Supplementary material to: Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections
Chih-Wei Wang,1 Kerwin Hui,1 and Jeng-Da Chai1, 2,⇤
1Department of Physics, National Taiwan University, Taipei 10617, Taiwan
2Center for Theoretical Sciences and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan
⇤ Author to whom correspondence should be addressed. Electronic mail: jdchai@phys.ntu.edu.tw
LIST OF TABLES
I Root-mean-square error (in kcal/mol) of SLC-LDA-D3 for the training set as a function of !SR and !LR (in bohr 1). 5 II Root-mean-square error (in kcal/mol) of SLC-PBE-D3 for the training set as a function of !SR and !LR (in bohr 1). 5 III Nonhydrogen transfer barrier heights (in kcal/mol) of the NHTBH38/04 set [1]. . . 5 IV Hydrogen transfer barrier heights (in kcal/mol) of the HTBH38/04 set [1]. . . 8 V Interaction energies (in kcal/mol) of the S22 set [2, 3]. . . 11 VI The 23 core ionization energies (in eV) of 14 molecules taken from Ref. [4]. Bold type denotes the atom at which
the 1s electron is ionized. The relativistic corrections are not considered. . . 12 VII The 23 core ionization energies (in eV) of 14 molecules taken from Ref. [4]. Bold type denotes the atom at which
the 1s electron is ionized. The relativistic corrections (0.12 eV for C, 0.24 eV for N, 0.45 eV for O, and 0.75 eV for F) [5] are subtracted from the reference values. . . 14 VIII The 38 core excitation energies (in eV) of 13 molecules taken from Ref. [6]. The relativistic corrections are not
considered. . . 15 IX The 38 core excitation energies (in eV) of 13 molecules taken from Ref. [6]. The relativistic corrections [(0.12 eV
for C, 0.24 eV for N, 0.45 eV for O, and 0.75 eV for F) [5] and (3.4 eV for Si, 4.6 eV for P, 5.9 eV for S, and 7.9 eV for Cl) [6]] are subtracted from the reference values. . . 17 X Interaction energies (in kcal/mol) of the S66 set [7]. . . 19 XI Atomization energies (in eV) of the AE113 database [8, 9]. The atomization energies are calculated without the
zero-point energy correction. . . 23 XII Vertical ionization potentials (in eV) of the IP131 database [8], calculated using IP(1) = Etotal(N 1) Etotal(N ). 28 XIII Vertical ionization potentials (in eV) of the IP131 database [8], calculated using IP(2) = ✏HOMO(N ). . . 33 XIV Vertical electron affinities (in eV) of the EA131 database [8, 9], calculated using EA(1) = Etotal(N ) Etotal(N + 1). 39 XV Vertical electron affinities (in eV) of the EA131 database [8, 9], calculated using EA(2) = ✏HOMO(N + 1). . . 44 XVI Vertical electron affinities (in eV) of the EA131 database [8, 9], calculated using EA(3) = ✏LUMO(N ). . . 50 XVIIFundamental gaps (in eV) of the FG131 database [8, 9], calculated using Eg(1) = Etotal(N 1) + Etotal(N + 1)
2Etotal(N ). . . 56
XVIIIFundamental gaps (in eV) of the FG131 database [8, 9], calculated using Eg(2) = ✏HOMO(N + 1) ✏HOMO(N ). . . . 61 XIX Fundamental gaps (in eV) of the FG131 database [8, 9], calculated using Eg(3) = ✏LUMO(N ) ✏HOMO(N ). . . 67 XX The 19 valence and 23 Rydberg excitation energies (in eV) of nitrogen gas (N2), carbon monoxide (CO), water
(H2O), ethylene (C2H4), and formaldehyde (CH2O) taken from Ref. [10]. . . 72 XXI The lowest charge-transfer excitation energies (in eV) of C2H4· · · C2F4 dimer along the intermolecular distance
R [11]. . . 75
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TABLES
TABLE I. Root-mean-square error (in kcal/mol) of SLC-LDA-D3 for the training set as a function of !SR and !LR (in bohr 1).
!LR\!SR 0.8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.30 19.13 16.86 28.33 34.73 38.49 41.04 42.91 44.33 0.35 19.24 10.66 19.42 25.56 29.24 31.75 33.59 34.99 0.40 21.34 10.84 12.82 18.19 21.67 24.08 25.87 27.23 0.45 23.76 13.48 9.65 12.98 15.91 18.09 19.74 21.03 0.50 24.80 16.31 10.64 10.63 12.33 13.97 15.33 16.44
TABLE II. Root-mean-square error (in kcal/mol) of SLC-PBE-D3 for the training set as a function of !SR and !LR (in bohr 1).
!LR\!SR 0.8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.30 11.90 8.60 6.00 8.06 9.24 9.81 10.17 10.44 0.35 13.26 9.70 5.36 5.87 6.78 7.27 7.60 7.85 0.40 14.80 11.11 5.94 4.90 5.20 5.51 5.75 5.96 0.45 16.32 12.66 7.12 5.34 5.02 5.03 5.11 5.21 0.50 17.83 14.20 8.54 6.44 5.85 5.72 5.70 5.71
TABLE III: Nonhydrogen transfer barrier heights (in kcal/mol) of the NHTBH38/04 set [1].
Reaction Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 Heavy-atom transfer reactions
H + N2O ! OH + N2
Vf 18.14 9.97 17.86 20.68 19.23 17.47 18.16 15.31 17.59 20.18
Vr 83.22 52.46 77.26 81.91 80.58 77.75 78.82 85.59 79.02 81.91
H + F H ! HF + H
Vf 42.18 27.07 40.39 44.78 43.10 40.56 41.46 37.83 40.09 43.74
Vr 42.18 27.07 40.39 44.78 43.10 40.56 41.46 37.83 40.09 43.74
H + ClH! HCl + H
Vf 18.00 9.64 18.30 23.17 20.71 18.19 19.33 17.30 17.99 22.25
Vr 18.00 9.64 18.30 23.17 20.71 18.19 19.33 17.30 17.99 22.25
H + F CH3 ! HF + CH3
Vf 30.38 18.51 32.56 33.44 32.11 30.02 30.98 30.25 32.09 33.45
Vr 57.02 41.00 56.65 55.78 55.35 54.47 54.75 57.90 56.16 55.38
H + F2 ! HF + F
Vf 2.27 -9.86 0.32 1.99 0.89 -0.60 0.10 -1.56 0.30 2.26
Vr 106.18 80.86 102.53 103.62 104.26 103.96 104.08 108.23 103.81 104.40 CH3+ F Cl! CH3F + Cl
Vf 7.43 -6.48 9.39 4.61 3.88 2.76 3.61 9.22 8.61 5.54
Vr 60.17 41.63 63.40 59.96 58.48 56.55 57.85 65.59 62.69 60.96
Nucleophilic substitution reactions F + CH3F ! F CH3+ F
Vf -0.34 -8.31 0.96 -2.61 -2.27 -1.37 -1.55 3.03 1.16 -1.34
Vr -0.34 -8.31 0.96 -2.61 -2.27 -1.37 -1.55 3.03 1.16 -1.34
F · · · CH3F ! F CH3· · · F
Vf 13.38 7.06 14.37 13.29 13.25 12.85 13.06 16.66 14.86 13.54
Vr 13.38 7.06 14.37 13.29 13.25 12.85 13.06 16.66 14.86 13.54
Cl + CH3Cl! ClCH3+ Cl
Vf 3.10 -3.80 8.42 6.22 4.72 3.70 4.38 8.56 7.82 6.48
Vr 3.10 -3.80 8.42 6.22 4.72 3.70 4.38 8.56 7.82 6.48
Cl · · · CH3Cl! ClCH3· · · Cl
Vf 13.61 7.15 17.80 17.69 16.04 14.30 15.20 18.38 17.81 17.24
Vr 13.61 7.15 17.80 17.69 16.04 14.30 15.20 18.38 17.81 17.24
F + CH3Cl! F CH3+ Cl
Vf -12.54 -19.52 -9.42 -11.70 -13.14 -13.58 -13.14 -9.57 -9.94 -11.43
Vr 20.11 12.31 23.54 20.15 20.79 21.26 21.33 26.89 23.87 21.89
F · · · CH3Cl! F CH3· · · Cl
Vf 2.89 -0.67 5.42 5.41 4.20 3.07 3.60 5.59 5.36 4.96
Vr 29.62 21.45 32.11 30.89 31.08 30.50 30.91 35.79 32.90 31.72
OH + CH3F ! HOCH3+ F
Vf -2.78 -10.59 -1.19 -4.00 -3.67 -3.31 -3.19 1.35 -1.01 -2.84
Vr 17.33 9.14 21.34 17.87 17.58 17.90 17.89 22.68 21.01 18.47
OH · · · CH3F ! HOCH3· · · F
Vf 10.96 3.88 11.88 11.62 11.54 10.57 11.06 14.69 12.39 11.75
Vr 47.20 43.21 52.43 49.19 49.36 49.20 49.43 54.19 52.50 50.19
Unimolecular and association reactions H + N2 ! HN2
Vf 14.69 5.19 12.14 15.46 13.99 12.32 12.96 11.36 12.33 15.20
Vr 10.72 9.08 13.10 15.08 14.32 13.40 13.74 13.10 12.72 14.42
H + CO! HCO
Vf 3.17 -1.69 2.32 5.64 4.55 3.37 3.71 1.27 2.29 5.33
Vr 22.68 24.66 26.04 27.07 26.74 26.20 26.24 24.79 25.37 26.13 H + C2H4 ! CH3CH2
Vf 1.72 -0.14 2.05 4.95 4.09 3.03 3.42 0.44 1.80 4.54
Vr 41.75 40.19 47.53 48.46 47.01 45.37 46.01 46.97 47.22 47.82
CH3+ C2H4 ! CH3CH2CH2
Vf 6.85 1.50 6.98 4.80 5.03 4.57 4.93 8.35 6.06 4.90
Vr 32.97 29.76 39.34 36.71 35.37 33.85 34.64 37.18 39.06 37.03
HCN ! HNC
Vf 48.16 45.60 46.67 45.86 46.28 46.42 46.19 46.35 46.24 45.26
Vr 33.11 30.50 33.20 32.79 33.13 33.27 33.07 33.59 32.57 32.36
MSE -8.52 1.39 1.32 0.55 -0.45 0.04 1.99 1.29 1.38
MAE 8.62 2.47 2.32 1.75 1.51 1.53 3.32 2.38 2.13
rms 10.61 3.07 2.82 2.08 2.00 1.89 3.77 2.86 2.55
TABLE IV: Hydrogen transfer barrier heights (in kcal/mol) of the HTBH38/04 set [1].
Reaction Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 H + HCl! H2+ Cl
Vf 5.70 0.56 5.85 6.55 5.24 4.08 4.71 2.61 5.54 6.44
Vr 8.70 -1.95 5.78 6.58 5.30 4.58 4.98 8.27 5.98 6.34
OH + H2! H + H2O
Vf 5.10 -6.36 2.74 3.24 2.54 2.22 2.48 4.45 3.27 3.11
Vr 21.20 13.69 21.14 20.38 19.50 18.77 19.13 17.23 20.34 20.44
CH3+ H2! H + CH4
Vf 12.10 3.82 9.98 10.25 9.58 9.06 9.36 11.35 9.69 9.80
Vr 15.30 9.32 14.87 16.29 15.05 13.54 14.22 11.74 14.56 16.10
OH + CH4! CH3+ H2O
Vf 6.70 -5.65 4.88 4.46 3.89 3.04 3.43 6.24 5.09 4.27
Vr 19.60 8.91 18.39 15.56 15.37 15.11 15.22 18.62 17.30 15.30
H + H2 ! H2+ H
Vf 9.60 3.64 7.89 12.37 10.73 9.21 9.77 5.84 7.84 11.67
Vr 9.60 3.64 7.89 12.37 10.73 9.21 9.77 5.84 7.84 11.67
OH + N H3! H2O + N H2
Vf 3.20 -11.94 2.93 2.80 1.60 -0.02 0.85 4.90 3.32 2.71
Vr 12.70 -0.71 13.00 12.06 10.96 9.69 10.38 14.55 12.67 11.89
HCl + CH3! Cl + CH4
Vf 1.70 -5.94 1.28 -0.58 -1.19 -1.86 -1.45 1.80 0.60 -0.77
Vr 7.90 -2.95 6.10 5.49 4.34 3.11 3.69 7.85 5.91 5.43
OH + C2H6! H2O + C2H5
Vf 3.40 -9.03 2.42 1.76 1.16 0.17 0.56 3.47 2.40 1.49
Vr 19.90 10.76 20.06 17.27 17.18 16.57 16.82 19.97 18.64 16.90
F + H2! HF + H
Vf 1.80 -12.97 -2.87 -3.79 -3.89 -3.70 -3.55 -1.06 -1.71 -2.85
Vr 33.40 25.12 32.70 29.79 29.17 29.01 29.20 27.67 30.93 29.99
O + CH4! OH + CH3
Vf 13.70 -0.79 9.83 10.40 9.84 9.20 9.55 12.28 10.44 10.48
Vr 8.10 -0.57 7.98 4.78 4.83 4.67 4.71 7.74 7.36 4.60
H + P H3! P H2+ H2
Vf 3.10 -1.79 2.90 5.86 4.63 3.28 3.79 0.73 2.63 5.36
Vr 23.20 17.91 23.04 25.29 24.15 23.46 23.78 25.51 23.02 24.72 H + HO ! H2+ O
Vf 10.70 3.75 10.52 10.68 9.82 8.84 9.17 6.66 10.16 10.48
Vr 13.10 -1.98 7.48 10.25 9.35 8.89 9.15 10.81 8.37 10.06
H + H2S ! H2+ HS
Vf 3.50 -1.22 3.77 6.89 5.52 4.05 4.62 1.63 3.53 6.38
Vr 17.30 9.10 15.69 18.48 17.19 16.31 16.64 18.96 15.81 17.85
O + HCl! OH + Cl
Vf 9.80 -10.54 7.88 8.39 6.94 5.47 6.42 10.89 8.52 8.38
Vr 10.40 -7.33 10.84 8.84 7.46 5.92 6.71 12.39 10.74 8.71
N H2+ CH3 ! CH4+ N H
Vf 8.00 0.71 9.29 6.92 6.49 5.65 6.13 9.44 8.73 6.60
Vr 22.40 10.56 20.18 20.01 19.34 18.41 18.99 22.02 19.97 19.89
N H2+ C2H5 ! C2H6+ N H
Vf 7.50 2.89 10.88 8.76 8.41 7.26 7.83 10.81 9.98 8.26
Vr 18.30 7.51 17.63 17.44 16.72 15.69 16.23 19.27 17.19 17.18
C2H6+ N H2 ! NH3+ C2H5
Vf 10.40 1.44 11.31 10.92 10.03 8.60 9.26 12.33 10.74 10.33
Vr 17.40 9.99 18.90 17.17 16.70 15.29 16.00 19.17 17.63 16.56
N H2+ CH4 ! CH3+ N H3
Vf 14.50 4.39 13.70 13.43 12.56 11.28 11.95 14.98 13.37 12.96
Vr 17.80 7.71 17.15 15.26 14.69 13.65 14.21 17.71 16.23 14.80
s-trans cis-C5H8 ! s-trans cis-C5H8
Vf 38.40 31.19 40.09 42.88 41.46 39.07 39.92 44.37 39.90 41.80
Vr 38.40 31.19 40.09 42.88 41.46 39.07 39.92 44.37 39.90 41.80
MSE -9.67 -0.77 -0.66 -1.55 2.57 -2.08 -0.27 -1.03 -0.96
MAE 9.67 1.39 2.11 2.27 2.70 2.40 1.99 1.41 2.04
rms 10.37 1.90 2.47 2.60 3.10 2.75 2.59 1.77 2.33
TABLE V: Interaction energies (in kcal/mol) of the S22 set [2, 3].
Complex Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 Hydrogen bonded complexes
NH3 dimer [C2h] -3.133 -2.83 -2.35 -3.66 -3.59 -3.08 -3.09 -2.82 -2.85 -3.27
H2O dimer [Cs] -4.989 -4.91 -4.37 -5.65 -5.59 -4.97 -5.04 -4.95 -4.69 -5.21
Formic acid dimer [C2h] -18.753 -18.08 -17.79 -20.11 -19.95 -19.28 -19.51 -19.20 -18.88 -19.83 Formamide dimer [C2h] -16.062 -14.69 -14.00 -16.77 -16.65 -16.17 -16.26 -15.73 -15.40 -16.40 Uracil dimer [C2h] -20.641 -18.45 -17.54 -20.31 -20.29 -20.43 -20.51 -20.19 -19.61 -20.56 2-pyridone· · · 2-aminopyridine [C1] -16.934 -15.27 -13.80 -16.39 -16.37 -17.06 -16.98 -16.28 -16.36 -16.93 Adenine· · · thymine WC [C1] -16.66 -14.29 -13.04 -16.04 -15.90 -16.46 -16.43 -15.94 -15.91 -16.47
Dispersion complexes
CH4 dimer [D3d] -0.527 -0.08 0.13 -0.43 -0.57 -0.57 -0.61 -0.74 -0.69 -0.56
C2H4 dimer [D2d] -1.472 -0.31 -0.15 -1.90 -1.77 -1.79 -1.54 -1.52 -1.53 -1.46
Benzene· · · CH4 [C3] -1.448 -0.01 0.01 -1.58 -1.43 -1.70 -1.64 -1.38 -1.57 -1.68
Benzene dimer [C2h] -2.654 1.90 1.64 -2.27 -1.52 -3.16 -3.00 -1.99 -2.89 -3.18
Pyrazine dimer [Cs] -4.255 0.73 0.36 -3.73 -2.91 -4.27 -4.15 -3.40 -4.13 -4.27
Uracil dimer [C2] -9.805 -2.69 -3.24 -8.92 -7.85 -9.79 -9.83 -9.49 -9.83 -9.96
Indole· · · benzene [C1] -4.524 2.24 1.73 -3.68 -2.46 -5.10 -4.61 -3.13 -4.49 -4.90
Adenine· · · thymine stack [C1] -11.73 -1.33 -2.57 -10.38 -8.49 -11.86 -11.26 -10.08 -11.32 -11.76
Mixed complexes
Ethene· · · ethine [C2v] -1.496 -1.16 -0.87 -1.62 -1.66 -1.63 -1.65 -1.59 -1.61 -1.63 Benzene· · · H2O [Cs] -3.275 -2.03 -2.13 -3.56 -3.39 -3.50 -3.58 -3.52 -3.73 -3.71 Benzene· · · NH3 [Cs] -2.312 -0.91 -0.95 -2.44 -2.30 -2.53 -2.56 -2.42 -2.60 -2.63 Benzene· · · HCN [Cs] -4.541 -2.81 -3.30 -4.90 -4.61 -4.79 -4.65 -4.41 -4.80 -4.88
Benzene dimer [C2v] -2.717 -0.10 -0.21 -2.37 -2.11 -2.89 -2.82 -2.37 -2.75 -2.94
Indole· · · benzene T-shape [C1] -5.627 -2.02 -2.27 -4.87 -4.46 -5.64 -5.52 -5.14 -5.77 -5.75
Phenol dimer [C1] -7.097 -3.86 -3.84 -6.93 -6.48 -6.99 -7.00 -6.83 -6.73 -7.14
MSE 2.71 2.82 0.10 0.47 -0.14 -0.07 0.34 0.11 -0.20
MAE 2.71 2.82 0.53 0.79 0.19 0.18 0.45 0.30 0.23
rms 3.73 3.58 0.63 1.11 0.25 0.25 0.61 0.39 0.33
TABLE VI: The 23 core ionization energies (in eV) of 14 molecules taken from Ref. [4]. Bold type denotes the atom at which the 1s electron is ionized. The relativistic corrections are not considered.
Molecule Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 C2H2 290.82 269.16 275.23 275.90 279.36 280.14 279.93 292.73 287.04 287.76 CH4 290.91 268.37 274.41 275.13 278.54 279.29 279.09 291.82 286.15 286.91 CH3OH 292.42 269.96 276.09 276.81 280.22 280.96 280.76 293.53 287.83 288.59 CH3CN 292.45 270.03 276.22 276.85 280.32 281.09 280.88 293.79 288.04 288.74 CH3CN 292.98 270.39 276.50 277.19 280.61 281,37 281.16 293.93 288.24 288.99
HCN 293.40 270.38 276.51 277.15 280.63 281.42 281.19 294.09 288.32 289.04 H2CO 294.47 271.57 277.78 278.47 281.91 282.67 282.46 295.34 289.55 290.31 CO 296.21 272.02 278.23 278.88 282.39 283.17 282.95 295.99 290.13 290.87 CO2 297.69 273.66 280.33 280.95 284.44 285.21 284.99 298.14 292.14 292.87 NH3 405.56 379.92 385.83 386.69 391.09 392.19 391.86 409.67 403.09 403.97 CH3CN 405.64 380.34 386.40 387.17 391.64 392.76 392.42 410.37 403.74 404.57 HCN 406.78 381.10 387.12 387.89 392.37 393.50 393.15 411.13 404.47 405.31 NNO 408.71 382.89 389.27 390.02 394.50 395.63 395.28 413.43 406.61 407.45 N2 409.98 383.12 389.27 390.02 394.52 395.67 395.31 413.38 406.63 407.46 NNO 412.59 386.30 393.02 393.76 398.20 399.26 398.94 417.13 410.30 411.12 CH3OH 539.11 510.22 516.05 516.94 522.38 523.87 523.37 546.62 539.34 540.28 H2CO 539.48 510.77 516.56 517.41 522.89 524.39 523.89 547.21 539.90 540.80 H2O 539.90 510.28 516.15 517.07 522.50 523.97 523.48 546.76 539.43 540.40 CO2 541.28 512.36 518.34 519.16 524.64 526.13 525.64 549.05 541.66 542.55 NNO 541.42 512.97 518.72 519.56 525.06 526.61 526.08 549.40 542.04 542.95 CO 542.55 513.06 518.98 519.76 525.26 526.76 526.26 549.66 542.33 543.17 HF 694.23 659.88 665.77 666.71 673.16 675.00 674.35 703.26 695.36 696.38 F2 696.69 662.88 668.98 669.87 676.34 678.19 677.54 706.57 698.58 699.58
MSE -26.25 -20.15 -19.39 -14.88 -13.74 -14.10 4.25 -2.36 -1.53
MAE 26.25 20.15 19.39 14.88 13.74 14.10 4.27 2.77 2.53
rms 26.48 20.47 19.70 15.10 13.91 14.29 5.27 3.36 2.91
TABLE VII: The 23 core ionization energies (in eV) of 14 molecules taken from Ref. [4]. Bold type denotes the atom at which the 1s electron is ionized. The relativistic corrections (0.12 eV for C, 0.24 eV for N, 0.45 eV for O, and 0.75 eV for F) [5] are subtracted from the reference values.
Molecule Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 C2H2 290.70 269.16 275.23 275.90 279.36 280.14 279.93 292.73 287.04 287.76 CH4 290.79 268.37 274.41 275.13 278.54 279.29 279.09 291.82 286.15 286.91 CH3OH 292.30 269.96 276.09 276.81 280.22 280.96 280.76 293.53 287.83 288.59 CH3CN 292.33 270.03 276.22 276.85 280.32 281.09 280.88 293.79 288.04 288.74 CH3CN 292.86 270.39 276.50 277.19 280.61 281,37 281.16 293.93 288.24 288.99 HCN 293.28 270.38 276.51 277.15 280.63 281.42 281.19 294.09 288.32 289.04 H2CO 294.35 271.57 277.78 278.47 281.91 282.67 282.46 295.34 289.55 290.31 CO 296.09 272.02 278.23 278.88 282.39 283.17 282.95 295.99 290.13 290.87 CO2 297.57 273.66 280.33 280.95 284.44 285.21 284.99 298.14 292.14 292.87 NH3 405.32 379.92 385.83 386.69 391.09 392.19 391.86 409.67 403.09 403.97 CH3CN 405.40 380.34 386.40 387.17 391.64 392.76 392.42 410.37 403.74 404.57 HCN 406.54 381.10 387.12 387.89 392.37 393.50 393.15 411.13 404.47 405.31 NNO 408.47 382.89 389.27 390.02 394.50 395.63 395.28 413.43 406.61 407.45 N2 409.74 383.12 389.27 390.02 394.52 395.67 395.31 413.38 406.63 407.46 NNO 412.35 386.30 393.02 393.76 398.20 399.26 398.94 417.13 410.30 411.12 CH3OH 538.66 510.22 516.05 516.94 522.38 523.87 523.37 546.62 539.34 540.28 H2CO 539.03 510.77 516.56 517.41 522.89 524.39 523.89 547.21 539.90 540.80 H2O 539.45 510.28 516.15 517.07 522.50 523.97 523.48 546.76 539.43 540.40 CO2 540.83 512.36 518.34 519.16 524.64 526.13 525.64 549.05 541.66 542.55
NNO 540.97 512.97 518.72 519.56 525.06 526.61 526.08 549.40 542.04 542.95 CO 542.10 513.06 518.98 519.76 525.26 526.76 526.26 549.66 542.33 543.17 HF 693.48 659.88 665.77 666.71 673.16 675.00 674.35 703.26 695.36 696.38 F2 695.94 662.88 668.98 669.87 676.34 678.19 677.54 706.57 698.58 699.58
MSE -25.95 -19.86 -19.10 -14.59 -13.45 -13.81 4.54 -2.07 -1.24
MAE 25.95 19.86 19.10 14.59 13.45 13.81 4.55 2.78 2.60
rms 26.16 20.15 19.38 14.78 13.60 13.97 5.62 3.30 2.93
TABLE VIII: The 38 core excitation energies (in eV) of 13 molecules taken from Ref. [6]. The relativistic corrections are not considered.
Excitation Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 Core!Valence
C2H4 C(1s)! ⇡* 284.7 268.07 269.02 269.74 273.37 274.76 274.20 284.98 280.51 281.23 C2H2 C(1s)! ⇡* 285.8 268.92 269.99 270.69 274.34 275.74 275.18 286.02 281.52 282.22 H2CO C(1s) ! ⇡* 286.0 269.25 269.79 270.48 274.08 275.51 274.93 285.48 281.18 281.85 CO C(1s) ! ⇡* 287.4 270.40 270.79 271.37 274.93 276.35 275.78 286.38 282.18 282.78 CO2 C(1s) ! ⇡* 290.8 273.74 274.49 275.08 278.62 280.01 279.44 289.97 285.73 286.33 N2 N(1s)! ⇡* 401.0 381.56 382.07 382.83 387.32 389.03 388.34 403.64 398.66 399.42 H2CO O(1s) ! ⇡* 530.8 508.53 509.21 510.13 515.48 517.45 516.66 537.09 531.52 532.43 CO O(1s)! ⇡* 534.2 511.37 512.23 513.14 518.59 520.59 519.79 540.48 534.72 535.64 HF F(1s) ! * 687.4 659.07 660.67 661.81 668.40 670.68 669.71 696.00 689.59 690.68 SiH4 Si(1s) ! * 1842.5 1779.27 1781.21 1782.55 1794.84 1799.52 1797.60 1852.21 1843.94 1845.54 PH3 P(1s) ! * 2145.8 2075.69 2077.03 2078.32 2091.78 2096.99 2094.85 2154.80 2146.59 2148.12
H2S S(1s) ! * 2473.1 2395.39 2396.48 2397.78 2412.37 2418.02 2415.71 2481.33 2473.07 2474.61 SO2 S(1s) ! ⇡* 2473.8 2396.11 2396.92 2398.22 2412.79 2418.47 2416.14 2481.35 2473.12 2474.67 HCl Cl(1s)! * 2823.9 2739.15 2740.77 2742.07 2757.51 2763.51 2761.06 2831.99 2823.59 2825.08 Cl2 Cl(1s)! u* 2821.3 2737.15 2738.27 2739.59 2754.88 2760.83 2758.40 2828.90 2820.64 2822.15
Core!Rydberg
C2H4 C(1s)! 3s 287.1 268.59 271.54 272.41 275.96 276.93 276.54 288.25 283.25 284.08 C2H2 C(1s)! 3s 287.7 268.88 271.81 272.66 276.25 277.21 276.82 288.57 283.54 284.36 C2H2 C(1s)! 3p⇡ 288.7 269.60 272.84 273.66 277.24 278.08 277.76 289.96 284.64 285.45 C2H2 C(1s)! 3p 288.8 269.21 272.32 273.12 276.75 277.76 277.38 289.16 284.08 284.88 H2CO C(1s) ! 3sa1 290.2 271.21 273.98 274.86 278.42 279.44 279.01 290.59 285.62 286.45 H2CO C(1s) ! 3pb2 291.3 271.87 274.91 275.77 279.46 280.46 280.07 291.96 286.72 287.58 H2CO C(1s) ! 3pa1 291.7 271.77 274.97 275.84 279.39 280.29 279.92 291.64 286.66 287.49 CO C(1s) ! 3s 292.4 272.05 274.96 275.79 279.49 280.44 280.04 292.14 286.81 287.65 CO C(1s) ! 3p⇡ 293.3 272.58 275.78 276.58 280.24 281.08 280.75 293.14 287.65 288.48 CO C(1s) ! 3p 293.5 272.53 275.74 276.55 280.24 281.12 280.79 293.14 287.66 288.49 CO2 C(1s) ! 3s 292.7 272.78 274.99 275.72 279.60 281.03 280.43 291.85 286.79 287.58 CO2 C(1s) ! 3p⇡ 295.0 274.12 277.74 278.55 282.22 283.08 282.73 295.19 289.56 290.39 N2 N(1s)! 3s 406.2 383.23 385.80 386.75 391.46 392.81 392.24 409.28 403.09 404.02 N2 N(1s)! 3p⇡ 407.1 383.82 386.66 387.59 392.28 393.54 393.03 410.37 404.00 404.93 N2 N(1s)! 3p 407.3 383.77 386.88 387.80 392.50 393.71 393.23 410.70 404.26 405.18 H2CO O(1s) ! 3sa1 535.4 510.30 513.14 514.20 519.85 521.54 520.86 543.15 536.40 537.43 H2CO O(1s) ! 3pa1 536.3 510.95 514.00 515.06 520.70 522.26 521.65 544.32 537.36 538.38 CO O(1s)! 3s 538.9 513.06 515.39 516.39 522.13 523.86 523.14 545.37 538.63 539.60 CO O(1s)! 3p⇡ 539.9 513.58 516.37 517.35 523.07 524.66 524.02 546.71 539.72 540.68
H2S S(1s) ! 4p 2476.3 2396.11 2399.32 2400.71 2415.18 2420.27 2418.20 2485.48 2476.55 2478.13 SO2 S(1s) ! 4p 2478.4 2400.56 2402.69 2404.00 2418.65 2424.29 2421.98 2487.91 2479.43 2480.98 HCl Cl(1s)! 4p⇡ 2827.8 2740.76 2743.73 2745.09 2760.58 2766.13 2763.87 2836.44 2827.28 2828.81 Cl2 Cl(1s)! 4p 2828.5 2741.19 2743.97 2745.32 2760.78 2766.55 2764.20 2836.39 2827.47 2829.01
Core!Valence MSE -42.32 -41.30 -40.31 -31.95 -28.74 -30.05 4.81 -1.46 -0.38
(15) MAE 42.32 41.30 40.31 31.95 28.74 30.05 5.12 2.22 2.53
rms 50.91 49.93 48.96 39.29 35.56 37.08 6.25 2.91 2.84
Core!Rydberg MSE -32.26 -29.35 -28.38 -22.26 -20.35 -21.12 3.36 -2.93 -1.93
(23) MAE 32.26 29.35 28.38 22.26 20.35 21.12 3.50 3.22 2.94
rms 39.91 37.64 36.78 29.43 26.90 27.93 4.94 3.81 3.26
TABLE IX: The 38 core excitation energies (in eV) of 13 molecules taken from Ref. [6]. The relativistic corrections [(0.12 eV for C, 0.24 eV for N, 0.45 eV for O, and 0.75 eV for F) [5] and (3.4 eV for Si, 4.6 eV for P, 5.9 eV for S, and 7.9 eV for Cl) [6]] are subtracted from the reference values.
Excitation Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 Core!Valence
C2H4 C(1s)! ⇡* 284.58 268.07 269.02 269.74 273.37 274.76 274.20 284.98 280.51 281.23 C2H2 C(1s)! ⇡* 285.68 268.92 269.99 270.69 274.34 275.74 275.18 286.02 281.52 282.22 H2CO C(1s) ! ⇡* 285.88 269.25 269.79 270.48 274.08 275.51 274.93 285.48 281.18 281.85 CO C(1s) ! ⇡* 287.28 270.40 270.79 271.37 274.93 276.35 275.78 286.38 282.18 282.78 CO2 C(1s) ! ⇡* 290.68 273.74 274.49 275.08 278.62 280.01 279.44 289.97 285.73 286.33 N2 N(1s)! ⇡* 400.76 381.56 382.07 382.83 387.32 389.03 388.34 403.64 398.66 399.42
H2CO O(1s) ! ⇡* 530.35 508.53 509.21 510.13 515.48 517.45 516.66 537.09 531.52 532.43 CO O(1s)! ⇡* 533.75 511.37 512.23 513.14 518.59 520.59 519.79 540.48 534.72 535.64 HF F(1s) ! * 686.65 659.07 660.67 661.81 668.40 670.68 669.71 696.00 689.59 690.68 SiH4 Si(1s) ! * 1839.1 1779.27 1781.21 1782.55 1794.84 1799.52 1797.60 1852.21 1843.94 1845.54 PH3 P(1s) ! * 2141.2 2075.69 2077.03 2078.32 2091.78 2096.99 2094.85 2154.80 2146.59 2148.12 H2S S(1s) ! * 2467.2 2395.39 2396.48 2397.78 2412.37 2418.02 2415.71 2481.33 2473.07 2474.61 SO2 S(1s) ! ⇡* 2467.9 2396.11 2396.92 2398.22 2412.79 2418.47 2416.14 2481.35 2473.12 2474.67 HCl Cl(1s)! * 2816.0 2739.15 2740.77 2742.07 2757.51 2763.51 2761.06 2831.99 2823.59 2825.08 Cl2 Cl(1s)! u* 2813.4 2737.15 2738.27 2739.59 2754.88 2760.83 2758.40 2828.90 2820.64 2822.15
Core!Rydberg
C2H4 C(1s)! 3s 286.98 268.59 271.54 272.41 275.96 276.93 276.54 288.25 283.25 284.08 C2H2 C(1s)! 3s 287.58 268.88 271.81 272.66 276.25 277.21 276.82 288.57 283.54 284.36 C2H2 C(1s)! 3p⇡ 288.58 269.60 272.84 273.66 277.24 278.08 277.76 289.96 284.64 285.45 C2H2 C(1s)! 3p 288.68 269.21 272.32 273.12 276.75 277.76 277.38 289.16 284.08 284.88 H2CO C(1s) ! 3sa1 290.08 271.21 273.98 274.86 278.42 279.44 279.01 290.59 285.62 286.45 H2CO C(1s) ! 3pb2 291.18 271.87 274.91 275.77 279.46 280.46 280.07 291.96 286.72 287.58 H2CO C(1s) ! 3pa1 291.58 271.77 274.97 275.84 279.39 280.29 279.92 291.64 286.66 287.49 CO C(1s) ! 3s 292.28 272.05 274.96 275.79 279.49 280.44 280.04 292.14 286.81 287.65 CO C(1s) ! 3p⇡ 293.18 272.58 275.78 276.58 280.24 281.08 280.75 293.14 287.65 288.48 CO C(1s) ! 3p 293.38 272.53 275.74 276.55 280.24 281.12 280.79 293.14 287.66 288.49 CO2 C(1s) ! 3s 292.58 272.78 274.99 275.72 279.60 281.03 280.43 291.85 286.79 287.58 CO2 C(1s) ! 3p⇡ 294.88 274.12 277.74 278.55 282.22 283.08 282.73 295.19 289.56 290.39 N2 N(1s)! 3s 405.96 383.23 385.80 386.75 391.46 392.81 392.24 409.28 403.09 404.02 N2 N(1s)! 3p⇡ 406.86 383.82 386.66 387.59 392.28 393.54 393.03 410.37 404.00 404.93
N2 N(1s)! 3p 407.06 383.77 386.88 387.80 392.50 393.71 393.23 410.70 404.26 405.18 H2CO O(1s) ! 3sa1 534.95 510.30 513.14 514.20 519.85 521.54 520.86 543.15 536.40 537.43 H2CO O(1s) ! 3pa1 535.85 510.95 514.00 515.06 520.70 522.26 521.65 544.32 537.36 538.38 CO O(1s)! 3s 538.45 513.06 515.39 516.39 522.13 523.86 523.14 545.37 538.63 539.60 CO O(1s)! 3p⇡ 539.45 513.58 516.37 517.35 523.07 524.66 524.02 546.71 539.72 540.68 H2S S(1s) ! 4p 2470.4 2396.11 2399.32 2400.71 2415.18 2420.27 2418.20 2485.48 2476.55 2478.13 SO2 S(1s) ! 4p 2472.5 2400.56 2402.69 2404.00 2418.65 2424.29 2421.98 2487.91 2479.43 2480.98 HCl Cl(1s)! 4p⇡ 2819.9 2740.76 2743.73 2745.09 2760.58 2766.13 2763.87 2836.44 2827.28 2828.81 Cl2 Cl(1s)! 4p 2820.6 2741.19 2743.97 2745.32 2760.78 2766.55 2764.20 2836.39 2827.47 2829.01
Core!Valence MSE -39.78 -38.76 -37.77 -29.41 -26.20 -27.51 7.35 1.08 2.16
(15) MAE 39.78 38.76 37.77 29.41 26.20 27.51 7.61 4.42 4.96
rms 47.20 46.21 45.23 35.54 31.80 33.33 9.73 4.80 5.50
Core!Rydberg MSE -30.89 -27.98 -27.01 -20.89 -18.97 -19.75 4.73 -1.56 -0.56
(23) MAE 30.89 27.98 27.01 20.89 18.97 19.75 4.83 4.23 4.12
rms 37.32 34.99 34.11 26.74 24.21 25.24 7.43 4.67 4.69
TABLE X: Interaction energies (in kcal/mol) of the S66 set [7].
Complex Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3 Hydrogen bonded complexes
Water· · · Water -4.918 -4.87 -4.37 -5.62 -5.56 -4.93 -5.01 -4.96 -4.69 -5.17
Water· · · MeOH -5.592 -5.16 -4.70 -6.18 -6.10 -5.56 -5.64 -5.68 -5.33 -5.81
Water· · · MeNH2 -6.908 -7.15 -6.34 -7.58 -7.57 -7.33 -7.34 -7.08 -7.03 -7.43
Water· · · Peptide -8.103 -7.28 -6.98 -9.03 -8.82 -8.13 -8.27 -8.23 -7.90 -8.50
MeOH· · · MeOH -5.757 -5.08 -4.54 -6.04 -6.00 -5.69 -5.75 -5.78 -5.45 -5.88
MeOH· · · MeNH2 -7.554 -7.19 -6.29 -7.93 -7.93 -7.99 -7.92 -7.68 -7.68 -7.95
MeOH· · · Peptide -8.230 -7.18 -6.64 -8.81 -8.64 -8.39 -8.47 -8.33 -8.07 -8.64
MeOH· · · Water -5.009 -4.78 -4.22 -5.50 -5.46 -4.94 -5.03 -4.97 -4.70 -5.16
MeNH2· · · MeOH -3.059 -2.22 -1.68 -3.16 -3.16 -3.05 -3.11 -3.19 -3.00 -3.13
MeNH2· · · MeNH2 -4.160 -3.08 -2.51 -4.61 -4.43 -4.36 -4.16 -3.88 -3.92 -4.28
MeNH2· · · Peptide -5.419 -3.39 -3.08 -5.86 -5.54 -5.54 -5.51 -5.21 -5.19 -5.68
MeNH2· · · Water -7.266 -7.14 -6.45 -7.96 -7.89 -7.52 -7.52 -7.32 -7.25 -7.66
Peptide· · · MeOH -6.187 -4.53 -4.24 -6.36 -6.22 -6.14 -6.22 -6.25 -6.00 -6.35
Peptide· · · MeNH2 -7.454 -6.12 -5.42 -7.53 -7.46 -7.91 -7.73 -7.41 -7.49 -7.77
Peptide· · · Peptide -8.630 -6.36 -6.04 -8.72 -8.50 -8.94 -8.95 -8.83 -8.69 -9.03
Peptide· · · Water -5.124 -4.32 -3.96 -5.41 -5.36 -4.88 -5.07 -5.09 -4.85 -5.20
Uracil· · · Uracil (BP) -17.182 -15.49 -14.38 -17.19 -17.16 -17.26 -17.36 -16.98 -16.49 -17.39
Water· · · Pyridine -6.857 -6.82 -6.01 -7.34 -7.31 -7.06 -7.16 -7.02 -6.83 -7.21
MeOH· · · Pyridine -7.410 -6.92 -6.01 -7.50 -7.50 -7.57 -7.65 -7.46 -7.32 -7.65
AcOH· · · AcOH -19.093 -18.59 -18.12 -20.50 -20.34 -19.84 -20.06 -19.76 -19.39 -20.37 AcNH2· · · AcNH2 -16.265 -15.02 -14.14 -16.94 -16.83 -16.50 -16.58 -16.04 -15.69 -16.72 AcOH· · · Uracil -19.491 -18.31 -17.58 -20.20 -20.10 -19.87 -20.03 -19.70 -19.22 -20.22 AcNH2· · · Uracil -19.189 -17.67 -16.83 -19.56 -19.51 -19.44 -19.52 -19.12 -18.65 -19.60
MSE 0.88 1.49 -0.46 -0.37 -0.17 -0.23 -0.05 0.18 -0.34
MAE 0.90 1.49 0.46 0.38 0.21 0.23 0.15 0.23 0.34
rms 1.10 1.63 0.56 0.48 0.28 0.31 0.20 0.29 0.43
Dispersion complexes
Benzene· · · Benzene (pi-pi) -2.822 1.22 1.11 -2.38 -1.84 -3.26 -3.25 -2.47 -3.10 -3.35
Pyridine· · · Pyridine (pi-pi) -3.895 0.48 0.22 -3.43 -2.81 -4.32 -4.24 -3.51 -4.17 -4.34 Uracil· · · Uracil (pi-pi) -9.829 -2.51 -3.13 -8.91 -7.79 -9.74 -9.77 -9.36 -9.78 -9.92 Benzene· · · Pyridine (pi-pi) -3.439 0.81 0.61 -2.99 -2.40 -3.86 -3.81 -3.05 -3.71 -3.91 Benzene· · · Uracil (pi-pi) -5.713 0.36 -0.25 -5.08 -4.06 -5.79 -5.80 -5.11 -5.87 -6.07 Pyridine· · · Uracil (pi-pi) -6.819 -0.74 -1.33 -6.22 -5.23 -6.80 -6.82 -6.29 -6.86 -7.06
Benzene· · · Ethene -1.432 0.76 0.89 -1.58 -1.26 -1.71 -1.80 -1.15 -1.59 -1.91
Uracil· · · Ethene -3.380 -0.34 -0.44 -3.48 -3.00 -3.54 -3.59 -3.19 -3.48 -3.74
Uracil· · · Ethyne -3.738 -1.03 -1.16 -4.02 -3.59 -3.72 -3.82 -3.41 -3.63 -3.94
Pyridine· · · Ethene -1.872 0.45 0.59 -2.02 -1.67 -2.10 -2.16 -1.56 -1.95 -2.25
Pentane· · · Pentane -3.776 0.42 0.68 -4.17 -3.48 -5.32 -4.34 -4.05 -4.34 -4.54
Pentane· · · Neopentane -2.613 0.18 0.59 -2.47 -2.13 -3.38 -2.88 -2.61 -2.81 -3.08
Neopentane· · · Neopentane -1.777 0.14 0.52 -2.70 -2.35 -3.58 -3.08 -2.75 -2.98 -3.31 Neopentane· · · Cyclopentane -2.404 0.11 0.62 -3.02 -2.56 -4.10 -3.31 -3.05 -3.21 -3.52 Cyclopentane· · · Cyclopentane -2.997 0.05 0.54 -1.69 -1.59 -2.38 -2.22 -1.98 -2.11 -2.38 Benzene· · · Cyclopentane -3.575 0.30 0.24 -3.41 -2.82 -4.38 -4.00 -3.49 -3.96 -4.10
Benzene· · · Neopentane -2.895 0.09 0.12 -2.77 -2.41 -3.50 -3.42 -2.97 -3.35 -3.54
Uracil· · · Pentane -4.848 0.52 0.34 -4.65 -3.77 -5.63 -5.21 -4.91 -5.30 -5.37
Uracil· · · Cyclopentane -4.138 0.58 0.59 -3.72 -3.01 -4.68 -4.30 -4.07 -4.34 -4.45
Uracil· · · Neopentane -3.712 0.08 0.08 -3.41 -2.91 -4.22 -4.03 -3.85 -4.04 -4.14
Ethene· · · Pentane -2.005 0.01 0.29 -2.32 -2.04 -2.59 -2.22 -2.08 -2.19 -2.24
Ethyne· · · Pentane -1.748 -0.09 0.17 -1.94 -1.81 -2.05 -2.03 -1.87 -1.99 -2.00
Peptide· · · Pentane -4.264 0.07 0.14 -4.55 -3.79 -5.13 -4.55 -4.26 -4.52 -4.73
MSE 3.72 3.73 0.12 0.67 -0.53 -0.30 0.12 -0.24 -0.44
MAE 3.72 3.73 0.42 0.74 0.59 0.38 0.32 0.33 0.50
rms 4.00 3.92 0.51 0.92 0.77 0.47 0.42 0.44 0.58
Mixed complexes
Benzene· · · Benzene (TS) -2.876 -0.19 -0.30 -2.61 -2.31 -3.12 -3.02 -2.67 -3.00 -3.07 Pyridine· · · Pyridine (TS) -3.535 -0.75 -0.87 -3.42 -3.05 -3.72 -3.60 -3.28 -3.52 -3.62 Benzene· · · Pyridine (TS) -3.331 -0.61 -0.82 -3.13 -2.80 -3.62 -3.50 -3.15 -3.51 -3.57 Benzene· · · Ethyne (CH-pi) -2.867 -1.23 -1.41 -3.03 -2.82 -3.02 -2.91 -2.70 -2.96 -3.00 Ethyne· · · Ethyne (TS) -1.524 -1.20 -0.89 -1.71 -1.73 -1.56 -1.56 -1.48 -1.48 -1.57 Benzene· · · AcOH (OH-pi) -4.707 -2.32 -2.62 -4.57 -4.22 -4.64 -4.75 -4.60 -5.05 -4.97 Benzene· · · AcNH2 (NH-pi) -4.361 -2.34 -2.29 -4.45 -4.18 -4.51 -4.56 -4.43 -4.60 -4.62 Benzene· · · Water (OH-pi) -3.277 -1.98 -2.10 -3.61 -3.40 -3.50 -3.57 -3.48 -3.73 -3.72 Benzene· · · MeOH (OH-pi) -4.188 -1.86 -1.95 -4.26 -3.89 -4.41 -4.35 -4.14 -4.54 -4.51 Benzene· · · MeNH2 (NH-pi) -3.231 -0.77 -0.83 -3.28 -2.93 -3.58 -3.49 -3.18 -3.54 -3.61 Benzene· · · Peptide (NH-pi) -5.282 -1.68 -2.02 -5.05 -4.56 -5.79 -5.62 -5.23 -5.80 -5.81 Pyridine· · · Pyridine (CH-N) -4.146 -2.49 -2.18 -4.21 -4.01 -3.89 -3.85 -3.54 -3.54 -4.05 Ethyne· · · Water (CH-O) -2.850 -2.63 -2.30 -3.23 -3.24 -2.73 -2.86 -2.91 -2.73 -2.94 Ethyne· · · AcOH (OH-pi) -4.868 -4.10 -3.78 -5.65 -5.41 -4.98 -5.10 -4.79 -4.91 -5.28
Pentane· · · AcOH -2.912 0.07 0.30 -2.99 -2.59 -3.37 -3.21 -3.21 -3.29 -3.30
Pentane· · · AcNH2 -3.534 -0.26 -0.01 -3.81 -3.28 -4.14 -3.87 -3.68 -3.85 -3.99
Benzene· · · AcOH -3.801 -0.53 -0.84 -3.82 -3.32 -4.12 -4.05 -3.64 -4.07 -4.26
Peptide· · · Ethene -2.999 -0.95 -0.74 -3.27 -3.00 -3.14 -3.14 -3.05 -3.06 -3.17
Pyridine· · · Ethyne -3.991 -3.64 -3.04 -4.20 -4.24 -4.15 -4.20 -4.04 -3.94 -4.19
MeNH2· · · Pyridine -3.968 -1.73 -1.44 -4.11 -3.78 -4.08 -3.99 -3.65 -3.78 -4.09
MSE 2.05 2.11 -0.11 0.17 -0.19 -0.15 0.07 -0.13 -0.25
MAE 2.05 2.11 0.20 0.33 0.24 0.18 0.16 0.23 0.26
rms 2.28 2.27 0.26 0.38 0.28 0.21 0.21 0.29 0.30
MSE 2.22 2.46 -0.15 0.16 -0.30 -0.23 0.04 -0.06 -0.35
MAE 2.23 2.46 0.37 0.49 0.35 0.26 0.21 0.27 0.37
rms 2.75 2.80 0.47 0.65 0.51 0.35 0.30 0.35 0.46
TABLE XI: Atomization energies (in eV) of the AE113 database [8, 9]. The atomization energies are calculated with- out the zero-point energy correction.
Molecule Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3
CH3 13.32 13.44 13.38 13.27 13.30 13.31 13.30 13.65 13.33 13.24
CH4 18.19 18.21 18.11 18.11 18.14 18.16 18.15 18.58 18.06 18.10
NH 3.60 3.84 3.70 3.66 3.65 3.65 3.65 3.73 3.69 3.65
NH2 7.91 8.18 5.95 7.94 7.94 7.95 7.94 8.11 7.93 7.93
NH3 12.91 13.10 12.83 12.86 12.88 12.90 12.89 13.16 12.78 12.87
OH 4.65 4.78 4.65 4.60 4.63 4.65 4.64 4.73 4.60 4.60
H2O 10.11 10.18 9.97 9.92 9.97 10.02 10.00 10.20 9.85 9.94
HF 6.16 6.18 6.06 6.04 6.04 6.07 6.06 6.16 5.93 6.01
SiH3 9.88 9.62 9.77 9.86 9.89 9.88 9.88 10.24 9.71 9.84
SiH4 14.07 13.58 13.78 14.07 14.07 14.04 14.05 14.53 13.72 14.04
PH3 10.46 10.40 10.25 10.48 10.57 10.62 10.61 10.84 10.22 10.50
SH2 7.93 7.90 7.72 7.86 7.92 7.96 7.96 8.05 7.69 7.88
HCl 4.65 4.64 4.52 4.58 4.60 4.63 4.63 4.67 4.50 4.59
HCCH 17.49 18.00 17.45 17.35 17.39 17.40 17.39 17.47 17.38 17.31
CH2CH2 24.38 24.80 24.35 24.28 24.33 24.35 24.34 24.63 24.28 24.26
CH3CH3 30.84 31.09 30.88 30.82 30.84 30.85 30.85 31.40 30.80 30.81
HCN 13.51 14.17 13.51 13.47 13.46 13.45 13.45 13.42 13.46 13.47
CO 11.22 11.70 11.26 11.19 11.17 11.17 11.17 11.13 11.15 11.22
HCO 12.01 12.78 12.20 12.05 12.06 12.09 12.07 12.06 12.07 12.05
CH2O 16.20 16.78 16.26 16.17 16.19 16.22 16.21 16.31 16.12 16.17
CH3OH 22.22 22.57 22.23 22.13 22.17 22.21 22.19 22.55 22.08 22.15
N2 9.85 10.56 9.91 9.95 9.86 9.79 9.82 9.71 9.88 9.98
NH2NH2 18.82 19.49 18.90 18.91 18.90 18.90 18.90 19.15 18.81 18.95
NO 6.57 7.23 6.74 6.52 6.48 6.45 6.46 6.89 6.59 6.53
O2 5.20 6.24 5.60 5.51 5.44 5.42 5.43 5.31 5.46 5.53
HOOH 11.62 12.19 11.51 11.42 11.46 11.52 11.50 11.56 11.32 11.46
F2 1.67 2.25 1.60 1.61 1.54 1.52 1.53 1.36 1.42 1.56
CO2 16.85 18.13 17.20 16.95 16.97 17.03 17.00 16.76 16.96 16.98
P2 4.99 5.30 4.39 4.71 4.93 5.07 5.01 4.47 4.36 4.74
S2 4.41 4.97 4.26 4.38 4.48 4.57 4.54 4.08 4.23 4.42
Cl2 2.53 2.82 2.36 2.41 2.47 2.54 2.51 2.22 2.34 2.45
NaCl 4.32 4.13 4.18 4.46 4.46 4.35 4.36 4.25 4.14 4.39
SiO 8.25 8.48 8.02 8.12 8.14 8.13 8.13 8.03 7.89 8.13
CS 7.37 7.79 7.01 7.17 7.22 7.28 7.26 6.89 6.99 7.18
ClO 2.74 3.53 2.85 2.81 2.85 2.90 2.88 2.63 2.77 2.84
ClF 2.68 3.12 2.67 2.67 2.67 2.68 2.68 2.52 2.55 2.66
SiH3SiH3 23.19 22.49 22.82 23.30 23.27 23.19 23.23 23.76 22.72 23.25
CH3Cl 17.08 17.35 17.05 17.07 17.09 17.10 17.10 17.23 16.98 17.06
CH3SH 20.50 20.72 20.39 20.47 20.52 20.54 20.54 20.73 20.32 20.48
SO2 10.97 12.09 11.03 10.92 10.99 11.07 11.04 10.68 10.81 11.00
BF3 20.40 20.93 20.65 20.37 20.35 20.30 20.31 20.39 20.22 20.29
BCl3 14.02 14.67 14.17 14.18 14.19 14.18 14.18 13.67 14.07 14.16
AlCl3 13.57 13.35 13.35 13.52 13.49 13.42 13.46 13.06 13.23 13.51
CF4 20.80 21.94 21.35 21.00 20.91 20.82 20.88 20.83 20.83 20.97
CCl4 13.59 14.57 13.59 13.70 13.67 13.62 13.65 12.83 13.49 13.70
OCS 14.45 15.64 14.53 14.47 14.53 14.63 14.59 14.14 14.37 14.50
CS2 12.00 13.09 11.70 11.83 11.96 12.12 12.05 11.35 11.62 11.85
CF2O 18.21 19.53 18.71 18.42 18.38 18.36 18.38 18.21 18.33 18.41
SiF4 24.92 24.58 24.54 24.59 24.44 24.24 24.33 24.35 23.94 24.45
N2O 11.66 13.51 11.97 11.89 11.82 11.82 11.83 11.38 11.80 11.90
NF3 8.94 10.67 9.47 9.40 9.22 9.11 9.17 8.90 9.10 9.35
PF3 15.64 15.99 15.62 15.59 15.59 15.52 15.56 15.52 15.21 15.58
O3 6.26 8.04 6.10 6.00 5.95 6.01 5.98 5.40 5.82 5.99
F2O 4.04 5.35 4.15 4.11 4.02 3.98 4.00 3.71 3.87 4.07
ClF3 5.43 7.12 5.70 5.60 5.54 5.54 5.54 5.09 5.32 5.54
CF2CF2 25.54 27.50 26.37 25.91 25.84 25.78 25.81 25.56 25.80 25.83
CF3CN 27.77 29.67 28.40 28.06 27.94 27.83 27.89 27.61 27.96 28.02
CH3CCH 30.43 31.26 30.57 30.39 30.43 30.42 30.42 30.65 30.46 30.36
CH2CCH2 30.40 31.42 30.56 30.39 30.45 30.48 30.46 30.63 30.46 30.36 cylC3H4 29.45 30.45 29.83 29.65 29.59 29.52 29.57 29.72 29.71 29.60 cylC3H6 36.91 37.68 37.33 37.15 37.09 37.02 37.06 37.50 37.22 37.12 CH3CH2CH3 43.58 44.02 43.72 43.61 43.62 43.63 43.62 44.31 43.63 43.60 CH3CCCH3 43.32 44.48 43.60 43.37 43.39 43.37 43.37 43.73 43.47 43.33 cylC4H6 43.28 44.43 43.73 43.43 43.40 43.39 43.40 43.67 43.61 43.42
isobutane 56.37 56.98 56.57 56.44 56.42 56.42 56.41 57.25 56.49 56.42
benzene 59.14 61.17 59.69 59.19 59.26 59.29 59.28 59.26 59.53 59.19
CH2F2 18.99 19.62 19.22 19.08 19.04 19.01 19.03 19.18 18.93 19.03
CF3H 19.92 20.84 20.31 20.07 20.01 19.94 19.98 20.02 19.90 20.03
CH2Cl2 16.05 16.55 16.05 16.09 16.11 16.11 16.11 15.93 15.97 16.09
CCl3H 14.87 15.61 14.87 14.95 14.94 14.91 14.94 14.44 14.78 14.95
CH3NO2 26.01 27.91 26.45 26.29 26.24 26.22 26.24 26.14 26.19 26.31
CH3SiH3 27.22 26.95 27.05 27.26 27.26 27.22 27.24 27.82 26.97 27.23
HCOOH 21.49 22.50 21.71 21.49 21.54 21.58 21.56 21.61 21.47 21.53
CH3CONH2 37.48 38.87 37.89 37.70 37.69 37.69 37.70 37.96 37.69 37.72 cylNHC2H4 31.11 32.10 31.53 31.39 31.32 31.26 31.30 31.57 31.41 31.39
NCCN 21.59 23.39 21.85 21.68 21.64 21.62 21.62 21.23 21.73 21.67
CH3NHCH3 37.66 38.33 37.83 37.75 37.75 37.76 37.75 38.31 37.72 37.76
CH2CO 23.03 24.26 23.35 23.13 23.17 23.22 23.20 23.17 23.18 23.14
cylOC2H4 28.18 29.11 28.55 28.33 28.30 28.28 28.30 28.53 28.37 28.35
OCHCHO 27.39 28.84 27.69 27.47 27.48 27.49 27.49 27.40 27.44 27.48
CH3CH2OH 35.06 35.62 35.17 35.02 35.05 35.07 35.06 35.57 35.00 35.04 CH3OCH3 34.55 35.15 34.67 34.54 34.58 34.59 34.59 35.11 34.50 34.56 cylSC2H4 27.06 27.78 27.20 27.18 27.16 27.14 27.17 27.15 27.10 27.18 CH3SOCH3 36.89 37.82 36.98 36.92 36.96 36.99 36.99 37.19 36.81 36.95
CH2CHF 24.81 25.62 25.00 24.84 24.85 24.85 24.85 25.01 24.80 24.80
CH3CH2Cl 29.96 30.42 30.03 30.00 30.02 30.01 30.02 30.28 29.96 30.00
CH2CHCl 23.51 24.22 23.55 23.49 23.53 23.54 23.54 23.53 23.46 23.48
CH3CClO 28.90 30.11 29.13 29.00 29.02 29.04 29.04 28.96 28.96 29.01
prplCl 42.65 43.35 42.81 42.75 42.74 42.73 42.74 43.14 42.72 42.74
NC3H9 50.20 51.08 50.45 50.35 50.33 50.32 50.32 51.03 50.34 50.36
cylOC4H4 42.99 44.80 43.60 43.07 43.12 43.14 43.15 43.15 43.37 43.11
cylNHC4H4 46.34 48.23 47.02 46.54 46.56 46.58 46.58 46.62 46.85 46.56
NO2 9.80 11.75 7.41 10.14 10.07 10.08 10.09 9.66 10.07 10.15
SF6 20.77 21.99 21.20 20.79 20.66 20.46 20.59 20.33 20.42 20.76
CFCl3 15.22 16.35 15.41 15.42 15.37 15.30 15.34 14.71 15.20 15.40
CClF3 18.85 20.06 19.32 19.10 19.01 18.92 18.98 18.74 18.90 19.07
CBrF3 18.34 19.60 18.81 18.55 18.46 18.37 18.43 18.16 18.36 18.51
HCCF 17.19 18.19 17.45 17.23 17.24 17.24 17.24 17.17 17.24 17.18
HCCCN 25.93 27.58 26.11 25.88 25.90 25.90 25.89 25.61 25.98 25.84
NCCCCN 34.15 36.94 34.64 34.26 34.27 34.27 34.24 33.66 34.46 34.22
C2N2 21.59 23.39 21.85 21.68 21.64 21.62 21.62 21.23 21.73 21.67
C3O2 28.58 31.24 29.25 28.77 28.88 29.03 28.94 28.40 28.93 28.78
FCN 13.19 14.37 13.45 13.31 13.27 13.25 13.26 13.04 13.26 13.29
HCCCCH 30.05 31.55 30.19 29.89 29.97 30.00 29.96 29.81 30.04 29.83
H2CS 14.07 14.45 13.85 13.92 14.00 14.06 14.04 13.92 13.78 13.92
HCONH2 24.56 25.70 24.86 24.70 24.73 24.75 24.74 24.84 24.67 24.72
CH2CHCHO 35.76 37.06 35.97 35.76 35.81 35.83 35.82 35.91 35.79 35.75 CH2CCl2 22.48 23.46 22.60 22.55 22.57 22.55 22.57 22.26 22.49 22.54
CHFCF2 25.31 26.91 25.91 25.57 25.52 25.48 25.50 25.38 25.47 25.50
CH2CF2 25.38 26.57 25.80 25.54 25.52 25.50 25.52 25.55 25.48 25.49
CH3F 18.31 18.64 18.39 18.32 18.32 18.32 18.32 18.60 18.22 18.29
CF2Cl2 16.97 18.17 17.33 17.23 17.15 17.06 17.11 16.67 17.01 17.20
SiF2 12.93 12.95 12.70 12.86 12.79 12.67 12.72 12.68 12.40 12.78
MSE 0.83 0.10 0.05 0.05 0.04 0.05 0.04 -0.03 0.04
MAE 0.88 0.27 0.11 0.10 0.10 0.10 0.28 0.17 0.11
rms 1.06 0.41 0.15 0.13 0.14 0.13 0.34 0.23 0.14
TABLE XII: Vertical ionization potentials (in eV) of the IP131 database [8], calculated using IP(1) = Etotal(N 1) Etotal(N ).
Molecule Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3
H 13.60 13.60 13.77 13.64 13.65 13.68 13.67 13.90 13.76 13.66
He 24.59 24.47 24.63 24.67 24.65 24.71 24.69 25.19 24.55 24.62
Li 5.39 5.57 3.74 5.31 5.29 5.36 5.36 5.82 5.58 5.39
Be 9.32 9.00 9.03 8.91 8.86 8.83 8.85 9.55 9.05 8.96
B 8.30 8.67 8.76 8.39 8.51 8.55 8.52 9.04 8.74 8.39
C 11.26 11.54 11.68 11.30 11.40 11.44 11.41 11.99 11.64 11.32
N 14.53 14.74 14.89 14.53 14.59 14.63 14.60 15.21 14.82 14.53
O 13.62 14.07 14.12 13.83 13.83 13.82 13.81 14.31 14.03 13.79
F 17.42 17.68 17.78 17.51 17.52 17.54 17.52 18.02 17.58 17.44
Ne 21.57 21.70 21.82 21.61 21.58 21.62 21.58 22.05 21.52 21.45
Na 5.14 5.35 5.20 4.87 4.87 4.95 4.94 5.58 5.22 4.95
Mg 7.65 7.62 7.47 7.65 7.60 7.48 7.48 8.03 7.50 7.56
Al 5.99 6.07 6.20 5.89 5.95 6.00 5.98 6.37 6.17 5.91
Si 8.15 8.20 8.32 8.03 8.07 8.11 8.10 8.51 8.29 8.05
P 10.49 10.49 10.62 10.39 10.39 10.41 10.42 10.83 10.59 10.41
S 10.36 10.43 10.52 10.41 10.46 10.49 10.48 10.96 10.49 10.44
Cl 12.97 12.98 13.07 12.96 13.01 13.03 13.02 13.53 13.03 13.00
Ar 15.76 15.72 15.83 15.75 15.76 15.79 15.78 16.29 15.78 15.78
CH3 9.84 10.02 10.11 9.72 9.76 9.77 9.76 10.33 10.08 9.73
CH4 13.60 13.96 14.23 14.19 14.19 14.16 14.18 14.70 14.23 14.21
NH 13.49 13.80 13.92 13.56 13.60 13.63 13.61 14.20 13.86 13.57
NH2 12.00 12.18 10.17 12.14 12.10 12.08 12.10 12.64 12.16 12.18
NH3 10.82 10.97 10.97 10.95 10.93 10.93 10.93 11.45 10.95 10.98
OH 13.02 13.30 13.34 13.17 13.18 13.17 13.16 13.70 13.26 13.16
H2O 12.62 12.81 12.83 12.75 12.73 12.73 12.73 13.25 12.75 12.75
HF 16.12 16.34 16.40 16.27 16.23 16.24 16.23 16.74 16.23 16.21
SiH3 8.74 8.95 9.11 8.77 8.84 8.88 8.86 9.35 9.09 8.79
SiH4 12.30 12.14 12.82 12.74 12.68 12.58 12.63 13.27 12.77 12.76
PH3 10.59 10.48 10.52 10.48 10.53 10.56 10.55 10.98 10.53 10.53
SH2 10.50 10.41 10.46 10.39 10.43 10.46 10.45 10.87 10.43 10.42
HCl 12.77 12.73 12.79 12.72 12.75 12.77 12.77 13.23 12.76 12.75
HCCH 11.49 11.41 11.36 11.21 11.25 11.28 11.27 11.74 11.33 11.24
CH2CH2 10.68 10.62 10.50 10.39 10.42 10.44 10.43 10.88 10.48 10.41
CH3CH3 11.99 11.91 12.60 12.56 12.49 12.38 12.43 13.10 12.59 12.57
HCN 13.61 13.75 13.70 13.53 13.56 13.59 13.58 14.09 13.66 13.55
CO 14.01 13.86 14.17 14.19 14.16 14.12 14.15 14.84 14.18 14.26
HCO 9.31 9.77 10.14 9.92 9.96 9.97 9.96 10.56 10.12 9.94
CH2O 10.89 10.75 10.94 10.85 10.86 10.85 10.85 11.36 10.89 10.86
CH3OH 10.96 10.69 11.04 10.96 10.93 10.90 10.91 11.48 10.99 10.96
N2 15.58 15.40 16.06 15.92 15.94 15.90 15.91 16.71 16.06 15.98
NH2NH2 8.98 9.40 9.80 9.74 9.71 9.67 9.69 10.31 9.79 9.77
NO 9.26 9.91 10.29 10.04 10.12 10.15 10.13 10.76 10.25 10.06
O2 12.30 12.58 13.07 12.89 12.97 13.00 12.98 13.66 13.03 12.92
HOOH 11.70 11.30 11.83 11.73 11.73 11.71 11.72 12.39 11.79 11.76
F2 15.70 15.39 16.03 15.90 15.97 15.99 15.97 16.71 15.97 15.93
CO2 13.78 13.67 14.00 13.87 13.85 13.83 13.84 14.44 13.93 13.88
P2 10.62 10.52 10.43 10.30 10.38 10.45 10.42 10.70 10.39 10.32
S2 9.55 9.47 9.97 9.81 9.75 9.69 9.73 10.29 9.94 9.83
Cl2 11.49 11.21 11.76 11.67 11.62 11.54 11.58 12.22 11.72 11.69
NaCl 9.80 9.35 9.28 9.23 9.27 9.29 9.28 9.72 9.25 9.24
SiO 11.61 11.31 11.67 11.54 11.57 11.54 11.56 12.14 11.64 11.58
CS 11.34 11.29 12.96 11.54 11.50 11.49 11.51 12.07 11.52 11.59
ClO 11.01 10.77 11.23 11.08 11.09 11.06 11.07 11.69 11.18 11.09
ClF 12.77 12.43 12.85 12.74 12.76 12.76 12.76 13.37 12.81 12.78
SiH3SiH3 10.53 10.29 10.59 10.48 10.49 10.48 10.50 10.97 10.57 10.51
CH3Cl 11.29 11.10 11.43 11.34 11.34 11.32 11.33 11.86 11.39 11.37
CH3SH 9.44 9.26 9.43 9.35 9.37 9.38 9.38 9.84 9.40 9.38
SO2 12.50 12.14 13.61 12.58 12.59 12.55 12.56 13.26 12.68 12.63
BF3 15.96 14.47 15.77 15.63 15.59 15.46 15.52 16.57 15.75 15.70
BCl3 11.64 10.81 12.04 11.95 11.79 11.55 11.68 12.54 12.01 11.97
AlCl3 12.01 10.89 12.29 12.20 12.03 11.76 11.90 12.79 12.27 12.22
CF4 16.20 14.56 16.05 15.88 15.86 15.73 15.79 16.93 16.02 15.97
CCl4 11.69 10.55 11.95 11.87 11.68 11.40 11.54 12.48 11.92 11.88
OCS 11.19 11.25 11.34 11.23 11.27 11.32 11.30 11.74 11.30 11.27
CS2 10.09 10.04 10.10 10.00 10.03 10.08 10.07 10.46 10.06 10.03
CF2O 13.60 13.17 13.63 13.49 13.50 13.48 13.49 14.11 13.55 13.50
SiF4 16.40 14.47 16.16 15.99 15.91 15.71 15.81 17.01 16.13 16.08
N2O 12.89 12.91 12.95 12.81 12.84 12.87 12.85 13.35 12.88 12.82
NF3 13.60 12.95 13.58 13.49 13.51 13.49 13.49 14.21 13.53 13.51
PF3 12.20 11.29 11.63 11.59 11.64 11.64 11.64 12.28 11.64 11.66
O3 12.73 12.64 13.38 13.29 13.29 13.23 13.25 13.59 13.35 13.32
F2O 13.26 12.73 13.52 13.40 13.45 13.44 13.44 14.19 13.48 13.43
ClF3 13.05 12.00 13.02 12.92 12.92 12.84 12.87 13.72 13.00 12.97
CF2CF2 10.69 10.10 10.55 10.41 10.48 10.48 10.47 11.13 10.52 10.44
CF3CN 14.30 13.49 14.09 13.92 13.94 13.92 13.93 14.55 14.05 13.94
CH3CCH 10.37 10.21 10.36 10.23 10.25 10.24 10.25 10.75 10.34 10.25
CH2CCH2 10.20 10.08 10.15 10.04 10.06 10.07 10.07 10.55 10.13 10.07
cylC3H4 9.86 9.71 9.86 9.73 9.73 9.72 9.73 10.23 9.84 9.74
cylC3H6 10.54 10.74 10.96 10.84 10.83 10.81 10.82 11.36 10.94 10.86 CH3CH2CH3 11.51 11.10 11.94 11.91 11.83 11.68 11.75 12.46 11.94 11.93
CH3CCCH3 9.79 9.30 9.56 9.44 9.45 9.42 9.43 9.95 9.54 9.46
cylC4H6 9.43 9.41 9.50 9.37 9.38 9.39 9.39 9.86 9.48 9.39
isobutane 11.13 10.74 11.52 11.51 11.44 11.30 11.36 11.99 11.48 11.51
benzene 9.25 9.27 9.39 9.26 9.27 9.26 9.27 9.74 9.37 9.28
CH2F2 13.27 12.43 13.23 13.16 13.16 13.10 13.12 13.90 13.22 13.20
CF3H 15.50 13.54 14.48 14.41 14.40 14.32 14.35 15.20 14.46 14.45
CH2Cl2 11.40 10.70 11.74 11.63 11.52 11.33 11.43 12.21 11.68 11.65
CCl3H 11.50 10.53 11.70 11.61 11.46 11.23 11.35 12.20 11.66 11.62
CH3NO2 11.29 11.01 11.58 11.73 11.68 11.58 11.63 12.40 11.79 11.76
CH3SiH3 11.60 11.26 11.77 11.65 11.65 11.62 11.64 12.18 11.75 11.68
HCOOH 11.50 11.11 11.34 11.24 11.23 11.21 11.22 11.77 11.27 11.24
CH3CONH2 10.00 9.66 10.54 9.87 9.85 9.81 9.82 10.37 9.89 9.87
cylNHC2H4 9.85 9.62 9.84 9.76 9.75 9.72 9.73 10.27 9.82 9.79
NCCN 13.51 13.14 13.58 13.40 13.38 13.32 13.35 14.00 13.54 13.43
CH3NHCH3 8.95 8.77 9.02 8.97 8.95 8.91 8.93 9.46 9.00 8.99
CH2CO 9.64 9.71 9.80 9.70 9.74 9.75 9.74 10.25 9.78 9.73
cylOC2H4 10.57 10.47 10.74 10.64 10.63 10.60 10.61 11.14 10.69 10.65
OCHCHO 10.60 9.99 10.84 10.76 10.73 10.60 10.66 11.43 10.82 10.79
CH3CH2OH 10.64 10.19 10.72 10.65 10.62 10.56 10.58 11.18 10.67 10.65
CH3OCH3 10.10 9.73 10.10 10.02 10.00 9.96 9.97 10.52 10.05 10.03
cylSC2H4 9.05 8.93 9.07 8.98 9.00 9.01 9.02 9.46 9.04 9.01
CH3SOCH3 9.10 8.81 9.06 8.98 8.97 8.94 8.95 9.49 9.03 9.00
CH2CHF 10.63 10.37 10.46 10.33 10.37 10.39 10.38 10.89 10.43 10.36
CH3CH2Cl 11.06 10.66 11.15 11.08 11.07 11.02 11.05 11.59 11.12 11.09
CH2CHCl 10.20 9.83 10.12 10.00 9.98 9.94 9.97 10.52 10.09 10.02
CH3CClO 11.03 10.75 11.98 11.09 11.06 11.01 11.03 11.59 11.12 11.09
prplCl 10.88 10.36 11.02 10.95 10.92 10.84 10.88 11.46 10.99 10.96
NC3H9 8.54 8.25 8.46 8.43 8.40 8.36 8.38 8.89 8.44 8.43
cylOC4H4 8.90 8.90 9.00 8.86 8.87 8.87 8.87 9.37 8.97 8.87
cylNHC4H4 8.23 8.27 8.31 8.19 8.21 8.21 8.21 8.68 8.29 8.21
NO2 11.23 11.18 9.01 11.70 11.74 11.71 11.71 12.51 11.88 11.74
SF6 15.70 13.73 15.52 15.44 15.40 15.22 15.31 16.48 15.57 15.53
CFCl3 11.76 10.84 12.07 11.98 11.83 11.59 11.71 12.59 12.04 12.00
CClF3 13.08 12.56 13.11 13.02 13.04 13.02 13.03 13.61 13.07 13.05
CBrF3 12.08 11.70 12.06 11.90 11.95 11.95 11.97 12.57 12.04 11.99
HCCF 11.50 11.17 11.30 11.16 11.20 11.22 11.21 11.75 11.28 11.19
HCCCN 11.75 11.37 11.68 11.52 11.51 11.48 11.50 12.08 11.65 11.55
NCCCCN 11.84 11.51 12.07 11.91 11.87 11.80 11.83 12.50 12.04 11.93
C2N2 13.51 13.14 13.58 13.40 13.38 13.32 13.35 14.00 13.54 13.43
C3O2 10.80 10.76 10.85 10.72 10.77 10.81 10.79 11.30 10.81 10.75
FCN 13.65 13.31 13.49 13.33 13.37 13.39 13.38 13.96 13.46 13.36
HCCCCH 10.30 9.93 10.19 10.04 10.04 10.01 10.02 10.59 10.17 10.07
H2CS 9.38 9.26 9.36 9.26 9.30 9.32 9.32 9.75 9.32 9.29
HCONH2 10.40 10.23 10.91 10.30 10.29 10.27 10.28 10.80 10.31 10.30
CH2CHCHO 10.10 9.81 10.13 10.04 10.02 9.98 10.00 10.54 10.08 10.04
CH2CCl2 10.00 9.56 10.00 9.88 9.85 9.78 9.82 10.41 9.97 9.90
CHFCF2 10.62 10.01 10.33 10.20 10.26 10.27 10.26 10.85 10.30 10.23
CH2CF2 10.70 10.38 10.58 10.45 10.50 10.51 10.51 11.06 10.55 10.48
CH3F 13.04 12.72 13.25 13.17 13.16 13.12 13.14 13.78 13.21 13.18
CF2Cl2 12.24 11.51 12.46 12.38 12.28 12.13 12.21 12.96 12.42 12.39
SiF2 11.08 10.83 11.00 11.10 11.10 11.07 11.09 11.64 11.03 11.14
MSE -0.26 0.10 0.00 0.00 -0.03 -0.02 0.57 0.09 0.02
MAE 0.36 0.28 0.19 0.18 0.19 0.18 0.58 0.20 0.18
rms 0.52 0.46 0.26 0.26 0.27 0.26 0.64 0.28 0.26
TABLE XIII: Vertical ionization potentials (in eV) of the IP131 database [8], calculated using IP(2) = ✏HOMO(N ).
Molecule Ref. PBE LC-!PBE !B97 !B97X !B97X-D !B97X-D3 SLC-LDA-D3 SLC-PBE-D3 SLC-B97-D3
H 13.60 7.59 12.21 11.91 11.62 11.05 11.38 12.68 12.21 11.98
He 24.59 15.76 21.19 21.13 20.90 20.26 20.62 22.41 21.30 21.28
Li 5.39 3.22 3.78 5.32 5.31 5.21 5.30 5.83 5.61 5.38
Be 9.32 5.61 8.92 8.76 8.63 8.29 8.49 9.33 8.94 8.81
B 8.30 4.17 8.21 7.91 7.73 7.24 7.51 8.66 8.20 7.92
C 11.26 6.10 10.69 10.36 10.14 9.57 9.88 11.30 10.68 10.41
N 14.53 8.31 13.27 12.94 12.72 12.14 12.46 14.12 13.30 13.03
O 13.62 7.60 12.60 12.38 12.12 11.49 11.83 13.39 12.63 12.43
F 17.42 10.32 15.58 15.43 15.23 14.63 14.96 16.76 15.67 15.57
Ne 21.57 13.38 18.83 18.73 18.63 18.08 18.39 20.47 19.06 19.02
Na 5.14 3.03 5.24 4.82 4.91 4.87 4.92 5.58 5.26 4.87
Mg 7.65 4.70 7.50 7.35 7.31 7.08 7.22 7.92 7.52 7.37
Al 5.99 3.09 6.20 5.88 5.77 5.47 5.66 6.39 6.18 5.90
Si 8.15 4.61 8.23 7.93 7.72 7.30 7.55 8.49 8.20 7.95
P 10.49 6.30 10.33 10.08 9.78 9.26 9.57 10.69 10.31 10.10
S 10.36 6.15 10.31 10.08 9.83 9.31 9.60 10.83 10.29 10.11
Cl 12.97 8.14 12.60 12.45 12.15 11.56 11.88 13.24 12.59 12.48
Ar 15.76 10.30 15.00 14.89 14.56 13.92 14.28 15.77 15.01 14.95
CH3 9.84 5.42 9.80 9.41 9.15 8.59 8.90 10.27 9.79 9.44
CH4 13.60 9.45 14.00 13.91 13.60 12.99 13.32 14.69 14.01 13.95
NH 13.49 7.92 12.81 12.49 12.24 11.65 11.97 13.59 12.82 12.56
NH2 12.00 7.22 9.88 11.65 11.36 10.75 11.09 12.52 11.81 11.72
NH3 10.82 6.18 10.72 10.64 10.33 9.73 10.06 11.48 10.74 10.70
OH 13.02 7.38 12.30 12.16 11.89 11.27 11.61 13.21 12.34 12.24
H2O 12.62 7.24 12.11 12.02 11.73 11.11 11.45 13.06 12.15 12.11
HF 16.12 9.65 14.82 14.73 14.50 13.89 14.23 16.06 14.92 14.90
SiH3 8.74 5.37 9.13 8.78 8.59 8.16 8.41 9.46 9.12 8.81
SiH4 12.30 8.52 12.76 12.66 12.37 11.82 12.13 13.34 12.76 12.69
PH3 10.59 6.72 10.61 10.49 10.26 9.77 10.04 11.14 10.62 10.54
SH2 10.50 6.31 10.42 10.30 10.01 9.46 9.77 10.95 10.40 10.33
HCl 12.77 8.05 12.46 12.37 12.05 11.44 11.78 13.10 12.45 12.40
HCCH 11.49 7.20 11.35 11.21 10.92 10.36 10.67 11.88 11.34 11.23
CH2CH2 10.68 6.74 10.70 10.55 10.28 9.75 10.05 11.18 10.68 10.57
CH3CH3 11.99 8.17 12.51 12.43 12.15 11.59 11.90 13.17 12.52 12.46
HCN 13.61 9.02 13.41 13.25 12.94 12.35 12.68 14.02 13.40 13.28
CO 14.01 9.04 13.84 13.75 13.44 12.81 13.16 14.69 13.87 13.83
HCO 9.31 5.16 9.61 9.40 9.17 8.63 8.93 10.32 9.64 9.46
CH2O 10.89 6.26 10.68 10.58 10.36 9.82 10.13 11.51 10.71 10.66
CH3OH 10.96 6.26 10.84 10.75 10.49 9.92 10.24 11.68 10.87 10.83
N2 15.58 10.28 15.30 15.17 14.91 14.29 14.63 16.29 15.34 15.27
NH2NH2 8.98 5.30 9.74 9.66 9.38 8.80 9.12 10.49 9.76 9.72
NO 9.26 4.52 9.38 9.15 8.93 8.35 8.67 10.26 9.40 9.23
O2 12.30 6.84 11.94 11.79 11.59 11.01 11.33 13.08 12.02 11.92
HOOH 11.70 6.46 11.34 11.24 10.98 10.38 10.71 12.32 11.38 11.34
F2 15.70 9.48 14.74 14.64 14.47 13.90 14.22 16.09 14.87 14.83
CO2 13.78 9.09 13.54 13.41 13.18 12.65 12.95 14.38 13.56 13.49
P2 10.62 7.15 10.64 10.49 10.30 9.90 10.14 10.96 10.61 10.49
S2 9.55 5.83 9.88 9.70 9.41 8.88 9.19 10.33 9.85 9.72
Cl2 11.49 7.33 11.60 11.50 11.20 10.63 10.95 12.21 11.58 11.52
NaCl 9.80 5.30 9.34 9.25 8.96 8.41 8.71 9.94 9.34 9.27
SiO 11.61 7.48 11.59 11.44 11.25 10.77 11.05 12.25 11.60 11.51
CS 11.34 7.40 11.88 11.78 11.50 10.92 11.25 12.58 11.88 11.84
ClO 11.01 6.30 10.87 10.73 10.48 9.91 10.23 11.64 10.88 10.79
ClF 12.77 7.86 12.43 12.33 12.04 11.45 11.78 13.20 12.44 12.38
SiH3SiH3 10.53 7.19 10.94 10.82 10.59 10.13 10.39 11.41 10.93 10.84
CH3Cl 11.29 7.12 11.39 11.31 11.00 10.43 10.75 12.01 11.39 11.33
CH3SH 9.44 5.57 9.60 9.49 9.21 8.68 8.98 10.13 9.59 9.51
SO2 12.50 8.08 12.48 12.35 12.13 11.61 11.90 13.29 12.50 12.43
BF3 15.96 10.07 15.15 15.01 14.84 14.28 14.59 16.38 15.25 15.19
BCl3 11.64 7.72 12.00 11.90 11.59 11.02 11.34 12.61 11.98 11.92
AlCl3 12.01 8.02 12.27 12.17 11.86 11.30 11.61 12.87 12.26 12.19
CF4 16.20 10.42 15.55 15.43 15.26 14.69 15.01 16.81 15.65 15.61
CCl4 11.69 7.69 11.99 11.90 11.59 11.01 11.33 12.61 11.97 11.92
OCS 11.19 7.50 11.35 11.22 10.99 10.53 10.80 11.89 11.33 11.26
CS2 10.09 6.82 10.31 10.18 9.97 9.57 9.80 10.75 10.28 10.21
CF2O 13.60 8.52 13.33 13.20 12.97 12.39 12.71 14.31 13.36 13.30
SiF4 16.40 10.69 15.73 15.61 15.42 14.85 15.17 16.92 15.82 15.77
N2O 12.89 8.40 12.58 12.44 12.23 11.74 12.02 13.33 12.58 12.50
NF3 13.60 8.45 13.21 13.13 12.90 12.33 12.64 14.20 13.23 13.21
PF3 12.20 7.36 11.54 11.44 11.21 10.69 10.98 12.29 11.57 11.52
O3 12.73 8.02 12.88 12.78 12.55 11.97 12.29 13.75 12.93 12.88
F2O 13.26 7.72 12.91 12.81 12.62 12.03 12.35 14.12 12.99 12.95
ClF3 13.05 8.00 12.78 12.68 12.44 11.87 12.19 13.74 12.81 12.77
CF2CF2 10.69 6.31 10.57 10.42 10.22 9.71 9.99 11.31 10.55 10.47
CF3CN 14.30 9.57 14.06 13.90 13.60 13.00 13.33 14.72 14.04 13.93
CH3CCH 10.37 6.49 10.55 10.42 10.14 9.60 9.90 11.07 10.53 10.44
CH2CCH2 10.20 6.56 10.51 10.38 10.12 9.60 9.89 11.03 10.50 10.40
cylC3H4 9.86 6.11 10.01 9.88 9.62 9.11 9.40 10.51 10.00 9.90
cylC3H6 10.54 7.07 11.24 11.11 10.83 10.28 10.59 11.82 11.23 11.14
CH3CH2CH3 11.51 7.75 12.00 11.93 11.66 11.11 11.41 12.64 12.00 11.96