[Wien] density matrix is not positive

Wed Jan 8 15:40:02 CET 2020

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
>> >>>
>> >>>
>> >>>
>> >>> _______________________________________________
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>> --
>>
>>                                        P.Blaha
>> --------------------------------------------------------------------------
>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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>
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