Supporting information to: Long-range corrected hybrid density functionals with improved dispersion corrections

improved dispersion corrections

You-Sheng Lin,¹ Guan-De Li,¹ Shan-Ping Mao,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

TABLE S1. Vertical IPs of IP131 database (page SI 2).

TABLE S2. Vertical EAs of EA115 database (page SI 7).

TABLE S3. Fundamental gaps of FG115 database (page SI 11).

TABLE S4. Atomic energies from H to Ar (page SI 15).

TABLE S5. NHTBH38/04 barrier heights (page SI 16).

TABLE S6. HTBH38/04 barrier heights (page SI 17).

TABLE S7. Interaction energies for S22 (page SI 18).

TABLE S8. Reaction energies (page SI 19).

TABLE S9. Binding energies of noncovalent interactions (page SI 19).

Reference (page SI 21).

⇤ Author to whom correspondence should be addressed. Electronic mail: jdchai@phys.ntu.edu.tw.

TABLE S1: -✏N(N ) (in eV) by DFT methods in the IP131 database. [1]

Molecule Reference !M06-D3 !B97X-D3 M06-2X

H (Hydrogen atom) 13.60 11.67 11.37 10.31

He (Helium atom) 24.59 21.24 20.62 20.56

Li (Lithium atom) 5.39 5.25 5.30 4.19

Be (Beryllium atom) 9.32 8.57 8.49 7.26

B (Boron atom) 8.30 7.70 7.51 6.17

C (Carbon atom) 11.26 10.23 9.87 8.84

N (Nitrogen atom) 14.53 12.92 12.46 11.78

O (Oxygen atom) 13.62 12.29 11.83 11.21

F (Fluorine atom) 17.42 15.53 14.96 14.82

Ne (Neon atom) 21.57 19.01 18.39 18.66

Na (Sodium atom) 5.14 5.09 4.92 4.19

Mg (Magnesium atom) 7.65 7.32 7.21 6.17

Al (Aluminum atom) 5.99 5.63 5.66 4.30

Si (Silicon atom) 8.15 7.64 7.56 6.26

P (Phosphorus atom) 10.49 9.76 9.55 8.35

S (Sulfur atom) 10.36 9.79 9.60 8.51

Cl (Chlorine atom) 12.97 12.21 11.89 10.96

Ar (Chlorine atom) 15.76 14.66 14.28 13.57

CH₃ (Methyl radical) 9.84 9.14 8.89 7.83

CH₄ (Methane) 13.60 13.65 13.33 12.43

NH (Imidogen) 13.49 12.35 11.97 11.26

NH₂ (Amino radical) 12.00 11.45 11.07 10.28

NH₃ (Ammonia) 10.82 10.42 10.06 9.30

OH (Hydroxyl radical) 13.02 12.08 11.59 11.07

H₂O (Water) 12.62 11.91 11.45 10.96

HF (Hydrogen fluoride) 16.12 14.77 14.23 14.06

SiH₃ (Silyl) 8.74 8.57 8.40 7.21

SiH₄ (Silane) 12.30 12.38 12.13 11.07

PH₃ (Phosphine) 10.59 10.23 10.04 8.95

H₂S (Hydrogen sulfide) 10.50 10.04 9.76 8.76

HCl (Hydrogen chloride) 12.77 12.13 11.78 10.91

C₂H₂ (Acetylene) 11.49 11.02 10.66 9.74

C₂H₄ (Ethylene) 10.68 10.39 10.04 9.08

C₂H₆ (Ethane) 11.99 12.16 11.89 10.99

HCN (Hydrogen cyanide) 13.61 13.03 12.68 11.80

CO (Carbon monoxide) 14.01 13.49 13.14 12.29

HCO (Formyl radical) 9.31 9.22 8.92 8.05

CH₂O (Formaldehyde) 10.89 10.50 10.12 9.52

CH₃OH (Methyl alcohol) 10.96 10.64 10.23 9.66

N₂ (Nitrogen diatomic) 15.58 15.07 14.63 13.98

N₂H₄ (Hydrazine) 8.98 9.44 9.11 8.38

NO (Nitric oxide) 9.26 9.08 8.68 8.05

O₂ (Oxygen diatomic) 12.30 11.80 11.32 11.04

H₂O₂ (Hydrogen peroxide) 11.70 11.15 10.72 10.28

F₂ (Fluorine diatomic) 15.70 14.77 14.23 14.23

CO₂ (Carbon dioxide) 13.78 13.27 12.95 12.32

P₂ (Phosphorus diatomic) 10.62 10.28 10.15 9.03

S₂ (Sulfur diatomic) 9.55 9.38 9.19 8.13

Cl₂ (Chlorine diatomic) 11.49 11.23 10.93 10.09

NaCl (Sodium Chloride) 9.80 9.03 8.70 7.83

SiO (Silicon monoxide) 11.61 11.29 11.04 10.09

CS (Carbon monosulfide) 11.34 11.51 11.23 10.20

ClO (Monochlorine monoxide) 11.01 10.58 10.23 9.49

ClF (Chlorine monofluoride) 12.77 12.13 11.78 11.04

Si₂H₆ (Disilane) 10.53 10.55 10.39 9.28

CH₃Cl (Methyl chloride) 11.29 11.07 10.74 9.87

CH₃SH (Methanethiol) 9.44 9.22 8.98 8.00

SO₂ (Sulfur dioxide) 12.50 12.21 11.89 11.15

BF₃ (Borane, trifluoro-) 15.96 15.10 14.58 14.50

BCl₃ (Borane, trichloro-) 11.64 11.64 11.34 10.50 AlCl₃ (Aluminum trichloride) 12.01 11.91 11.61 10.77

CF₄ (Carbon tetrafluoride) 16.20 15.53 15.01 14.96

CCl₄ Carbon tetrachloride) 11.69 11.64 11.32 10.50

OCS (Carbonyl sulfide) 11.19 10.99 10.80 9.85

CS₂ (Carbon disulfide) 10.09 9.93 9.79 8.84

CF₂O (Carbonic difluoride) 13.60 13.14 12.70 12.32

SiF₄ (Silicon tetrafluoride) 16.40 15.67 15.15 15.01

N₂O (Nitrous oxide) 12.89 12.29 12.02 11.29

NF₃ (Nitrogen trifluoride) 13.60 13.00 12.62 12.13

PF₃ (Phosphorus trifluoride) 12.20 11.18 10.99 10.04

O₃ (Ozone) 12.73 12.76 12.29 11.67

F₂O (Difluorine monoxide) 13.26 12.89 12.35 12.21

ClF₃ (Chlorine trifluoride) 13.05 12.59 12.19 11.72

C₂F₄ (Tetrafluoroethylene) 10.69 10.28 9.98 9.25

CF₃CN (Acetonitrile, trifluoro-) 14.30 13.68 13.33 12.54

CH₃CCH (Propyne) 10.37 10.20 9.90 8.98

CH₂CCH₂ (Allene) 10.20 10.17 9.87 8.95

C₃H₄ (Cyclopropene) 9.86 9.68 9.38 8.51

C₃H₆ (Cyclopropane) 10.54 10.91 10.58 9.60

C₃H₈ (Propane) 11.51 11.67 11.40 10.53

CH₃CCCH₃ (2-Butyne) 9.79 9.55 9.28 8.38

C₄H₆ (Cyclobutene) 9.43 9.55 9.28 8.35

CH₃CH(CH₃)CH₃ (Isobutane) 11.13 11.45 11.15 10.25

C₆H₆ (Benzene) 9.25 9.55 9.30 8.40

CH₂F₂ (Methane, difluoro-) 13.27 12.65 12.29 11.75

CHF₃ (Methane, trifluoro-) 15.50 13.90 13.52 13.06

CH₂Cl₂ (Methylene chloride) 11.40 11.34 11.02 10.17

CHCl₃ (Chloroform) 11.50 11.34 11.02 10.20

CH₃NO₂ (Methane, nitro-) 11.29 11.48 11.04 10.64

CH₃SiH₃ (Methyl silane) 11.60 11.70 11.42 10.36

HCOOH (Formic acid) 11.50 11.07 10.66 10.12

CH₃CONH₂ (Acetamide) 10.00 10.06 9.66 9.08

C₂H₅N (Aziridine) 9.85 9.74 9.41 8.62

C₂N₂ (Cyanogen) 13.51 13.14 12.84 12.00

CH₃NHCH₃ (Dimethylamine) 8.95 8.98 8.68 7.92

CH₂CO (Ketene) 9.64 9.55 9.28 8.38

C₂H₄O (Ethylene oxide) 10.57 10.64 10.20 9.71

C₂H₂O₂ (Ethanedial) 10.60 10.53 10.17 9.49

CH₃CH₂OH (Ethanol) 10.64 10.50 10.12 9.49

CH₃OCH₃ (Dimethyl ether) 10.10 10.04 9.66 9.03

C₂H₄S (Thiirane) 9.05 9.00 8.76 7.81

CH₃SOCH₃ (Dimethyl sulfoxide) 9.10 9.14 8.84 8.05

CH₂CHF (Ethene, fluoro-) 10.63 10.25 9.96 9.06

CH₃CH₂Cl (Ethyl chloride) 11.06 10.91 10.61 9.74

CH₂CHCl (Ethene, chloro-) 10.20 9.98 9.68 8.79

CH₃CClO (Acetyl Chloride) 11.03 11.15 10.80 10.15

CH₂ClCH₂CH₃ (Propane, 1-chloro-) 10.88 10.88 10.55 9.68

N(CH₃)₃ (Trimethylamine) 8.54 8.65 8.35 7.56

C₄H₄O (Furan) 8.90 9.03 8.76 7.83

C₄H₅N (Pyrrole) 8.23 8.40 8.16 7.26

NO₂ (Nitrogen dioxide) 11.23 11.10 10.69 10.15

SF₆ (Sulfur Hexafluoride) 15.70 15.23 14.72 14.72

CFCl₃ (Trichloromonofluoromethane) 11.76 11.70 11.40 10.58 CF₃Cl (Methane, chlorotrifluoro-) 13.08 12.73 12.40 11.61 CF₃Br (Bromotrifluoromethane) 12.08 11.67 11.42 10.55

HCCF (Fluoroacetylene) 11.50 10.91 10.58 9.71

HCCCN (Cyanoacetylene) 11.75 11.42 11.12 10.28

C₄N₂ (2-Butynedinitrile) 11.84 11.86 11.61 10.80

C₂N₂ (Cyanogen) 13.51 13.14 12.84 12.00

C₃O₂ (Carbon suboxide) 10.80 10.64 10.44 9.66

FCN (Cyanogen fluoride) 13.65 12.84 12.48 11.70

C₄N₂ (Diacetylene) 10.30 10.06 9.79 8.89

H₂CS (Thioformaldehyde) 9.38 9.17 8.92 7.97

CHONH₂ (Formamide) 10.40 10.28 9.90 9.36

CH₂CHCHO (Acrolein) 10.10 10.31 9.90 9.30

CH₂CCl₂ (Ethene, 1,1-dichloro-) 10.00 9.96 9.71 8.79

C₂HF₃ (Trifluoroethylene) 10.62 10.06 9.79 8.98

CH₂CF₂ (Ethene, 1,1-difluoro-) 10.70 10.36 10.06 9.22

CH₃F (Methyl fluoride) 13.04 12.62 12.21 11.70

CF₂Cl₂ (Difluorodichloromethane) 12.24 12.10 11.78 10.96

SiF₂ (Silicon difluoride) 11.08 10.64 10.50 9.41

MSE -0.39 -0.72 -1.48

MAE 0.45 0.72 1.48

rms 0.66 0.93 1.57

TABLE S2: -✏N +1(N + 1) and -✏N +1(N ) (in eV) by DFT methods in the EA115 database. [1]

Reference !M06-D3 !B97X-D3 M06-2X

Molecule -✏_{N +1}(N + 1) -✏_{N +1}(N ) -✏_{N +1}(N + 1) -✏_{N +1}(N ) -✏_{N +1}(N + 1) -✏_{N +1}(N )

H (Hydrogen atom) 0.75 1.12 -0.52 1.03 -0.53 -0.33 -0.52

He (Helium atom) -2.63 -4.22 -6.12 -4.16 -4.38 -5.22 -2.67

Li (Lithium atom) 0.62 0.71 -0.60 0.71 -0.24 -0.16 0.24

Be (Beryllium atom) -0.36 -0.35 -0.79 -0.35 -0.44 -1.28 0.54

B (Boron atom) 0.25 0.54 0.08 0.30 0.33 -0.76 1.39

C (Carbon atom) 1.25 1.36 1.36 0.98 1.66 -0.11 2.72

N (Nitrogen atom) -0.22 -0.14 -0.14 -0.35 0.22 -1.60 1.71

O (Oxygen atom) 1.45 1.28 1.71 0.87 2.15 -0.03 3.05

F (Fluorine atom) 3.44 2.75 3.94 2.28 4.57 1.69 4.76

Ne (Neon atom) -5.31 -7.15 -7.81 -7.34 -6.99 -7.97 -5.17

Na (Sodium atom) 0.54 0.71 -0.73 0.68 -0.27 -0.14 0.16

Mg (Magnesium atom) -0.23 -0.41 -0.92 -0.30 -0.46 -1.03 0.33

Al (Aluminum atom) 0.45 0.52 0.00 0.41 0.19 -0.57 1.25

Si (Silicon atom) 1.42 1.44 1.17 1.25 1.31 0.11 2.39

P (Phosphorus atom) 0.74 0.87 0.60 0.79 0.98 -0.35 2.39

S (Sulfur atom) 2.10 2.18 2.20 1.96 2.50 0.84 3.51

Cl (Chlorine atom) 3.69 3.51 3.94 3.21 4.27 2.20 5.09

Ar (Chlorine atom) -2.81 -3.24 -4.24 -3.43 -3.51 -3.92 -2.09

CH₃ (Methyl radical) -0.07 0.19 -0.49 0.03 -0.19 -1.06 1.20

CH₄ (Methane) -0.62 -0.95 -2.31 -0.95 -1.20 -1.50 -0.08

NH (Imidogen) 0.33 0.44 0.16 0.14 0.54 -0.95 1.80

NH₂ (Amino radical) 0.74 0.84 0.46 0.54 0.82 -0.46 1.93

NH₃ (Ammonia) -0.56 -0.92 -2.34 -0.92 -1.17 -1.58 0.08

OH (Hydroxyl radical) 1.83 1.69 1.74 1.28 2.20 0.46 2.94

H₂O (Water) -0.56 -0.95 -2.31 -0.92 -1.17 -1.77 0.16

HF (Hydrogen fluoride) -0.63 -1.01 -2.37 -0.98 -1.17 -1.93 0.16

SiH₃ (Silyl) 0.93 1.06 0.68 0.95 1.14 -0.14 2.58

SiH₄ (Silane) -1.11 -1.06 -2.42 -1.09 -1.33 -1.52 -0.19

PH₃ (Phosphine) -1.21 -0.84 -2.18 -0.92 -1.14 -1.36 -0.03

H₂S (Hydrogen sulfide) -0.49 -1.85 -2.12 -1.71 -1.09 -2.50 0.05

HCl (Hydrogen chloride) -0.52 -0.79 -2.04 -0.84 -1.06 -1.55 0.11

C₂H₂ (Acetylene) -1.90 -2.48 -2.20 -2.53 -1.22 -3.21 -0.24

C₂H₄ (Ethylene) -1.86 -1.90 -2.18 -2.01 -1.39 -2.83 -0.19

C₂H₆ (Ethane) -0.62 -0.95 -2.34 -0.98 -1.22 -1.44 -0.05

HCN (Hydrogen cyanide) -0.48 -2.04 -2.20 -1.99 -1.12 -2.88 -0.03

CO (Carbon monoxide) -1.50 -1.77 -1.80 -1.82 -1.33 -2.72 -0.27

HCO (Formyl radical) 0.02 0.05 0.05 -0.11 0.30 -1.12 1.52

CH₂O (Formaldehyde) -0.55 -1.12 -1.06 -1.25 -0.73 -2.09 0.35

CH₃OH (Methyl alcohol) -0.55 -0.87 -2.20 -0.87 -1.12 -1.47 0.05

N₂ (Nitrogen diatomic) -2.24 -2.48 -2.04 -2.67 -1.58 -3.64 -0.63

N₂H₄ (Hydrazine) -0.45 -1.50 -2.23 -1.41 -1.06 -2.01 0.27

NO (Nitric oxide) -0.42 -0.52 0.11 -0.84 0.54 -1.69 1.47

O₂ (Oxygen diatomic) -0.08 -0.41 0.38 -0.76 0.79 -1.52 1.66

H₂O₂ (Hydrogen peroxide) -0.92 -1.44 -2.34 -1.36 -1.31 -2.12 0.08

F₂ (Fluorine diatomic) 0.42 -0.03 1.20 -0.44 1.82 -0.84 2.26

CO₂ (Carbon dioxide) -0.65 -4.11 -2.45 -4.38 -1.36 -1.88 0.05

P₂ (Phosphorus diatomic) 0.48 0.63 0.49 0.54 0.76 -0.60 1.74

S₂ (Sulfur diatomic) 1.53 1.52 1.47 1.36 1.71 0.33 2.83

Cl₂ (Chlorine diatomic) 0.75 0.68 0.68 0.49 1.09 -0.46 2.04

NaCl (Sodium Chloride) 0.65 0.65 -0.33 0.68 0.44 -0.14 1.63

SiO (Silicon monoxide) 0.03 -0.11 -0.19 -0.11 0.14 -1.17 1.22

CS (Carbon monosulfide) -0.09 0.05 0.00 -0.08 0.30 -1.22 1.36

ClO (Monochlorine monoxide) 2.19 2.01 2.28 1.71 2.50 0.95 3.54

ClF (Chlorine monofluoride) 0.44 0.22 0.52 0.03 0.98 -0.95 1.88

Si₂H₆ (Disilane) -0.69 -1.25 -2.23 -1.22 -1.25 -1.69 -0.08

CH₃Cl (Methyl chloride) -0.51 -0.79 -2.12 -0.79 -1.06 -1.39 0.08

CH₃SH (Methanethiol) -0.50 -0.79 -2.12 -0.82 -1.09 -1.31 0.11

SO₂ (Sulfur dioxide) 0.81 0.79 1.03 0.57 1.39 -0.41 2.42

BF₃ (Borane, trifluoro-) -1.04 -1.09 -2.61 -1.20 -1.39 -1.69 0.11

BCl₃ (Borane, trichloro-) -0.17 -0.84 -0.46 -1.03 -0.27 -1.20 0.95

AlCl₃ (Aluminum trichloride) 0.06 0.05 -0.65 -0.08 -0.33 -0.71 1.01

CF₄ (Carbon tetrafluoride) -1.33 -1.74 -3.51 -1.85 -2.09 -2.26 -0.46

CCl₄ Carbon tetrachloride) -0.46 -0.22 -0.76 -0.24 -0.38 -1.06 0.68

OCS (Carbonyl sulfide) -0.74 -1.28 -1.36 -1.41 -1.03 -2.31 0.03

CS₂ (Carbon disulfide) 0.01 0.24 -0.05 0.11 0.19 -0.95 1.20

CF₂O (Carbonic difluoride) -2.37 -2.39 -2.01 -1.41 -1.60 -3.13 -0.08

SiF₄ (Silicon tetrafluoride) -0.81 -1.03 -2.37 -1.25 -1.33 -1.60 0.16

N₂O (Nitrous oxide) -2.01 -2.26 -2.01 -2.53 -1.63 -3.35 -0.49

NF₃ (Nitrogen trifluoride) -2.06 -2.69 -3.21 -2.80 -2.64 -3.37 -1.33

PF₃ (Phosphorus trifluoride) -1.23 -1.52 -2.45 -1.50 -1.66 -2.12 -0.38

O₃ (Ozone) 1.93 2.31 2.80 1.88 3.18 1.33 4.16

F₂O (Difluorine monoxide) -0.31 -0.63 -0.03 -0.87 0.49 -1.66 1.14

ClF₃ (Chlorine trifluoride) 1.20 1.01 1.20 0.79 1.63 -0.08 2.56

C₂F₄ (Tetrafluoroethylene) -1.65 -2.31 -2.91 -2.37 -1.74 -2.80 -0.16

CH₃CCH (Propyne) -1.13 -1.77 -2.15 -1.63 -1.12 -2.26 0.03

CH₂CCH₂ (Allene) -0.56 -1.55 -2.37 -1.47 -1.25 -2.07 -0.08

C₃H₄ (Cyclopropene) -1.82 -1.85 -2.26 -1.96 -1.33 -2.72 -0.19

C₃H₆ (Cyclopropane) -0.65 -1.09 -2.58 -1.12 -1.36 -1.55 -0.14

CH₂F₂ (Methane, difluoro-) -0.58 -1.01 -2.37 -0.92 -1.22 -1.71 -0.03

CHF₃ (Methane, trifluoro-) -0.60 -1.06 -2.42 -0.98 -1.28 -1.90 -0.08

CH₂Cl₂ (Methylene chloride) -0.49 -0.76 -1.90 -0.73 -1.06 -1.41 0.14

CHCl₃ (Chloroform) -0.83 -0.73 -1.41 -0.73 -0.95 -1.47 0.22

CH₃NO₂ (Methane, nitro-) -0.37 -0.16 -0.38 -0.44 0.00 -1.22 0.98

CH₃SiH₃ (Methyl silane) -0.53 -0.87 -2.18 -0.87 -1.14 -1.36 0.03

HCOOH (Formic acid) -0.57 -2.01 -2.18 -2.09 -1.31 -2.88 -0.03

CH₃CONH₂ (Acetamide) -0.31 -1.60 -2.01 -1.50 -0.90 -2.12 0.33

C₂N₂ (Cyanogen) -0.19 -0.05 0.14 -0.16 0.44 -1.20 1.44

CH₂CO (Ketene) -0.51 -1.39 -1.47 -1.31 -1.14 -2.01 0.00

C₂H₄O (Ethylene oxide) -0.86 -1.01 -2.42 -0.98 -1.28 -1.58 -0.08

C₂H₂O₂ (Ethanedial) 0.69 0.84 0.84 0.71 1.14 -0.27 2.18

CH₃CH₂OH (Ethanol) -0.53 -0.87 -2.23 -0.84 -1.12 -1.39 0.08

CH₃OCH₃ (Dimethyl ether) -0.58 -0.92 -2.28 -0.92 -1.17 -1.41 -0.03

C₂H₄S (Thiirane) -0.78 -1.20 -2.20 -1.20 -1.25 -1.69 -0.05

CH₂CHF (Ethene, fluoro-) -0.88 -2.01 -2.28 -2.12 -1.31 -2.94 -0.14

CH₃CH₂Cl (Ethyl chloride) -0.51 -0.82 -2.23 -0.82 -1.12 -1.31 0.08

CH₂CHCl (Ethene, chloro-) -1.11 -1.39 -1.80 -1.52 -1.22 -2.39 -0.08

CH₃CClO (Acetyl Chloride) -0.85 -0.84 -1.20 -0.98 -0.90 -1.82 0.19

NO₂ (Nitrogen dioxide) 1.44 1.36 1.60 1.06 1.90 0.24 3.05

CFCl₃ (Trichloromonofluoromethane) -0.68 -0.57 -1.03 -0.63 -0.65 -1.44 0.46 CF₃Cl (Methane, chlorotrifluoro-) -1.06 -1.55 -2.31 -1.52 -1.71 -2.04 -0.38

HCCF (Fluoroacetylene) -0.55 -0.90 -2.07 -0.82 -1.12 -1.47 -0.05

HCCCN (Cyanoacetylene) -0.36 -0.57 -0.57 -0.63 -0.30 -1.63 0.76

C₄N₂ (2-Butynedinitrile) 0.68 0.95 0.87 0.90 1.14 -0.11 2.18

C₂N₂ (Cyanogen) -0.19 -0.05 0.14 -0.16 0.44 -1.20 1.44

C₃O₂ (Carbon suboxide) -0.74 -0.73 -0.52 -0.87 -0.27 -1.82 0.79

FCN (Cyanogen fluoride) -0.66 -3.84 -1.96 -4.03 -1.06 -1.63 0.33

C₄N₂ (Diacetylene) -0.64 -1.09 -1.31 -1.14 -1.03 -2.07 0.08

H₂CS (Thioformaldehyde) 0.28 0.41 0.35 0.27 0.57 -0.82 1.66

CHONH₂ (Formamide) -0.35 -2.45 -2.18 -2.42 -1.01 -1.41 0.24

CH₂CCl₂ (Ethene, 1,1-dichloro-) -1.07 -0.92 -1.47 -0.90 -1.20 -1.47 0.00

C₂HF₃ (Trifluoroethylene) -0.54 -1.03 -2.45 -0.98 -1.28 -1.69 -0.03

CH₂CF₂ (Ethene, 1,1-difluoro-) -1.03 -2.18 -2.50 -2.23 -1.31 -3.02 -0.05

CH₃F (Methyl fluoride) -0.58 -0.95 -2.28 -0.90 -1.17 -1.60 -0.03

CF₂Cl₂ (Difluorodichloromethane) -0.90 -1.20 -1.60 -1.25 -1.17 -1.90 -0.03

SiF₂ (Silicon difluoride) 0.10 0.00 -0.11 -0.03 0.22 -1.12 1.31

MSE -0.34 -0.78 -0.42 -0.11 -1.15 1.01

MAE 0.42 0.90 0.48 0.49 1.15 1.05

rms 0.69 1.15 0.75 0.58 1.22 1.14

TABLE S3: HOMO-LUMO gap results by DFT methods in the FG115 database. [1]

Molecule Reference !M06-D3 !B97X-D3 M06-2X

H (Hydrogen atom) 12.86 12.19 11.90 10.83

He (Helium atom) 27.23 27.36 25.00 23.28

Li (Lithium atom) 4.22 5.85 5.55 3.94

Be (Beryllium atom) 9.66 9.36 8.92 6.72

B (Boron atom) 7.99 7.62 7.18 4.79

C (Carbon atom) 9.97 8.87 8.21 6.12

N (Nitrogen atom) 14.74 13.06 12.24 10.06

O (Oxygen atom) 12.14 10.58 9.68 8.16

F (Fluorine atom) 13.98 11.59 10.39 10.06

Ne (Neon atom) 26.91 26.82 25.38 23.83

Na (Sodium atom) 4.14 5.82 5.20 4.03

Mg (Magnesium atom) 7.76 8.24 7.67 5.85

Al (Aluminum atom) 5.53 5.63 5.47 3.05

Si (Silicon atom) 6.73 6.47 6.26 3.86

P (Phosphorus atom) 9.78 9.17 8.60 5.96

S (Sulfur atom) 8.23 7.59 7.10 5.00

Cl (Chlorine atom) 9.30 8.27 7.62 5.88

Ar (Chlorine atom) 18.65 18.90 17.79 15.67

CH₃ (Methyl radical) 9.86 9.63 9.08 6.64

CH₄ (Methane) 15.06 15.97 14.52 12.51

NH (Imidogen) 13.17 12.19 11.42 9.47

NH₂ (Amino radical) 11.34 10.99 10.25 8.35

NH₃ (Ammonia) 11.54 12.76 11.23 9.22

OH (Hydroxyl radical) 11.27 10.34 9.38 8.13

H₂O (Water) 13.35 14.23 12.62 10.80

HF (Hydrogen fluoride) 16.91 17.14 15.40 13.90

SiH₃ (Silyl) 7.95 7.89 7.26 4.62

SiH₄ (Silane) 14.03 14.80 13.46 11.26

PH₃ (Phosphine) 11.83 12.40 11.18 8.98

H₂S (Hydrogen sulfide) 11.00 12.16 10.85 8.70

HCl (Hydrogen chloride) 13.36 14.17 12.84 10.80

C₂H₂ (Acetylene) 13.43 13.22 11.89 9.98

C₂H₄ (Ethylene) 12.57 12.57 11.42 9.28

C₂H₆ (Ethane) 13.41 14.50 13.11 11.04

HCN (Hydrogen cyanide) 14.31 15.23 13.79 11.83

CO (Carbon monoxide) 15.57 15.29 14.47 12.57

HCO (Formyl radical) 9.56 9.17 8.62 6.53

CH₂O (Formaldehyde) 11.56 11.56 10.85 9.17

CH₃OH (Methyl alcohol) 11.67 12.84 11.34 9.60

N₂ (Nitrogen diatomic) 17.88 17.11 16.21 14.61

N₂H₄ (Hydrazine) 10.30 11.67 10.17 8.11

NO (Nitric oxide) 10.11 8.98 8.13 6.58

O₂ (Oxygen diatomic) 12.52 11.42 10.53 9.38

H₂O₂ (Hydrogen peroxide) 12.65 13.49 12.02 10.20

F₂ (Fluorine diatomic) 15.53 13.57 12.40 11.97

CO₂ (Carbon dioxide) 14.58 15.72 14.31 12.27

P₂ (Phosphorus diatomic) 10.19 9.79 9.38 7.29

S₂ (Sulfur diatomic) 7.96 7.92 7.48 5.30

Cl₂ (Chlorine diatomic) 10.93 10.55 9.85 8.05

NaCl (Sodium Chloride) 8.64 9.36 8.27 6.20

SiO (Silicon monoxide) 11.60 11.48 10.91 8.87

CS (Carbon monosulfide) 11.58 11.51 10.93 8.84

ClO (Monochlorine monoxide) 8.86 8.30 7.72 5.96

ClF (Chlorine monofluoride) 12.43 11.61 10.80 9.17

Si₂H₆ (Disilane) 11.33 12.78 11.64 9.36

CH₃Cl (Methyl chloride) 12.01 13.19 11.80 9.79

CH₃SH (Methanethiol) 10.01 11.34 10.06 7.89

SO₂ (Sulfur dioxide) 11.74 11.18 10.50 8.73

BF₃ (Borane, trifluoro-) 17.22 17.71 15.97 14.39

BCl₃ (Borane, trichloro-) 12.07 12.10 11.61 9.55

AlCl₃ (Aluminum trichloride) 12.14 12.57 11.94 9.76

CF₄ (Carbon tetrafluoride) 17.85 19.04 17.11 15.42

CCl₄ Carbon tetrachloride) 11.97 12.40 11.70 9.82

OCS (Carbonyl sulfide) 12.13 12.35 11.83 9.82

CS₂ (Carbon disulfide) 10.19 9.98 9.60 7.64

CF₂O (Carbonic difluoride) 16.08 15.15 14.31 12.40

SiF₄ (Silicon tetrafluoride) 16.95 18.03 16.48 14.85

N₂O (Nitrous oxide) 15.01 14.31 13.65 11.78

NF₃ (Nitrogen trifluoride) 15.76 16.21 15.26 13.46

PF₃ (Phosphorus trifluoride) 13.00 13.63 12.65 10.42

O₃ (Ozone) 11.06 9.96 9.11 7.51

F₂O (Difluorine monoxide) 13.82 12.92 11.86 11.07

ClF₃ (Chlorine trifluoride) 11.79 11.40 10.55 9.17

C₂F₄ (Tetrafluoroethylene) 12.45 13.19 11.72 9.41

CH₃CCH (Propyne) 11.70 12.35 11.02 8.95

CH₂CCH₂ (Allene) 10.83 12.54 11.12 9.03

C₃H₄ (Cyclopropene) 11.87 11.94 10.72 8.70

C₃H₆ (Cyclopropane) 11.64 13.49 11.94 9.74

CH₂F₂ (Methane, difluoro-) 14.15 15.01 13.52 11.78

CHF₃ (Methane, trifluoro-) 15.44 16.32 14.80 13.14

CH₂Cl₂ (Methylene chloride) 12.18 13.25 12.08 10.04

CHCl₃ (Chloroform) 12.38 12.76 11.97 9.98

CH₃NO₂ (Methane, nitro-) 11.95 11.86 11.04 9.66

CH₃SiH₃ (Methyl silane) 12.35 13.87 12.57 10.34

HCOOH (Formic acid) 11.98 13.25 11.97 10.15

CH₃CONH₂ (Acetamide) 10.05 12.08 10.55 8.76

C₂N₂ (Cyanogen) 13.90 13.00 12.40 10.55

CH₂CO (Ketene) 10.32 11.02 10.42 8.38

C₂H₄O (Ethylene oxide) 11.68 13.06 11.48 9.79

C₂H₂O₂ (Ethanedial) 10.04 9.68 9.03 7.32

CH₃CH₂OH (Ethanol) 11.38 12.73 11.23 9.41

CH₃OCH₃ (Dimethyl ether) 10.79 12.32 10.83 9.06

C₂H₄S (Thiirane) 9.93 11.21 10.01 7.86

CH₂CHF (Ethene, fluoro-) 11.55 12.54 11.26 9.19

CH₃CH₂Cl (Ethyl chloride) 11.74 13.14 11.72 9.66

CH₂CHCl (Ethene, chloro-) 11.35 11.78 10.91 8.87

CH₃CClO (Acetyl Chloride) 11.97 12.35 11.70 9.96

NO₂ (Nitrogen dioxide) 9.79 9.49 8.79 7.10

CFCl₃ (Trichloromonofluoromethane) 12.61 12.73 12.05 10.12 CF₃Cl (Methane, chlorotrifluoro-) 14.27 15.04 14.12 12.00

HCCF (Fluoroacetylene) 12.04 12.97 11.70 9.76

HCCCN (Cyanoacetylene) 12.20 12.00 11.42 9.52

C₄N₂ (2-Butynedinitrile) 11.52 10.99 10.47 8.62

C₂N₂ (Cyanogen) 13.90 13.00 12.40 10.55

C₃O₂ (Carbon suboxide) 11.64 11.15 10.72 8.87

FCN (Cyanogen fluoride) 14.33 14.80 13.55 11.37

C₄N₂ (Diacetylene) 11.00 11.37 10.83 8.81

H₂CS (Thioformaldehyde) 9.18 8.81 8.35 6.31

CHONH₂ (Formamide) 10.81 12.46 10.91 9.11

CH₂CCl₂ (Ethene, 1,1-dichloro-) 11.17 11.42 10.91 8.79

C₂HF₃ (Trifluoroethylene) 11.11 12.51 11.07 9.00

CH₂CF₂ (Ethene, 1,1-difluoro-) 11.81 12.87 11.37 9.28

CH₃F (Methyl fluoride) 14.09 14.91 13.38 11.72

CF₂Cl₂ (Difluorodichloromethane) 13.33 13.71 12.95 10.99

SiF₂ (Silicon difluoride) 11.04 10.74 10.28 8.11

MSE 0.23 -0.75 -2.64

MAE 0.77 0.83 2.64

rms 0.93 1.07 2.73

TABLE S4. Atomic energies (in kcal/mol) from the H atom to the Ar atom [2].

Atom Reference !M06-D3 !B97X-D3 M06-2X

H -313.76 -312.64 -315.17 -312.62

He -1822.12 -1820.15 -1823.18 -1820.89

Li -4692.56 -4691.39 -4697.55 -4693.69

Be -9203.92 -9197.60 -9202.20 -9201.54

B -15470.58 -15467.52 -15469.02 -15467.26

C -23748.12 -23749.38 -23746.81 -23745.48

N -34255.28 -34257.81 -34253.17 -34252.40

O -47105.50 -47109.47 -47105.58 -47102.06

F -62584.04 -62588.74 -62584.45 -62579.51

Ne -80909.66 -80910.05 -80907.17 -80899.63

Na -101816.42 -101813.89 -101817.11 -101806.82

Mg -125535.30 -125537.51 -125537.98 -125533.86

Al -152074.59 -152075.96 -152077.91 -152071.75

Si -181575.73 -181576.46 -181577.36 -181570.29

P -214143.51 -214140.10 -214140.40 -214131.83

S -249818.09 -249816.58 -249817.64 -249809.65

Cl -288747.57 -288747.09 -288747.12 -288738.36

Ar -331036.74 -331037.14 -331036.75 -331026.76

MSE 0.22 -0.17 4.95

MAE 2.17 1.64 5.07

rms 2.69 2.07 6.20

TABLE S5. Non-hydrogen transfer barrier heights (in kcal/mol) of the NHTBH38/04 set [3].

Reactions Eref !M06-D3 !B97X-D3 M06-2X

Heavy-atom transfer reactions

H + N₂O ! OH + N2 V^f 18.14 17.99 18.16 16.90

V^r 83.22 82.68 78.82 81.59

H + FH ! HF + H V^f 42.18 40.24 41.46 38.38

V^r 42.18 40.24 41.46 38.38

H + ClH ! HCl + H V^f 18 20.49 19.33 18.07

V^r 18 20.49 19.33 18.07

H + FCH₃ ! HF + CH3 V^f 30.38 30.37 30.98 30.67

V^r 57.02 54.06 54.75 53.97

H + F₂ ! HF + F V^f 2.27 1.56 0.10 1.97

V^r 106.18 103.77 104.08 108.93

CH₃+ FCl ! CH3F + Cl V^f 7.43 5.19 3.61 4.84

V^r 60.17 58.37 57.85 59.44

Nucleophilic substitution reactions

F + CH₃F ! FCH3 + F V^f -0.34 -1.79 -1.55 -0.48

V^r -0.34 -1.79 -1.55 -0.48

F · · · CH₃F ! FCH₃· · · F V^f 13.38 13.59 13.06 15.39

V^r 13.38 13.59 13.06 15.39

Cl + CH₃Cl ! ClCH3+ Cl V^f 3.1 4.26 4.38 2.17

V^r 3.1 4.26 4.38 2.17

Cl · · · CH₃Cl ! ClCH₃· · · Cl V^f 13.61 15.13 15.20 13.77

V^r 13.61 15.13 15.20 13.77

F + CH₃Cl ! FCH3+ Cl V^f -12.54 -13.21 -13.14 -14.94

V^r 20.11 22.24 21.33 23.86

F · · · CH3Cl ! FCH3· · · Cl V^f 2.89 3.79 3.60 3.37

V^r 29.62 32.20 30.91 34.06

OH + CH₃F ! HOCH₃+ F V^f -2.78 -3.34 -3.19 -2.70

V^r 17.33 16.77 17.89 16.93

OH · · · CH3F ! HOCH3· · · F V^f 10.96 11.59 11.06 12.71

V^r 47.2 49.10 49.43 50.85

Unimolecular and association reactions

H + N₂ ! HN2 V^f 14.69 14.18 12.96 13.61

V^r 10.72 12.56 13.74 11.27

H + CO ! HCO V^f 3.17 3.97 3.71 3.52

V^r 22.68 24.75 26.24 22.75

H + C₂H₄ ! CH3CH₂ V^f 1.72 3.71 3.42 2.72

V^r 41.75 44.44 46.01 43.67

CH₃+ C₂H₄ ! CH₃CH₂CH₂ V^f 6.85 6.14 4.93 5.77

V^r 32.97 34.67 34.64 34.21

HCN ! HNC V^f 48.16 46.27 46.19 45.78

V^r 33.11 32.44 33.07 32.80

MSE 0.18 0.04 0.00

MAE 1.40 1.53 1.41

rms 1.62 1.89 1.91

TABLE S6. Hydrogen transfer barrier heights (in kcal/mol) of the HTBH38/04 set [3, 4].

Reactions Eref !M06-D3 !B97X-D3 M06-2X

H + HCl ! H₂+ Cl V^f 5.7 5.75 4.71 4.36

V^r 8.7 4.86 4.98 6.25

OH + H₂ ! H + H2O V^f 5.1 2.15 2.48 4.74

V^r 21.2 19.76 19.13 21.00

CH₃+ H₂ ! H + CH4 V^f 12.1 9.40 9.36 11.89

V^r 15.3 15.83 14.22 15.52

OH + CH₄ ! CH₃+ H₂O V^f 6.7 3.79 3.43 5.02

V^r 19.6 14.97 15.22 17.65

H + H₂ ! H2+ H V^f 9.6 9.87 9.77 11.57

V^r 9.6 9.87 9.77 11.57

OH + NH₃ ! H₂O + NH₂ V^f 3.2 1.70 0.85 2.31

V^r 12.7 10.75 10.38 12.02

HCl + CH₃ ! Cl + CH4 V^f 1.7 -0.32 -1.45 -0.17

V^r 7.9 5.22 3.69 5.35

OH + C₂H₆ ! H2O + C₂H₅ V^f 3.4 0.87 0.56 2.41

V^r 19.9 16.75 16.82 19.04

F + H₂ ! HF + H V^f 1.8 -2.55 -3.55 0.52

V^r 33.4 30.79 29.20 32.13

O + CH₄ ! OH + CH3 V^f 13.7 10.81 9.55 11.46

V^r 8.1 4.78 4.71 6.38

H + PH₃ ! PH₂+ H₂ V^f 3.1 3.81 3.79 3.45

V^r 23.2 22.57 23.78 25.32

H + HO ! H2+ O V^f 10.7 9.29 9.17 9.81

V^r 13.1 8.88 9.15 11.25

H + H₂S ! H2+ HS V^f 3.5 4.96 4.62 4.37

V^r 17.3 15.58 16.64 17.95

O + HCl ! OH + Cl V^f 9.8 7.67 6.42 6.80

V^r 10.4 7.18 6.71 7.24

NH₂+ CH₃ ! CH4+ NH V^f 8 6.59 6.13 6.50

V^r 22.4 20.55 18.99 20.59

NH₂+ C₂H₅ ! C₂H₆+ NH V^f 7.5 8.38 7.83 7.85

V^r 18.3 17.64 16.23 17.93

C₂H₆+ NH₂ ! NH3+ C₂H₅ V^f 10.4 9.85 9.26 9.95

V^r 17.4 16.67 16.00 16.88

NH₂+ CH₄ ! CH3+ NH₃ V^f 14.5 12.67 11.95 12.50

V^r 17.8 14.80 14.21 15.42

s-trans cis-C₅H₈ ! s-trans cis-C₅H₈ V^f 38.4 41.39 39.92 39.08

V^r 38.4 41.39 39.92 39.08

MSE -1.54 -2.08 -0.81

MAE 2.08 2.40 1.32

rms 2.41 2.75 1.56

TABLE S7. Interaction energies (in kcal/mol) for the S22 set with new reference values. [5] The counterpoise corrections are used to reduce the basis set superposition errors. Monomer deformation energies are not included.

Complex [Symmetry] Eref !M06-D3 !B97X-D3 M06-2X

Hydrogen bonded complexes

(NH₃)₂ [C2h] -3.133 -3.21 -3.09 -3.18

(H₂O)₂[Cs] -4.989 -5.17 -5.04 -5.02

Formic acid dimer [C_2h] -18.753 -19.44 -19.52 -19.09

Formamide dimer [C2h] -16.062 -16.21 -16.26 -15.61

Uracil dimer [C2h] -20.641 -20.31 -20.51 -19.47

2-pyridoxine·2-aminopyridine [C1] -16.934 -16.53 -16.98 -15.56

Adenine·thymine WC [C1] -16.66 -16.12 -16.43 -15.03

MSE 0.03 -0.09 0.60

MAE 0.34 0.21 0.72

Dispersion complexes

(CH₄)₂ [D3d] -0.527 -0.40 -0.61 -0.48

(C₂H₄)₂ [D2d] -1.472 -1.77 -1.54 -1.62

Benzene·CH4[C₃] -1.448 -1.59 -1.64 -1.35

Benzene dimer [C2h] -2.654 -2.82 -3.00 -2.68

Pyrazine dimer [Cs] -4.255 -4.03 -4.15 -4.17

Uracil dimer [C2] -9.805 -9.80 -9.83 -9.80

Indole·benzene [C1] -4.524 -4.56 -4.61 -4.64

Adenine·thymine stack [C1] -11.73 -11.78 -11.26 -12.26

MSE -0.04 -0.03 -0.07

MAE 0.13 0.17 0.13

Mixed complexes

Ethene·ethine [C2v] -1.496 -1.32 -1.65 -1.35

Benzene·H2O [Cs] -3.275 -3.50 -3.58 -3.57

Benzene·NH₃ [Cs] -2.312 -2.45 -2.56 -2.34

Benzene·HCN [Cs] -4.541 -4.71 -4.65 -4.85

Benzene dimer [C2v] -2.717 -2.65 -2.82 -2.33

Indole·benzene T-shape [C1] -5.627 -5.38 -5.52 -5.04

Phenol dimer [C1] -7.097 -7.08 -7.00 -6.56

MSE 0.00 -0.10 0.15

MAE 0.15 0.16 0.33

MSE -0.01 -0.07 0.21

MAE 0.20 0.18 0.38

rms 0.26 0.24 0.59

TABLE S8. Comparison of errors of di↵erent functionals for the reaction energies (in kcal/mol) of the 30 chemical reactions in the NHTBH38/04 and HTBH38/04 database [3, 4].

Reactions E_ref !M06-D3 !B97X-D3 M06-2X

H + N₂O ! OH + N2 -65.08 -64.69 -60.66 -64.69

H + FCH₃ ! HF + CH₃ -26.64 -23.69 -23.76 -23.30

H + F₂ ! HF + F -103.91 -102.21 -103.99 -106.96

CH₃+ FCl ! CH3F + Cl -52.74 -53.18 -54.25 -54.60

F + CH₃Cl ! FCH₃+ Cl -32.65 -35.45 -34.48 -38.80

F · · · CH₃Cl ! FCH₃· · · Cl -26.73 -28.41 -27.32 -30.68

OH + CH₃F ! HOCH3+ F -20.11 -20.11 -21.09 -19.63

OH · · · CH3F ! HOCH3· · · F -36.24 -37.51 -38.37 -38.14

H + N₂ ! HN₂ 3.97 1.63 -0.78 2.34

H + CO ! HCO -19.51 -20.78 -22.52 -19.23

H + C₂H₄ ! CH3CH₂ -40.03 -40.74 -42.59 -40.95

CH₃+ C₂H₄ ! CH₃CH₂CH₂ -26.12 -28.53 -29.71 -28.45

HCN ! HNC 15.05 13.83 13.12 12.98

H + HCl ! H2+ Cl -3.0 0.89 -0.28 -1.89

OH + H₂ ! H + H₂O -16.1 -17.62 -16.66 -16.26

CH₃+ H₂ ! H + CH₄ -3.2 -6.43 -4.86 -3.64

OH + CH₄ ! CH3+ H₂O -12.9 -11.19 -11.80 -12.63

OH + NH₃ ! H2O + NH₂ -9.5 -9.05 -9.53 -9.70

HCl + CH₃ ! Cl + CH₄ -6.2 -5.54 -5.14 -5.52

OH + C₂H₆ ! H2O + C₂H₅ -16.5 -15.87 -16.26 -16.63

F + H₂ ! HF + H -31.6 -33.34 -32.74 -31.61

O + CH₄ ! OH + CH₃ 5.6 6.02 4.84 5.08

H + PH₃ ! PH₂+ H₂ -20.1 -18.76 -19.99 -21.87

H + HO ! H2+ O -2.4 0.41 0.02 -1.45

H + H₂S ! H2+ HS -13.8 -10.63 -12.01 -13.58

O + HCl ! OH + Cl -0.6 0.49 -0.30 -0.44

NH₂+ CH₃ ! CH4+ NH -14.4 -13.96 -12.86 -14.09

NH₂+ C₂H₅ ! C2H₆+ NH -10.8 -9.27 -8.39 -10.08

C₂H₆+ NH₂ ! NH₃+ C₂H₅ -7.0 -6.82 -6.74 -6.93

NH₂+ CH₄ ! CH3+ NH₃ -3.3 -2.13 -2.27 -2.92

MSE 0.13 -0.16 -0.59

MAE 1.51 1.65 1.21

rms 1.82 2.06 1.84

TABLE S9. Binding energies (in kcal/mol) of several sets of noncovalent interactions. The first three sets are taken from Ref. [6] with monomer deformation energies taken into considerations. The last three sets are taken from Ref. [7] without

considering monomer deformation energies. The counter-point corrections are applied for all the cases.

Complex E_ref !M06-D3 !B97X-D3 M06-2X Charge-transfer complexes

C₂H₄· · · F2 1.06 0.85 0.80 1.06

NH₃· · · F₂ 1.81 1.58 1.50 1.56

C₂H₂· · · ClF 3.81 4.00 3.76 4.40

HCN· · · ClF 4.86 4.71 4.43 4.68

NH₃· · · Cl₂ 4.88 4.76 4.82 4.98

H₂O· · · ClF 5.36 5.65 5.38 5.70

NH₃· · · ClF 10.62 10.26 10.92 10.02

MSE -0.08 -0.11 0.00

MAE 0.22 0.20 0.29

Dipole-dipole interaction complexes

H₂S· · · H2S 1.66 1.58 1.71 1.38

HCl· · · HCl 2.01 1.87 1.83 1.70

H₂S· · · HCl 3.35 3.46 3.52 3.22

CH₃Cl· · · HCl 3.55 3.50 3.29 3.37

HCN· · · CH₃SH 3.59 3.69 3.81 3.60

CH₃SH· · · HCl 4.16 5.00 4.97 4.85

MSE 0.13 0.14 -0.03

MAE 0.22 0.28 0.27

Weak interaction complexes

He· · · Ne 0.04 -0.20 0.02 0.13

He· · · Ar 0.06 -0.21 0.04 0.14

Ne· · · Ne 0.08 -0.23 -0.02 0.16

Ne· · · Ar 0.13 -0.22 0.01 0.19

CH₄· · · Ne 0.22 -0.12 0.15 0.27

C₆H₆· · · Ne 0.47 0.23 0.30 0.68

CH₄· · · CH₄ 0.51 0.47 0.60 0.52

MSE -0.26 -0.06 0.08

MAE 0.26 0.09 0.08

Hydrogen-bonded DNA base pairs

G· · · A HB -11.30 -12.61 -13.30 -11.42

C· · · G WC -30.70 -32.05 -32.49 -30.77

G· · · C WC -31.40 -31.99 -32.38 -30.77

MSE -1.09 -1.59 0.15

MAE 1.09 1.59 0.27

Interstrand base pairs

G· · · G IS -5.20 -5.08 -5.62 -4.64

G· · · G IS 0.80 1.19 0.92 1.97

C· · · C IS 3.10 3.54 3.29 3.43

MSE 0.32 -0.04 0.69

MAE 0.32 0.25 0.69

Stacked base pairs

A· · · G S -6.50 -6.21 -6.17 -5.61

C· · · G S -12.40 -11.08 -10.76 -10.03

G· · · C S -11.60 -11.00 -11.04 -10.03

MSE 0.74 0.84 1.61

MAE 0.74 0.84 1.61

MSE -0.06 -0.09 0.27

MAE 0.38 0.41 0.41

[1] Lin, Y.-S.; Tsai, C.-W.; Li, G.-D.; Chai, J.-D. J. Chem. Phys. 2012, 136, 154109.

[2] Chakravorty, S. J.; Gwaltney, S. R.; Davidson, E. R.; Parpia, F. A.; Fischer, C. F. Phys. Rev. A 1993, 47, 3649.

[3] Zhao, Y.; Gonz´alez-Garc´ıa, N.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 2012.Zhao, Y.; Gonz´alez-Garc´ıa, N.; Truhlar, D. G.

J. Phys. Chem. A 2006, 110, 4942(E).

[4] Zhao, Y.; Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 2715.

[5] Marshall, M. S.; Burns, L. A.; Sherrill, C. D. J. Chem. Phys. 2011, 135, 194102.

[6] Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2005, 109, 5656.

[7] Jureˇcka, P.; ˇSponer, J.; ˇCern´y, J.; Hobza, P. Phys. Chem. Chem. Phys. 2006, 8, 1985.