Supplementary material to: Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections

(1)

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 Chai^{1, 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

(2)

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 E_g(1) = E_total(N 1) + E_total(N + 1)

2Etotal(N ). . . 56

(3)

XVIIIFundamental gaps (in eV) of the FG131 database [8, 9], calculated using E_g(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

(4)

[1] Y. Zhao, B. J. Lynch, and D. G. Truhlar, J. Phys. Chem. A 108, 2715 (2004); Y. Zhao, N. Gonz´alez-Garc´ıa, and D. G. Truhlar, J.

Phys. Chem. A 109, 2012 (2005); 110, 4942(E) (2006).

[2] P. Jureˇcka, J. ˇSponer, J. ˇCern´y, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006).

[3] M. S. Marshall, L. A. Burns, and C. D. Sherrill, J. Chem. Phys. 135, 194102 (2011).

[4] N. A. Besley, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Phys. 130, 124308 (2009).

[5] T. M. Maier, H. Bahmann, A. V. Arbuznikov, and M. Kaupp, J. Chem. Phys. 144, 074106 (2016).

[6] N. A. Besley, M. J. G. Peach, and D. J. Tozer, Phys. Chem. Chem. Phys. 11, 10350 (2009).

[7] J. ˘Rez´a˘c, K. E. Riley, and P. Hobza, J. Chem. Theory Comput. 7, 2427 (2011).

[8] Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys. 136, 154109 (2012).

[9] C.-W. Tsai, Y.-C. Su, G.-D. Li, and J.-D. Chai, Phys. Chem. Chem. Phys. 15, 8352 (2013).

[10] S. Hirata and M. Head-Gordon, Chem. Phys. Lett. 314, 291 (1999).

[11] Y. Tawada, T. Tsuneda, S. Yanagisawa, T. Yanai, and K. Hirao, J. Chem. Phys. 120, 8425 (2004).

(5)

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

(6)

V^f 18.14 9.97 17.86 20.68 19.23 17.47 18.16 15.31 17.59 20.18

V^r 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

V^f 42.18 27.07 40.39 44.78 43.10 40.56 41.46 37.83 40.09 43.74

V^r 42.18 27.07 40.39 44.78 43.10 40.56 41.46 37.83 40.09 43.74

H + ClH! HCl + H

V^f 18.00 9.64 18.30 23.17 20.71 18.19 19.33 17.30 17.99 22.25

V^r 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

V^f 30.38 18.51 32.56 33.44 32.11 30.02 30.98 30.25 32.09 33.45

V^r 57.02 41.00 56.65 55.78 55.35 54.47 54.75 57.90 56.16 55.38

H + F2 ! HF + F

V^f 2.27 -9.86 0.32 1.99 0.89 -0.60 0.10 -1.56 0.30 2.26

V^r 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

V^f 7.43 -6.48 9.39 4.61 3.88 2.76 3.61 9.22 8.61 5.54

V^r 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

V^f -0.34 -8.31 0.96 -2.61 -2.27 -1.37 -1.55 3.03 1.16 -1.34

V^r -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

V^f 13.38 7.06 14.37 13.29 13.25 12.85 13.06 16.66 14.86 13.54

V^r 13.38 7.06 14.37 13.29 13.25 12.85 13.06 16.66 14.86 13.54

(7)

Cl + CH3Cl! ClCH3+ Cl

V^f 3.10 -3.80 8.42 6.22 4.72 3.70 4.38 8.56 7.82 6.48

V^r 3.10 -3.80 8.42 6.22 4.72 3.70 4.38 8.56 7.82 6.48

Cl · · · CH3Cl! ClCH3· · · Cl

V^f 13.61 7.15 17.80 17.69 16.04 14.30 15.20 18.38 17.81 17.24

V^r 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

V^f -12.54 -19.52 -9.42 -11.70 -13.14 -13.58 -13.14 -9.57 -9.94 -11.43

V^r 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

V^f 2.89 -0.67 5.42 5.41 4.20 3.07 3.60 5.59 5.36 4.96

V^r 29.62 21.45 32.11 30.89 31.08 30.50 30.91 35.79 32.90 31.72

OH + CH3F ! HOCH3+ F

V^f -2.78 -10.59 -1.19 -4.00 -3.67 -3.31 -3.19 1.35 -1.01 -2.84

V^r 17.33 9.14 21.34 17.87 17.58 17.90 17.89 22.68 21.01 18.47

OH · · · CH3F ! HOCH3· · · F

V^f 10.96 3.88 11.88 11.62 11.54 10.57 11.06 14.69 12.39 11.75

V^r 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

V^f 14.69 5.19 12.14 15.46 13.99 12.32 12.96 11.36 12.33 15.20

V^r 10.72 9.08 13.10 15.08 14.32 13.40 13.74 13.10 12.72 14.42

H + CO! HCO

V^f 3.17 -1.69 2.32 5.64 4.55 3.37 3.71 1.27 2.29 5.33

(8)

V^r 22.68 24.66 26.04 27.07 26.74 26.20 26.24 24.79 25.37 26.13 H + C2H4 ! CH3CH2

V^f 1.72 -0.14 2.05 4.95 4.09 3.03 3.42 0.44 1.80 4.54

V^r 41.75 40.19 47.53 48.46 47.01 45.37 46.01 46.97 47.22 47.82

CH₃+ C₂H₄ ! CH3CH₂CH₂

V^f 6.85 1.50 6.98 4.80 5.03 4.57 4.93 8.35 6.06 4.90

V^r 32.97 29.76 39.34 36.71 35.37 33.85 34.64 37.18 39.06 37.03

HCN ! HNC

V^f 48.16 45.60 46.67 45.86 46.28 46.42 46.19 46.35 46.24 45.26

V^r 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

V^f 5.70 0.56 5.85 6.55 5.24 4.08 4.71 2.61 5.54 6.44

V^r 8.70 -1.95 5.78 6.58 5.30 4.58 4.98 8.27 5.98 6.34

OH + H₂! H + H2O

V^f 5.10 -6.36 2.74 3.24 2.54 2.22 2.48 4.45 3.27 3.11

V^r 21.20 13.69 21.14 20.38 19.50 18.77 19.13 17.23 20.34 20.44

CH3+ H2! H + CH4

(9)

V^f 12.10 3.82 9.98 10.25 9.58 9.06 9.36 11.35 9.69 9.80

V^r 15.30 9.32 14.87 16.29 15.05 13.54 14.22 11.74 14.56 16.10

OH + CH₄! CH3+ H₂O

V^f 6.70 -5.65 4.88 4.46 3.89 3.04 3.43 6.24 5.09 4.27

V^r 19.60 8.91 18.39 15.56 15.37 15.11 15.22 18.62 17.30 15.30

H + H₂ ! H2+ H

V^f 9.60 3.64 7.89 12.37 10.73 9.21 9.77 5.84 7.84 11.67

V^r 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

V^f 3.20 -11.94 2.93 2.80 1.60 -0.02 0.85 4.90 3.32 2.71

V^r 12.70 -0.71 13.00 12.06 10.96 9.69 10.38 14.55 12.67 11.89

HCl + CH3! Cl + CH4

V^f 1.70 -5.94 1.28 -0.58 -1.19 -1.86 -1.45 1.80 0.60 -0.77

V^r 7.90 -2.95 6.10 5.49 4.34 3.11 3.69 7.85 5.91 5.43

OH + C₂H₆! H2O + C₂H₅

V^f 3.40 -9.03 2.42 1.76 1.16 0.17 0.56 3.47 2.40 1.49

V^r 19.90 10.76 20.06 17.27 17.18 16.57 16.82 19.97 18.64 16.90

F + H₂! HF + H

V^f 1.80 -12.97 -2.87 -3.79 -3.89 -3.70 -3.55 -1.06 -1.71 -2.85

V^r 33.40 25.12 32.70 29.79 29.17 29.01 29.20 27.67 30.93 29.99

O + CH₄! OH + CH3

V^f 13.70 -0.79 9.83 10.40 9.84 9.20 9.55 12.28 10.44 10.48

V^r 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

V^f 3.10 -1.79 2.90 5.86 4.63 3.28 3.79 0.73 2.63 5.36

(10)

V^r 23.20 17.91 23.04 25.29 24.15 23.46 23.78 25.51 23.02 24.72 H + HO ! H2+ O

V^f 10.70 3.75 10.52 10.68 9.82 8.84 9.17 6.66 10.16 10.48

V^r 13.10 -1.98 7.48 10.25 9.35 8.89 9.15 10.81 8.37 10.06

H + H₂S ! H2+ HS

V^f 3.50 -1.22 3.77 6.89 5.52 4.05 4.62 1.63 3.53 6.38

V^r 17.30 9.10 15.69 18.48 17.19 16.31 16.64 18.96 15.81 17.85

O + HCl! OH + Cl

V^f 9.80 -10.54 7.88 8.39 6.94 5.47 6.42 10.89 8.52 8.38

V^r 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

V^f 8.00 0.71 9.29 6.92 6.49 5.65 6.13 9.44 8.73 6.60

V^r 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

V^f 7.50 2.89 10.88 8.76 8.41 7.26 7.83 10.81 9.98 8.26

V^r 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

V^f 10.40 1.44 11.31 10.92 10.03 8.60 9.26 12.33 10.74 10.33

V^r 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

V^f 14.50 4.39 13.70 13.43 12.56 11.28 11.95 14.98 13.37 12.96

V^r 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

V^f 38.40 31.19 40.09 42.88 41.46 39.07 39.92 44.37 39.90 41.80

V^r 38.40 31.19 40.09 42.88 41.46 39.07 39.92 44.37 39.90 41.80

(11)

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 [C_2h] -3.133 -2.83 -2.35 -3.66 -3.59 -3.08 -3.09 -2.82 -2.85 -3.27

H₂O dimer [C_s] -4.989 -4.91 -4.37 -5.65 -5.59 -4.97 -5.04 -4.95 -4.69 -5.21

Formic acid dimer [C_2h] -18.753 -18.08 -17.79 -20.11 -19.95 -19.28 -19.51 -19.20 -18.88 -19.83 Formamide dimer [C_2h] -16.062 -14.69 -14.00 -16.77 -16.65 -16.17 -16.26 -15.73 -15.40 -16.40 Uracil dimer [C_2h] -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 [D_3d] -0.527 -0.08 0.13 -0.43 -0.57 -0.57 -0.61 -0.74 -0.69 -0.56

C₂H₄ dimer [D_2d] -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 [C_2h] -2.654 1.90 1.64 -2.27 -1.52 -3.16 -3.00 -1.99 -2.89 -3.18

Pyrazine dimer [C_s] -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

(12)

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 [C_s] -3.275 -2.03 -2.13 -3.56 -3.39 -3.50 -3.58 -3.52 -3.73 -3.71 Benzene· · · NH3 [C_s] -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 [C_2v] -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

(13)

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

(14)

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

(15)

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

(16)

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

(17)

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

(18)

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

(19)

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

(20)

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

(21)

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

(22)

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

(23)

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 without 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

(24)

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

(25)

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

(26)

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

(27)

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

(28)

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) = E_total(N 1) E_total(N ).

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

(29)

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

(30)

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

(31)

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

(32)

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

(33)

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 ).

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

(34)

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

(35)

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

(36)

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