From owner-chemistry@ccl.net Wed Sep 21 22:33:01 2005
From: "CCL" <owner-chemistry[]server.ccl.net>
To: CCL
Subject: CCL: Summary) spin contamination and S**2
Message-Id: <-29262-050921162414-14473-fgmcqWsJBX3C35vqwQRwUA[]server.ccl.net>
X-Original-From: "Telkuni Tsuru" <telkuni[]venus.dti.ne.jp>
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Date: Thu, 22 Sep 2005 05:16:56 +0900
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Sent to CCL by: "Telkuni Tsuru" [telkuni[]venus.dti.ne.jp]

--Replace strange characters with the "at" sign to recover email address--.

Hello, CCLers.

A few days ago I've sent the following question:

----- Original Question -----
Sent: Monday, September 19, 2005 5:28 AM
Subject: CCL: spin contamination and S**2
> I like to ask the relationship between the spin contamination and
> S**2 value.
>
> As mentioned before, S**2 shows the spin state, singlet(=0 [+/- 10%]),
> doublet (=0.75 [+/- 10%]), triplet (=2.0 [+/- 10%]), etc. When one
> molecule's multiplicity is singlet and its S**2 is 0.5, can I say that
> the molecule has spin contamination ?
> And the same manner, the multiplicity is doublet and its S**2 is 1.2,
> can I say that the molecule has spin contamination too ?
>
> (What should I call "S**2"?  Is it "S star 2"?)
>
>   All responses, I will appreciate.
>   I will summarize them and send to CCL.


I've received useful replies. To say simply, when S**2 is grater than 
S(S+1), the system has spin contamination.

Thank you very much.


///////////////// Summary //////////////////
--- 1) from dr. Marcel Swart ---
Hello Telkuni,

yes, "S squared" of 0.5 for a singlet, and 1.2 for a doublet are spin
contaminated.
There are some correction schemes available to "project out" the pure state;
we've recently reported some results for iron porphyrins in:
J. Phys. Chem. A 2005, 109, 3411


--- 2) from Pr. Xavier Assfeld ---
Hi,

for S**2 pronounce "S squared" (S multiplied by S). It is the expectation
value of the total spin operator.
If for a wavefunction of a singlet you get a S**2 value greater than 0 then
it is spin contaminated. Spin contamination can only arises with states of
higher multiplicity and of the same parity (odd or even) than the desired
state.
Hope this helps.

       ...Xav

--- 3) from Wang, Dongqi ---
Dear Telkuni,

  according to my understanding, you can compare the S**2 (S Square) value
with the scheme of S(S+1). if they are not equal, generally it's safe for
you to say your calculation has spin contamination. according to this
scheme, S**2 is 0 for singlet and 0.75 for doublet.

  i remember there is topic in Young's webpage. you can find the link from
CCL homepage.

good luck.
wang


//////////////////////////////////


  Sincerely yours,
----------------------------------------------------
        Telkuni Tsuru     telkuni[]venus.dti.ne.jp