The ABINIT Users Mailing List ( CLOSED )

["D. R. Hamann" <drh@bell-labs.com>]

Dear Alexey,

I believe I have identified your problem.  In short, it is the FHI model core charge, which has discontinuous higher derivatives.

My conclusions were drawn as follows:  Using your .in and pseudopotential files, I basically reproduced your error, 1.6% discrepancy between the optimized acell (stress zero) and the Murnaghan energy fit minimum (this was with 4.5.2).  My summary results are attached as MnN_GGA.txt.

I then proceeded to "bracket" your case, first with LDA using well-established *.pspnc pseudopotentials from Psps_for_tests.  Since Mn was not available, I did FeN and CrN keeping everything but ixc and znucl unchanged.  These gave excellent agreement (FeN_LDA.txt and CrN_LDA.txt).  (CrN gave seriously non-Murnaghan behavior, so I settled for a polynomial fit close to the energy minimum.)

To test whether this could be a GGA issue, I redid FeN with your ixc=7, and still got excellent agreement (FeN_GGA.txt).

This left me little to suspect but the model core charge, a quantity which proved very troublesome in my development of the strain perturbation.  I simply stripped the core charge out of your Mn potential (N was already coreless) and got excellent agreement between Murnaghan and optimization (MnN_GGA_no_core.txt).  (At least some of the ~3% shift in acell is likely an artifact of the inconsistency between unscreening and rescreening the psp with this quick-and-dirty test.)

The issue is not the presence or absence of a core charge.  I deliberately chose the *.pspnc's because they do have core charges.  However, unlike the FHI psp's, these use an analytic function for the core models and the Abinit routines that process these for the rest of the code do everything analytically.  The numerical FHI charges are processed by psp6cc.f in 4.2.4.  I found that even with an analytic charge input as a numerical table, this routine treated derivatives inconsistently and produced systematic errors.  In more recent version (4.4+ and maybe 4.3) my revised routine psp6cc_drh.F90 is the default, which leads to accurate comparisons between numerical and analytic derivatives for sufficiently smooth model charges.  A problem can still arise, however, for "spliced" functions because up to 4th derivatives are used in spline interpolations.  These problems are undoubtedly worse for GGA.

I note that you're using an fhi e-mail address.  I don't know if any of your FHI colleagues (former colleagues?) are still interested in the psp code, but it would be a welcome service to the community if an improved core model could solve this problem.

Best regards,

Don Hamann


Alexey Dick wrote:

Dear all,

In case someone needs more details to resolve the problem i send the complete input environment (input files/pseudopotentials), output and result files. Please find them attached as "cell_optimization.tar.gz" file. I hope this can help to fix the problem. Thank you for support,

With best wishes,
Alexey

=============================================
Alexey Dick
Abteilung Computer-Gestütztes Material-Design
Max-Planck-Institut für Eisenvorschung GmbH
Max-Planck-Str. 1
40237 Düsseldorf, Germany
Tel: +49(211)6792-283
=============================================

Dear Don,

Thank you very much for your hint. Although i have tried to increase accuracy toldfe to 1.0d-10 (without any changes, that guided me to conclusion that accuracy is rather sufficient), i have not checked if zero stresses and the total energy minimum are at the same lattice constant. As suggested, i have performed re-run for both automatic and Murnaghan search with tolvrs=1.0d-18, so to be on the safe site (this convergence parameter is indeed much more strict than toldfe - thanks for hint).  I also used denser lattice constant sampling (frankly speaking this was redundant) for Murnaghan fit, so to avoid questions if Murnaghan curve sampling is accurate enough.

Unfortunately, it looks that the problem is neither the ill-defined input variables nor convergence issue. Below are the stresses and total energies extracted from extremly accurate Murnaghan run:

############ Stress #############
aLat(Bohr)  sigma_11 (hartree/bohr^3)
7.35         -1.23147819E-03
7.40         -8.45468113E-04
7.45         -4.65923605E-04
7.50         -1.74591372E-04
7.55          1.63329532E-04
7.60          4.13679164E-04
7.65          6.53594477E-04
7.70          8.62113102E-04
7.75          1.07866157E-03
7.80          1.25115526E-03
7.85          1.42121770E-03
7.90          1.57836802E-03
7.95          1.70864643E-03
8.00          1.82422595E-03
8.05          1.90873470E-03

######### Total energy ############
aLat(Bohr)   total energy(H)
7.35         -3.2212485167E+01
7.40         -3.2216000760E+01
7.45         -3.2218779803E+01
7.50         -3.2220836207E+01
7.55         -3.2222217502E+01
7.60         -3.2222978000E+01
7.65         -3.2223168461E+01
7.70         -3.2222828145E+01
7.75         -3.2221962141E+01
7.80         -3.2220657425E+01
7.85         -3.2218868223E+01
7.90         -3.2216697215E+01
7.95         -3.2214101724E+01
8.00         -3.2211156261E+01
8.05         -3.2207923512E+01

Again, the Murnaghan total energy minimum -32.22317H found at 7.6419Bohr, that one can also easily see from the data above. The zero stress is, however, located between 7.50 and 7.55Bohr. The exact value, found by built-in automatic search is 7.5246Bohr, that corresponds to -32.22161H (sigma_11=1.58335955E-10 hartree/bohr^3).

With best wishes,
Alexey

=============================================
Alexey Dick
Abteilung Computer-Gestütztes Material-Design
Max-Planck-Institut für Eisenvorschung GmbH
Max-Planck-Str. 1
40237 Düsseldorf, Germany
Tel: +49(211)6792-283
=============================================

-- 
D. R. Hamann				Phone: 908-582-4454
Director, Theoretical Materials    	Fax:   908-582-4702
  Physics Research (retired)		email: drh@physics.bell-labs.com
Bell Laboratories 
Lucent Technologies
700 Mountain Ave, Room 1D-371
Murray Hill, NJ 07974-0636 USA

MnN, rocksalt
ixc = 7 (PW91 GGA)

psps:
        mn:eq:lda:tm:23t-24t-1.0e-23t:p1.02:ls.cpi
        n:ca:lda:tm:145t-145t-145t:p0.0:ld.cpi

        acell = 7.644726278 (Murnaghan fit)
        acell = 7.5240301931E+00 (optimization)
        difference 1.6%  BAD!

acell              etot               sigma(1 1)

6.5000000000E+00  -3.1976460762E+01  -1.66036158E-02
6.6000000000E+00  -3.2028089407E+01  -1.35763930E-02
6.7000000000E+00  -3.2071608462E+01  -1.08823646E-02
6.8000000000E+00  -3.2107969297E+01  -8.54561777E-03
6.9000000000E+00  -3.2137989141E+01  -6.68684068E-03
7.0000000000E+00  -3.2162397122E+01  -5.11585788E-03
7.1000000000E+00  -3.2181847363E+01  -3.77030544E-03
7.2000000000E+00  -3.2196999664E+01  -2.61283133E-03
7.3000000000E+00  -3.2208338582E+01  -1.64075272E-03
7.4000000000E+00  -3.2216174033E+01  -8.53469852E-04
7.5000000000E+00  -3.2221007815E+01  -1.79073145E-04
7.6000000000E+00  -3.2223143130E+01   4.18856758E-04
7.7000000000E+00  -3.2222993742E+01   8.72370914E-04
7.8000000000E+00  -3.2220819667E+01   1.25435729E-03
7.9000000000E+00  -3.2216851841E+01   1.58013677E-03
8.0000000000E+00  -3.2211309290E+01   1.82393584E-03
8.1000000000E+00  -3.2204504552E+01   2.02202862E-03
8.2000000000E+00  -3.2196606275E+01   2.16005557E-03
8.3000000000E+00  -3.2187808002E+01   2.25170313E-03
8.4000000000E+00  -3.2178256204E+01   2.30331286E-03
8.5000000000E+00  -3.2168133026E+01   2.33486521E-03
FeN, rocksalt
ixc = 2 (LDA)
Psps_for_tests/26fe.pspnc, 7n.pspnc

        acell = 7.58777019 (Murnaghan fit)
        acell = 7.5838364606E+00 (optimization)
        difference 0.05%

acell              etot               sigma(1 1)

6.5000000000E+00  -3.5155930779E+01  -1.55389705E-02
6.6000000000E+00  -3.5201086803E+01  -1.27331355E-02
6.7000000000E+00  -3.5238772059E+01  -1.02273870E-02
6.8000000000E+00  -3.5269879205E+01  -8.03316048E-03
6.9000000000E+00  -3.5295288765E+01  -6.36086967E-03
7.0000000000E+00  -3.5315748438E+01  -4.96542601E-03
7.1000000000E+00  -3.5331878134E+01  -3.77115180E-03
7.2000000000E+00  -3.5344267253E+01  -2.72534047E-03
7.3000000000E+00  -3.5353356165E+01  -1.83971852E-03
7.4000000000E+00  -3.5359278047E+01  -1.10591532E-03
7.5000000000E+00  -3.5362428368E+01  -4.73550934E-04
7.6000000000E+00  -3.5363134011E+01   9.12888771E-05
7.7000000000E+00  -3.5361805435E+01   5.09902177E-04
7.8000000000E+00  -3.5358656409E+01   8.78214380E-04
7.9000000000E+00  -3.5353835029E+01   1.20228232E-03
8.0000000000E+00  -3.5347553799E+01   1.43778175E-03
8.1000000000E+00  -3.5340154342E+01   1.62464117E-03
8.2000000000E+00  -3.5331889024E+01   1.72700682E-03
8.3000000000E+00  -3.5322941051E+01   1.78952389E-03
8.4000000000E+00  -3.5313434528E+01   1.83191592E-03
8.5000000000E+00  -3.5303450479E+01   1.86138805E-03
CrN, rocksalt
ixc = 2 (LDA)
Psps_for_tests/24cr.pspnc, 7n.pspnc

        acell = 8.04569 (4th-order polynomial fit to * energies below
                        because of non-Murnaghan behavior)
        acell = 8.0497458154E+00 (optimization)
        difference 0.05%

acell              etot               sigma(1 1)

6.5000000000E+00  -2.6525701981E+01  -2.43552724E-02
6.6000000000E+00  -2.6599148805E+01  -2.33773805E-02
6.7000000000E+00  -2.6666082858E+01  -1.92471788E-02
6.8000000000E+00  -2.6724868483E+01  -1.48046280E-02
6.9000000000E+00  -2.6773118037E+01  -1.14283802E-02
7.0000000000E+00  -2.6808047468E+01  -8.00751537E-03
7.1000000000E+00  -2.6831650293E+01  -5.25661830E-03
7.2000000000E+00  -2.6848516954E+01  -3.67877875E-03
7.3000000000E+00  -2.6862659406E+01  -3.02707876E-03
7.4000000000E+00  -2.6874322738E+01  -2.63047822E-03
7.5000000000E+00  -2.6884377070E+01  -2.62814074E-03
7.6000000000E+00  -2.6892908238E+01  -1.44853141E-03
7.7000000000E+00  -2.6897096997E+01  -2.41923057E-04
7.8000000000E+00  -2.6899463749E+01* -6.35080989E-04
7.9000000000E+00  -2.6900763314E+01* -7.20515292E-05
8.0000000000E+00  -2.6901455138E+01*  8.37540578E-05
8.1000000000E+00  -2.6901247597E+01*  5.30090489E-04
8.2000000000E+00  -2.6897023749E+01*  1.40992562E-03
8.3000000000E+00  -2.6887293756E+01   2.39430386E-03
8.4000000000E+00  -2.6873830636E+01   2.67197163E-03
8.5000000000E+00  -2.6858506100E+01   2.61985678E-03
FeN, rocksalt
ixc = 7 (PW91 GGA)
Psps_for_tests/26fe.pspnc, 7n.pspnc

        acell = 7.58408468 (Murnaghan fit)
        acell = 7.5815197220E+00 (optimization)
        difference 0.03%

acell              etot               sigma(1 1)

6.5000000000E+00  -3.5162899362E+01  -1.54956823E-02
6.6000000000E+00  -3.5207913207E+01  -1.26937729E-02
6.7000000000E+00  -3.5245462741E+01  -1.01916523E-02
6.8000000000E+00  -3.5276444538E+01  -8.00084504E-03
6.9000000000E+00  -3.5301738307E+01  -6.33177018E-03
7.0000000000E+00  -3.5322091059E+01  -4.93923997E-03
7.1000000000E+00  -3.5338116686E+01  -3.74758643E-03
7.2000000000E+00  -3.5350413822E+01  -2.70420972E-03
7.3000000000E+00  -3.5359419450E+01  -1.82079151E-03
7.4000000000E+00  -3.5365261228E+01  -1.08897844E-03
7.5000000000E+00  -3.5368337365E+01  -4.58517194E-04
7.6000000000E+00  -3.5368972293E+01   1.04604994E-04
7.7000000000E+00  -3.5367585036E+01   5.21647740E-04
7.8000000000E+00  -3.5364380903E+01   8.88596166E-04
7.9000000000E+00  -3.5359509037E+01   1.21144435E-03
8.0000000000E+00  -3.5353179513E+01   1.44578334E-03
8.1000000000E+00  -3.5345742785E+01   1.63164665E-03
8.2000000000E+00  -3.5337432932E+01   1.73308000E-03
8.3000000000E+00  -3.5328453473E+01   1.79470996E-03
8.4000000000E+00  -3.5318910764E+01   1.83628630E-03
8.5000000000E+00  -3.5308904666E+01   1.86504790E-03
MnN, rocksalt
ixc = 7 (PW91 GGA)

psps:
        mn_no_core_charge.cpi ( from 
mn:eq:lda:tm:23t-24t-1.0e-23t:p1.02:ls.cpi)
        n:ca:lda:tm:145t-145t-145t:p0.0:ld.cpi

        acell = 7.87568173 (Murnaghan fit)
        acell = 7.8765483734E+00 (optimization)
        difference 0.01%

acell              etot               sigma(1 1)

6.5000000000E+00  -2.2514692693E+01  -2.37110752E-02
6.6000000000E+00  -2.2584531224E+01  -1.98989493E-02
6.7000000000E+00  -2.2644569135E+01  -1.65196326E-02
6.8000000000E+00  -2.2695873669E+01  -1.35753234E-02
6.9000000000E+00  -2.2739404044E+01  -1.11611139E-02
7.0000000000E+00  -2.2775983150E+01  -9.09020406E-03
7.1000000000E+00  -2.2806400577E+01  -7.31414909E-03
7.2000000000E+00  -2.2831403601E+01  -5.77515168E-03
7.3000000000E+00  -2.2851596759E+01  -4.46904418E-03
7.4000000000E+00  -2.2867392465E+01  -3.37709206E-03
7.5000000000E+00  -2.2879336476E+01  -2.42504728E-03
7.6000000000E+00  -2.2887847230E+01  -1.60081291E-03
7.7000000000E+00  -2.2893374368E+01  -9.36125802E-04
7.8000000000E+00  -2.2896266576E+01  -3.70196953E-04
7.9000000000E+00  -2.2896818383E+01   1.15561409E-04
8.0000000000E+00  -2.2895321139E+01   5.03902131E-04
8.1000000000E+00  -2.2892058778E+01   8.38121967E-04
8.2000000000E+00  -2.2887230363E+01   1.10842320E-03
8.3000000000E+00  -2.2881029999E+01   1.32240850E-03
8.4000000000E+00  -2.2873650264E+01   1.48196035E-03
8.5000000000E+00  -2.2865326682E+01   1.60117510E-03