Supplementary Information: Heats of formation of solids with error estimation: the
mBEEF functional with and without fitted reference energies.
Mohnish Pandey1 and Karsten W. Jacobsen,1
1Center for Atomic-scale Materials Design, Department of Physics,
Technical University of Denmark, DK - 2800 Kongens Lyngby, Denmark
(Dated: April 14, 2015)
TABLE I: Energies (in eV/atom) of the reference states of elements
before and after the fitting
Element μPBE μFERE
PBE μRPBE μFERE
RPBE μPBE+U μFERE
PBE+U μTPSS μFERE
TPSS μmBEEF μFERE
mBEEF
Li -1.904 -1.68 -1.796 -1.521 -1.904 -1.685 -2.481 -2.391 -4.62 -4.536
Be -3.699 -3.413 -3.412 -3.056 -3.699 -3.406 -4.668 -4.24 -7.528 -7.406
B -6.691 -6.612 -6.296 -6.244 -6.691 -6.682 -7.84 -7.646 -11.726 -11.773
Na -1.322 -1.116 -1.201 -0.974 -1.322 -1.112 -4.701 -4.492 -15.925 -15.915
Mg -1.614 -1.152 -1.422 -0.902 -1.614 -1.154 -5.343 -4.949 -18.121 -17.919
Al -3.745 -3.058 -3.489 -2.714 -3.745 -3.103 -7.765 -7.049 -22.134 -21.773
Si -5.393 -5.351 -5.094 -5.052 -5.393 -5.299 -9.543 -9.68 -25.89 -25.908
K -1.232 -0.977 -1.133 -0.818 -1.232 -0.975 -7.092 -6.937 -32.652 -32.589
Ca -1.663 -1.702 -1.473 -1.397 -1.663 -1.65 -8.06 -7.708 -35.485 -35.57
Zn -1.201 -0.805 -0.818 -0.405 -1.201 -0.798 -8.592 -8.056 -61.628 -61.3
Ga -2.899 -2.324 -2.544 -1.954 -2.899 -2.382 -10.126 -9.52 -66.906 -66.399
Ge -4.499 -4.206 -4.161 -3.833 -4.499 -4.229 -11.448 -11.441 -72.126 -71.683
As -4.648 -5.026 -4.278 -4.731 -4.648 -4.945 -11.764 -12.12 -75.744 -76.153
Rb -0.926 -0.646 -0.814 -0.469 -0.926 -0.618 -8.185 -7.772 -87.101 -87.036
Sr -1.677 -1.309 -1.488 -1.003 -1.677 -1.277 -8.095 -8.374 -91.307 -91.402
Cd -0.958 -0.858 -0.563 -0.479 -0.958 -0.853 -6.97 -6.766 -130.798 -130.821
In -2.793 -2.42 -2.426 -2.043 -2.793 -2.511 -8.594 -8.168 -137.051 -136.79
Sn -4.149 -3.924 -3.815 -3.519 -4.149 -3.953 -9.468 -9.515 -142.951 -142.552
Sb -4.463 -4.799 -4.093 -4.46 -4.463 -4.66 -9.599 -10.057 -147.587 -147.917
Te -3.188 -3.314 -2.834 -3.016 -3.188 -3.268 -8.042 -8.177 -150.633 -150.804
Cs -0.813 -0.504 -0.699 -0.333 -0.813 -0.437 -4.551 -3.886 -161.584 -161.519
Ba -0.208 -1.365 0.024 -1.049 -0.208 -1.312 -4.588 -4.762 -166.612 -166.602
Hg -0.917 -0.902 -0.543 -0.505 -0.917 -0.909 12.263 12.372 -308.363 -308.362
Tl -2.569 -2.72 -2.17 -2.399 -2.569 -2.69 11.337 11.435 -316.931 -317.061
Pb -3.875 -4.086 -3.49 -3.678 -3.875 -4.037 11.282 10.815 -325.376 -325.429
Bi -4.717 -5.16 -4.334 -4.786 -4.717 -5.154 11.223 10.45 -333.537 -333.615
Sc -4.667 -4.183 -4.366 -3.763 -3.29 -2.878 -11.312 -11.112 -40.093 -39.857
Ti -6.701 -6.818 -6.296 -6.27 -4.303 -4.529 -13.529 -13.779 -44.225 -44.465
Y -4.696 -4.104 -4.384 -3.668 -3.289 -2.844 -12.161 -11.813 -97.841 -97.554
Zr -7.409 -7.269 -7.007 -6.778 -4.934 -4.981 -14.826 -14.851 -104.147 -104.108
Nb -10.387 -10.523 -9.867 -9.918 -6.985 -7.41 -17.614 -17.889 -110.943 -110.977
Mo -11.265 -11.707 -10.693 -11.062 -7.716 -8.104 -18.546 -18.813 -115.777 -115.834
Ru -9.498 -10.24 -8.839 -9.597 -6.297 -7.733 -16.396 -16.939 -121.956 -122.391
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