CSF expansions 2

Posted by Willem Van den Heuvel on January 20, 2009 at 14:59:22:

In a previous message (/molcas/wwwboard/messages/670.html), the following CSF expansions were given:

uud = 1/sqrt(6) * ( 2|aab| - |aba| - |baa| )
udu = 1/sqrt(2) * ( |aba| - |baa| ),

where a and b represent alpha and beta spin. Both have spin S=1/2 and Ms=1/2. I have used the algorithm given by Shavitt in a Lecture Note on GUGA [1] and find, for Ms=1/2:

uud = 1/sqrt(6) * ( -2|aab| + |aba| + |baa| )
udu = 1/sqrt(2) * ( |aba| - |baa| ),

so with opposite sign for uud but equal sign for udu.

Which one is correct?

ref: [1] I. Shavitt, in 'The Unitary Group', ed. J. Hinze, Lecture Notes in Chemistry 22, Springer-Verlag, Berlin, 1981, p.55.

Best regards,

Willem Van den Heuvel

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Comments:
: In a previous message (/molcas/wwwboard/messages/670.html), the following CSF expansions were given: : uud = 1/sqrt(6) * ( 2|aab| - |aba| - |baa| ) : udu = 1/sqrt(2) * ( |aba| - |baa| ), : where a and b represent alpha and beta spin. Both have spin S=1/2 and Ms=1/2. I have used the algorithm given by Shavitt in a Lecture Note on GUGA [1] and find, for Ms=1/2: : uud = 1/sqrt(6) * ( -2|aab| + |aba| + |baa| ) : udu = 1/sqrt(2) * ( |aba| - |baa| ), : so with opposite sign for uud but equal sign for udu. : Which one is correct? : ref: [1] I. Shavitt, in 'The Unitary Group', ed. J. Hinze, Lecture Notes in Chemistry 22, Springer-Verlag, Berlin, 1981, p.55. : : Best regards, : Willem Van den Heuvel

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