Table 3 Elemental ground-state structures and chemical potentials predicted by DFT at 0 K

From: The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies

Potential	DFT ground state μ_i (eV/atom)					Exp. LT			Exp. RT
	ID	SG	Fit-none	Fit-partial	Fit-all	ID	SG	ΔE (eV/atom)	ID	SG	ΔE (eV/atom)
H		I4/mmm	−3.327	−3.394	−3.434					Gas
He	A5	I41/amd	−0.004	−0.004	−0.004	A3	P6₃/mmc	0.006		Gas
LLsv	C19	$R \bar{3} m$	−1.907	−1.907	−1.731				A2	$Im \bar{3} m$	0.003
Be	A3	P6₃/mmc	−3.755	−3.755	−3.653
B		$R \bar{3} m$	−6.678	−6.678	−6.656
C	A9	P6₃/mmc	−9.217	−9.217	−9.044
N		$Pa \bar{3}$	−8.235	−8.122	−8.195					Gas
O		C2/m	−4.844	−4.485	−4.523					Gas
F	A11	Cmca	−1.666	−1.429	−1.443		C2/c	0.006		Gas
Ne	A1	$Fm \bar{3} m$	−0.029	−0.029	−0.029					Gas
Na_pv	A3	P6₃/mmc	−1.303	−1.212	−1.196				A1	$Fm \bar{3} m$	0.003
Mg	A3	P6₃/mmc	−1.542	−1.542	−1.417
Al	A1	$Fm \bar{3} m$	−3.746	−3.746	−3.660
Si	A4	$Fd \bar{3} m$	−5.425	−5.425	−5.386
P		$P \bar{1}$	−5.405	−5.161	−5.175	A17	Cmca	0.031
S		P21	−4.114	−3.839	−3.868
Cl		Cmca	−1.820	−1.465	−1.479					Gas
Ar	A3	P6₃/mmc	−0.006	−0.006	−0.006	A1	$Fm \bar{3} m$	0.009		Gas
K_sv	A7	$R \bar{3} m$	−1.097	−1.097	−0.987	A2	$Im \bar{3} m$	0.000
Ca_pv	A1	$Fm \bar{3} m$	−1.978	−1.978	−1.780
Sc_sv	A3	P6₃/mmc	−6.328	−6.328	−6.344
Ti		P6/mmm	−7.776	−7.712	−7.702				A3	P6₃/mmc	0.014
V	A2	$Im \bar{3} m$	−8.941	−8.941	−8.898
Cr	A2	$Im \bar{3} m$	−9.508	−9.508	−9.463
Mn	A12	$I \bar{4} 3m$	−9.027	−9.027	−8.898
Fe	A2	$Im \bar{4} 3m$	−8.308	−8.308	−8.499
Co	A3	P6₃/mmc	−7.090	−7.090	−7.078
Ni	A1	$Fm \bar{3} m$	−5.567	−5.567	−5.587
Cu	A1	$Fm \bar{3} m$	−3.716	−3.716	−3.710
Zn	A3	P6₃/mmc	−1.266	−1.266	−1.157
Ga_d	A11	Cmca	−3.032	−3.032	−2.902
Ge_d	A4	$Fd \bar{3} m$	−4.624	−4.624	−4.522
As	A7	$R \bar{3} m$	−4.652	−4.652	−4.593
Se	A8	P3₁21	−3.481	−3.481	−3.374
Br		Cmca	−1.606	−1.317	−1.333					Liquid
Kr	A3	P6₃/mmc	−0.004	−0.004	−0.004	A1	$Fm \bar{3} m$	0.003		Gas
Rb_sv	C19	$R \bar{3} m$	−0.963	−0.963	−0.881	A2	$Im \bar{3} m$	0.001
Sr_sv	A1	$Fm \bar{3} m$	−1.683	−1.683	−1.549
Y_sv	A3	P6₃/mmc	−6.464	−6.464	−6.449
Zr_sv	A3	P6₃/mmc	−8.547	−8.547	−8.438
Nb_pv	A2	$Im \bar{3} m$	−10.094	−10.094	−10.017
Mo_pv	A2	$Im \bar{3} m$	−10.848	−10.848	−10.921
Tc_pv	A3	P6₃/mmc	−10.361	−10.361	−10.457
Ru	A3	P6₃/mmc	−9.202	−9.202	−9.210
Rh	A1	$Fm \bar{3} m$	−7.269	−7.269	−7.319
Pd	A1	$Fm \bar{3} m$	−5.177	−5.177	−5.197
Ag	A3′	P6₃/mmc	−2.822	−2.822	−2.907	A1	$Fm \bar{3} m$	0.000
Cd	A3	P6₃/mmc	−0.900	−0.900	−0.861
In_d	A6	I4/mmm	−2.720	−2.720	−2.609
Sn_d	A4	$Fd \bar{3} m$	−4.007	−3.895	−3.938				A5	I41/amd	0.042
Sb	A7	$R \bar{3} m$	−4.118	−4.118	−4.155
Te	A8	P3₁21	−3.142	−3.142	−3.027
I		Cmca	−1.509	−1.344	−1.365
Xe	A6	I4/mmm	0.003	0.003	−0.640	A1	$Fm \bar{3} m$	0.004		Gas
Cs_sv	A3	P6₃/mmc	−0.855	−0.855	−0.744	A2	$Im \bar{3} m$	0.002
Ba_sv	A2	$Im \bar{3} m$	−1.924	−1.924	−1.479
La	A3′	P6₃/mmc	−4.935	−4.935	−4.959
Ce_3	A3′	P6₃/mmc	−4.777	−4.777	−4.564	A1	$Fm \bar{3} m$	0.006	A3′	P6₃/mmc	0.000
Pr_3	A3′	P6₃/mmc	−4.775	−4.775	−4.627
Nd_3	A3′	P6₃/mmc	−4.763	−4.763	−4.697
Pm_3	A3′	P6₃/mmc	−4.745	−4.745	−4.716
Sm_3	A3′	P6₃/mmc	−4.715	−4.715	−4.606				C19	$R \bar{3} m$	0.004
Eu_2	A2	$Im \bar{3} m$	−1.888	−1.888	−1.708
Gd_3	A3′	P6₃/mmc	−4.655	−4.655	−4.718	A3	P6₃/mmc	0.017
Tb_3	C19	$R \bar{3} m$	−4.629	−4.629	−4.731	A20	Cmcm	0.017	A3	P6₃/mmc	0.012
Dy_3	C19	$R \bar{3} m$	−4.602	−4.602	−4.660	A20	Cmcm	0.013	A3	P6₃/mmc	0.008
Ho_3	C19	$R \bar{3} m$	−4.577	−4.577	−4.573	A3	P6₃/mmc	0.003
Er_3	A3	P6₃/mmc	−4.563	−4.563	−4.582
Tm_3	A3	P6₃/mmc	−4.475	−4.475	−4.451
Yb_2	A1	$Fm \bar{3} m$	−1.513	−1.513	−1.125	A3	P6₃/mmc	0.007	A1	$Fm \bar{3} m$	0.000
Lu_3	A3	P6₃/mmc	−4.524	−4.524	−4.549
Hf_pv	A3	P6₃/mmc	−9.955	−9.955	−9.902
Ta_pv	A2	$Im \bar{3} m$	−11.853	−11.853	−11.941
W_pv	A2	$Im \bar{3} m$	−12.960	−12.960	−13.130
Re	A3	P6₃/mmc	−12.423	−12.423	−12.378
Os_pv	A3	P6₃/mmc	−11.226	−11.226	−11.374
Ir	A1	$Fm \bar{3} m$	−8.855	−8.855	−8.953
Pt	A1	$Fm \bar{3} m$	−6.056	−6.056	−6.162
Au	A1	$Fm \bar{3} m$	−3.267	−3.267	−3.283
Hg	A12	$I \bar{4} 3m$	−0.298	−0.376	−0.374	A_a	I4/mmm	0.074		Liquid
Tl_d	A3	P6₃/mmc	−2.359	−2.359	−2.480
Pb_d	A1	$Fm \bar{3} m$	−3.704	−3.704	−3.951
Bi_d	A7	$R \bar{3} m$	−4.039	−4.039	−4.199
Ac	A3′	P6₃/mmc	−4.106	−4.106	−4.106	A1	$Fm \bar{3} m$	0.012
Th	A1	$Fm \bar{3} m$	−7.413	−7.413	−7.237
Pa	A1	$Fm \bar{3} m$	−9.496	−9.496	−9.497	A_a	I4/mmm	0.017
U	A20	Cmcm	−11.292	−11.292	−11.032
Np		Pnma	−12.940	−12.940	−12.797
Pu		P2₁/m	−14.298	−14.298	−13.950

Abbreviations: DFT, density functional theory; Exp. LT, experimentally observed lowest temperature; Exp. RT, experimentally observed room temperature PAW-PBE, projected augmented wave-Perdew, Burke and Ernzerhof; VASP, Vienna Ab-initio Simulation Package.
The ‘Potential’ column corresponds to VASP PAW-PBE potential names for the elements used in the current work. The ID and SG columns list the Strukturbericht designation and the space group of the crystal structures, respectively. The ‘fit-none’ chemical potentials are the DFT ground-state total energies of each element, whereas the ‘fit-partial’ and ‘fit-all’ correspond to the chemical-potential correction schemes described in the section ‘Formation Energy Calculation’. The ‘Exp. LT’ and/or ‘Exp. RT’ ground states^29,30 are given if they differ from the DFT-predicted 0-K ground state (RT only provided if it differs from LT), along with the difference between the DFT-predicted total energy of the Exp. LT or RT structure and DFT ground-state energy (energy difference only provided if the DFT ground state differs from Exp. LT or Exp. RT).

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Table 3 Elemental ground-state structures and chemical potentials predicted by DFT at 0 K

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