Supplementary material to: Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2 functional

Supplementary material to: Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2

functional

Jeng-Da Chai

and Shan-Ping Mao

1

Department of Physics, National Taiwan University, Taipei 10617, Taiwan

2

Center for Theoretical Sciences and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan

(Dated: April 20, 2012)

TABLE I: Nonhydrogen transfer barrier heights (in kcal/mol) of the NHTBH38/04 set [1]. The notation used for characterizing statistical errors is as follows: mean signed errors (MSEs), mean absolute errors (MAEs), and root-mean-square (rms) errors.

Reactions Eref LDA PBE TPSS PBE0 PBE0-DH PBE0-2 B3LYP B2PLYP B2PLYP-D3 MP2

Heavy-atom transfer reactions

H + N2O! OH + N² V^f 18.14 2.69 9.97 7.33 13.91 17.41 23.58 11.37 16.67 16.48 36.05

V^r 83.22 32.09 52.46 60.16 68.79 76.63 81.25 72.81 76.62 76.34 88.32

H + FH! HF + H V^f 42.18 18.48 27.07 25.89 33.74 38.71 43.35 31.01 36.65 36.60 46.57

V^r 42.18 18.48 27.07 25.89 33.74 38.71 43.35 31.01 36.65 36.60 46.57

H + ClH! HCl + H V^f 18.00 2.27 9.64 7.03 13.38 16.03 19.26 12.41 15.70 15.66 22.64

V^r 18.00 2.27 9.64 7.03 13.38 16.03 19.26 12.41 15.70 15.66 22.64 H + FCH3! HF + CH3 V^f 30.38 13.36 18.51 16.40 25.71 30.23 33.87 21.79 26.55 26.26 36.14 V^r 57.02 31.72 41.00 42.28 49.75 54.86 58.38 48.64 52.70 52.15 60.23

H + F2! HF + F V^f 2.27 -15.97 -9.86 -11.44 -4.60 -0.44 11.20 -7.54 0.86 0.78 28.32

V^r 106.18 69.40 80.86 84.02 99.02 109.16 121.25 96.16 106.41 106.32 133.73 CH3+ FCl! CH3F + Cl V^f 7.43 -11.50 -6.48 -5.36 0.79 4.97 10.02 -1.58 2.51 1.81 18.72 V^r 60.17 37.67 41.63 42.81 53.46 60.14 66.55 50.96 56.69 56.25 75.15 Nucleophilic substitution reactions

F + CH3F! FCH3+ F V^f -0.34 -12.18 -8.31 -8.80 -2.67 -0.71 0.00 -3.93 -3.20 -3.76 0.37 V^r -0.34 -12.18 -8.31 -8.80 -2.67 -0.71 0.00 -3.93 -3.20 -3.76 0.37 F · · · CH3F! FCH3· · · F V^f 13.38 6.55 7.06 6.24 11.69 13.57 14.40 10.23 11.30 11.43 14.75 V^r 13.38 6.55 7.06 6.24 11.69 13.57 14.40 10.23 11.30 11.43 14.75

Cl + CH3Cl! ClCH3+ Cl V^f 3.10 -6.74 -3.80 -4.99 0.87 2.92 4.32 -0.57 1.02 0.12 5.50

V^r 3.10 -6.74 -3.80 -4.99 0.87 2.92 4.32 -0.57 1.02 0.12 5.50 Cl · · · CH3Cl! ClCH3· · · Cl V^f 13.61 6.74 7.15 5.68 11.29 13.41 15.14 9.22 11.36 11.32 16.54 V^r 13.61 6.74 7.15 5.68 11.29 13.41 15.14 9.22 11.36 11.32 16.54 F + CH3Cl! FCH3+ Cl V^f -12.54 -23.45 -19.52 -20.87 -15.45 -13.75 -12.13 -16.55 -15.05 -15.78 -10.28 V^r 20.11 10.10 12.31 13.42 19.44 21.77 21.83 18.26 18.63 17.85 20.70 F · · · CH3Cl! FCH3· · · Cl V^f 2.89 -1.04 -0.67 -2.18 1.66 2.96 4.29 0.31 1.74 1.75 5.66 V^r 29.62 21.65 21.45 22.23 28.35 30.86 31.38 26.62 27.69 27.70 30.64 OH + CH3F! HOCH3+ F V^f -2.78 -14.36 -10.59 -10.74 -4.97 -2.97 -2.20 -5.83 -5.06 -5.77 -1.71 V^r 17.33 5.70 9.14 8.02 15.94 18.22 18.50 14.13 14.60 13.98 17.96 OH · · · CH3F! HOCH3· · · F V^f 10.96 3.39 3.88 3.33 8.82 10.87 11.94 7.69 8.99 8.93 12.58 V^r 47.20 47.53 43.21 40.74 49.06 51.09 51.22 45.46 46.16 45.89 50.20 Unimolecular and association reactions

H+N2! HN2 V^f 14.69 -2.19 5.19 2.34 8.50 11.54 17.32 7.47 12.33 12.27 27.64

V^r 10.72 9.44 9.09 8.87 11.64 12.55 11.91 10.88 10.71 10.66 8.64

H + CO! HCO V^f 3.17 -7.57 -1.69 -5.14 0.31 1.83 3.85 -0.59 1.82 1.59 5.93

V^r 22.68 26.34 24.66 24.06 25.47 25.51 24.52 24.60 24.10 23.94 22.70

H + C H ! CHCH V^f 1.72 -5.34 -0.14 -4.34 0.67 1.50 4.24 -0.18 1.84 1.47 9.35

MSE -12.41 -8.52 -9.09 -3.13 -0.32 2.34 -4.57 -2.00 -2.29 5.37

MAE 12.62 8.62 9.16 3.63 1.57 2.44 4.69 2.19 2.44 5.48

rms 16.13 10.61 10.55 4.63 2.19 3.71 5.71 2.69 2.95 8.45

TABLE II: Hydrogen transfer barrier heights (in kcal/mol) of the HTBH38/04 set [1, 2]. The notation used for characterizing statistical errors is as follows: mean signed errors (MSEs), mean absolute errors (MAEs), and root-mean-square (rms) errors.

Reactions Eref LDA PBE TPSS PBE0 PBE0-DH PBE0-2 B3LYP B2PLYP B2PLYP-D3 MP2

H + HCl! H2+ Cl V^f 5.70 -3.14 0.56 -3.91 2.94 4.88 7.64 -0.77 2.84 2.74 10.68

V^r -8.70 8.70 -1.95 -1.10 1.66 3.90 5.90 3.73 5.45 5.34 7.45 OH + H2! H + H2O V^f 5.10 -18.39 -6.36 -3.88 -0.02 3.16 5.51 0.51 2.92 2.74 7.27 V^r 21.20 11.33 13.69 8.04 17.31 20.24 25.39 13.36 18.55 18.37 31.87 CH3+ H2! H + CH4 V^f 12.10 -5.35 3.82 5.12 6.89 8.83 10.84 8.73 10.23 9.95 12.76 V^r 15.30 4.94 9.32 5.58 11.90 13.92 16.73 9.53 12.78 12.52 19.76 OH + CH4! CH3+ H2O V^f 6.70 -17.22 -5.65 -1.77 1.62 4.91 6.50 1.92 3.89 3.44 7.19 V^r 19.60 2.21 8.91 9.69 13.94 16.90 20.50 13.98 16.96 16.51 24.79

H + H2! H2+ H V^f 9.60 -2.70 3.64 -0.86 5.63 7.47 10.24 4.22 7.12 7.09 13.24

V^r 9.60 -2.70 3.64 -0.86 5.63 7.47 10.24 4.22 7.12 7.09 13.24 OH + NH3! H2O + NH2 V^f 3.20 -23.88 -11.94 -7.99 -2.28 2.16 4.60 -2.62 0.12 -0.36 6.40 V^r 12.70 -10.71 -0.71 2.29 7.41 11.49 14.91 7.32 10.41 9.93 18.62 HCl + CH3! Cl + CH4 V^f 1.70 -13.74 -5.94 -4.04 -2.49 -0.67 0.74 -1.59 -0.19 -0.76 1.87 V^r -7.90 7.90 -2.95 -0.77 1.24 3.45 4.88 3.70 4.96 4.41 5.64 OH + C2H6! H2O + C2H5 V^f 3.40 -20.98 -9.03 -5.00 -1.23 2.22 4.00 -1.05 1.12 0.55 4.94 V^r 19.90 4.79 10.76 11.26 15.66 18.30 21.52 15.63 18.20 17.44 25.50 F + H2! HF + H V^f 1.80 -24.20 -12.97 -10.36 -4.90 -0.73 2.44 -6.03 -1.67 -1.85 4.37 V^r 33.40 25.72 25.12 19.19 28.41 31.46 37.89 23.76 30.40 30.22 46.07 O + CH4! OH + CH3 V^f 13.70 -10.69 -0.79 4.14 7.16 11.53 14.42 6.79 10.47 10.15 15.88 V^r 8.10 -9.27 -0.57 0.51 3.94 6.48 8.93 4.44 6.76 6.42 11.49 H + PH3! PH2+ H2 V^f 3.10 -7.35 -1.79 -5.21 0.35 1.86 3.70 -1.10 1.28 1.10 5.50 V^r 23.20 9.24 17.91 17.68 20.12 21.43 22.79 22.72 23.48 23.25 24.04

H + HO! H2+ O V^f 10.70 -1.69 3.75 -1.31 7.13 9.66 13.34 4.14 8.17 8.05 17.76

V^r 13.10 -13.40 -1.98 1.86 5.33 9.62 12.94 5.69 9.34 9.21 15.15

H + H2S! H2+ HS V^f 3.50 -6.73 -1.22 -4.71 1.05 2.69 4.69 -0.58 1.93 1.71 6.66

V^r -17.30 17.30 9.10 10.13 12.06 13.75 15.13 15.54 16.22 15.98 16.11 O + HCl! OH+Cl V^f 9.80 -23.13 -10.55 -3.92 2.22 14.62 12.39 0.96 13.30 13.21 15.25 V^r -10.40 10.40 -7.33 -4.28 2.74 13.69 11.04 3.90 14.75 14.66 14.63 NH2+ CH3! CH4+ NH V^f 8.00 -8.37 0.71 2.46 5.05 7.26 9.00 6.13 7.74 7.28 10.61 V^r 22.40 2.16 10.56 15.34 16.42 19.62 22.03 17.09 19.58 19.13 23.70 NH2+ C2H5! C2H6+ NH V^f 7.50 -5.76 2.89 4.57 6.89 8.71 9.86 8.20 9.14 8.39 10.93 V^r 18.30 -1.57 7.51 12.64 13.70 16.98 19.38 14.54 16.98 16.41 21.06 C2H6+ NH2! NH3+ C2H5 V^f 10.40 -9.69 1.44 5.61 7.26 9.81 10.87 8.73 9.85 9.17 11.19 V^r 17.40 2.91 9.99 11.59 14.45 16.57 18.08 15.47 16.64 15.77 19.54 NH2+ CH4! CH3+ NH3 V^f 14.50 -6.16 4.39 8.33 9.87 12.37 13.49 11.27 12.47 11.92 13.84 V^r 17.80 0.10 7.71 9.51 12.50 15.03 17.18 13.39 15.26 14.71 19.23

TABLE III: Interaction energies (in kcal/mol) of the S22 set [3, 4]. The counterpoise corrections are used to reduce the basis set superposition errors. Monomer deformation energies are not included. The notation used for characterizing statistical errors is as follows: mean signed errors (MSEs), mean absolute errors (MAEs), and root-mean-square (rms) errors.

Complex Eref LDA PBE TPSS PBE0 PBE0-DH PBE0-2 B3LYP B2PLYP B2PLYP-D3 MP2

Hydrogen bonded complexes

(NH3)2[C2h] -3.17 -5.10 -2.83 -2.29 -2.77 -2.83 -2.93 -2.19 -2.56 -3.04 -2.92 (H2O)2[Cs] -5.02 -7.78 -4.91 -4.44 -4.92 -4.96 -4.89 -4.49 -4.66 -5.05 -4.61 Formic acid dimer [C_2h] -18.80 -26.82 -18.08 -17.61 -18.86 -19.21 -18.75 -17.29 -17.52 -18.75 -17.16 Formamide dimer [C2h] -16.12 -21.82 -14.69 -14.02 -15.27 -15.64 -15.55 -13.97 -14.49 -15.85 -14.68 Uracil dimer [C2h] -20.69 -26.15 -18.45 -17.76 -19.16 -19.72 -19.91 -17.87 -18.67 -20.44 -19.22 2-pyridoxine2-aminopyridine [C1] -17.00 -22.77 -15.27 -14.38 -15.35 -15.84 -16.42 -13.72 -14.93 -16.97 -16.29 Adeninethymine WC [C1] -16.74 -21.99 -14.29 -13.28 -14.50 -15.09 -15.69 -12.82 -14.15 -16.37 -15.47

MSE -4.98 1.29 1.97 0.96 0.61 0.49 2.17 1.51 0.15 1.03

MAE 4.98 1.29 1.97 0.97 0.72 0.49 2.17 1.51 0.16 1.03

Dispersion complexes

(CH4)2[D3d] -0.53 -0.83 -0.08 0.18 -0.04 -0.09 -0.25 0.40 0.06 -0.36 -0.42 (C2H4)2[D2d] -1.50 -2.49 -0.31 0.33 -0.35 -0.58 -1.00 0.51 -0.28 -1.40 -1.35 BenzeneCH4[C3] -1.45 -2.01 -0.01 0.52 -0.08 -0.41 -1.04 0.82 -0.13 -1.32 -1.64 Benzene dimer [C2h] -2.62 -2.62 1.90 3.00 1.80 0.60 -1.94 3.84 0.82 -2.21 -4.58 Pyrazine dimer [Cs] -4.20 -4.46 0.73 1.91 0.52 -0.82 -3.57 2.56 -0.69 -3.86 -6.38 Uracil dimer [C2] -9.74 -10.15 -2.69 -0.96 -3.29 -4.99 -7.91 -0.86 -4.72 -9.34 -10.32 Indolebenzene [C1] -4.59 -4.38 2.24 3.69 2.02 0.17 -3.67 4.81 0.34 -4.01 -7.56 Adeninethymine stack [C1] -11.66 -11.96 -1.33 0.75 -2.14 -4.86 -9.69 1.46 -4.55 -10.93 -13.87

MSE -0.33 4.59 5.71 4.34 3.17 0.90 6.23 3.39 0.36 -1.23

MAE 0.38 4.59 5.71 4.34 3.17 0.90 6.23 3.39 0.36 1.29

Mixed complexes

Etheneethine [C2v] -1.51 -2.27 -1.16 -0.84 -1.18 -1.26 -1.41 -0.64 -0.99 -1.53 -1.52 BenzeneH2O [Cs] -3.29 -4.44 -2.04 -1.44 -2.21 -2.54 -2.98 -1.21 -2.04 -3.21 -3.25 BenzeneNH3 [Cs] -2.32 -3.03 -0.92 -0.35 -1.03 -1.36 -1.94 -0.08 -1.01 -2.22 -2.43 BenzeneHCN [Cs] -4.55 -5.85 -2.81 -2.26 -3.28 -3.83 -4.46 -1.93 -3.07 -4.56 -4.78 Benzene dimer [C2v] -2.71 -3.05 -0.10 0.59 -0.28 -0.95 -2.19 1.02 -0.63 -2.58 -3.36 Indolebenzene T-shape [C1] -5.62 -6.26 -2.03 -1.08 -2.36 -3.32 -5.03 -0.50 -2.79 -5.35 -6.53 Phenol dimer [C1] -7.09 -9.01 -3.87 -2.93 -4.18 -4.96 -6.23 -2.94 -4.71 -6.95 -7.23

MSE -0.98 2.03 2.68 1.80 1.27 0.41 2.97 1.69 0.10 -0.29

MAE 0.98 2.03 2.68 1.80 1.27 0.41 2.97 1.69 0.11 0.30

MSE -2.01 2.72 3.56 2.46 1.75 0.61 3.90 2.25 0.21 -0.21

MAE 2.03 2.72 3.56 2.46 1.78 0.61 3.90 2.25 0.22 0.89

rms 3.08 3.72 4.64 3.45 2.49 0.78 5.02 2.79 0.29 1.23

TABLE IV: Interaction energies (in kcal/mol) of the S66 set [5]. The counterpoise corrections are used to reduce the basis set superposition errors. Monomer deformation energies are not included. The notation used for characterizing statistical errors is as follows: mean signed errors (MSEs), mean absolute errors (MAEs), and root-mean-square (rms) errors.

Eref LDA PBE TPSS PBE0 PBE0-DH PBE0-2 B3LYP B2PLYP B2PLYP-D3 MP2 Hydrogen bonded complexes

Water! Water -4.92 -7.64 -4.87 -4.41 -4.90 -4.94 -4.88 -4.48 -4.66 -5.04 -4.62

Water! MeOH -5.59 -8.47 -5.16 -4.63 -5.20 -5.33 -5.43 -4.71 -5.08 -5.71 -5.31

Water! MeNH2 -6.91 -10.61 -7.15 -6.66 -7.01 -7.01 -6.94 -6.34 -6.55 -7.16 -6.64 Water! Peptide -8.10 -11.73 -7.28 -6.57 -7.49 -7.72 -7.82 -6.73 -7.22 -8.19 -7.52

MeOH! MeOH -5.76 -8.46 -5.08 -4.51 -5.10 -5.26 -5.46 -4.54 -5.02 -5.80 -5.45

MeOH! MeNH2 -7.55 -11.28 -7.19 -6.50 -7.05 -7.16 -7.32 -6.08 -6.63 -7.65 -7.23 MeOH! Peptide -8.23 -11.86 -7.18 -6.39 -7.30 -7.56 -7.78 -6.40 -7.04 -8.27 -7.62

MeOH! Water -5.01 -7.62 -4.78 -4.28 -4.79 -4.85 -4.87 -4.33 -4.58 -5.07 -4.69

MeNH2! MeOH -3.06 -4.65 -2.22 -1.62 -2.17 -2.31 -2.61 -1.54 -2.14 -3.02 -2.81

MeNH2! MeNH2 -4.16 -6.56 -3.08 -2.27 -3.01 -3.24 -3.67 -2.08 -2.91 -4.04 -3.94 MeNH2! Peptide -5.42 -7.74 -3.39 -2.40 -3.53 -3.98 -4.67 -2.39 -3.59 -5.32 -5.09 MeNH2! Water -7.27 -11.10 -7.14 -6.52 -7.06 -7.15 -7.22 -6.27 -6.67 -7.45 -7.03 Peptide! MeOH -6.19 -8.33 -4.53 -3.76 -4.72 -5.09 -5.63 -3.88 -4.82 -6.07 -5.93 Peptide ... MeNH2 -7.45 -10.30 -6.12 -5.32 -6.12 -6.44 -6.96 -4.95 -5.94 -7.35 -7.22 Peptide ... Peptide -8.63 -11.10 -6.36 -5.46 -6.64 -7.16 -7.84 -5.43 -6.65 -8.48 -8.14 Peptide ... Water -5.12 -7.05 -4.32 -3.75 -4.46 -4.64 -4.83 -3.87 -4.37 -5.04 -4.84 Uracil ... Uracil (BP) -17.18 -22.91 -15.49 -14.74 -15.98 -16.47 -16.69 -14.73 -15.55 -17.29 -16.10 Water ... Pyridine -6.86 -10.21 -6.82 -6.33 -6.64 -6.69 -6.76 -6.10 -6.42 -7.14 -6.63 MeOH ... Pyridine -7.41 -10.64 -6.92 -6.32 -6.73 -6.86 -7.14 -6.03 -6.58 -7.61 -7.21 AcOH ... AcOH -19.09 -27.31 -18.59 -17.99 -19.24 -19.58 -19.20 -17.72 -18.01 -19.34 -17.73 AcNH2 ... AcNH2 -16.27 -22.15 -15.02 -14.27 -15.48 -15.85 -15.85 -14.21 -14.80 -16.25 -15.08 AcOH ... Uracil -19.49 -26.45 -18.31 -17.64 -18.96 -19.39 -19.28 -17.59 -18.11 -19.64 -18.21 AcNH2 ... Uracil -19.19 -25.20 -17.67 -16.94 -18.31 -18.79 -18.83 -16.97 -17.64 -19.26 -18.00

MSE -3.67 0.88 1.55 0.74 0.50 0.31 1.63 1.04 -0.06 0.51

MAE 3.67 0.90 1.55 0.76 0.55 0.32 1.63 1.04 0.12 0.51

Dispersion complexes

Benzene ... Benzene (pi-pi) -2.82 -2.42 1.22 2.23 1.18 0.18 -2.04 2.91 0.30 -2.34 -4.41 Pyridine ... Pyridine (pi-pi) -3.90 -3.66 0.48 1.54 0.34 -0.79 -3.17 2.20 -0.63 -3.47 -5.65 Uracil ... Uracil (pi-pi) -9.83 -10.27 -2.51 -0.75 -3.14 -4.90 -7.90 -0.64 -4.59 -9.33 -10.34 Benzene ... Pyridine (pi-pi) -3.44 -3.15 0.81 1.86 0.72 -0.36 -2.68 2.53 -0.22 -2.99 -5.11 Benzene ... Uracil (pi-pi) -5.71 -5.51 0.35 1.75 0.01 -1.49 -4.34 2.31 -1.25 -5.01 -7.00 Pyridine ... Uracil (pi-pi) -6.82 -6.73 -0.74 0.65 -1.12 -2.63 -5.44 1.06 -2.46 -6.17 -8.04

Benzene ... Ethene -1.43 -1.80 0.76 1.50 0.82 0.32 -0.84 2.03 0.54 -1.02 -2.08

Uracil ... Ethene -3.38 -3.94 -0.34 0.58 -0.52 -1.22 -2.51 0.88 -0.91 -2.99 -3.65

Benzene ... Cyclopentane -3.58 -4.01 0.30 1.41 0.18 -0.72 -2.52 1.93 -0.43 -3.29 -4.26 Benzene ... Neopentane -2.90 -3.27 0.10 1.01 0.00 -0.67 -2.04 1.49 -0.35 -2.65 -3.36 Uracil ... Pentane -4.85 -5.62 0.52 2.09 0.27 -0.91 -3.09 2.41 -0.62 -4.52 -4.99 Uracil ... Cyclopentane -4.14 -4.59 0.58 1.96 0.44 -0.58 -2.54 2.22 -0.43 -3.81 -4.31 Uracil ... Neopentane -3.71 -4.15 0.08 1.21 -0.07 -0.87 -2.39 1.47 -0.66 -3.46 -3.73 Ethene ... Pentane -2.01 -3.12 0.01 0.93 0.03 -0.36 -1.17 1.20 -0.09 -1.87 -1.92 Ethyne ... Pentane -1.75 -2.52 -0.10 0.65 -0.06 -0.39 -1.12 1.00 -0.12 -1.48 -1.85 Peptide ... Pentane -4.26 -5.66 0.07 1.61 -0.07 -0.97 -2.65 1.83 -0.65 -4.00 -4.09

MSE -0.55 3.72 4.86 3.61 2.77 1.11 5.24 3.01 0.34 -0.46

MAE 0.66 3.72 4.86 3.61 2.77 1.11 5.24 3.01 0.34 0.54

Mixed complexes

Benzene ... Benzene (TS) -2.88 -3.17 -0.19 0.56 -0.36 -1.03 -2.29 0.96 -0.73 -2.72 -3.50 Pyridine ... Pyridine (TS) -3.54 -4.14 -0.75 0.08 -0.97 -1.68 -2.95 0.34 -1.38 -3.43 -4.09 Benzene ... Pyridine (TS) -3.33 -3.75 -0.61 0.14 -0.84 -1.53 -2.78 0.53 -1.17 -3.20 -3.90 Benzene ... Ethyne (CH-pi) -2.87 -3.66 -1.23 -0.68 -1.48 -1.94 -2.64 -0.36 -1.47 -2.84 -3.19 Ethyne ... Ethyne (TS) -1.52 -2.35 -1.20 -0.88 -1.21 -1.28 -1.39 -0.70 -1.01 -1.52 -1.47 Benzene ... AcOH (OH-pi) -4.71 -5.94 -2.32 -1.57 -2.65 -3.28 -4.18 -1.16 -2.61 -4.41 -4.78 Benzene ... AcNH2 (NH-pi) -4.36 -5.73 -2.34 -1.55 -2.59 -3.10 -3.86 -1.36 -2.60 -4.23 -4.38 Benzene ... Water (OH-pi) -3.28 -4.58 -1.98 -1.36 -2.17 -2.52 -2.98 -1.11 -1.99 -3.20 -3.25 Benzene ... MeOH (OH-pi) -4.19 -5.46 -1.86 -0.99 -2.03 -2.61 -3.58 -0.58 -2.07 -3.95 -4.37 Benzene ... MeNH2 (NH-pi) -3.23 -4.08 -0.77 0.08 -0.90 -1.48 -2.55 0.47 -1.08 -3.00 -3.52 Benzene ... Peptide (NH-pi) -5.28 -6.04 -1.68 -0.66 -2.01 -2.90 -4.45 -0.14 -2.32 -5.00 -5.79 Pyridine ... Pyridine (CH-N) -4.15 -5.61 -2.49 -1.81 -2.60 -3.02 -3.66 -1.75 -2.79 -4.01 -4.04 Ethyne ... Water (CH-O) -2.85 -4.31 -2.63 -2.29 -2.74 -2.81 -2.81 -2.34 -2.57 -2.93 -2.68 Ethyne ... AcOH (OH-pi) -4.87 -7.50 -4.10 -3.50 -4.30 -4.50 -4.62 -3.26 -3.80 -4.83 -4.44

Pentane ... AcOH -2.91 -3.97 0.07 1.24 0.02 -0.57 -1.71 1.42 -0.32 -2.71 -2.71

Pentane ... AcNH2 -3.53 -4.95 -0.26 1.04 -0.32 -0.98 -2.23 1.25 -0.66 -3.31 -3.30 Benzene ... AcOH -3.80 -4.39 -0.52 0.41 -0.81 -1.60 -2.99 0.80 -1.15 -3.49 -4.19 Peptide ... Ethene -3.00 -4.17 -0.95 -0.06 -1.06 -1.49 -2.25 0.06 -1.18 -2.88 -2.86 Pyridine ... Ethyne -3.99 -5.74 -3.64 -3.31 -3.65 -3.78 -3.94 -3.10 -3.51 -4.14 -3.93 MeNH2 ... Pyridine -3.97 -5.48 -1.73 -0.79 -1.73 -2.25 -3.28 -0.58 -2.03 -3.78 -4.20

MSE -1.14 2.05 2.82 1.89 1.40 0.56 3.08 1.79 0.13 -0.12

MAE 1.14 2.05 2.82 1.89 1.40 0.56 3.08 1.79 0.16 0.26

MSE -1.82 2.22 3.09 2.09 1.56 0.66 3.33 1.96 0.14 -0.02

MAE 1.85 2.23 3.09 2.10 1.58 0.67 3.33 1.96 0.21 0.45

rms 2.52 2.75 3.63 2.61 1.98 0.81 3.89 2.25 0.25 0.62

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