Dear CCL
subscribers,
 I have Three questions about running TDDFT, TDHF,
and CIS with Gaussian 09, Revision C.01, that need your help.
 Thank you so much in advance for your suggestions, advices, and
comments.
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(1)Â TDA for removing Negative/Imaginary excitation
energy :
 In TDDFT, TDHF, CIS calculations,
using Gaussian, some excitation energies are written as negative values,
e.g.,
********************
TD B3LYP;
excitation energy =Â -0.6141 eV :
ÂExcited StateÂÂ
1:ÂÂÂÂÂ Triplet-SGUÂÂÂ -0.6141
eV -2019.02 nm f=-0.0000Â
<S**2>=2.000
ÂÂÂÂÂÂ 4 ->Â
5ÂÂÂÂÂÂÂÂ
0.80601
ÂÂÂÂÂÂ 4 ->
10ÂÂÂÂÂÂÂ
-0.11570
ÂÂÂÂÂÂ 4 <-Â
5ÂÂÂÂÂÂÂÂ 0.39989
********************
Note: the above problem of negative excitation
energy, which could be originated from the instability of wave function, still
persists even I used "Stable=Opt" in Gaussian.
Some papers
actually refer these negative values as "imaginary" numbers or
imaginary excitation energies (e.g., see DOI:Â
10.1063/1.2786997ÂandÂ
10.1021/cr0505627Â).
And the papers also show that the imaginary excitation energies could be
re-calculated to become "real" excitation energies by Tamm-Dancoff
Approximation (TDA).
->> Since
there is No TDA available in the Revision C.01 of Gaussian 09, I just wonder a
bit is it correct that the TDA implemented in the Revision D.01 of Gaussian 09
can be used to perform TDA-DFT (e.g., TDA-B3LYP) calculations that may possibly
solve the above problem of Negative/Imaginary excitation energy ?
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(2)Â Normalization procedure for
"de-excitation" :
In a TDDFT calculation, we found,
e.g.,
********************
TD
B3LYP:
ÂExcited
StateÂÂ 1:Â 3.003-?SymÂÂÂ 0.1776 eV 6981.48
nm f=0.0000 <S**2>=2.004
ÂÂÂÂÂ 5A ->Â
6AÂÂÂÂÂÂÂ
1.03714
ÂÂÂÂÂ 5A <-Â
6AÂÂÂÂÂÂÂ
0.28145
********************
The above coefficient of "5A
-> 6A" is already larger than unity (1.03714 > 1.0). And
we have another coefficient for the de-excitation "5A <-Â 6A",
0.28145 .
Interestingly, (1.03714)^2 - (0.28145)^2 = 0.996.
->> So, I
just wonder a bit is it true that if there is a coefficient associated with
de-excitation, then the square of this coefficient should be subtracted (instead
of being added) during a normalization process ?Â
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(3)Â Physical meaning for "de-excitation"
:
Just a quick follow-up question about
de-excitation.
->> I just wonder
a bit whether or not there is any physical meaning for de-excitation, e.g., the
above "5A <-Â 6A" ?
->> Or, is it just a pure mathematical construct as what this paper,
DOI:Â
10.1021/jp308662xÂ, suggested ?
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 Just feel free to give me any
suggestions, advices, and comments.
 Thank you
very much in advance again.