www.sciencemag.org/content/351/6280/aad3000/suppl/DC1 Supplementary Materials for Reproducibility in density functional theory calculations of solids Kurt Lejaeghere,* Gustav Bihlmayer, Torbjörn Björkman, Peter Blaha, Stefan Blügel, Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso, Stefano de Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Claudia Draxl, Marcin Dułak, Olle Eriksson, José A. Flores-Livas, Kevin F. Garrity, Luigi Genovese, Paolo Giannozzi, Matteo Giantomassi, Stefan Goedecker, Xavier Gonze, Oscar Grånäs, E. K. U. Gross, Andris Gulans, François Gygi, D. R. Hamann, Phil J. Hasnip, N. A. W. Holzwarth, Diana Iuşan, Dominik B. Jochym, François Jollet, Daniel Jones, Georg Kresse, Klaus Koepernik, Emine Küçükbenli, Yaroslav O. Kvashnin, Inka L. M. Locht, Sven Lubeck, Martijn Marsman, Nicola Marzari, Ulrike Nitzsche, Lars Nordström, Taisuke Ozaki, Lorenzo Paulatto, Chris J. Pickard, Ward Poelmans, Matt I. J. Probert, Keith Refson, Manuel Richter, Gian-Marco Rignanese, Santanu Saha, Matthias Scheffler, Martin Schlipf, Karlheinz Schwarz, Sangeeta Sharma, Francesca Tavazza, Patrik Thunström, Alexandre Tkatchenko, Marc Torrent, David Vanderbilt, Michiel J. van Setten, Veronique Van Speybroeck, John M. Wills, Jonathan R. Yates, Guo-Xu Zhang, Stefaan Cottenier* *Corresponding author. E-mail: [email protected] (K.L.); [email protected] (S.C.) Published 25 March 2016, Science 351, aad3000 (2016) DOI: 10.1126/science.aad3000 This PDF file includes: Materials and Methods Fig. S1 Tables S1 to S42 Full Reference List
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Reproducibility in density functional theory calculations of solids Kurt Lejaeghere,* Gustav Bihlmayer, Torbjörn Björkman, Peter Blaha, Stefan Blügel, Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso, Stefano de Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Claudia Draxl, Marcin Dułak, Olle Eriksson, José A. Flores-Livas, Kevin F. Garrity, Luigi
Genovese, Paolo Giannozzi, Matteo Giantomassi, Stefan Goedecker, Xavier Gonze, Oscar Grånäs, E. K. U. Gross, Andris Gulans, François Gygi, D. R. Hamann, Phil J.
Hasnip, N. A. W. Holzwarth, Diana Iuşan, Dominik B. Jochym, François Jollet, Daniel Jones, Georg Kresse, Klaus Koepernik, Emine Küçükbenli, Yaroslav O. Kvashnin, Inka
L. M. Locht, Sven Lubeck, Martijn Marsman, Nicola Marzari, Ulrike Nitzsche, Lars Nordström, Taisuke Ozaki, Lorenzo Paulatto, Chris J. Pickard, Ward Poelmans, Matt I. J. Probert, Keith Refson, Manuel Richter, Gian-Marco Rignanese, Santanu Saha, Matthias
Scheffler, Martin Schlipf, Karlheinz Schwarz, Sangeeta Sharma, Francesca Tavazza, Patrik Thunström, Alexandre Tkatchenko, Marc Torrent, David Vanderbilt, Michiel J. van Setten, Veronique Van Speybroeck, John M. Wills, Jonathan R. Yates, Guo-Xu
Materials and MethodsWe compared 40 DFT methods in terms of the ∆ gauge. ∆ expresses the root-mean-square
difference between the equations of state of two codes, averaged over a benchmark set of 71elemental crystals. The space groups and magnetic states for these crystals are listed in Ta-ble S1. The cif-files for these structures, as well as the ∆ calculation script, can be found in theSupplementary Material of Reference (26).
As mentioned in the main article, the ∆ value between codes a and b for element i is definedby:
∆i(a, b) =
√√√√√1.06V0,i∫
0.94V0,i
(Eb,i(V ) − Ea,i(V ))2
0.12V0,i
dV (1)
which is then averaged over every crystal in the benchmark set. Although V0,i was originallyproposed to represent the equilibrium volume predicted by the WIEN2k code, the results reportedhere are based on the average equilibrium volume of codes a and b to allow for a more symmetriccomparison (Delta calculation package version 3.0 (66)).
To maximize the comparability of the codes, the following protocol is used. Ea,i(V ) andEb,i(V ) are obtained by performing a 4-parameter Birch-Murnaghan fit (67) to 7 equidistantE(V ) data points between 0.94Vcif,i and 1.06Vcif,i (with Vcif,i the volume in the cif file). Theenergy is moreover shifted in such a way that the energy at the fitted equilibrium volume is zero.Only for FHI-aims, GBRV12/ABINIT, GPAW09/ABINIT, GPAW09/GPAW, Vdb2/DACAPO,FHI98pp/ABINIT, and HGH/ABINIT was the lattice constant instead varied over 5 equidis-tant points in a ±2 % interval, but we found the ∆ values of both approaches to differ by less than0.1 meV/atom. To avoid artefacts due to different geometry optimizers, only the volume of theelemental crystal is scaled; the cell shape and atomic positions are not relaxed. This guaranteesthat every evaluated code calculates exactly the same crystals in exactly the same geometries. Ev-erything is calculated at the scalar relativistic level. Finally, computational settings are taken ashigh as possible (basis set size, number of k-points, ...) to ensure that all results are numericallyconverged.
The definition (1) naturally leads to larger ∆ values when the bulk modulus increases, be-cause the equation of state over a given volume interval also reaches higher energies. To obtain amore relative energy difference, Jollet et al. rescaled each ∆i to the value for an average volumeVref and bulk modulus Bref (27):
∆1,i(a, b) =VrefBref
V0,iB0,i
∆i(a, b) (2)
leading to an average of ∆1. An equivalent approach is to divide each ∆i by the average rms-
2
height of the equation of state:
∆rel,i(a, b) = 2
√√√√√√√√√
1.06V0,i∫0.94V0,i
(Eb,i(V ) − Ea,i(V ))2 dV
1.06V0,i∫0.94V0,i
(Eb,i(V ) + Ea,i(V ))2 dV
(3)
Both methods were implemented in the ∆ calculation package 3.0 (66).Kucukbenli et al., on the other hand, defined ∆′ (and analogously ∆′
1) to obtain a rigorousdistance measure, satisfying the triangular inequality between three codes or methods (28):
∆′i(a, b) =
√√√√√√
1.06Vcif,i∫
0.94Vcif,i
(Eb,i(V ) − Ea,i(V ))2
0.12Vcif,i
dV (4)
They used the EOS central volume Vcif,i, which is based on a VASP geometry optimization, as areference.
Fig. S1. ∆-values between all considered DFT methods (in meV/atom). Methods are listedalphabetically for each of four categories, i.e. all-electron (AE), PAW, ultrasoft (USPP) andnorm-conserving pseudopotential methods (NCPP). The tags stand for code, code/specifi-cation (AE) or potential set/code (PAW/USPP/NCPP), and are explained in full inTables S3–S42. The colour code ranges from green over yellow to red (small to large ∆ values).The mixed potential set SSSP was added to the ultrasoft category, in agreement with its prevalentpotential type. Both the code settings and the DFT-predicted equation-of-state parameters behindthese numbers are listed in Tables S3–S42.
4
Table S1. Reference structures for the calculation of the ∆ gauge. Elemental crystal struc-tures are represented by their space group number (top) and in the Pearson notation (middle)(with hRx standing for x atoms in the hexagonal setting of the rhombohedral unit cell). The tagon the bottom indicates the magnetic state of each elemental crystal: nm stands for nonmagnetic,fm for ferromagnetic and afm for antiferromagnetic.
5
Table S2. Precision as a function of numerical convergence. For some all-electron codes,i.e. FHI-aims, FPLO and WIEN2k, the influence of numerical settings on equation-of-state isdemonstrated. Results are expressed in terms of ∆ (in meV/atom) and are referenced with re-spect to the ultimate-precision settings. The corresponding code settings and the DFT-predictedequation-of-state parameters are listed in Tables S5 (FHI-aims default, FHI-aims/tight), Ta-bles S9 (FPLO default, FPLO/default), Tables S13 (WIEN2k default, WIEN2k/default),Tables S6 (FHI-aims enhanced, FHI-aims/really tight), Tables S10 (FPLO enhanced,FPLO/T+F), Tables S14 (WIEN2k enhanced, WIEN2k/enhanced), Tables S7 (FHI-aimsultimate, FHI-aims/tier2), Tables S11 (FPLO ultimate, FPLO/T+F+s) and Tables S15(WIEN2k ultimate, WIEN2k/acc). The ultimate-precision results are the ones used in Fig. 4 ofthe main article.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S3.2basis set size see Table S3.2 (Rmin
MT Kmax)k-mesh density see Table S3.2 (k-mesh in the full 1st Brillouin zone of
the primitive cell)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.0005 Ha
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S3.2 (RMT )radial mesh 200-700 radial mesh points on a logarithmic grid
up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 12
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 9density and potential
ADDITIONAL COMMENTS
Use Elk version 3.1.5 or beyond. Set the internal flag vhighq to .True. for a highly accurate calculation togetherwith the k-mesh and core-valence partition in the table in order to acquire the results described here.
7
Table S3.2. Elk calculation settings and results per element. Muffin-tin radius RMT , basisset size Rmin
MTKmax, k-mesh in the full 1st Brillouin zone of the primitive cell kpts, valence,equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
valence scalar relativistic (IORA) (53 )assignment of core / valence states see Table S4.2basis set size see Table S4.2 (Rmin
MT Kmax)k-mesh density see Table S4.2 (k-mesh in the full 1st Brillouin zone of
the primitive cell)reciprocal-space integration method Gaussian smearing with a fictitious
temperature corresponding to 0.001 Ry
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S4.2 (RMT )radial mesh 400–1500 radial mesh points on an inverse
cubic grid up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 12
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 12density and potential
largest vector in Fourier expansion 35a−10 for I,
of charge density 40a−10 for H, He, O, Cl, Ar and Xe,
45a−10 for Ne
and 30a−10 for remaining elements
ADDITIONAL COMMENTS
none
10
Table S4.2. exciting calculation settings and results per element. Muffin-tin radius RMT ,basis set size Rmin
MTKmax, k-point mesh in the full 1st Brillouin zone of the primitive cell kpts,valence, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk mod-ulus B1.
Eqs. (55)/(56) of (42)assignment of core / valence states treated on equal footingbasis set size default for “tight” settings – see Table S5.2k-mesh density see Table S5.3 (k-point grid kpts, and the number of
irreducible k-points in the full 1st Brillouin zoneof the primitive cell # k)
reciprocal-space integration method Gaussian smearing with a fictitiousbroadening corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
Hartree potential lhartree = 6multicentre expansionlogarithmic mesh for free-atom see Table S5.2 (number of points # Nlog betweenquantities 0.001/Z and 100.0 bohr)radial integration mesh see Table S5.2 (number of shells per atom # Nrad,
distributed according to Eq. (18) of (42))anchor distance of radial int. mesh 7 Asmallest (innermost) Lebedev grid 110 pointslargest (outermost) Lebedev grid 434 pointsbasis function confinement ronset see Table S5.2, w = 2.0 A
Eq. (9) of (42)
ADDITIONAL COMMENTS
Radial integration mesh:The “anchor distance of the radial mesh” is the radius of the second-most distant radial integration shell,specified by the “radial base” keyword in FHI-aims. A detailed explanation of the construction of radialintegration grids in FHI-aims can be found in the Appendix of (70).
Basis set character and angular momenta:The set of radial functions used is characterized according to their angular momenta. Each basis setconsists of the core and valence radial functions of a spherical free atom and further groups of radialfunctions, organized in “tiers” (levels). For each element, the table lists the closest noble gas configuration+ valence shells included in the free atom + default radial functions for “tight” settings.
The ASE script (46) used to generate these data is available online (48).
13
Table S5.2. FHI-aims/tight basis function settings per element. Basis set size, numberof logarithmic grid points Nlog, number of radial grid points Nrad and basis function onset radiusronset.
Table S5.3. FHI-aims/tight calculation settings and results per element. k-point meshin the full 1st Brillouin zone of the primitive cell kpts and number of irreducible k-points # k,equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
kpts [–] # k [–] V0 [A3/atom] B0 [GPa] B1 [–]H 28 x 28 x 20 7840 17.3962 10.3122 2.7059He 40 x 40 x 22 17600 18.0531 0.8652 0.5915Li 38 x 38 x 38 27436 20.2567 13.8364 3.5623Be 52 x 52 x 28 37856 7.9071 123.6848 3.4431B 26 x 26 x 24 8112 7.2391 237.5952 3.4102C 48 x 48 x 12 13824 11.6294 209.0859 3.5920N 16 x 16 x 16 2048 28.8022 54.0235 3.6858O 26 x 24 x 24 7488 18.5125 51.3340 3.9229F 16 x 28 x 14 3136 19.1428 34.2611 4.0537Ne 22 x 22 x 22 5324 24.4318 1.1094 7.0758Na 32 x 32 x 32 16384 37.4501 7.7355 3.6748Mg 36 x 36 x 20 12960 23.0275 36.2098 3.9417Al 24 x 24 x 24 6912 16.4910 77.7480 5.0823Si 32 x 32 x 32 16384 20.4816 88.4431 4.2398P 30 x 8 x 22 2640 21.4463 68.2171 4.3542S 38 x 38 x 38 27436 17.2140 83.8991 4.0258Cl 12 x 24 x 12 1728 38.8495 18.9573 4.3883Ar 16 x 16 x 16 2048 52.8424 0.7432 7.5319K 20 x 20 x 20 4000 73.7482 3.6144 4.0770Ca 18 x 18 x 18 2916 42.2587 17.6785 3.4926Sc 34 x 34 x 20 11560 24.5979 55.2055 3.3369Ti 40 x 40 x 22 17600 17.3744 112.5817 3.6003V 34 x 34 x 34 19652 13.4454 182.7162 3.9668Cr 36 x 36 x 36 23328 11.7796 182.8542 7.0136Mn 28 x 28 x 28 10976 11.3916 120.6594 0.0158Fe 36 x 36 x 36 23328 11.3130 196.5445 4.8490Co 46 x 46 x 24 25392 10.8582 214.0374 4.6214Ni 28 x 28 x 28 10976 10.8904 198.4243 4.9492Cu 28 x 28 x 28 10976 11.9694 140.2334 5.0546Zn 44 x 44 x 20 19360 15.2241 74.4107 5.2677Ga 22 x 12 x 22 2904 20.3697 48.9570 5.4808Ge 30 x 30 x 30 13500 23.9581 59.2613 4.9265As 30 x 30 x 10 4500 22.6350 68.0797 4.2800Se 26 x 26 x 20 6760 29.8545 46.8488 4.4591Br 12 x 24 x 12 1728 39.6550 22.2302 4.8489Kr 16 x 16 x 16 2048 66.6112 0.6016 7.2097Rb 18 x 18 x 18 2916 93.1829 2.6807 3.6910Sr 16 x 16 x 16 2048 54.9431 10.2226 5.9551Y 32 x 32 x 18 9216 32.8086 42.1174 3.0932Zr 36 x 36 x 20 12960 23.3839 94.2078 3.3116Nb 30 x 30 x 30 13500 18.1072 171.2023 3.6924Mo 32 x 32 x 32 16384 15.7737 261.8191 4.3708Tc 42 x 42 x 22 19404 14.4183 301.9407 4.5713Ru 42 x 42 x 24 21168 13.7499 314.2909 4.9149Rh 26 x 26 x 26 8788 14.0416 257.7568 5.2159
16
Pd 26 x 26 x 26 8788 15.3243 169.0745 5.5660Ag 24 x 24 x 24 6912 17.8657 90.6303 6.0521Cd 38 x 38 x 18 12996 22.8702 43.6603 6.9053In 30 x 30 x 20 9000 27.5167 35.8111 5.0756Sn 26 x 26 x 26 8788 36.9687 35.7730 5.0415Sb 26 x 26 x 8 2704 31.8284 50.1747 4.5919Te 26 x 26 x 16 5408 35.1597 44.3034 4.7039I 12 x 22 x 10 1320 50.6789 18.4046 5.0541Xe 14 x 14 x 14 1372 88.0742 0.4745 5.6768Cs 16 x 16 x 16 2048 120.5143 2.0882 3.0910Ba 20 x 20 x 20 4000 63.5384 8.6375 1.6486Lu 32 x 32 x 18 9216 29.1181 47.6255 3.3819Hf 36 x 36 x 20 12960 22.5453 107.8083 3.3978Ta 30 x 30 x 30 13500 18.2850 194.4320 3.5048W 32 x 32 x 32 16384 16.1354 303.1029 4.1867Re 42 x 42 x 22 19404 14.9498 365.0171 4.4286Os 42 x 42 x 24 21168 14.2745 398.3862 4.8135Ir 26 x 26 x 26 8788 14.5011 347.9583 5.1384Pt 26 x 26 x 26 8788 15.6488 248.7646 5.4799Au 24 x 24 x 24 6912 17.9711 139.4401 5.9992Hg 24 x 24 x 28 8064 29.8640 7.1374 10.2806Tl 32 x 32 x 18 9216 31.4701 26.3197 5.5324Pb 20 x 20 x 20 4000 31.9992 39.5202 5.6947Bi 26 x 26 x 8 2704 36.9530 42.6549 4.6156Po 30 x 30 x 30 13500 37.6237 45.1643 4.9981Rn 14 x 14 x 14 1372 93.9401 0.5193 6.4423
17
Table S6.1. Overview of the most important features and settings of theFHI-aims/really tight calculations.
FHI-aims/really tight
name and version of the code: FHI-aims 081213 (42, 70)type of basis set: numeric atom-centred orbital basis functionsmethod: all-electron
Eqs. (55)/(56) of (42)assignment of core / valence states treated on equal footingbasis set size default for “really tight” settings – see Table S6.2k-mesh density see Table S6.3 (k-point grid kpts, and the number of
irreducible k-points in the full 1st Brillouin zoneof the primitive cell # k)
reciprocal-space integration method Gaussian smearing with a fictitiousbroadening corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
Hartree potential lhartree = 8multicentre expansionlogarithmic mesh for free-atom see Table S6.2 (number of points # Nlog betweenquantities 0.001/Z and 100.0 bohr)radial integration mesh see Table S6.2 (number of shells per atom # Nrad,
distributed according to Eq. (18) of (42))anchor distance of radial int. mesh 7 Asmallest (innermost) Lebedev grid 110 pointslargest (outermost) Lebedev grid 590 pointsbasis function confinement ronset see Table S6.2, w = 2.0 A
Eq. (9) of (42)
ADDITIONAL COMMENTS
Radial integration mesh:The “anchor distance of the radial mesh” is the radius of the second-most distant radial integration shell,specified by the “radial base” keyword in FHI-aims. A detailed explanation of the construction of radialintegration grids in FHI-aims can be found in the Appendix of (70).
Basis set character and angular momenta:The set of radial functions used is characterized according to their angular momenta. Each basis setconsists of the core and valence radial functions of a spherical free atom and further groups of radialfunctions, organized in “tiers” (levels). For each element, the table lists the closest noble gas configuration+ valence shells included in the free atom + default radial functions for “really tight” settings.
The ASE script (46) used to generate these data is available online (48).
18
Table S6.2. FHI-aims/really tight basis function settings per element. Basis set size,number of logarithmic grid points Nlog, number of radial grid points Nrad and basis functiononset radius ronset.
Table S6.3. FHI-aims/really tight calculation settings and results per element. k-point mesh in the full 1st Brillouin zone of the primitive cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
kpts [–] # k [–] V0 [A3/atom] B0 [GPa] B1 [–]H 28 x 28 x 20 7840 17.3955 10.3244 2.7385He 40 x 40 x 22 17600 18.0461 0.8494 1.1724Li 38 x 38 x 38 27436 20.2584 13.8120 3.4520Be 52 x 52 x 28 37856 7.9069 123.7151 3.4723B 26 x 26 x 24 8112 7.2393 237.3241 3.4365C 48 x 48 x 12 13824 11.6300 209.1781 3.5981N 16 x 16 x 16 2048 28.8025 54.0466 3.6934O 26 x 24 x 24 7488 18.5125 51.3380 3.9259F 16 x 28 x 14 3136 19.1427 34.2735 4.0643Ne 22 x 22 x 22 5324 24.4391 1.1878 6.9161Na 32 x 32 x 32 16384 37.4512 7.7498 3.6534Mg 36 x 36 x 20 12960 23.0276 36.2237 3.9165Al 24 x 24 x 24 6912 16.4906 77.6090 5.0682Si 32 x 32 x 32 16384 20.4816 88.4550 4.2422P 30 x 8 x 22 2640 21.4475 68.2086 4.3350S 38 x 38 x 38 27436 17.2129 83.8978 4.0272Cl 12 x 24 x 12 1728 38.8503 18.9735 4.3515Ar 16 x 16 x 16 2048 52.8166 0.7159 8.6188K 20 x 20 x 20 4000 73.7990 3.5420 3.6339Ca 18 x 18 x 18 2916 42.2586 17.6922 3.5068Sc 34 x 34 x 20 11560 24.5982 55.1859 3.3562Ti 40 x 40 x 22 17600 17.3742 112.5512 3.6095V 34 x 34 x 34 19652 13.4447 182.7881 3.9742Cr 36 x 36 x 36 23328 11.7791 182.8957 7.0271Mn 28 x 28 x 28 10976 11.3898 120.8318 0.0489Fe 36 x 36 x 36 23328 11.3124 196.5112 4.8600Co 46 x 46 x 24 25392 10.8581 214.0187 4.6290Ni 28 x 28 x 28 10976 10.8897 198.4342 4.9314Cu 28 x 28 x 28 10976 11.9697 140.2311 5.0538Zn 44 x 44 x 20 19360 15.2233 74.3654 5.3050Ga 22 x 12 x 22 2904 20.3706 49.0547 5.4655Ge 30 x 30 x 30 13500 23.9595 59.2474 4.9094As 30 x 30 x 10 4500 22.6362 68.0924 4.2943Se 26 x 26 x 20 6760 29.8549 46.8519 4.4654Br 12 x 24 x 12 1728 39.6548 22.2281 4.8550Kr 16 x 16 x 16 2048 66.5689 0.6176 6.7113Rb 18 x 18 x 18 2916 93.2587 2.6583 3.3988Sr 16 x 16 x 16 2048 54.9390 10.2206 5.9713Y 32 x 32 x 18 9216 32.8087 42.1152 3.0595Zr 36 x 36 x 20 12960 23.3835 94.2045 3.3246Nb 30 x 30 x 30 13500 18.1056 171.3739 3.7435Mo 32 x 32 x 32 16384 15.7738 261.7850 4.3718Tc 42 x 42 x 22 19404 14.4184 301.9200 4.5750Ru 42 x 42 x 24 21168 13.7500 314.2912 4.9135Rh 26 x 26 x 26 8788 14.0413 257.7028 5.2127
21
Pd 26 x 26 x 26 8788 15.3236 169.1674 5.5597Ag 24 x 24 x 24 6912 17.8646 90.6812 6.0497Cd 38 x 38 x 18 12996 22.8703 43.6359 6.8925In 30 x 30 x 20 9000 27.5272 35.8265 4.8812Sn 26 x 26 x 26 8788 36.9675 35.7455 5.0669Sb 26 x 26 x 8 2704 31.8318 50.1728 4.5787Te 26 x 26 x 16 5408 35.1605 44.3231 4.6968I 12 x 22 x 10 1320 50.6794 18.4117 5.0405Xe 14 x 14 x 14 1372 87.8741 0.5371 6.8563Cs 16 x 16 x 16 2048 120.5269 2.0693 3.0468Ba 20 x 20 x 20 4000 63.4673 8.6386 1.7559Lu 32 x 32 x 18 9216 29.1190 47.5978 3.3767Hf 36 x 36 x 20 12960 22.5451 107.8392 3.3980Ta 30 x 30 x 30 13500 18.2845 194.5152 3.4984W 32 x 32 x 32 16384 16.1348 303.1631 4.2057Re 42 x 42 x 22 19404 14.9498 364.9963 4.4396Os 42 x 42 x 24 21168 14.2746 398.3392 4.8159Ir 26 x 26 x 26 8788 14.5006 347.9727 5.1331Pt 26 x 26 x 26 8788 15.6484 248.9114 5.4790Au 24 x 24 x 24 6912 17.9699 139.3879 6.0004Hg 24 x 24 x 28 8064 29.8634 7.1355 10.2613Tl 32 x 32 x 18 9216 31.4711 26.3250 5.5058Pb 20 x 20 x 20 4000 31.9976 39.5440 5.7070Bi 26 x 26 x 8 2704 36.9551 42.6522 4.6769Po 30 x 30 x 30 13500 37.6207 45.2537 5.0490Rn 14 x 14 x 14 1372 93.5297 0.5336 6.4481
22
Table S7.1. Overview of the most important features and settings of the FHI-aims/tier2calculations.
FHI-aims/tier2
name and version of the code: FHI-aims 081213 (42, 70)type of basis set: numeric atom-centred orbital basis functionsmethod: all-electron
Eqs. (55)/(56) of (42)assignment of core / valence states treated on equal footingbasis set size tier2 – see Table S7.2k-mesh density see Table S7.3 (k-point grid kpts, and the number of
irreducible k-points in the full 1st Brillouin zoneof the primitive cell # k)
reciprocal-space integration method Gaussian smearing with a fictitiousbroadening corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
Hartree potential lhartree = 8multicentre expansionlogarithmic mesh for free-atom see Table S7.2 (number of points # Nlog betweenquantities 0.001/Z and 100.0 bohr)radial integration mesh see Table S7.2 (number of shells per atom # Nrad,
distributed according to Eq. (18) of (42))anchor distance of radial int. mesh 7 Asmallest (innermost) Lebedev grid 110 pointslargest (outermost) Lebedev grid 590 pointsbasis function confinement ronset see Table S7.2, w = 2.0 A
Eq. (9) of (42)
ADDITIONAL COMMENTS
Radial integration mesh:The “anchor distance of the radial mesh” is the radius of the second-most distant radial integration shell,specified by the “radial base” keyword in FHI-aims. A detailed explanation of the construction of radialintegration grids in FHI-aims can be found in the Appendix of (70).
Basis set character and angular momenta:The set of radial functions used is characterized according to their angular momenta. Each basis setconsists of the core and valence radial functions of a spherical free atom and further groups of radialfunctions, organized in “tiers” (levels). For each element, the table lists the closest noble gas configuration+ valence shells included in the free atom + tier1 + tier2 radial functions.
The ASE script (46) used to generate these data is available online (48).
23
Table S7.2. FHI-aims/tier2 basis function settings per element. Basis set size, numberof logarithmic grid points Nlog, number of radial grid points Nrad and basis function onset radiusronset.
Table S7.3. FHI-aims/tier2 calculation settings and results per element. k-point meshin the full 1st Brillouin zone of the primitive cell kpts and number of irreducible k-points # k,equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
kpts [–] # k [–] V0 [A3/atom] B0 [GPa] B1 [–]H 28 x 28 x 20 7840 17.3955 10.3244 2.7385He 40 x 40 x 22 17600 18.0461 0.8494 1.1724Li 38 x 38 x 38 27436 20.2584 13.8120 3.4520Be 52 x 52 x 28 37856 7.9069 123.7151 3.4723B 26 x 26 x 24 8112 7.2393 237.3241 3.4365C 48 x 48 x 12 13824 11.6300 209.1781 3.5981N 16 x 16 x 16 2048 28.8025 54.0466 3.6934O 26 x 24 x 24 7488 18.5125 51.3380 3.9259F 16 x 28 x 14 3136 19.1427 34.2735 4.0643Ne 22 x 22 x 22 5324 24.4391 1.1878 6.9161Na 32 x 32 x 32 16384 37.0854 7.7625 3.7955Mg 36 x 36 x 20 12960 22.9569 35.9978 3.9894Al 24 x 24 x 24 6912 16.4921 77.7749 5.0377Si 32 x 32 x 32 16384 20.4535 88.6201 4.2489P 30 x 8 x 22 2640 21.4435 68.1001 4.3366S 38 x 38 x 38 27436 17.2125 83.9136 4.0230Cl 12 x 24 x 12 1728 38.8211 18.9341 4.3405Ar 16 x 16 x 16 2048 52.4645 0.7327 8.6099K 20 x 20 x 20 4000 73.8148 3.5802 3.6558Ca 18 x 18 x 18 2916 42.2161 17.6892 3.4734Sc 34 x 34 x 20 11560 24.6089 54.6364 3.3974Ti 40 x 40 x 22 17600 17.3902 111.5900 3.6297V 34 x 34 x 34 19652 13.4479 182.2043 3.9567Cr 36 x 36 x 36 23328 11.7715 185.0625 6.9532Mn 28 x 28 x 28 10976 11.4777 119.6118 0.0802Fe 36 x 36 x 36 23328 11.3392 194.4014 4.6849Co 46 x 46 x 24 25392 10.8513 214.1797 4.6796Ni 28 x 28 x 28 10976 10.8872 198.1638 4.9449Cu 28 x 28 x 28 10976 11.9615 140.0409 5.2277Zn 44 x 44 x 20 19360 15.1941 75.4154 5.5155Ga 22 x 12 x 22 2904 20.3013 49.1819 5.4723Ge 30 x 30 x 30 13500 23.8905 59.3238 4.9369As 30 x 30 x 10 4500 22.5901 68.2982 4.2925Se 26 x 26 x 20 6760 29.7404 47.0304 4.4686Br 12 x 24 x 12 1728 39.4566 22.3752 4.8436Kr 16 x 16 x 16 2048 66.2448 0.6297 6.6440Rb 18 x 18 x 18 2916 91.1656 2.8045 3.5574Sr 16 x 16 x 16 2048 54.3677 11.4507 5.3802Y 32 x 32 x 18 9216 32.8355 41.4725 3.1396Zr 36 x 36 x 20 12960 23.3940 93.7535 3.2944Nb 30 x 30 x 30 13500 18.1270 170.4048 3.7274Mo 32 x 32 x 32 16384 15.7887 259.4884 4.3507Tc 42 x 42 x 22 19404 14.4381 299.1265 4.5298Ru 42 x 42 x 24 21168 13.7635 312.1158 4.8757Rh 26 x 26 x 26 8788 14.0431 257.0866 5.1885
26
Pd 26 x 26 x 26 8788 15.3106 168.8863 5.5095Ag 24 x 24 x 24 6912 17.8455 91.0431 5.9975Cd 38 x 38 x 18 12996 22.8392 43.9964 6.9580In 30 x 30 x 20 9000 27.5167 35.8699 4.8709Sn 26 x 26 x 26 8788 36.8318 35.8545 5.0021Sb 26 x 26 x 8 2704 31.7533 50.3972 4.5283Te 26 x 26 x 16 5408 34.9740 44.7145 4.6885I 12 x 22 x 10 1320 50.2501 18.6164 5.0436Xe 14 x 14 x 14 1372 86.8790 0.5681 7.2531Cs 16 x 16 x 16 2048 116.7703 2.0044 4.1222Ba 20 x 20 x 20 4000 63.0761 8.8520 2.2069Lu 32 x 32 x 18 9216 29.0652 47.0124 3.5308Hf 36 x 36 x 20 12960 22.5418 107.5910 3.4407Ta 30 x 30 x 30 13500 18.2835 193.6651 3.5015W 32 x 32 x 32 16384 16.1399 301.5926 4.2144Re 42 x 42 x 22 19404 14.9559 363.3583 4.4155Os 42 x 42 x 24 21168 14.2799 396.7276 4.8143Ir 26 x 26 x 26 8788 14.4993 347.6047 5.2287Pt 26 x 26 x 26 8788 15.6401 248.0916 5.4707Au 24 x 24 x 24 6912 17.9752 138.6731 6.1054Hg 24 x 24 x 28 8064 29.5950 7.7226 9.8983Tl 32 x 32 x 18 9216 31.4374 26.6619 5.5187Pb 20 x 20 x 20 4000 31.9622 39.9991 5.6218Bi 26 x 26 x 8 2704 36.9073 42.5965 4.6508Po 30 x 30 x 30 13500 37.5659 45.4307 5.0102Rn 14 x 14 x 14 1372 93.0392 0.5344 6.8771
27
Table S8.1. Overview of the most important features and settings of the FLEUR calcula-tions.
FLEUR
name and version of the code: FLEUR 0.26 (71)type of basis set: linearized augmented plane waves (+ local orbitals)method: all-electron
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S8.2basis set size see Table S8.2 (Kmax)k-mesh density see Table S8.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.001 Ry
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S8.2 (RMT)radial mesh 981 radial mesh points on a logarithmic grid
up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 6
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 12density and potential
largest vector in Fourier expansion 3 × the magnitude of Kmax
of charge density
ADDITIONAL COMMENTS
if RMT ≤ 1.5 an APW+lo basisset was used
28
Table S8.2. FLEUR calculation settings and results per element. Muffin-tin radius RMT,maximum wavevector Kmax, number of k-points in the full 1st Brillouin zone of the primitivecell # k, semicore and valence shells, equilibrium volume per atom V0, bulk modulus B0, pressurederivative of the bulk modulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Section additional comments and Table S9.2basis set size default (see below): 5-33 basis orbitals
(typical basis set size of 20)k-mesh density see Table S9.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method linear tetrahedron method (72)
METHOD-SPECIFIC INFORMATION
numerical settings all settings are default settings except fork-mesh (see Table S9.2)
ADDITIONAL COMMENTS
In Table S9.2, the basis set is denoted in the following way: semi-core orbitals are separated by a /, Dnlmeans double basis orbitals, e.g. D3p=3p4p. Ultra soft elements require a (non default) fixed compact supportradius (as was used in the FPLO/T+F+s set of calculations, see Table S11.1). For this reason some of thoseelements (Xe, Rn, Hg) are excluded from the tables. The use of the linear tetrahedron method allows to keepthe relatively small default k-mesh, except for the cases C, Al, Ag, where we used a higher k-point numberfor testing reasons.
31
Table S9.2. FPLO/default calculation settings and results per element. k-point meshin the full 1st Brillouin zone of the primitive cell kpts and number of irreducible k-points #k, valence, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Section additional comments and Table S10.2basis set size enhanced (see below): 21-56 basis orbitals
(typical basis set size of 35)k-mesh density see Table S10.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method linear tetrahedron method (72)
METHOD-SPECIFIC INFORMATION
numerical settings all settings are default settingsexcept for the basis and k-mesh(see below and Table S10.2).
ADDITIONAL COMMENTS
We enhanced the default basis according to the following scheme. The core and semi-core orbitals stayuntouched. A double valence basis orbital (e.g. 3d4d) becomes a triple basis orbital (e.g. 3d4d5d) withthe charge parameter Q3 = Q2 + 2 and compression parameter P3 = max(0.85, P2). A single valence basisorbital becomes a double basis orbital with Q2 = Q1 + 2 and P2 = max(0.85, P1). An additional f-orbital isadded with Q = 4 and P = 1. For H and He additionally a single d-orbital (Q = 5, P = 1) is added to thedefault basis. In Table S10.2, the basis set is denoted in the following way: semi-core orbitals are separated bya /, Dnl means double basis orbitals, e.g. D3p=3p4p, Tnl means triple basis orbitals, e.g. T3p=3p4p5p. Theadditional nominal 5f orbital for Lu is of course not identical to the 5f part of its T4f basis states but rather aneffective 7f state. Ultra soft elements require a (non default) fixed compact support radius (as was used in theFPLO/T+F+s set of calculations, see Table S11.1). For this reason some of those elements (Xe, Rn, Hg) areexcluded from the tables. The use of the linear tetrahedron method allows to keep the relatively small defaultk-mesh, except for the cases C, Al, Ag, where we used a higher k-point number for testing reasons.
34
Table S10.2. FPLO/T+F calculation settings and results per element. k-point mesh in thefull 1st Brillouin zone of the primitive cell kpts and number of irreducible k-points # k, valence,equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Section additional comments and Table S11.2basis set size enhanced (see below): 21-56 basis orbitals
(typical basis set size of 35)k-mesh density see Table S11.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method linear tetrahedron method (72)
METHOD-SPECIFIC INFORMATION
numerical settings all settings are default settingsexcept for the basis, the compact support andk-mesh (see below and Table S11.2).
ADDITIONAL COMMENTS
We enhanced the default basis according to the following scheme. The core and semi-core orbitals stay untouched.A double valence basis orbital (e.g. 3d4d) becomes a triple basis orbital (e.g. 3d4d5d) with the charge parameterQ3 = Q2 + 2 and compression parameter P3 = max(0.85, P2). A single valence basis orbital becomes a doublebasis orbital with Q2 = Q1 + 2 and P2 = max(0.85, P1). An additional f-orbital is added with Q = 4 and P = 1.For H and He additionally a single d-orbital (Q = 5, P = 1) is added to the default basis. The compact supportradius was fixed for all volumes to its default value at the equilibrium volume. This option is only needed for verysoft elements. We use it for all elements for consistency. In Table S11.2, the basis set is denoted in the followingway: semi-core orbitals are separated by a /, Dnl means double basis orbitals, e.g. D3p=3p4p, Tnl means triple basisorbitals, e.g. T3p=3p4p5p. The additional nominal 5f orbital for Lu is of course not identical to the 5f part of its T4fbasis states but rather an effective 7f state. The use of the linear tetrahedron method allows to keep the relativelysmall default k-mesh, except for the cases C, Al, Ag, where we used a higher k-point number for testing reasons.
37
Table S11.2. FPLO/T+F+s calculation settings and results per element. k-point mesh in thefull 1st Brillouin zone of the primitive cell kpts and number of irreducible k-points # k, valence,equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S12.2basis set size see Table S12.2k-mesh density see Table S12.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method modified tetrahedron method on a Fourier
quadrature mesh (73)
METHOD-SPECIFIC INFORMATION
muffin-tin radii 95% of touching, rescaled with volume,except for O and Xe, which had fixedradii of 1.10 and 2.70 bohr radii, respectively
radial mesh 450-600 radial mesh points on a logarithmicgrid, selected automatically.
wave function ` cutoff 8potential and density ` cutoff 8interstitial Fourier mesh see Table S12.2
basis set specification
The default choice (repository revision 1904) is described by the letter ‘V’, indicating ‘valence’, i.e. basisfunctions corresponding to the selected valence electrons, always including s, p and d basis functions abovethe completely filled semi-core shells. Basis functions for the interstitial are spherical Hankel functions atkinetic energies 0.3, -0.6 and -2.3 Ry, the first one being replaced by the average kinetic energy over theinterstitial. s and p basis functions are by default attached to all three tails, d functions, occupied f functionsand semi-core states to tails 1 and 2 and higher polarization functions are attached to only the “interstitialaverage” tail. The most common basis setting is then describable as V+4f, indicating that f electrons wereadded to the normal setting.More complex variations are denoted by specifically singling out the modified shells and describe themseparately after the ‘V+’ symbol, specifying the choice of linearization energy in parentheses () andattached tails in square brackets []. For example, the Na basis (V+4f, including 2s, 2p and 3s electrons)could explicitly be given as:2s(0)[1,2] 2p(0)[1,2] 3s(20)[1,2,3] 3s(21)[1,2,3] 3d(0)[1,2] 4f(0)[1]The meaning of the choices of linearization energies are explained in the RSPt manual.
ADDITIONAL COMMENTS
The LMTO basis set required for high accuracy varies predictably across the periodic table, with the notableexception of Cl, which required a very large basis. The reason for this anomaly is not clear, but goodconvergence was nevertheless achievable. This appears to be a special feature of the Cl dimeric crystalwhich has not been observed in other Cl compounds. A very large basis was also required for the 5d series,where a crossover of the 4f and 5p semi-core bands occur.
40
Table S12.2. RSPt calculation settings and results per element. Basis (see explanation under‘basis set specification’, Table S12.1), interstitial Fourier mesh, number of k-points in the full 1stBrillouin zone of the primitive cell # k, valence, equilibrium volume per atom V0, bulk modulusB0, pressure derivative of the bulk modulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S13.2basis set size see Table S13.2 (Rmin
MT Kmax)k-mesh density see Table S13.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.001 Ry
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S13.2 (RMT )radial mesh 781 radial mesh points on a logarithmic grid
up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 6
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 6density and potential
largest vector in Fourier expansion 3 × the magnitude of the smallest vectorof charge density
IFFT-factor 4
ADDITIONAL COMMENTS
none
43
Table S13.2. WIEN2k/default calculation settings and results per element. Muffin-tinradius RMT , basis set size Rmin
MTKmax, number of k-points in the full 1st Brillouin zone of theprimitive cell # k, valence, equilibrium volume per atom V0, bulk modulus B0, pressure derivativeof the bulk modulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S14.2basis set size see Table S14.2 (Rmin
MT Kmax)k-mesh density see Table S14.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.001 Ry
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S14.2 (RMT )radial mesh 781 radial mesh points on a logarithmic grid
up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 6
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 6density and potential
largest vector in Fourier expansion 3 × the magnitude of the smallest vectorof charge density
IFFT-factor 4
ADDITIONAL COMMENTS
Compared to WIEN2k/default (Tables S13), this data set uses larger numbers of k-points and largerRmin
MT Kmax, but the muffin-tin radii have remained the same.
46
Table S14.2. WIEN2k/enhanced calculation settings and results per element. Muffin-tinradius RMT , basis set size Rmin
MTKmax, number of k-points in the full 1st Brillouin zone of theprimitive cell # k, valence, equilibrium volume per atom V0, bulk modulus B0, pressure derivativeof the bulk modulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S15.2basis set size see Table S15.2 (Rmin
MT Kmax)k-mesh density see Table S15.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.001 Ry
METHOD-SPECIFIC INFORMATION
muffin-tin radii see Table S15.2 (RMT )radial mesh 781 radial mesh points on a logarithmic grid
up to the muffin-tin radiuslargest `-value of wave function 12largest `-value of nonspherical 6
Hamiltonian and overlap matrixelements inside the spheres
largest `-value in expansion of 6density and potential
largest vector in Fourier expansion 3 × the magnitude of the smallest vectorof charge density
IFFT-factor 4
ADDITIONAL COMMENTS
none
49
Table S15.2. WIEN2k/acc calculation settings and results per element. Muffin-tin radiusRMT , basis set size Rmin
MTKmax, number of k-points in the full 1st Brillouin zone of the primitivecell # k, valence, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of thebulk modulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S16.2 (Zval)basis set size plane-wave cutoff energy = 100 Ryk-mesh density see Table S16.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
energy cutoff for the double grid 300 Ry
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
52
Table S16.2. GBRV12/ABINIT calculation settings and results per element. Valence Zval,k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S17.2 (Zval)basis set size real-space grid spacing = 0.075 Ak-mesh density see Table S17.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.1 eV
METHOD-SPECIFIC INFORMATION
none
ADDITIONAL COMMENTS
none
55
Table S17.2. GPAW06/GPAW calculation settings and results per element. Valence Zval, k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S18.2 (Zval)basis set size plane-wave cutoff energy = 100 Ryk-mesh density see Table S18.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
energy cutoff for the double grid 300 Ry
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
58
Table S18.2. GPAW09/ABINIT calculation settings and results per element. Valence Zval,k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S19.2 (Zval)basis set size real-space grid spacing = 0.08 Ak-mesh density see Table S19.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
none
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
61
Table S19.2. GPAW09/GPAW calculation settings and results per element. Valence Zval, k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S20.2basis set size cutoff energy = 20 Hak-mesh density 6 750/N k-points in the
full first Brillouin zone of an N -atom cellreciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.002 Ha
METHOD-SPECIFIC INFORMATION
PAW radii see Table S20.2 (RPAW )PAW cutoff energy 20 HaPAW cutoff augmentation energy 40 HaPartial-wave basis size 2 elements per `-value
except for H, He, Li (one p element)and Ga, Ge, In, K, Kr, Pb and Sn (one d element)
ADDITIONAL COMMENTS
PAW dataset generator ATOMPAW 3.1.0.2 (82)
64
Table S20.2. JTH01/ABINIT calculation settings and results per element. Valence, PAWradius RPAW , equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S21.2basis set size cutoff energy = 20 Hak-mesh density 6 750/N k-points in the
full first Brillouin zone of an N -atom cellreciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.002 Ha
METHOD-SPECIFIC INFORMATION
PAW radii see Table S21.2 (RPAW )PAW cutoff energy 20 HaPAW cutoff augmentation energy 40 HaPartial-wave basis size 2 elements per `-value
except for H, He, Li (one p element)and In, K, Kr, Pb, Rb and Sn (one d element)
ADDITIONAL COMMENTS
PAW dataset generator ATOMPAW 4.0.0.8 (82)
67
Table S21.2. JTH02/ABINIT calculation settings and results per element. Valence, PAWradius RPAW , equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S24.2 (valence Zval)basis set size see Table S24.2 (cutoff energy Ecut)k-mesh density see Table S24.2 (k-point grid kpts in the full 1st Brillouin
zone of the primitive (∗) or conventional cell)reciprocal-space integration method Blochl tetrahedron method (91)
METHOD-SPECIFIC INFORMATION
FFT grid wavevectors up to 2Gcut = 2√
2meEcut
h2 includedaugmentation charge grid wavevectors up to 4Gcut included
ADDITIONAL COMMENTS
none
76
Table S24.2. VASP2007/VASP calculation settings per element. PAW potential, valenceZval, cutoff energy Ecut, k-mesh in the full 1st Brillouin zone of the conventional cell kpts (ofthe primitive cell for elements with an asterisk∗).
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S25.2 (valence Zval)basis set size see Table S25.2 (cutoff energy Ecut)k-mesh density see Table S25.2 (k-point grid kpts in the full 1st Brillouin
zone of the primitive (∗) or conventional cell)reciprocal-space integration method Blochl tetrahedron method (91)
METHOD-SPECIFIC INFORMATION
FFT grid wavevectors up to 2Gcut = 2√
2meEcut
h2 includedaugmentation charge grid wavevectors up to 4Gcut included
ADDITIONAL COMMENTS
none
81
Table S25.2. VASP2012/VASP calculation settings per element. PAW potential, valenceZval, cutoff energy Ecut, k-mesh in the full 1st Brillouin zone of the conventional cell kpts (ofthe primitive cell for elements with an asterisk∗).
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S26.2 (valence Zval)basis set size see Table S26.2 (cutoff energy Ecut)k-mesh density see Table S26.2 (k-point grid kpts in the full 1st Brillouin
zone of the primitive (∗) or conventional cell)reciprocal-space integration method Blochl tetrahedron method (91)
METHOD-SPECIFIC INFORMATION
FFT grid wavevectors up to 2Gcut = 2√
2meEcut
h2 includedaugmentation charge grid wavevectors up to 4Gcut included
ADDITIONAL COMMENTS
Aspherical contributions from the gradient corrections inside the PAW spheres have been included.
86
Table S26.2. VASPGW2015/VASP calculation settings per element. PAW potential, valenceZval, cutoff energy Ecut, k-mesh in the full 1st Brillouin zone of the conventional cell kpts (ofthe primitive cell for elements with an asterisk∗).
(Koelling-Harmon) (54)assignment of core / valence states see Table S27.2 (Zval)basis set size wave function cutoff = 50 Ryk-mesh density 20× 20× 20reciprocal-space integration method Marzari-Vanderbilt cold smearing (87) with a fictitious
temperature corresponding to 0.002 Ry(0.02 Ry when required to achieve convergence)
METHOD-SPECIFIC INFORMATION
wave function cutoff 50 Rydensity cutoff 250 Ry
ADDITIONAL COMMENTS
none
91
Table S27.2. GBRV12/QE calculation settings and results per element. Valence Zval, equi-librium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
Table S28.1. Overview of the most important features and settings of the GBRV14/CASTEPcalculations.
GBRV14/CASTEP
name and version of the code: CASTEP 9.0 (Hg revision 6666 Jun 05 2015) (92)type of basis set: plane wavesmethod: ultrasoft pseudopotentials (GBRV 1.4 (33, 78))
(Koelling-Harmon) (54)assignment of core / valence states see Table S28.2basis set size cutoff energy = 816 eVk-mesh density see Table S28.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.0754 A
−1
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
METHOD-SPECIFIC INFORMATION
size of FFT grid for augmentation 2 × FFT grid for soft density (Ec,ρ = 16Ec,φ)
ADDITIONAL COMMENTS
Basis set, “fine” FFT grid, k-point density and plane-wave cutoff were chosen uniformly across the periodic ta-ble to achieve high convergence. Less stringent critera, determined individually per element will still give highconvergence in almost all cases at a substantially reduced computational cost.
94
Table S28.2. GBRV14/CASTEP calculation settings and results per element. Valence, Monkhorst-Pack k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irre-ducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of thebulk modulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S29.2 (Zval)basis set size wave function cutoff = 100 Ryk-mesh density see Table S29.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Gaussian smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
wave function cutoff 100 Rydensity cutoff 400 Ry
ADDITIONAL COMMENTS
none
97
Table S29.2. GBRV14/QE calculation settings and results per element. Valence Zval, k-pointmesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
Table S30.1. Overview of the most important features and settings of the OTFG7/CASTEPcalculations.
OTFG7/CASTEP
name and version of the code: CASTEP 8.0 (92)type of basis set: plane wavesmethod: ultrasoft pseudopotentials (“On-The-Fly” Vanderbilt-type version C7 (33))
(Koelling-Harmon) (54)assignment of core / valence states see Table S30.2basis set size cutoff energy = 700 eVk-mesh density see Table S30.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.0125 A
−1
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
METHOD-SPECIFIC INFORMATION
pseudopotential library CASTEP “on-the-fly” method. Default in 7.0, availableas “C7” library in later releases
pseudopotential core radii see Table S30.2 (rc)local channel see Table S30.2 (lloc)non-local core radii 2.0 a0 for Mg, Ca, Ni; 2.61 a0 for Li; 1.6 a0 for N; 1.3 a0
for O; 2.15 a0 for Cu;2.3 a0 for Ag; rc otherwisenumber of projectors mostly 2 per valence l channel, plus 1 per semi-core stateprojector generation KE-Optimized RRKJ - see Table S30.2 for qcaugmentation function pseudization between 0.5 rc and rc dependent on element
radiuspseudization radius for NLCC core same as for augmentation functions
chargesize of FFT grid for augmentation 1.5 × FFT grid for soft density (Ec,ρ = 9Ec,φ)
ADDITIONAL COMMENTS
none
100
Table S30.2. OTFG7/CASTEP calculation settings and results per element. Valence, pseu-dopotential core radius rc, local channel lloc, projector wave vector cutoff qc, Monkhorst-Packk-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
Table S31.1. Overview of the most important features and settings of the OTFG9/CASTEPcalculations.
OTFG9/CASTEP
name and version of the code: CASTEP 9.0 (92)type of basis set: plane wavesmethod: ultrasoft pseudopotentials (“On-The-Fly” Vanderbilt-type version C9 (33))
(Koelling-Harmon) (54)assignment of core / valence states see Table S31.2basis set size cutoff energy = 816 eVk-mesh density see Table S31.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.0754 A
−1.
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
pseudopotential core radii see Table S31.2 (rc)local channel see Table S31.2 (lloc)non-local core radii 2.0 a0 for Mn, Fe, Co, Ni, Cu; rc otherwisenumber of projectors 2 per valence l channel, plus 1 per semi-core state.projector generation KE-Optimized RRKJ - see Table S31.2 for qcaugmentation function pseudization 1.0 a0 (V, Fe, Co, Ni, Cu, Zn); 0.7 a0 (Cr, Mn);
radius 0.7 rc otherwisepseudization radius for NLCC core same as for augmentation functions
chargesize of FFT grid for augmentation 2 × FFT grid for soft density (Ec,ρ = 16Ec,φ)
ADDITIONAL COMMENTS
Basis set, “fine” FFT grid, k-point density and plane-wave cutoff were chosen uniformly across the periodic tableto achieve high convergence. Less stringent critera, determined individually per element will still give high conver-gence in almost all cases at a substantially reduced computational cost.The C9 set of potentials is identical to C8 for the elements in the Delta test suite, except for Cr and Mn, for whichthe augmentation pseudization radius rinner was reduced from 1.0 a0 to 0.7 a0.
103
Table S31.2. OTFG9/CASTEP calculation settings and results per element. Valence, pseu-dopotential core radius rc, local channel lloc, projector wave vector cutoff qc, Monkhorst-Packk-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
Table S32.1. Overview of the most important features and settings of the SSSP/QE calcu-lations.
SSSP/QE
name and version of the code: QUANTUM ESPRESSO 5.1 (84)type of basis set: plane wavesmethod: mixed projector-augmented wave, ultrasoft pseudopotentials and norm-conserving
(Koelling-Harmon) (54)assignment of core / valence states see Table S32.2basis set size see Table S32.2 (wave function cutoff ewfc
cut )k-mesh density 20 × 20 × 20reciprocal-space integration method Marzari-Vanderbilt cold smearing (87) with a fictitious
temperature corresponding to 0.002 Ry(0.02 Ry when required to achieve convergence)
METHOD-SPECIFIC INFORMATION
wave function cutoff see Table S32.2 (ewfccut )
density cutoff see Table S32.2 (erhocut )
ADDITIONAL COMMENTS
Optimally efficient potentials have been selected for each element (see Table S32.2). The investigatedlibraries are: pslibrary.0.3.1 (US and PAW), pslibrary.1.0.0 (US and PAW), GBRV v1.2 and v1.4 (US),and SG15 (NC). The selection criteria for the SSSP efficiency are: smallest ∆, convergence of thephonons mode within 2 %, convergence of the standard heat of formation with respect to theisolated atom (within 3 meV), not too computationally costly. The pseudopotential for N (labeledas THEOS) has been obtained tuning the matching radius starting from the pseudopotential in pslib031US to improve the ∆.
106
Table S32.2. SSSP/QE calculation settings per element. Potential library from which the usedpotential is taken, wave function cutoff ewfc
cut , density cutoff erhocut , valence.
library ewfccut [Ry] erhocut [Ry] valence
H pslib031 US 58 276 1s1
He SG15 100 400 1s2
Li GBRV-1.4 50 250 1s22s0.552p0
Be SG15 100 400 1s22s2
B pslib031 PAW 86 340 2s22p1
C GBRV-1.2 50 250 2s22p2
N THEOS 100 400 2s22p3
O pslib031 PAW 94 374 2s22p4
F GBRV-1.4 50 250 2s22p5
Ne pslib100 PAW 110 530 2s22p6
Na GBRV-1.2 50 250 2s22p63s1
Mg GBRV-1.4 50 250 2s22p63s1.7
Al pslib100 PAW 60 290 3s23p1
Si pslib100 US 56 219 3s23p2
P pslib100 US 44 219 3s23p3
S GBRV-1.2 50 250 3s23p4
Cl pslib100 US 57 282 3s23p5
Ar pslib100 US 63 281 3s23p6
K pslib100 US 56 350 3s23p64s14p0
Ca GBRV-1.2 50 250 3s23p64s24p0
Sc GBRV-1.2 50 250 3s23p63d14s24p0
Ti GBRV-1.4 50 250 3s23p63d14s2
V GBRV-1.2 50 250 3s23p63d34s2
Cr pslib100 PAW 125 1150 3s23p63d44s2
Mn pslib100 PAW 120 1410 3s23p63d54s2
Fe pslib031 PAW 128 1564 3s23p63d64s24p0
Co GBRV-1.2 50 250 3s23p63d74s14p0
Ni GBRV-1.4 50 250 3s23p63d84s04p0
Cu GBRV-1.2 50 250 3s23p63d84s24p0
Zn GBRV-1.2 50 250 3s23p63d104s24p0
Ga pslib100 PAW 120 490 3d104s24p1
Ge pslib100 PAW 90 480 3d104s24p2
As pslib031 US 40 206 4s24p3
Se GBRV-1.2 50 250 4s24p4
Br GBRV-1.4 50 250 4s24p5
Kr pslib031 US 56 440 4s24p6
Rb SG15 100 400 4s24p65s15p0
Sr pslib100 US 50 331 4s24p65s25p0
Y GBRV-1.2 50 250 4s24p64d15s25p0
Zr GBRV-1.2 50 250 4s24p64d25s25p0
Nb pslib031 PAW 84 728 4s24p64d45s1
Mo SG15 100 400 4s24p64d45s2
Tc SG15 100 400 4s24p64d55s2
Ru SG15 100 400 4s24p64d65s2
Rh pslib100 PAW 110 730 4s24p64d75s2
Pd pslib100 PAW 120 1080 4s24p64d85s2
107
Ag GBRV-1.4 50 250 4s24p64d105s0.5
Cd pslib031 US 74 358 4d9.55s25p0.5
In pslib031 US 96 380 4d105s25p1
Sn GBRV-1.2 50 250 4d105s25p1
Sb GBRV-1.4 50 250 4d105s25p2
Te GBRV-1.2 50 250 5s25p4
I GBRV-1.2 50 250 5s25p5
Xe pslib100 US 56 269 4d105s25p6
Cs GBRV-1.2 50 250 5s25p65d06s16p0
Ba SG15 100 400 5s25p65d16s1
Lu N/A N/A N/A N/AHf pslib100 PAW 100 640 4d104f145s25p65d26s2
Ta pslib100 US 69 663 4f145s25p65d36s2
W GBRV-1.2 50 250 5s25p65d3.96s26p0
Re GBRV-1.2 50 250 5s25p65d4.56s26p0
Os pslib100 US 88 563 4f145s25p65d66s26p0
Ir GBRV-1.2 50 250 5p65d8.56s06p0
Pt pslib100 US 100 500 4f145s25p65d86s2
Au SG15 100 400 5s05p65d96s2
Hg GBRV-1.2 50 250 5d106s26p0
Tl pslib100 US 57 263 5d106s26p1
Pb pslib031 PAW 94 378 5d106s26p2
Bi pslib031 PAW 86 344 5d106s26p3
Po pslib100 US 63 569 5d106s26p4
Rn pslib100 US 63 269 5d106s26p6
108
Table S32.3. SSSP/QE calculation results per element. Equilibrium volume per atom V0, bulkmodulus B0, pressure derivative of the bulk modulus B1.
Table S33.1. Overview of the most important features and settings of the Vdb/CASTEP cal-culations.
Vdb/CASTEP
name and version of the code: CASTEP 8.0 (92)type of basis set: plane wavesmethod: ultrasoft pseudopotentials (Legacy Vanderbilt-type Materials Studio set (33))
GENERAL INFORMATION
exchange-correlation functional Perdew-Burke-Ernzerhof (PBE) (43)relativistic scheme core scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S33.2basis set size cutoff energy = 700 eVk-mesh density see Table S33.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.125 A
−1
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
METHOD-SPECIFIC INFORMATION
size of FFT grid for augmentation 1.5 × FFT grid for soft density (Ec,ρ = 9Ec,φ)
ADDITIONAL COMMENTS
This is the set of pseudopotentials generated using the Vanderbilt USPP code and shipped with Accelrys MaterialsStudio in “.usp” file format. The “.uspcc” variants incorporating a non-linear core correction were used for Mn, Fe,Co, Ni, Y and Hf.
111
Table S33.2. Vdb/CASTEP calculation settings and results per element. Valence, Monkhorst-Pack k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number ofirreducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative ofthe bulk modulus B1.
(Koelling-Harmon) (54)assignment of core / valence states see Table S34.2 (Zval)basis set size plane-wave cutoff = 700 eVk-mesh density 8 k-points per A−1
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.06 eV
METHOD-SPECIFIC INFORMATION
plane-wave cutoff 700 eVdensity cutoff 1000 eV
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
114
Table S34.2. Vdb2/DACAPO calculation settings and results per element. Potential, valenceZval, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulusB1.
potential Zval [–] V0 [A3/atom] B0 [GPa] B1 [–]H ch e9g4.pseudo 1 17.683 10.617 2.728He N/A N/A N/A N/A N/ALi Li us cc.pseudo 1 22.156 12.196 3.532Be N/A N/A N/A N/A N/AB B us cc.pseudo 3 7.228 236.231 3.45C C us gga.pseudo 4 11.573 211.609 3.598N N us.pseudo 5 30.218 55.628 3.389O co gef e13 gga.pseudo 6 19.338 53.354 3.722F F pw91 us 7.3.4.pseudo 7 19.872 35.781 4.621Ne N/A N/A N/A N/A N/ANa Na tm lda cc.pseudo 1 35.524 8.072 3.724Mg mg us gga.pseudo 8 23.058 35.951 4.052Al Al us gga org.pseudo 3 16.455 77.26 5.027Si csi e8ag4.pseudo 4 20.403 88.872 4.307P P us.pseudo 5 21.427 67.695 4.196S S tm.pseudo 6 17.037 83.932 4.452Cl Cl us gga.pseudo 7 38.077 19.69 6.753Ar N/A N/A N/A N/A N/AK k us gga.pseudo 9 73.872 3.893 1.431Ca Ca us cc pw91.pseudo 10 42.217 17.175 1.979Sc Sc us cc pw91.pseudo 11 24.643 54.266 3.418Ti ti us gga.pseudo 12 17.404 111.643 3.831V V us pw91 13elec.pseudo 13 13.47 180.486 3.601Cr N/A N/A N/A N/A N/AMn Mn us gga.pseudo 7 10.748 277.287 4.329Fe Fe us gga d2.1.8.pseudo 8 11.626 162.557 8.238Co Co us gga.pseudo 9 10.973 214.957 5.157Ni Ni us gga.pseudo 10 10.954 203.148 4.772Cu Cu us gga.pseudo 11 12.306 133.614 5.029Zn N/A N/A N/A N/A N/AGa ga pw91 us 13elec.pseudo 13 20.345 49.928 3.377Ge ge pw91 us 14elec.pseudo 14 23.907 59.757 4.804As as pw91 us 15elec.pseudo 15 22.548 69.623 4.089Se N/A N/A N/A N/A N/ABr Br us.pseudo 17 39.468 22.404 4.667Kr N/A N/A N/A N/A N/ARb N/A N/A N/A N/A N/ASr Sr us cc pw91.pseudo 10 54.752 11.506 3.321Y Y us cc pw91.pseudo 11 32.899 40.972 3.065Zr N/A N/A N/A N/A N/ANb Nb us pw91 13elec.pseudo 13 18.093 170.578 3.971Mo Mo us.pseudo 6 16.182 267.884 4.531Tc N/A N/A N/A N/A N/ARu Ru us gga.pseudo 8 14.12 344.792 5.059Rh Rh us gga fl.pseudo 9 13.985 259.049 5.12Pd pd us gga.pseudo 10 15.82 170.298 5.644
115
Ag ag us.pseudo 11 17.744 92.462 5.863Cd Cd us gga.pseudo 12 22.766 44.499 6.813In N/A N/A N/A N/A N/ASn sn us f.pseudo 14 36.792 35.194 4.237Sb sb us gga.pseudo 15 31.192 54.089 4.649Te te tm.pseudo 16 38.558 41.165 4.833I I us.pseudo 17 49.319 19.099 5.063Xe N/A N/A N/A N/A N/ACs cs tm 7el.pseudo 7 123.835 1.793 3.432Ba Ba us cc pw91.pseudo 10 62.41 8.497 2.585Lu N/A N/A N/A N/A N/AHf N/A N/A N/A N/A N/ATa Ta us pw91 13elec.pseudo 13 18.21 194.071 3.724W W us pw91 6elec.pseudo 6 16.12 306.074 4.283Re re us gga 7elec.pseudo 7 14.689 371.713 4.44Os os us gga 7elec 7.3.4.pseudo 8 14.177 408.197 4.723Ir ir us gga flocal.pseudo 9 14.296 352.89 5.15Pt pt us gga.pseudo 10 15.971 243.678 5.562Au Au us gga.pseudo 11 18.227 138.628 5.811Hg N/A N/A N/A N/A N/ATl N/A N/A N/A N/A N/APb N/A N/A N/A N/A N/ABi Bi us gga.pseudo 15 36.777 43.893 4.081Po N/A N/A N/A N/A N/ARn N/A N/A N/A N/A N/A
116
Table S35.1. Overview of the most important features and settings of the FHI98pp/ABINITcalculations.
FHI98pp/ABINIT
name and version of the code: ABINIT 7.6.4 (75–77)type of basis set: plane wavesmethod: norm-conserving pseudopotentials (Troullier-Martins FHI (98, 99))
(Koelling-Harmon) (54)assignment of core / valence states see Table S35.2 (Zval)basis set size cut-off energy = 120 Ryk-mesh density see Table S35.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
number of symmetry operations 1
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
117
Table S35.2. FHI98pp/ABINIT calculation settings and results per element. Valence Zval,k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
valence scalar relativistic (Koelling-Harmon) (54)assignment of core / valence states see Table S36.2 (Zval)basis set size cut-off energy = 250 Ryk-mesh density see Table S36.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Fermi-Dirac smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
none
ADDITIONAL COMMENTS
The ASE script (46) used to generate these data is available online (48).
120
Table S36.2. HGH/ABINIT calculation settings and results per element. Valence Zval, k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number of irreduciblek-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivative of the bulkmodulus B1.
Table S37.1. Overview of the most important features and settings of the HGH-NLCC/BigDFTcalculations.
HGH-NLCC/BigDFT
name and version of the code: BigDFT 1.7.6 (104, 105)type of basis set: Daubechies waveletsmethod: norm-conserving pseudopotentials (HGHk, HGHk-sc and NLCC (101–103, 106, 107))
GENERAL INFORMATION
exchange-correlation functional Perdew-Burke-Ernzerhof (PBE) (43)relativistic scheme HGHk PSP generated with relativistic correctionsassignment of core / valence states see Table S37.2 (valence)basis set size full high-resolution grid, hgrid indicated in Table S37.2k-mesh density see Table S37.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 5 · 10−5 Ry
METHOD-SPECIFIC INFORMATION
pseudopotential families HGHk pseudopotentials generated by Krack (101–103)and hard-coded in BigDFT
HGHk-sc pseudopotentials generated by Krack (101–103)with semi-core electrons and hard-coded in BigDFT
NLCC pseudopotentials generated by Willand (106) andlater by S. Saha with non-linear core correctionsand available in the BigDFT wiki (107)
ADDITIONAL COMMENTS
In version 1.7.6, BigDFT cannot treat non orthorhombic systems. The six elements for whichthis is the case, are mentioned in Table S37.2.
123
Table S37.2. HGH-NLCC/BigDFT calculation settings per element. Potential type, real-space grid spacing hgrid, number of k-points in the full 1st Brillouin zone of the primitive cell# k, valence.
Table S38.1. Overview of the most important features and settings of the MBK2013/OpenMXcalculations.
MBK2013/OpenMX
name and version of the code: OpenMX 3.7 (108–111)type of basis set: optimized numerical pseudo-atomic orbitalsmethod: norm-conserving pseudopotentials (Morrison-Bylander-Kleinman 2013 (112, 113))
(Koelling-Harmon) (54)assignment of core / valence states see Table S38.2basis set size see Table S38.2k-mesh density see Table S38.2 (number of k-points in the full 1st
Brillouin zone of the primitive cell, # k)reciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.026 eV
METHOD-SPECIFIC INFORMATION
real-space mesh for integrations 400 Rydbergreal-space mesh for the Poisson 400 Rydberg
solver by FFTprojector expansion for OFF
the neutral atom potentialsone-dimensional radial mesh 900
in k-space (1DFFT.NumGridK)one-dimensional radial mesh 900
in r-space (1DFFT.NumGridR)cutoff energy for the one-dimensional 3 600 Rydberg
radial mesh in k-space(1DFFT.EnergyCutoff)
ADDITIONAL COMMENTS
In the pseudopotential generation, unbound states were calculated by Hamann’s scheme (113).
128
Table S38.2. MBK2013/OpenMX calculation settings per element. Basis set (BS), valenceand unbound states included in the pseudopotential generation and the occupation, which is givenby superscript, and cutoff radii in a.u., which is given in parentheses (States), and the number ofk-points in the full 1st Brillouin zone of the primitive cell (# k).
Table S39.1. Overview of the most important features and settings of theONCVPSP(PD0.1)/ABINIT calculations.
ONCVPSP(PD0.1)/ABINIT
name and version of the code: ABINIT 7.11.8 (75–77)type of basis set: plane wavesmethod: norm-conserving pseudopotentials (ONCVPSP 3.2.1 Pseudo-Dojo v0.1 (94, 114, 115))
GENERAL INFORMATION
exchange-correlation functional Perdew-Burke-Ernzerhof (PBE) (43)relativistic scheme core and valence scalar relativisticassignment of core / valence states see Table S39.2basis set size see Table S39.2 (Ecut)k-mesh density 6750 / N k-points in the first Brillouin zone
of a N-atom cellreciprocal-space integration method Fermi-Dirac smearing with a fictitious
temperature corresponding to 0.0036 Ha
METHOD-SPECIFIC INFORMATION
none
ADDITIONAL COMMENTS
RCmin and RCmax are the minimum and maximum core radii used to pseudize theall-electron wave-functions
The Ecut provided in Table S39.2 are the values at which the ∆ value is converged well within0.1 meV/atom. For many practical applications, a much smaller cutoff energy is alreadysufficient (usually 20 Ha less than the value of Ecut reported in Table S39.2).
The pseudopotentials are known formally as ONCVPSP-PBE-PDv0.1.
133
Table S39.2. ONCVPSP(PD0.1)/ABINIT calculation settings and results per element.Minimum and maximum core radii RCmin and RCmax, plane-wave cutoff Ecut, valence, equi-librium volume per atom V0, bulk modulus B0, pressure derivative of the bulk modulus B1.
Table S40.1. Overview of the most important features and settings of theONCVPSP(SG15)1/CASTEP calculations.
ONCVPSP(SG15)1/CASTEP
name and version of the code: CASTEP 9.0 (Hg revision 6666 Jun 05 2015) (92)type of basis set: plane wavesmethod: norm-conserving pseudopotentials (Schlipf-Gygi ONCVPSP 2015-01-24 (94, 95))
(Koelling-Harmon) (54)assignment of core / valence states see Table S40.2basis set size cutoff energy = 952 eVk-mesh density see Table S40.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.0754 A
−1
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
METHOD-SPECIFIC INFORMATION
size of FFT grid for augmentation N/A
ADDITIONAL COMMENTS
Basis set, “fine” FFT grid, k-point density and plane-wave cutoff were chosen uniformly across the periodic ta-ble to achieve high convergence. Less stringent criteria, determined individually per element will still give highconvergence in almost all cases at substantially reduced computational cost.
136
Table S40.2. ONCVPSP(SG15)1/CASTEP calculation settings and results per element. Va-lence, Monkhorst-Pack k-point mesh in the full 1st Brillouin zone of the conventional cell kpts andnumber of irreducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressurederivative of the bulk modulus B1.
Table S41.1. Overview of the most important features and settings of theONCVPSP(SG15)1/QE calculations.
ONCVPSP(SG15)1/QE
name and version of the code: QUANTUM ESPRESSO 5.1 (84)type of basis set: plane wavesmethod: norm-conserving pseudopotentials (Schlipf-Gygi ONCVPSP 2015-01-24 (94, 95))
(Koelling-Harmon) (54)assignment of core / valence states see Table S41.2 (Zval)basis set size wave function cutoff = 100 Ryk-mesh density see Table S41.2 (k-point mesh in the full 1st Brillouin
zone of the conventional cell kpts, and numberof irreducible k-points # k)
reciprocal-space integration method Gaussian smearing with a fictitioustemperature corresponding to 0.01 eV
METHOD-SPECIFIC INFORMATION
wave function cutoff 100 Rydensity cutoff 400 Ry
ADDITIONAL COMMENTS
none
139
Table S41.2. ONCVPSP(SG15)1/QE calculation settings and results per element. ValenceZval, k-point mesh in the full 1st Brillouin zone of the conventional cell kpts and number ofirreducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressure derivativeof the bulk modulus B1.
Table S42.1. Overview of the most important features and settings of theONCVPSP(SG15)2/CASTEP calculations.
ONCVPSP(SG15)2/CASTEP
name and version of the code: CASTEP 9.0 (Hg revision 6666 Jun 05 2015) (92)type of basis set: plane wavesmethod: norm-conserving pseudopotentials (Schlipf-Gygi ONCVPSP 2015-05-20 (94, 95))
(Koelling-Harmon) (54)assignment of core / valence states see Table S42.2basis set size cutoff energy = 952 eVk-mesh density see Table S42.2 for grid values and number of k-points
in the irreducible wedge of the 1st Brillouin zone (# k);this choice achieves spacing ∆k < 0.0754 A
−1
reciprocal-space integration method Gaussian smearing with a fictitious temperature corre-sponding to 0.2 eV
METHOD-SPECIFIC INFORMATION
size of FFT grid for augmentation N/A
ADDITIONAL COMMENTS
Basis set, “fine” FFT grid, k-point density and plane-wave cutoff were chosen uniformly across the periodic ta-ble to achieve high convergence. Less stringent criteria, determined individually per element will still give highconvergence in almost all cases at substantially reduced computational cost.
142
Table S42.2. ONCVPSP(SG15)2/CASTEP calculation settings and results per element. Va-lence, Monkhorst-Pack k-point mesh in the full 1st Brillouin zone of the conventional cell kpts andnumber of irreducible k-points # k, equilibrium volume per atom V0, bulk modulus B0, pressurederivative of the bulk modulus B1.
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