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 <[email protected]> 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 <[email protected]> > 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 <[email protected]> >> 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 >>> >>> [email protected] >>> >>> >>> 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 >>> > [email protected] >>> > >>> 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. 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