[Wien] What is U(R) in potential parameters (case.output1, SRC_lapw1/atpar.f P(J, JATOM))

[Laurence Marks]

I've seen a Cholesky error sometimes before, but always managed to get
around it by tweaking the linearization energies. I getting the
problem fairly consistently with the O1s states and I suspect that,
physically, it has something to do with the presence of relatively
large and long range potential gradients. The two O 1s energies are
very different,

          E( 0)=   -0.2545
             APW+lo
          E( 0)=   -1.2224
             LOCAL ORBITAL

It's the APW+lo energy which is the culprit.

The main APW parameters in one case (just the O 1s) are
          POTENTIAL PARAMETERS
           L     U(R)          U'(R)         DU/DE        DU'/DE      NORM-U'
           0  0.124693E-05  0.880980E+00  0.362319E+00  0.298987E+00
0.107629E+00     1 2 2

and the corresponding coefficients are
          LOCAL ORBITAL POTENTIAL PARAMETERS
           L     U(R)          U'(R)     NORM U1U2        NORM UE1U2
           0 -0.335520E+00  0.484669E+00  0.956748E+00 -0.953884E-01      0 1 0
LO COEFFICIENT: l,A,B,C   0            0.10000D+01      -0.34415D-05
    0.00000D+00
LO COEFFICIENT: l,A,B,C   0            0.10000D+01       0.00000D+00
    0.37164D-05

This will give a Cholesky error and/or nutty forces (1e5 or higher!!!)

If I change the level to lapw, things get sane (at least appear to,
have not rigorously checked, only done x lapw1 -nmat_only):
LO COEFFICIENT: l,A,B,C   0           -0.92227D+01       0.98800D+01
    0.10669D+02
LO COEFFICIENT: l,A,B,C   1            0.94072D+00       0.11296D+01
    0.00000D+00

Alternatively, if I shift the linearization energy down by -0.05 I get:
          POTENTIAL PARAMETERS
           L     U(R)          U'(R)         DU/DE        DU'/DE      NORM-U'
           0 -0.181123E-01  0.865678E+00  0.362173E+00  0.313018E+00
0.106558E+00      1 1 1

LO COEFFICIENT: l,A,B,C   0            0.99987D+00       0.50003D-01
    0.00000D+00
LO COEFFICIENT: l,A,B,C   0            0.10546D+01       0.00000D+00
   -0.56931D-01



On 1/17/07, Peter Blaha <pblaha at theochem.tuwien.ac.at> wrote:
> If you consider, how the LAPW-matrix elements are formed (see eg.
> J.Phys.F: Melal.Phys. 5, 2041 (1975)), you see that basically only the
> value of the radial wavefunctions at R=RMT enter. Thus the quantities
>
>      U(R)          U'(R)         DU/DE        DU'/DE      NORM-U'
>
> are U: radial wave function (actually it is R(r).r) at RMT
>      U':  dU/dr
>      DU/DE:  = u-dot = energy derivative
>      DU`/DE:     energy derivative of U'
>
> With these numbers the Hamilton and overlap matrix elements are formed.
>
> It was well known in the original APW method, where the logarithmic
> derivative entered the matrix elements and (u/u') could become infinity,
> that sometimes the secural equation became singular.
> LAPW has removed this problem (there is no division anymore), but I
> don't know if it might happen that when u (or one of the other
> parameter) is (nearly) zero, two rows of matrixelements become very
> similar leading to Cholesky-problems.
>
> Did you find any difference between APW+lo+LO and LAPW+LO (0 or 1 in
> case.in1) ?
>
> You think you always get problems connected with LOs ?
> It that always for MgO systems ?
>
> Are the two energies E1 and E2 for the energy parameters different enough ?
>
> PS: I had funny errors during Christmas: On two of our new Core2
> machines I got a Cholesky error when both processors where used by two
> jobs. However, when I repeat the lapw1 run the error did NOT show up
> anymore (No change, simply rerunning !!!). I did not find that when
> using only one processor and it occurred just a few times.
>
> Regards
>
> Laurence Marks schrieb:
> > Does anyone know what exactly U(R) in the potential parameters printed
> > in case.output1 by SRC_lapw1/atpar.f is, stored in the array
> > P(J,JATOM)? I've traced that when this gets small both B and C in the
> > APW+lo expansion get small, you can get a Cholesky factorization error
> > and also the forces can get inaccurate. Unfortunately my German is non
> > existent.
> >
>
> --
>
>                                        P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
> Email: blaha at theochem.tuwien.ac.at    WWW:
> http://info.tuwien.ac.at/theochem/
> --------------------------------------------------------------------------
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-- 
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
http://www.numis.northwestern.edu