[Wien] density matrix is not positive
pieper
pieper at ifp.tuwien.ac.at
Sat Jan 11 18:43:06 CET 2020
If I understand correctly, then the SCF cycle does not wade through some
river (to stay in the pedagogic example). It walks along the shore,
sometimes with one foot in the water (the density generated by mixer).
The other foot (the density generated from the wave functions) always
comes down on dry land. This way the SCF can step across cracks in
reality that are narrower than the step width.
This also explains why one apparently can be rather careless about
semi-positiveness of dmats when manipulating them to stabilize certain
solutions with the -orb option, correct?
I can appreciate that this has advantages if there are a lot of rivers.
I don't understand why this is always better than going for unitary
transformations only, because it does add a lot of definitely wrong
directions to explore. But I am happy to trust the experts.
So thanks a lot for the explanations,
Martin
---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564
Am 2020-01-08 16:10, schrieb Laurence Marks:
> 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 [1]
>
> 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 [1]
>>
>> 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 [1]
>>
>> 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
>>>>>
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>> --
>>
>> P.Blaha
>>
> --------------------------------------------------------------------------
>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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