[Wien] density matrix is not positive

Wed Jan 8 16:10:03 CET 2020

Yet more pedagogy...

Over the last few years I have been trying to add to the mixer algorithms
so it can sense when their might be piranha around. One of these is large
fluctuations of the potential; if these occur it becomes more cautious.
Another currently being tested for a future release is taking a step
backwards if something was not right. Slowly the mixer is becoming
smarter...I hope.

_____
Professor Laurence Marks
"Research is to see what everybody else has seen, and to think what nobody
else has thought", Albert Szent-Gyorgi
www.numis.northwestern.edu

On Wed, Jan 8, 2020, 08:40 Laurence Marks <laurence.marks at gmail.com> wrote:

> For pedagogical reasons, let me explain why forcing dmat to positive
> definite may not be good.
>
> The mixer is solving a fixed point problem, which with +U is for both the
> dmat and density. Currently it can explore all values, including ones which
> are not physically reasonable. If we limit it to positive definite then
> there are some forbidden regions. The problem may be slower if the mixer
> can't explore them.
>
> As an illustration, suppose your home is on the other side of a shallow
> stream. If you demand that your feet don't get wet, you may have to walk a
> long way to a bridge to get home. If you are OK with getting your feet wet,
> you just ford the river. Fine, so long as there are no pirhana fish (ghost
> bands) in the stream.
>
> _____
> Professor Laurence Marks
> "Research is to see what everybody else has seen, and to think what nobody
> else has thought", Albert Szent-Gyorgi
> www.numis.northwestern.edu
>
> On Wed, Jan 8, 2020, 07:01 Laurence Marks <laurence.marks at gmail.com>
> wrote:
>
>> Being more specific, the unmixed density matrix (dmat) produced by one
>> scf iteration is necessarily positive definite. The mixer produces a new
>> dmat that is a linear combination of prior dmats used, i.e.
>>
>>     dmat_(n+1) = sum_i c_i * dmat_i
>>
>> If some of the coefficients c_i are negative the new density matrix may
>> not be positive definite. A trivial example used two 1x1 matrices M=1 and
>> M=2.
>>
>> As Peter said, at convergence (:MV) the dmat must be positive definite
>> since the input is equal to the output.
>>
>> N.B., one could constrain the dmat to be positive definite. However,
>> mathematically this may converge slower, not faster.
>>
>> _____
>> Professor Laurence Marks
>> "Research is to see what everybody else has seen, and to think what
>> nobody else has thought", Albert Szent-Gyorgi
>> www.numis.northwestern.edu
>>
>> On Wed, Jan 8, 2020, 06:40 Peter Blaha <pblaha at theochem.tuwien.ac.at>
>> wrote:
>>
>>> The "new" (unmixed) dmat is always ok, only through mixing of the
>>> individual elements this may happen.
>>>
>>> When reaching scf, the "mixed" dmat = "unmixed" dmat and thus this
>>> should no longer occur.
>>>
>>> On 1/8/20 1:19 PM, pieper wrote:
>>> > Sorry for interrupting, but I am intrigued. I was not aware that the
>>> > density matrix can leave the physically meaningfull realm of
>>> > semi-positive operators.
>>> >
>>> > May I spoil this thread with the question why the mixer produces such
>>> > non-physical trial states? And if it does, what forces drive rho back
>>> to
>>> > proper density operators during convergence?
>>> >
>>> > ---
>>> > Dr. Martin Pieper
>>> > Karl-Franzens University
>>> > Institute of Physics
>>> > Universitätsplatz 5
>>> > A-8010 Graz
>>> > Austria
>>> > Tel.: +43-(0)316-380-8564
>>> >
>>> >
>>> > Am 2020-01-04 11:50, schrieb Peter Blaha:
>>> >> I repeated your calculations. Yes, intermediately I also got these
>>> >> density matrix warnings, but NOT with final convergence.
>>> >>
>>> >> Most likely, this warning should be removed from mixer (Laurence !),
>>> >> as it does not give any meaningful hint or it should be printed only
>>> >> if one is nearly converged (:DIS is lower than ...)
>>> >>
>>> >> I have a few other comments:
>>> >>
>>> >> You seem to start a Ferro-magnetic calculation. As was mentioned
>>> >> before, maybe an AFM structure is more stable. So check other possible
>>> >> magnetic configurations.
>>> >>
>>> >> You seem to start with init_lapw, and thus with the default
>>> >> (ferromagnetic) case.inst
>>> >>
>>> >> For magnetic oxides it is highly recommended to start with:
>>> >>
>>> >> instgen -ask
>>> >> This lets you define a possible AFM arrangement and in particular you
>>> >> should set the O-atoms as non-magnetic. This save a lot of scf cycles.
>>> >>
>>> >> -rkmax 7.5 is quite some "overkill". This rkmax value is for the small
>>> >> O-atoms and RKmax=6 (beginning) and 7 (final convergence) is
>>> >> sufficient.
>>> >>
>>> >> On the other hand, a HDLO for Nd-4f states is highly recommended.
>>> >>
>>> >> I never start the scf-cycle with "-orb" right after intitialization,
>>> >> but always do (at least a crude) GGA calculation before switching on
>>> >> -orb. Otherwise you may even more likely end up in some local minimum
>>> >> but not the ground state.
>>> >>
>>> >> I got a half-metallic solution with a spin-up 4f peak down at -3.5 eV
>>> >> and another one at EF. You expected that the 4f states are all removed
>>> >> from EF, but your compound seems to be "special" (is this compound
>>> >> experimentally known ??).
>>> >>
>>> >> The stoichiometry of Nd4 Ni3 O8  suggests Ni2+ ions, leaving a
>>> (Nd4)10+
>>> >> charge state, i.e. a Nd2.5+ state, which is very unusual. But I got
>>> >> 34f electrons, which hints to a Nd3+ and in fact one of your Oxygens
>>> >> has p-states above EF.
>>> >>
>>> >> With this half-filled 4f-DOS peak at EF also spin-orbit could be very
>>> >> important.
>>> >>
>>> >> And as always in such LDA+U calculations, play with the initial
>>> >> case.dmat file. In my case I have 2 4f orbitals "fully" occupied (and
>>> >> thus shifted down), but 2 others are partly occupied (close to 1/2)
>>> >> and thus not much shifted and pinned to EF.
>>> >>
>>> >> As mentioned before, additional symmetry splitting with AFM for the 2
>>> >> equivalent Nd atoms may lead to further splitting.
>>> >>
>>> >>
>>> >> Am 03.01.2020 um 10:30 schrieb Fan:
>>> >>> Thank you for your reply, Prof. Blaha. In fact, when I change
>>> >>> parameters in inorb, I always do 'rm case.dmat*' and 'rm case.vorb*'
>>> >>> , so I think it should not be the problem. But I do value your
>>> >>> suggestions, so I started a new session, only used the struct file
>>> of
>>> >>> Nd4Ni3O8 which is attached here, and then
>>> >>> init_lapw -b -rkmax 7.5 -numk 2000 -sp -vxc 5 -lvns 6
>>> >>> create inorb and indm by copying them from templates and modify them
>>> >>> accordingly
>>> >>> runsp_lapw -p -orb -i 200 -ec 0.0001 -cc 0.001 -NI
>>> >>> during the scf cycle, QTL-B warning appeared, but the value was very
>>> >>> small (2~3, still could be a trouble?), the density matrix warnings
>>> >>> appeared at about the 20th cycle and persisted.
>>> >>>
>>> >>> With regards.
>>> >>>
>>> >>> Fan
>>> >>>
>>> >>>
>>> >>>
>>> >>> _______________________________________________
>>> >>> Wien mailing list
>>> >>> Wien at zeus.theochem.tuwien.ac.at
>>> >>>
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=eysx4yGF3nTRYJls4yocWU7oyluqkIpCzgteUDW2VuM&e=
>>> >>> SEARCH the MAILING-LIST at:
>>> >>>
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=XZoEXEbnC0vsZmryXaVC0vs2dXpqNtKiIXUnYSvakb8&e=
>>> >>>
>>> > _______________________________________________
>>> > Wien mailing list
>>> > Wien at zeus.theochem.tuwien.ac.at
>>> >
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=eysx4yGF3nTRYJls4yocWU7oyluqkIpCzgteUDW2VuM&e=
>>> > SEARCH the MAILING-LIST at:
>>> >
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=XZoEXEbnC0vsZmryXaVC0vs2dXpqNtKiIXUnYSvakb8&e=
>>>
>>> --
>>>
>>>                                        P.Blaha
>>>
>>> --------------------------------------------------------------------------
>>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
>>> Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
>>> Email: blaha at theochem.tuwien.ac.at    WIEN2k:
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.wien2k.at&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=IFuBwsLNUiapb3xswmxvIshNj9YcJ3CeWvPJTzc9zdQ&e=
>>> WWW:
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.imc.tuwien.ac.at_TC-5FBlaha&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=y2JZilUAvnkeeS6STghDpGOnpRJjz_Sqk58GlJuUANo&e=
>>>
>>> --------------------------------------------------------------------------
>>> _______________________________________________
>>> Wien mailing list
>>> Wien at zeus.theochem.tuwien.ac.at
>>>
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=eysx4yGF3nTRYJls4yocWU7oyluqkIpCzgteUDW2VuM&e=
>>> SEARCH the MAILING-LIST at:
>>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tAI1trxDz-gl5vxcYhEQxGU9OoU6gcc7NYXBIo86OH8&s=XZoEXEbnC0vsZmryXaVC0vs2dXpqNtKiIXUnYSvakb8&e=
>>>
>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20200108/ab13308c/attachment.html>