# [CP2K:2945] Re: bug in cp_fm_invert ?

Hanning Chen chenh... at gmail.com
Fri Nov 26 04:05:31 UTC 2010

```Hi, Flo,

Thank you very much for your clarification. I was previously confused by
the definition of overlap matrix, SMO. Now, I agree with you that the
permutation operator is somehow problematic, and look forward to checking

Hanning

On Thu, Nov 25, 2010 at 5:07 AM, flo <fsch... at pci.uzh.ch> wrote:

> Hi Hanning,
>
> thanks for looking into it. The index problem is solved in a bit a
> hidden way. The definition of SMO in cp2k is
> C_2^T S C_1 = SMO =S_21
> note here as S, the overlap is symmetric it is valid
> S_21^T=(C_2^T S C_1)^T=C_1^T S C_2=S_12
> furthermore the definition of the matrices
> rest_MO(1)=C_2^T V C_1=V_21   and  rest_MO(2)=C_1^T V C_2=V_12
> as b is computed as
> rest_MO(2) _kj * (S_21)^-1_kj
> this is equivalent to
> (V_12)_kj*(S_21)^-1_kj= (V_12)_kj * [(S_21)^-1]^T_jk = (V_12)_kj *
> (S_12)^-1_jk
>
> Took me as well a little while to understand this again. But yet I
> could not see (remember), why tttt (the kind of permutation operator)
> is in there. I had the formula out of the Loewdin paper
> P.-O. Löwdin, Phys. Rev. 97, 1474 (1955).
> The formulas there are not as straightforward as yours and it could
> be, that I derived a wrong formula for the determinant of minors in
> formula 51 in this paper. Trying to derive it again, I am almost sure
> that this permutation operator is wrong. I will change this in the
> code and submit the changes as soon as possible.
>
> Thank you very for having a look into this,
>
> Flo
>
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