Subject: diradical singlets

From: "Dr. Heinz Schiffer" <[email-masked]>
Date: Fri, 15 Aug 1997 17:07:22 +0200

Hello all,

does anyone out there has experience with the calculation of singlet
states of diradicals within density functional theories ? If so, it
would be very nice to get some information of it.

To be more specific :

I have only an unrestricted (or spin-polarized) DFT code available to
handle open-shell systems. Within an unrestricted procedure you can 
only calculate electronic states, which can be described by a single
Slater determinant.

The triplet state of a diradical is therefore no problem, because the
triplet state can, e.g., be described by a single Slater determinant
(a_a,b_a). a_a is orbital a with alpha spin, b_a is orbital b with alpha
spin. The energy is h_aa + h_bb + J_ab - K_ab. h_aa and h_bb are the
expectation values of the one-electron operators with orbitals a and b,
respectively. J_ab and K_ab are the usual Coulomb and exchange energies.

The singlet state of a diradical represents a problem in so far, as it
is described by a linear combination of two Slater determinants :
1/sqrt(2) * [ (a_a,b_b) - (a_b,b_a) ]. a_a and b_a as above, a_b and
b_b are orbitals a and b with beta spin. The energy is h_aa + h_bb
+ J_ab + K_ab. Within an unrestricted (or spin-polarized) procedure,
you cannot use two determinants. Within the Roothaan open-shell
formalism of the Hartree-Fock method and the corresponding formalism
of the Kohn-Sham method, you can ! But as I mentioned above, I do not
have acces to such a program.

Now, there is a trick : The energy of the single Slater determinant
(a_a,b_b) is : h_aa + h_bb + J_ab. If you take that expression two times
and substract the energy of the triplet state from it, you end up with
the same energy expression as for the singlet state ! So, I tried to
do an unrestricted DFT calculation for the mixed state, described by
the single Slater determinant (a_a,b_b). And I got tremendous 
convergence problems : after several thousand iterations (with and
without DIIS, level shifts, damping, etc.) I always end up with a
wild oszillatory behaviour in the energy. Therefor my question, if
anyone has experience with such calculations.

Ciao,
Heinz
-- 
Dr. Heinz Schiffer              Phone   ++49-69-305-2330                        
Hoechst CR&T                    Fax     ++49-69-305-81162                       
Scientific Computing, G864      Email   [email-masked]           
65926 Frankfurt am Main                 [email-masked]