CCL:G: Broken Symmetry Singlet Excited State

 Sent to CCL by: "Cristian V. Diaconu" [cvdiaconu{=}rice.edu]
The value of S^2 you have to use is the one *before* projection (in the example you gave me 0.8631) After projection S^2 should be 0 for a singlet. In your example S^2 after "Annihilation of the first spin contaminant", in this case triplet, is 0.4136, and comes from higher spin components. This, unfortunately, means the formula you are using does not hold.
In the case of broken symmetry calculation for H2, the broken symmetry determinant is a mixture of pure singlet determinant and pure triplet determinant with S_z=0. The mixing ratio is related to your fSC. For H2 at infinite separation, the broken symmetry determinant is an equal mixture of singlet and triplet (S_z=0). This limiting case is the only case that DFT handles well. If your <S^2> is not close to 1, then the projection using this approach is not very good. See the following example for H2 at d(H-H) = 9.5 a0 (almost dissociated), and d(H-H) = 4.2 a0 (right around where the broken symmetry solution becomes more stable). 
 Chris
 Here's an example for H2 UB3LYP/6-311++G** guess=mix
 d(H-H) = 9.5 a0:
  SCF Done:  E(UB+HF-LYP) =  -1.00452667499     A.U. after    5 cycles
              Convg  =    0.5289D-08             -V/T =  2.0119
              S**2   =   1.0000
  KE= 9.927556920227D-01 PE=-2.202132474486D+00 EE= 9.958694958153D-02
  Annihilation of the first spin contaminant:
  S**2 before annihilation     1.0000,   after     0.0000
 d(H-H) = 4.2 a0:
  SCF Done:  E(UB+HF-LYP) =  -1.01321186020     A.U. after    8 cycles
              Convg  =    0.3446D-08             -V/T =  2.0689
              S**2   =   0.8435
  KE= 9.479387091822D-01 PE=-2.439555548275D+00 EE= 2.403097407996D-01
  Annihilation of the first spin contaminant:
  S**2 before annihilation     0.8435,   after     0.0000
 Sue Lam chsue2004#,#yahoo.com wrote:
 
 Hello Chris,
Thank you very much for your reply. I am studying a reaction, in which the transition state contain biradical character. I have tired to extract the energy of the pure singlet from the broken symmetry state by using the spin-correction procedure which was proposed by Yamaguchi et al (/Chem. Phys. Lett. /*1994*, /231/, 25–33)//
E(singlet) = E(broken symmetry from UDFT) + fSC[E(broken symmetry from UDFT – E(triplet from UDFT)) 
 
 Where fSC = 1<S^2> / [3<S^2> - 1<S^2>]
 
 S^2: expectation value of the total spin
The S^2 before and after the annihilation are listed in the Gaussian output. In my case, 
 
 Annihilation of the first spin contaminant:
 S^2 before annihilation     0.8631,   after     0.4136
I am not sure that whether I should use the S^2 before or after the annihilation for the projection method. 
 
 Best regards,
 Sue
--- On *Wed, 2/4/09, Cristian V. Diaconu cvdiaconu!A!rice.edu /<owner-chemistry*_*ccl.net>/* wrote: 
     From: Cristian V. Diaconu cvdiaconu!A!rice.edu
     <owner-chemistry*_*ccl.net>
     Subject: CCL:G: Broken Symmetry Singlet Excited State
     To: "L, Sue " <chsue2004*_*yahoo.com>
     Date: Wednesday, February 4, 2009, 2:15 PM
     Sent to CCL by: "Cristian V. Diaconu" [cvdiaconu~!~rice.edu]
     Hello Sue,
     The total energy reported by Gaussian is not for 'annihilated' wave
     function, but for the single determinant that it uses in the Kohn-Sham
 scheme
     (for DFT there isn't really any wave function).  There are ways to extract
     the energy of the pure singlet from the broken symmetry state, but for DFT
 they
     only work in certain cases.  Please look at discussions in:
     J. Chem. Phys. 121, 10026 (2004)
     J. Chem. Phys. 74, 5737 (1981)
     Coord. Chem. Rev. 238–239, 187 (2003)
     C. J. Cramer, in Essentials of Computational Chemistry. Theories and Models.
     (Wiley, Chichester, 2002), Chap. 14.4, pp. 456 – 459.
     For example, for a molecule with two unpaired electrons on two sites which
     interact weakly (e.g., H2 molecule stretched, with a large bond length, say
 10
     Angstroms), if <S^2> ~ 1,
     E(singlet) = 2 E(broken sym) - E(triplet)
     I hope this helps.  If you have further questions, please include a little
     detail on the system you are looking at.
     Best regards,
     Chris
     Sue L chsue2004(~)yahoo.com wrote:
     > Sent to CCL by: "Sue  L" [chsue2004..yahoo.com]
> Hi, > I am running a DFT open-shell singlet calculation using Gaussian 03 to 
     obtain a broken symmetry singlet excited state. Does anyone know whether the
     electronic energy calculated at the end based on the annihilated wave
 function
or not? > Thank you very much! > > Best regards, > Sue> > > 
     -- Cristian V. Diaconu
     Postdoctoral Research Associate
     Department of Chemistry - MS60
     Rice University
     PO Box 1892
     Houston, TX 77251-1892
     Phone: 713-348-3734
     Email: cvdiaconu-x-rice.eduhttp://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp-:-//www.ccl.net/chemistry/sub_unsub.shtmlhttp-:-//www.ccl.net/spammers.txt