Anomalous energy-volume results

Elk Users
2014-09-05
2014-09-15
  • D. R. Hamann

    D. R. Hamann - 2014-09-05

    I have been calculating energy-volume results to compare lattice constants and bulk moduli among several structures for monatomic and binary cubic materials to benchmark new pseudopotentials. Many results give excellent fits to the Burch-Murgnahan eos and close agreement with psp results, but I often encounter non-physical EV results which come and go with small changes in mt radii. Instead of typical concave eos trends, I get inflection points and sudden quasi-singular drops to lower energies at one or more volumes. I am using elk-2.3.22.

    AgCl input data and results for zincblende, rocksalt, and cesium cloride structures are attached as an example. These are script-driven calculations cycling through 11 acell values. The highq option is used. The mt radii are kept the same for all structures and volumes, their sum kept below the shortest bond encountered (4.50 au for zincblende). The first set, with Ag/Cl rmt of 1.8/2.0 give excellent eos fits and good agreement with psp results. The second set, with 1.9/2.1 give a good fit and nearly identical results for the CsCl structure, but anomalous, unfittable behavior for the zb and rs structures.

    What am I doing wrong?


    Zincblende prototype input (acell stepped by script)


    tasks
    0 :tasks #switched to 1 after first volume point

    xctype
    3

    sppath
    '../'

    ngridk
    10 10 10

    vkloff
    0.5 0.5 0.5

    nempty
    6

    highq
    .true.

    autokpt
    .false.

    stype
    3

    mixtype
    3

    swidth
    0.01

    maxscl
    100

    scrpath
    '/tmp/'

    scale
    11.596 :scale

    rgkmax
    9.00

    atoms
    2 : nspecies
    'Ag4.in1'
    1 : natoms
    0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt
    'Cl4.in2'
    1 : natoms
    0.25 0.25 0.25 0.0 0.0 0.0 : atposl, bfcmt
    avec
    0.5 0.5 0.0
    0.5 0.0 0.5
    0.0 0.5 0.5


    rocksalt input (last 12 lines, rest as above)


    atoms
    2 : nspecies
    'Ag4.in1'
    1 : natoms
    0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt
    'Cl4.in2'
    1 : natoms
    0.50 0.50 0.50 0.0 0.0 0.0 : atposl, bfcmt
    avec
    0.5 0.5 0.0
    0.5 0.0 0.5
    0.0 0.5 0.5


    CsCl input


    atoms
    2 : nspecies
    'Ag4.in1'
    1 : natoms
    0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt
    'Cl4.in2'
    1 : natoms
    0.50 0.50 0.50 0.0 0.0 0.0 : atposl, bfcmt

    avec
    1.0 0.0 0.0
    0.0 1.0 0.0
    0.0 0.0 1.0


    Ag4.in1 species file


    'Ag' : spsymb
    'silver' : spname
    -47.0000 : spzn
    196631.6997 : spmass
    0.291730E-06 1.8000 57.5790 600 : sprmin, rmt, sprmax, nrmt
    15 : spnst
    1 0 1 2.00000 T : spn, spl, spk, spocc, spcore
    2 0 1 2.00000 T
    2 1 1 2.00000 T
    2 1 2 4.00000 T
    3 0 1 2.00000 T
    3 1 1 2.00000 T
    3 1 2 4.00000 T
    3 2 2 4.00000 T
    3 2 3 6.00000 T
    4 0 1 2.00000 F
    4 1 1 2.00000 F
    4 1 2 4.00000 F
    4 2 2 4.00000 F
    4 2 3 6.00000 F
    5 0 1 1.000000 F
    1 : apword
    0.1500 0 F : apwe0, apwdm, apwve
    0 : nlx
    6 : nlorb
    0 2 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    1 2 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    2 2 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    0 3 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    -4.0000 0 T
    1 3 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    -2.5000 0 T
    2 3 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    -0.2735 0 T


    Cl4.in2 species file


    'Cl' : spsymb
    'chlorine' : spname
    -17.0000 : spzn
    64626.86545 : spmass
    0.485071E-06 2.0000 31.8449 400 : sprmin, rmt, sprmax, nrmt
    7 : spnst
    1 0 1 2.00000 T : spn, spl, spk, spocc, spcore
    2 0 1 2.00000 T
    2 1 1 2.00000 T
    2 1 2 4.00000 T
    3 0 1 2.00000 F
    3 1 1 2.00000 F
    3 1 2 3.00000 F
    1 : apword
    0.1500 0 F : apwe0, apwdm, apwve
    0 : nlx
    3 : nlorb
    0 2 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    1 2 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    0 3 : lorbl, lorbord
    0.1500 0 F : lorbe0, lorbdm, lorbve
    0.1500 1 F
    -0.9000 0 T


    Only species file changes (rmt) for Ag5, Cl5 "bad runs"


    Ag5.in1: 0.291730E-06 1.9000 57.5790 600 : sprmin, rmt, sprmax, nrmt

    Cl5.in2: 0.485071E-06 2.1000 31.8449 400 : sprmin, rmt, sprmax, nrmt


    Engegy-Volume results for Ag4, Cl4 "good runs"


    Zincblende
    acell volume energy
    11.4870 378.9307696 -5772.66720461
    11.3780 368.2457955 -5772.66885410
    11.2690 357.7635945 -5772.67021065
    11.1600 347.4822240 -5772.67128934
    11.0510 337.3997414 -5772.67199398
    10.9420 327.5142042 -5772.67230499
    10.8330 317.8236699 -5772.67210488
    10.7240 308.3261959 -5772.67137845
    10.6150 299.0198396 -5772.67006481
    10.5060 289.9026586 -5772.66801864
    10.3970 280.9727102 -5772.66526007

    Rocksalt
    10.6470 301.7322775 -5772.66941982
    10.5460 293.2265628 -5772.67130293
    10.4450 284.8822178 -5772.67288715
    10.3440 276.6976969 -5772.67405033
    10.2430 268.6714547 -5772.67485070
    10.1420 260.8019458 -5772.67514302
    10.0410 253.0876247 -5772.67489693
    9.9400 245.5269460 -5772.67403993
    9.8390 238.1183642 -5772.67252181
    9.7380 230.8603338 -5772.67018977
    9.6370 223.7513095 -5772.66696523

    CsCl
    6.5100 275.8944510 -5772.66020513
    6.4480 268.0865874 -5772.66211409
    6.3860 260.4274405 -5772.66366278
    6.3240 252.9155802 -5772.66485623
    6.2620 245.5495767 -5772.66559832
    6.2000 238.3280000 -5772.66583219
    6.1380 231.2494201 -5772.66554416
    6.0760 224.3124070 -5772.66455777
    6.0140 217.5155307 -5772.66285747
    5.9520 210.8573614 -5772.66032976
    5.8900 204.3364690 -5772.65688423


    Engegy-Volume results for Ag5, Cl5 "bad runs"


                                          "real bad points"
    

    Zincblende
    11.4870 378.9307696 -5772.77483690
    11.3780 368.2457955 -5772.81710399
    11.2690 357.7635945 -5772.67442349
    11.1600 347.4822240 -5772.67246876
    11.0510 337.3997414 -5772.67258303
    10.9420 327.5142042 -5772.67271469
    10.8330 317.8236699 -5772.67246058
    10.7240 308.3261959 -5772.67172634
    10.6150 299.0198396 -5772.67056783
    10.5060 289.9026586 -5772.70549017

    10.3970 280.9727102 -5772.66868590 *

    Rocksalt
    10.6470 301.7322775 -5772.69416444 *
    10.5460 293.2265628 -5772.67485178
    10.4450 284.8822178 -5772.67450914
    10.3440 276.6976969 -5772.67520257
    10.2430 268.6714547 -5772.67576497
    10.1420 260.8019458 -5772.67596663
    10.0410 253.0876247 -5772.67569184
    9.9400 245.5269460 -5772.67481974
    9.8390 238.1183642 -5772.67323678
    9.7380 230.8603338 -5772.67088085
    9.6370 223.7513095 -5772.66765736

    CsCl
    6.5100 275.8944510 -5772.66112013
    6.4480 268.0865874 -5772.66294566
    6.3860 260.4274405 -5772.66447716
    6.3240 252.9155802 -5772.66562699
    6.2620 245.5495767 -5772.66637377
    6.2000 238.3280000 -5772.66659338
    6.1380 231.2494201 -5772.66625218
    6.0760 224.3124070 -5772.66529671
    6.0140 217.5155307 -5772.66358226
    5.9520 210.8573614 -5772.66104369
    5.8900 204.3364690 -5772.65754373

     
  • John Kay Dewhurst

    Hi,

    It appears that the problem is being caused by conduction band local orbitals being switched on automatically by the 'highq' option.

    You can turn them off by adding

    lorbcnd
     .false.
    

    after the 'highq=.true.' block.

    I may remove this from the highq defaults for the next release based on your experience.

    Let me know if this works for you.

    Regards,
    Kay.

     
  • D. R. Hamann

    D. R. Hamann - 2014-09-07

    Hi Kay,

    Thanks for your prompt response. I ran several more AgCl tests with lorbcnd=.false., and my findings were somewhat mixed:
    1) With smaller Ag/Cl rmt = 1.8/2.0 and rgkmax=9, eos fits remained excellent and essentially unchanged.
    2) With larger Ag/Cl rmt = 1.9/2.1 and rgkmax=9, cc eos fit remained excellent, rs points at several largest volumes were visibly off the fit, and several zb points at smaller volumes were far off. Eos.in files for these are below (I couldn’t figure out how to attach plots).
    3) With Ag/Cl rmt = 1.9/2.1 and rgkmax = 10, rs failed to converge at the 4 smallest volumes with charge errors reported, and the zb fit was even worse at smaller volumes. cc remained good.
    4) With Ag/Cl rmt = 1.9/2.1 and rgkmax = 7.5, one zb run failed to converge, and rs had fairly bad points at larger volumes. cc was slightly worse.

    I haven’t gone back and tested any of my other problem systems with lorbcnd=.false., but there still appear to be unresolved issues.

    Regards,
    Don H.

    **********Ag/Cl rmt = 1.9/2.1, rgkmax=9.0, lorbcnd=.false.
    **********
    zincblende eos.in

    Ag5.in1Cl5.in2
    1
    3
    271 389 200
    11
    378.93076960 -5772.66698776
    368.24579550 -5772.66869583
    357.76359450 -5772.67007635
    347.48222400 -5772.67117915
    337.39974140 -5772.67186112
    327.51420420 -5772.67213299
    317.82366990 -5772.67189339
    308.32619590 -5772.67108888
    299.01983960 -5772.66949082
    289.90265860 -5772.66990823
    280.97271020 -5772.66535935

    rocksalt

    Ag5.in1Cl5.in2
    1
    3
    216 310 200
    11
    301.73227750 -5772.67114902
    293.22656280 -5772.67210210
    284.88221780 -5772.67353077
    276.69769690 -5772.67468361
    268.67145470 -5772.67542106
    260.80194580 -5772.67569886
    253.08762470 -5772.67545320
    245.52694600 -5772.67458205
    238.11836420 -5772.67297725
    230.86033380 -5772.67057437
    223.75130950 -5772.66727857

     
  • John Kay Dewhurst

    Dear Don,

    Two points:

    a) Large rgkmax can cause instability in the eigenvalue problem. This can be overcome by increasing gmaxvr (I set it to 20.0 to converge zb). If this doesn't work, then you can also set

    trimvg
     .true.
    

    ... which should hopefully cure the problem.

    b) Check that your muffin-tin radii are remaining constant across the volume range. The energy can change discontinuously if these are reduced at some volume. This effect can be converged away with large rgkmax because the kinetic energy at the muffin-tin surface becomes more accurate.

    I've now removed 'lorbcnd=.true.' from the highq defaults. This is only useful for excited state properties anyway.

    Thanks for the very clear description of the problem, by the way - I really appreciate that.

    Regards,
    Kay.

     
  • D. R. Hamann

    D. R. Hamann - 2014-09-07

    Dear Kay,

    Thanks again. My AgCl remained stable with one more test with smaller yet rmt = 1.7/1.9, so I'm satisfied with that. I just went back to one of my worst headaches at a completely different place in the periodic table, LiF. With rmts small enough to be sure that they weren't readjusted for any structure or volume, I had never avoided "s-shaped" EV curves for rs and cc (zb was OK). With the lorbcnd=.false. fix I got excellent fits for all three structures on my first try, with rgkmax=8.5. I'll keep your gmaxvr and trimvg suggestions in mind if I need to go further for some system.

    I'm also getting excellent agreement with my psps for cases with such good EV fits (PRB 88, 085117 (2013) if you're curious). The psp bulk moduli are being done with DFPT in Abinit rather than EV fits.

    Regards,
    Don

     
  • D. R. Hamann

    D. R. Hamann - 2014-09-09

    Dear Kay,

    A new case NOT solved by lorbcnd=.false., gmaxvr=20 (or 40) and trimvg=.true. is O in fcc, bcc, and sc structures (following the Trieste group’s psp testing protocol, arXiv:1404.3015). I found similar problems for F and N. A quick summary of my observations over a number of tests of this case, and a hopefully condensed input file and set of EV results follow.

    1) Singular EV behavior seems to occur at approximately the same unit-cell volume for all three structures.
    2) Very small rmt adjustments “tune” this volume (smaller rmt yields a larger volume value)
    3) Adjusting rgkmax (I tried 7.5 and 8.5) has a most a small effect on this volume.
    4) Omitting gmaxvr or setting it to high (20) and ridiculous (40) values has no effect.
    5) There are no warning messages.
    6) Nothing funny seems to happen to the single calculated l.o. energy spanning the singular volume.
    7) Tuning rmt to 1.75, which just avoids rmt readjustment, either removes the singularity or gets it far enough out of the scanned volume ranges to let me get good fits. I hope there’s another solution that doesn’t involve careful inspection and hand-tuning for many elements or compounds.

    Regards,
    Don


    fcc prototype input file


    tasks
    0 :tasks

    xctype
    3

    sppath
    '../'

    ngridk
    10 10 10

    vkloff
    0.5 0.5 0.5

    nempty
    6

    highq
    .true.

    lorbcnd
    .false.

    gmaxvr
    40.0

    trimvg
    .true.

    autokpt
    .false.

    stype
    3

    mixtype
    3

    swidth
    0.01

    maxscl
    50

    scrpath
    '/tmp/'

    scale
    6.106 :scale ** change according to values listed below **

    rgkmax
    7.50

    atoms
    1 : nspecies
    'O.in' :** elk-2.3.22/species/O.in with rmt = 1.64
    1 : natoms
    0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt
    avec :** change for bcc and sc

    0.5 0.5 0.0
    0.5 0.0 0.5
    0.0 0.5 0.5


    Energy-Volume results


    scale volume energy
    fcc
    6.0650 55.7740812 -74.6424843856
    6.0240 54.6505955 -74.6430034050
    5.9830 53.5422993 -74.6434271443
    5.9420 52.4490892 -74.6436842845
    5.9010 51.3708619 -74.6436520569
    5.8600 50.3075140 -74.6423978813
    5.8190 49.2589421 -74.6454908208
    5.7780 48.2250427 -74.6448732253
    5.7370 47.2057126 -74.6444451120
    5.6960 46.2008484 -74.6439458057
    5.6550 45.2103466 -74.6432872069

    bcc
    4.7720 54.3339538 -74.6486003874
    4.7400 53.2482120 -74.6491210603
    4.7080 52.1770315 -74.6494697615
    4.6760 51.1203139 -74.6494637837
    4.6440 50.0779610 -74.6479128854
    4.6120 49.0498745 -74.6515307522
    4.5800 48.0359560 -74.6511638959
    4.5480 47.0361073 -74.6508903066
    4.5160 46.0502301 -74.6505504072
    4.4840 45.0782259 -74.6500478062
    4.4520 44.1199967 -74.6493944465

    sc
    3.8290 56.1378918 -74.6710120194
    3.8030 55.0020626 -74.6717053328
    3.7770 53.8816584 -74.6722700574
    3.7510 52.7765737 -74.6726600853
    3.7250 51.6867031 -74.6727853303
    3.6990 50.6119411 -74.6720915904
    3.6730 49.5521822 -74.6750932061
    3.6470 48.5073210 -74.6741569665
    3.6210 47.4772521 -74.6736624903
    3.5950 46.4618699 -74.6730848558
    3.5690 45.4610690 -74.6723421497

     
  • John Kay Dewhurst

    Dear Don,

    I think 'gmaxvr=40' is too large and is causing some instability in the Poisson solver. You should never have to go much beyond 'gmaxvr=20'.

    Regards,
    Kay.

     
  • D. R. Hamann

    D. R. Hamann - 2014-09-10

    Dear Kay,

    gmaxvr=20 and 40 gave essentially identical bad behavior for these EV runs, as did leaving the default. I think the problem lies elsewhere, but I haven't a clue as to what else to try.

    Regards,
    Don

     
  • John Kay Dewhurst

    Dear Don,

    You're correct. Oxygen seems to be a tricky case for these muffin-tin radii. It's possible that ghost bands are being generated.

    I found that automatically determining the APW linearisation energies seems to fix the problem. Do this with

    autolinengy
     .true.
    

    Maybe I should enable this by default. I'll think about it.

    Regards,
    Kay.

     
    Last edit: John Kay Dewhurst 2014-09-11
  • D. R. Hamann

    D. R. Hamann - 2014-09-12

    Dear Kay,

    I've run N and F with autolinengy=.true., and the ghost quasi-divergences in these EV results seem to be controlled as well. I reran 17 elements with autolinengy set, all with rgkmax=7.5, lorbcnd=.false., gmaxvr-20, and trimvg-.true., and have these observations:

    1) rmt have to retuned to avoid lack of convergence at certain volumes for at least some structures comarped to the autolinengy-.false. deafault.

    2) The scatter of the EV points around the EV fits were generally worse with autolinengy than without (in cases where the ghost problems did not occur).

    3) Setting rgkmax=8.5 worsened the scatter with autolinengy=.true., but generally had no such effect with the default .false. It would probably be better to keep this default, and switch to .true. only when other attempts to fix ghost-like behavior fail.

    4) Less scatter generally coincided with better agreement of the lattice constants, bulk moduli, and structural energy difference with my psp results.

    I haven't completed binary-compound tests with the new features yet, but I believe you've given me enough advice to get valid results for the many more cases I hope to study.

    Thanks again,
    Don

     
  • John Kay Dewhurst

    Dear Don,

    Could you post the elk.in corresponding to worst case of the scattered data?

    It should be a prefectly smooth curve so I'd like to find out what's wrong.

    Regards,
    Kay.

     
  • D. R. Hamann

    D. R. Hamann - 2014-09-15

    Dear Kay,

    Here is an example which can display two types of bad behavior, both of which I can eliminate and one of which I can explain. This is for the “Trieste tests suite” on N. I’m sending the prototype fcc elk.in, and my three sets of scale values with badly scattered EV results. The elk-2.3.22/species/N.in file is used, with rmt=1.5, a value which is small enough to avoid rescaling for all structures.

    The scatter can be removed by restoring the default trimvg=.false. and the default gmaxvr. I can’t explain this.

    With the above changes, allowing lorbcnd=.true. gives smooth behavior and reasonable lattice constant and bulk modulus results for fcc and bcc, but a “ghost-resonance-like” behavior for sc just below the smallest scale value. This can be removed in two ways, either by leaving lorbcnd=.false. or by eliminating the third local orbital in N.in. With both, the LINENGY.OUT files indicate that two nearly identical local orbitals end up in the conduction band range for all structures. This doesn’t seem to produce the ghost problem within the scale ranges of fcc and bcc, however.

    My present opinion is that autolinengy=.true. is a safe option, probably giving somewhat better results. lorbcnd=.true. is probably also good in general, unless a variable-energy local orbital in the atom.in file gets boosted into the conduction-band range.

    Regards,
    Don


    prototype fcc elk.in


    tasks
    0 :tasks

    xctype
    3

    sppath
    '../'

    ngridk
    10 10 10

    vkloff
    0.5 0.5 0.5

    nempty
    6

    highq
    .true.

    lorbcnd
    .false.

    gmaxvr
    20.0

    trimvg
    .true.

    autokpt
    .false.

    stype
    3

    mixtype
    3

    swidth
    0.01

    maxscl
    30

    scrpath
    '/tmp/'

    scale
    6.054 :scale

    autolinengy
    .true.

    rgkmax
    8.50

    atoms
    1 : nspecies
    'N.in'
    1 : natoms
    0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt
    avec
    0.5 0.5 0.0
    0.5 0.0 0.5
    0.0 0.5 0.5


    fcc scale, Volume and Energy


    6.0130 54.3517611 -54.2300449036
    5.9720 53.2475225 -54.2308851844
    5.9310 52.1583424 -54.2314002694
    5.8900 51.0841172 -54.2319055951
    5.8490 50.0247438 -54.2321666788
    5.8080 48.9801185 -54.2322832409
    5.7670 47.9501382 -54.2322492729
    5.7260 46.9346993 -54.2323232098
    5.6850 45.9336985 -54.2323815726
    5.6440 44.9470325 -54.2318588424
    5.6030 43.9745978 -54.2312790242


    bcc scale, Volume and Energy


    4.6990 51.8783721 -54.2392160625
    4.6670 50.8257045 -54.2398840259
    4.6350 49.7873739 -54.2404314975
    4.6030 48.7632821 -54.2413522586
    4.5710 47.7533307 -54.2416609086
    4.5390 46.7574214 -54.2418186010
    4.5070 45.7754559 -54.2419551434
    4.4750 44.8073359 -54.2417918405
    4.4430 43.8529632 -54.2414519478
    4.4110 42.9122393 -54.2414672780
    4.3790 41.9850660 -54.2407639402


    sc scale, Volume and Energy


    3.5500 44.7388750 -54.2818382976
    3.5260 43.8376156 -54.2823652836
    3.5020 42.9485420 -54.2827589808
    3.4780 42.0715713 -54.2830107553
    3.4540 41.2066207 -54.2831196072
    3.4300 40.3536070 -54.2834685698
    3.4060 39.5124474 -54.2832871532
    3.3820 38.6830590 -54.2834738868
    3.3580 37.8653587 -54.2829824418
    3.3340 37.0592637 -54.2822967576
    3.3100 36.2646910 -54.2814081229

     

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