Posted by Per Åke Malmqvist on February 22, 2006 at 11:33:00:
In Reply to: Question on CSF expansions posted by Mariusz Radon on February 20, 2006 at 22:22:18:
: Can anyone tell me please if these CSFs expansions are correct. Particularly I'd like to be sure that phases are correct!
: uud = 1/sqrt(6) * ( 2|uud| - |udu| - |duu| )
: udu = 1/sqrt(2) * ( |udu| - |duu| )
OK, phases are correct. Perhaps a clearer notation would be
uud = 1/sqrt(6) * ( 2|aab| - |aba| - |baa| )
udu = 1/sqrt(2) * ( |aba| - |baa| )
using u and d for up- and down-coupling, but a and b for
alpha and beta spin, resp. The notation and phase rules are
those of the GUGA (Graphical Unitary Group Approach) of Shavitt,
except that the 'step numbers' (aka 'case numbers') '0,1,2,3' are
shown as the more easily understanding '0,u,d,2', showing the
occupation number, or u,d for single occupation.
Best regards,
Per Åke