Dear
Micaela and others!
The
f-sum rule may be stated as follows:
The
sum of all oscillator strengths, f(0,n), from a state |0> to all other states
|n> obeys the sum rule SUMMA(n) f(0,n) = N
--
> f(0,n) = N
--
n#0
where
N is the total number of electrons in the system (also called the
Thomas-Reiche-Kuhn sum rule).
This
formulation is taken from Poul Joergensen & Jens Oddershede: "Problems
in quantum chemistry", Addison-Wesley, Massachusetts, USA, 1983. Hence, the
f-value for an electronic transition is not limited to magnitudes below or
equal to unity, it may increase unity. As a matter of fact, it frequently does.
For example, the experimental oscillator strength for the first transition in
all-trans beta-carotene
is equal to f = 2.7. This is the value obtained by integration over the
absorption band in hexane with maximum at 22200 cm-1 and eps = 139400
(http://omlc.ogi.edu/spectra/PhotochemCAD), yielding f = 4.32E-9 *
INT[eps(nu)dnu] = 2.73. For the extremely strong
band with maximum at 44800 cm-1 and eps = 1.1E6, integration yields f >
7.
Yours, Jens >--<
------------------------------------------------------
JENS
SPANGET-LARSEN
Office: +45 4674 2710
Dept. of Science (18.1)
Fax: +45 4674
3011
Roskilde
University
Mobile: +45 2320 6246
P.O.Box
260
E-Mail:
spanget---ruc.dk
DK-4000 Roskilde, Denmark
http://www.ruc.dk/~spanget
------------------------------------------------------
From:
owner-chemistry+spanget==ruc.dk---ccl.net
[mailto:owner-chemistry+spanget==ruc.dk---ccl.net]
On Behalf Of Hao-Bo Guo guohaobo()gmail.com
Sent: 11. december 2013 19:03
To: Jens Spanget-Larsen
Subject: CCL: SV: TDDFT (CAM-B3LYP) oscillator strength too
high
"the sum of the oscillator strengths from one
sub-state to all other states is equal to the total number of electrons
N"
My understanding is the sum of
oscillator strengths equals to the number of electron(s) excited, which is 1,
for single electron excitation calculations w/ TDDFT.
Hao-Bo
On Wed, Dec 11, 2013 at 10:03 AM, Jens Spanget-Larsen
spanget]=[ruc.dk
<owner-chemistry!=cl.net> wrote:
Dear Micaela,
According to "IUPAC Glossary of terms used in photochemistry, 3rd Edition,
2005", the oscillator strength f is defined as:
f = (8*pi^2*m*c*nu)/(3*e^2*h) G * M^2
where m is the mass of the electron, c is the velocity of light, nu is the
wavenumber, e is the elementary charge, and h is the Planck constant. G is the
degeneracy of the final state, and M is the transition moment vector. Formally,
there is no upper limit
to nu and the length of M, and there is thus no reason why the magnitude of f
should not increase unity (however, according to the Thomas-Reiche-Kuhn sum
rule, the sum of the oscillator strengths from one sub-state to all other states
is equal to the total
number of electrons N).
Yors, Jens >--<
P.S. Experimentally, f is determined by integration over the entire absorption
band-width of the molar decadic absorption coefficient eps(nu), f =
INT[eps(nu)dnu].
------------------------------------------------------
JENS SPANGET-LARSEN Office:
+45 4674 2710
Dept. of Science (18.1) Fax:
+45 4674 3011
Roskilde University Mobile:
+45 2320 6246
P.O.Box 260
E-Mail: spanget#,#ruc.dk<mailto:spanget#,#ruc.dk>
DK-4000 Roskilde, Denmark
http://www.ruc.dk/~spanget
------------------------------------------------------
> From: owner-chemistry+spanget==ruc.dk#,#ccl.net [mailto:owner-chemistry+spanget==ruc.dk#,#ccl.net] On
Behalf Of Micaela Matta micaela.matta2+/-unibo.it
Sent: 11. december 2013 09:29
To: Jens Spanget-Larsen
Subject: CCL: SV: TDDFT (CAM-B3LYP) oscillator strength too high
Dear Jens,
I thught it to be unreasonable because oscillator strength must be less or equal
than one, and this had never happened to me before.
Thank you very much to all of you!
Micaela
2013/12/11 Somananda Sanyal somananda.sanyal]|[gmail.com<http://gmail.com>
<owner-chemistry..ccl.net<mailto:owner-chemistry..ccl.net>>
Dear Micaela,
The oscillator strength you are getting using CAM-B3LYp, or for
that matter many other functionals that I too have checked with, such f>1
results come.
As far as I know, it is because of the fact that the oscillator strengths are
not normalized, so that is why they come as greater than 1 value.
Thanks and regards,
Somanand Sanyal
*****************
Regards,
Somananda Sanyal.
Theoretical Sciences Unit,
JNCASR, Bangalore.
On Wed, Dec 11, 2013 at 4:23 AM, Jens Spanget-Larsen spanget,+,ruc.dk<http://ruc.dk>
<owner-chemistry],[ccl.net<mailto:owner-chemistry],[ccl.net>>
wrote:
Sent to CCL by: Jens Spanget-Larsen [spanget[]ruc.dk<http://ruc.dk>]
Dear Micaela,
why do you think that an oscillator strength f = 2.7 is unphysical? This is
certainly a large value, but it is not necessarily unreasonable. With
TD-PBE1PBE/6-31+G*, we obtained f = 2.2 for the first optically
allowed electronic transition in the D2d conformation
of diphenyldiacetylene, see Thulstrup et al., PCCP 13, 16168-16174 (2011).
Jens >--<
------------------------------------------------------
JENS SPANGET-LARSEN Office:
+45 4674 2710<tel:%2B45%204674%202710>
Dept. of Science (18.1) Fax:
+45 4674 3011<tel:%2B45%204674%203011>
Roskilde University Mobile:
+45 2320 6246<tel:%2B45%202320%206246>
P.O.Box 260
E-Mail: spanget{=}ruc.dk<http://ruc.dk>
DK-4000 Roskilde, Denmark
http://www.ruc.dk/~spanget
------------------------------------------------------
________________________________________
Fra: owner-chemistry+spanget==ruc.dk<http://ruc.dk>{=}ccl.net<http://ccl.net> [owner-chemistry+spanget==ruc.dk<http://ruc.dk>{=}ccl.net<http://ccl.net>]
på vegne af micaela matta micaela.matta2 ..
unibo.it<http://unibo.it> [owner-chemistry{=}ccl.net<http://ccl.net>]
Sendt: 10. december 2013 17:05
Til: Jens Spanget-Larsen
Emne: CCL: TDDFT (CAM-B3LYP) oscillator strength too high
Sent to CCL by: "micaela matta" [micaela.matta2 ..
unibo.it<http://unibo.it>]
Dear CCL suscribers,
I am running TD-DFT calculations on an organic molecule at level CAM-BLYP/6-
311G*. The first excited state has the correct energy compared to
experimental
results, but I obtained an unphysical f=2.7206!! How can I make sense of
this
result?
Thanks
Micaelahttp-:-//www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/chemistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txt<http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp:/www.ccl.net/chemistry/sub_unsub.shtmlhttp:/www.ccl.net/spammers.txt>
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or usehttp-:-//www.ccl.net/chemistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txt--_000_A94E15A372E6194CA8719D62642F674463C57C16MBX3adrucdk_
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<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">Dear
Micaela,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">According to “IUPAC Glossary of
terms used in photochemistry, 3rd Edition, 2005”, the oscillator
strength f is defined as:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">f = (8*pi^2*m*c*nu)/(3*e^2*h) G * M^2
<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">where m is the mass of the electron, c is
the velocity of light, nu is the wavenumber, e is the elementary charge, and h
is the Planck constant.
G is the
degeneracy of the final state, and M is the transition moment vector.
Formally, there is no upper limit to nu and the length of M, and there is thus
no reason why the magnitude of f should not increase unity (however, according
to the Thomas-Reiche-Kuhn sum
rule, the sum of the oscillator strengths from one sub-state to all other
states is equal to the total number of electrons
N).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">Yors, Jens
>--<<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">P.S. Experimentally, f is determined by
integration over the entire absorption band-width of the molar decadic
absorption coefficient eps(nu),
f = INT[eps(nu)dnu].<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">
</span><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"> JENS
SPANGET-LARSEN
Office: +45 4674
2710<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"> Dept. of Science
(18.1)
Fax:
+45 4674 3011<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"> Roskilde
University
Mobile: +45 2320
6246<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D"> P.O.Box
260
E-Mail:
<a href="" href="mailto:spanget">spanget#,#ruc.dk">spanget#,#ruc.dk</a><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">
</span><span style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">DK-4000 Roskilde,
Denmark
<a href="" href="http://www.ruc.dk/~spanget"
target="_blank">http://www.ruc.dk/~spanget">http://www.ruc.dk/~spanget</a><o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">
</span><span lang="EN-GB"
style="font-size:10.0pt;font-family:"Courier
New";color:#1F497D">------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US"
style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span
lang="EN-US"
style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">
owner-chemistry+spanget==ruc.dk#,#ccl.net
[mailto:owner-chemistry+spanget==ruc.dk#,#ccl.net]
<b>On Behalf Of </b>Micaela Matta micaela.matta2+/-http://unibo.it" target="_blank">unibo.it<br>
<b>Sent:</b> 11. december 2013 09:29<br>
<b>To:</b> Jens Spanget-Larsen<br>
<b>Subject:</b> CCL: SV: TDDFT (CAM-B3LYP) oscillator strength too
high<o:p></o:p></span></p>
<p
class="MsoNormal"><o:p> </o:p></p>
<div>
<div>
<div>
<div>
<p class="MsoNormal">Dear
Jens,<o:p></o:p></p>
</div>
<p class="MsoNormal">I thught it to be unreasonable because
oscillator strength must be less or equal than one, and this had never happened
to me before.
<o:p></o:p></p>
</div>
<p class="MsoNormal">Thank you very much to all of
you!<o:p></o:p></p>
</div>
<p
class="MsoNormal">Micaela<o:p></o:p></p>
<div>
<p class="MsoNormal"
style="margin-bottom:12.0pt"><o:p> </o:p></p>
<div>
<p class="MsoNormal">2013/12/11 Somananda Sanyal
somananda.sanyal]|[<a href="" href="http://gmail.com"
target="_blank">http://gmail.com">gmail.com</a> <<a
href=""
href="mailto:owner-chemistry..ccl.net">owner-chemistry..ccl.net"
target="_blank">owner-chemistry..ccl.net</a>><o:p></o:p></p>
<div>
<p
class="MsoNormal">Dear Micaela,<o:p></o:p></p>
<div>
<p class="MsoNormal"> The oscillator
strength you are getting using CAM-B3LYp, or for that matter many other
functionals that I too have checked with, such f>1 results
come.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">As far as I know, it is because of the fact
that the oscillator strengths are not normalized, so that is why they come as
greater than 1 value.<o:p></o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Thanks and
regards,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Somanand
Sanyal<o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal"><br clear="all">
<o:p></o:p></p>
<div>
<div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p
class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="color:silver">*****************</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Tahoma","sans-serif";color:#999999">Regards,</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Tahoma","sans-serif";color:#999999">Somananda
Sanyal.<br>
Theoretical Sciences Unit,<br>
JNCASR, Bangalore.</span><o:p></o:p></p>
</div>
</div>
</div>
<p class="MsoNormal"
style="margin-bottom:12.0pt"><o:p> </o:p></p>
<div>
<div>
<div>
<p class="MsoNormal">On Wed, Dec 11, 2013 at 4:23 AM, Jens
Spanget-Larsen spanget,+,<a href="" href="http://ruc.dk"
target="_blank">http://ruc.dk" target="_blank">ruc.dk</a>
<<a href="" href="mailto:owner-chemistry">owner-chemistry],[ccl.net"
target="_blank">owner-chemistry],[ccl.net</a>>
wrote:<o:p></o:p></p>
</div>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC
1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<p class="MsoNormal"><br>
Sent to CCL by: Jens Spanget-Larsen [spanget[]<a href="" href="http://ruc.dk"
target="_blank">http://ruc.dk" target="_blank">ruc.dk</a>]<br>
<br>
Dear Micaela,<br>
why do you think that an oscillator strength f = 2.7 is unphysical? This is
certainly a large value, but it is not necessarily unreasonable. With
TD-PBE1PBE/6-31+G*, we obtained f = 2.2 for the first
optically allowed electronic transition in the
D2d conformation
of diphenyldiacetylene, see Thulstrup et al., PCCP 13, 16168-16174
(2011).<br>
Jens >--<<br>
<br>
------------------------------------------------------<br>
JENS SPANGET-LARSEN
Office: <a href=""
href="tel:%2B45%204674%202710">tel:%2B45%204674%202710"
target="_blank">+45 4674 2710</a><br>
Dept. of Science (18.1) Fax:
<a href=""
href="tel:%2B45%204674%203011">tel:%2B45%204674%203011"
target="_blank">
+45 4674 3011</a><br>
Roskilde University
Mobile: <a href=""
href="tel:%2B45%202320%206246">tel:%2B45%202320%206246"
target="_blank">+45 2320 6246</a><br>
P.O.Box 260
E-Mail: spanget{=}<a
href="" href="http://ruc.dk" target="_blank">http://ruc.dk"
target="_blank">ruc.dk</a><br>
DK-4000 Roskilde, Denmark <a href=""
href="http://www.ruc.dk/~spanget"
target="_blank">http://www.ruc.dk/~spanget"
target="_blank">
http://www.ruc.dk/~spanget</a><br>
------------------------------------------------------<br>
<br>
________________________________________<br>
Fra: owner-chemistry+spanget==<a href="" href="http://ruc.dk"
target="_blank">http://ruc.dk" target="_blank">ruc.dk</a>{=}<a
href="" href="http://ccl.net" target="_blank">http://ccl.net"
target="_blank">ccl.net</a>
[owner-chemistry+spanget==<a href="" href="http://ruc.dk"
target="_blank">http://ruc.dk" target="_blank">ruc.dk</a>{=}<a
href="" href="http://ccl.net" target="_blank">http://ccl.net"
target="_blank">ccl.net</a>]
p&#229; vegne af micaela matta micaela.matta2 .. <a href=""
href="http://unibo.it" target="_blank">http://unibo.it"
target="_blank">
unibo.it</a>
[owner-chemistry{=}<a href="" href="http://ccl.net"
target="_blank">http://ccl.net" target="_blank">ccl.net</a>]<br>
Sendt: 10. december 2013 17:05<br>
Til: Jens Spanget-Larsen<br>
Emne: CCL: TDDFT (CAM-B3LYP) oscillator strength too high<br>
<br>
Sent to CCL by: "micaela matta" [micaela.matta2 ..
<a href="" href="http://unibo.it" target="_blank">http://unibo.it"
target="_blank">
unibo.it</a>]<br>
Dear CCL suscribers,<br>
<br>
I am running TD-DFT calculations on an organic molecule at level
CAM-BLYP/6-<br>
311G*. The first excited state has the correct energy compared to
experimental<br>
results, but I obtained an unphysical f=2.7206!! How can I make sense of
this<br>
result?<br>
Thanks<br>
<br>
Micaelahttp://<a href=""
href="http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp:/www.ccl.net/chemistry/sub_unsub.shtmlhttp:/www.ccl.net/spammers.txt"
target="_blank">http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp:/www.ccl.net/chemistry/sub_unsub.shtmlhttp:/www.ccl.net/spammers.txt"
target="_blank">www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/chemistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txt</a><br>
<br>
<br>
-= This is automatically added to each message by the mailing script =-
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--
University of Tennessee Knoxville
Plant Systems Biology Group
Oak Ridge National Laboratory
865-803-4432;
guoh1!=rnl.gov
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