contains spin multiplicity and state symmetries, e.g. -

 Excited State   1:   Singlet-A2     3.7169 eV  333.57 nm  f=0.0000
      20 -> 21         0.66862
      ..

But for a calculation on an open shell species, G98 uses the 
unrestricted-DFT procedure ("different [Kohn-Sham] MOs for alpha and 
beta spin") which means that the computed states are more or less 
spin-contaminated. In this case, G98 does not print a spin 
multiplicity, e.g. -   

 Excited State   1:   ?Spin  -A2     1.0282 eV 1205.70 nm  f=0.0000
     24B -> 25B        1.03710
     24B -> 27B       -0.16586
     ..

Hence,  ?Spin  indicates than the spin multiplicity is not well 
defined and is not available. The numbers below ?Spin are the CI 
coefficients of the excited configurations listed to the left: 24B -> 
25B, and so on (meaning, e.g.: the configuration derived by promoting 
an electron from beta spin-MO no. 24 to beta spin-MO no. 25). A large 
coefficient means that the configuration in question has a large 
weight in the state wave function. You may notice that in the example 
I give above, one of the coefficients exceeds unity, indicating that 
for TD calculations on open shell systems G98 does not normalize the 
states in the usual sense. - In my opinion, it would have been VERY 
HELPFUL if Gaussian would compute and print spin data for excited 
states, just as for the ground state where the expectation value of 
S**2 is given.

In the example you quote in your query, not even the wave function  
symmetry is printed, evidently because of a failure; if you look up 
the MO symmetries given in the printout, you will probably find that 
Gaussian failed to deduce symmetry labels for some of the MOs.

I am not quite sure of what you mean when you say "how can one 
extract an assignment for the transitions from a TD-DFT calculation 
in G98". To me, an 'assignment' means an assignment of experimentally 
observed transitions to theoretically predicted ones, and such an 
assignment can of course not be extracted from the G98 output. Do you 
mean: How can the calculated transitions be explained in terms of 
orbital contributions? If this is your question, you must look up the 
orbitals involved in the leading configurations listed in the output 
(the keyword POP=REGULAR gives you the five highest occupied and the 
five lowest unoccupied MOs; consult the manual).

Good Luck!

Yours, Jens >--<

P.S. Please say hello to dear old Heidelberg! I spent the years 
1979-1984 in Heidelberg as a member of Professor Gleiter's group.

NB! Please note new mail address: <[email-masked]>
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Department of Chemistry     Fax:            +45 4674 3011
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There was a discussion of ?Spin in the TD-DFT output about 5 months
ago on CCL - maybe you'll find your answer in the summary of that
discussion.
In short, I believe that the conclusion is that ?Spin is related to the
weight
of a particular excitation in a given state.

In order to assign the excitations I always look at the output orbitals
(e.g., using Molden) and assign the state according to the excitation
with the highest nominal ?Spin value. If you get any better suggestions
please
let me know because manually visualizing the orbitals is quite time
consuming.

Cheers,

Theis Solling

Dr. Theis I. Solling
California Institute of Technology
M/C 127-72
1200 E. California Blvd.
Pasadena, California 91125
Ph. (626)-395-6741

Dr. Remenyi,

This happens most commonly when the SCF orbitals cannot be labeled
properly.  Look back after the end of the SCF and see if any of
the orbitals, 65,68-74 and then 75 are labeled.  Even if not all of
them are labeled the first group must be the same any one will do.
Then if the reference is a singlet then the product will be the
symmetry.  Otherwise you need to look at the full orbital set.

Since this is a beta-beta excitation the spin state should be
the same as the ground state.

Rainer Remenyi
Anorganisch-Chemisches Institut
Im Neuenheimer Feld 270
69120 Heidelberg
Germany

phone           ++ 49 6221 54 8653
fax                ++ 49 6221 54 6617

e-mail: [email-masked]