Impact of Non-Empirically Tuning the Range-Separation Parameter of Long-Range Corrected Hybrid Functionals on Ionization Potentials, Electron Affinities, and Fundamental Gaps

Impact of Non-Empirically Tuning the Range-Separation Parameter of Long-Range Corrected Hybrid Functionals on Ionization Potentials, Electron Affinities, and Fundamental Gaps

Talapunur Vikramaditya,

Jeng-Da Chai,

and Shiang-Tai Lin

iT. Vikramaditya, Shiang-Tai Lin

Computational Molecular Engineering Laboratory,Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan.

ii Jeng-Da Chai

Department of Physics, Center for Theoretical Physics, and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan.

Supporting Information

Table 1. CCSD(T)//ATZ IP, EA and FG evaluated employing ∆SCF approach (30 compounds).

Compounds IP EA FG

Butyl amine 9.44 -0.57 10.01

Cyclohexyl amine 9.3 -0.53 9.83

Dimethyl amine 8.94 -0.61 9.55

Sec-Butyl amine 9.31 -0.56 9.87

Butanol 10.68 -0.74 11.42

Ethyleneglycol 10.97 -0.7 11.67

Phenol 9.2 -0.49 9.69

Quinol 8.99 -0.59 9.58

1-Butyne 10.38 -0.59 10.97

Butadine 9.22 -0.78 10

1,4-Cyclohexadine 9.08 -0.79 9.87

Benzene 9.43 -0.79 10.22

Naphthalene 8.23 -0.63 8.86

Acridine 8.06 0.54 7.52

Azulene 7.54 0.41 7.13

Furan 9.05 -0.83 9.88

Thiophene 9.39 -0.77 10.16

Pyridine 9.73 -0.74 10.47

Indole 7.93 -0.38 8.31

Quinoline 8.77 -0.59 9.36

Carbazole 7.78 -0.36 8.14

Benzonitrile 9.89 -0.32 10.21

meta Cyano Benzonitrile 10.41 0.52 9.89

TCNE 11.96 2.92 9.04

Fumeronitrile 11.41 0.88 10.53

Benzoquinone 10.17 1.47 8.7

F4- Benzoquinone 11.01 2.18 8.83

Benzaldehyde 9.85 -0.06 9.91

Maleic Anhydride 11.21 0.94 10.27

Pthalimide 10.02 0.55 9.47

Table 2. LC-ωPBE//ATZ IP, EA and FG evaluated employing ∆SCF approach with default range separation parameter (ω=0.40 bohr^-1). (30 compounds).

Compounds IP EA FG

Butyl amine 9.37 -0.58 9.95

Cyclohexyl amine 9.22 -0.57 9.79

Dimethyl amine 8.9 -0.62 9.52

Sec-Butyl amine 9.28 -0.59 9.87

Butanol 10.59 -0.56 11.15

Ethyleneglycol 10.83 -0.73 11.56

Phenol 9.16 -0.53 9.69

Quinol 8.94 -0.67 9.61

1-Butyne 10.25 -0.6 10.85

Butadine 9.1 -0.79 9.89

1,4-Cyclohexadine 9.03 -0.81 9.84

Benzene 9.42 -0.8 10.22

Naphthalene 8.31 -0.43 8.74

Acridine 8.12 0.75 7.37

Azulene 7.35 0.78 6.57

Furan 9.03 -0.81 9.84

Thiophene 9.42 -0.79 10.21

Pyridine 9.67 -0.89 10.56

Indole 8.01 -0.38 8.39

Quinoline 8.82 -0.02 8.84

Carbazole 7.84 -0.39 8.23

Benzonitrile 9.94 -0.09 10.03

meta Cyano Benzonitrile 10.49 0.78 9.71

TCNE 12.03 3.41 8.62

Fumeronitrile 11.41 1.26 10.15

Benzoquinone 10.67 1.74 8.93

F4- Benzoquinone 11.06 2.48 8.58

Benzaldehyde 9.8 0.15 9.65

Maleic Anhydride 11.63 1.23 10.4

Pthalimide 10.09 0.71 9.38

Table 3. Tuned IP, EA evaluated employing ∆SCF approach using eq. 3 with LC-ωPBE//ATZ (30 compounds).

Compounds ω IP EA

Butyl amine 0.35 9.36 -0.57

Cyclohexyl amine 0.33 9.18 -0.55

Dimethyl amine 0.35 8.89 -0.62

Sec-Butyl amine 0.34 9.26 -0.58

Butanol 0.38 10.56 -0.56

Ethyleneglycol 0.4 10.83 -0.73

Phenol 0.28 9.11 -0.5

Table 4. Tuned EA, evaluated employing ∆SCF approach using eq. 4 with LC-ωPBE//ATZ (26 compounds).

Compounds ω EA

Butyl amine 0.11 -0.42

Cyclohexyl amine 0.11 -0.39

Dimethyl amine 0.11 -0.45

Sec-Butyl amine 0.12 -0.43

Butanol 0.11 -0.40

Ethyleneglycol 0.39 -0.73

Phenol 0.13 -0.39

Quinol 0.18 -0.54

1-Butyne 0.11 -0.43

Butadine 0.27 -0.77

Naphthalene 0.24 -0.33

Acridine 0.23 0.82

Azulene 0.23 0.67

Thiophene 0.36 -0.79

Indole 0.21 -0.32

Quinoline 0.25 0.05

Carbazole 0.23 -0.47

Benzonitrile 0.26 -0.05

meta Cyano Benzonitrile 0.25 0.81

TCNE 0.27 3.35

Fumeronitrile 0.3 1.27

Benzoquinone 0.29 1.81

F4- Benzoquinone 0.3 2.49

Benzaldehyde 0.27 0.21

Maleic Anhydride 0.31 1.26

Pthalimide 0.26 0.78

Table 5. Tuned IP, EA, FG employing ∆SCF approach using eq. 5 with LC-ωPBE//ATZ (30 compounds).

Compounds ω IP EA FG

Butyl amine 0.35 9.36 -0.57 9.93

Cyclohexyl amine 0.33 9.18 -0.55 9.73

Dimethyl amine 0.35 8.89 -0.62 9.51

Sec-Butyl amine 0.34 9.26 -0.58 9.84

Butanol 0.38 10.56 -0.56 11.12

Ethyleneglycol 0.4 10.83 -0.73 11.56

Phenol 0.28 9.11 -0.5 9.61

Quinol 0.28 8.87 -0.63 9.5

1-Butyne 0.34 10.22 -0.59 10.81

Butadine 0.31 9.06 -0.78 9.84

Table 6. LC-ωPBE//ADZ IP, EA and FG evaluated employing ∆SCF approach with default range separation parameter (ω=0.40 bohr^-1). (30 compounds).

Compounds IP EA FG

Butyl amine 9.38 -0.73 10.11

Cyclohexyl amine 9.22 -0.71 9.93

Dimethyl amine 8.9 -0.77 9.67

Sec-Butyl amine 9.29 -0.74 10.03

Butanol 10.57 -0.71 11.28

Ethyleneglycol 10.8 -0.88 11.68

Phenol 9.13 -0.67 9.8

Quinol 8.92 -0.82 9.74

1-Butyne 10.19 -0.74 10.93

Butadine 9.04 -1 10.04

1,4-Cyclohexadine 8.99 -1.03 10.02

Benzene 9.37 -0.79 10.16

Naphthalene 8.27 -0.4 8.67

Acridine 8.08 0.77 7.31

Azulene 7.32 0.8 6.52

Furan 8.99 -1 9.99

Thiophene 9.42 -1.32 10.74

Pyridine 9.68 -0.88 10.56

Indole 7.97 -0.49 8.46

Quinoline 8.77 0 8.77

Carbazole 7.81 -0.48 8.29

Benzonitrile 9.89 -0.07 9.96

meta Cyano Benzonitrile 10.44 0.8 9.64

TCNE 11.96 3.42 8.54

Fumeronitrile 11.34 1.28 10.06

Benzoquinone 10.67 1.77 8.9

F4- Benzoquinone 11.07 2.54 8.53

Benzaldehyde 9.79 0.18 9.61

Maleic Anhydride 11.61 1.27 10.34

Pthalimide 10.05 0.75 9.3

Table 7. Tuned IP, EA, FG employing ∆SCF approach using eq. 5 with LC-ωPBE//ADZ (30 compounds).

Compounds ω IP EA FG

Butyl amine 0.35 9.36 -0.72 10.08

Cyclohexyl amine 0.33 9.18 -0.69 9.87

Dimethyl amine 0.35 8.88 -0.76 9.64

Table 8. HOMO, LUMO Energies and their gaps using default range separation parameter (0.40 bohr^-1) employing LC- ωPBE//ATZ. (30 compounds).

Compounds -HOMO -LUMO Gap(L-H)

Butyl amine 9.62 -0.76 10.38

Cyclohexyl amine 9.61 -0.75 10.36

Dimethyl amine 9.14 -0.77 9.91

Sec-Butyl amine 9.63 -0.76 10.39

Butanol 10.67 -0.74 11.41

Ethyleneglycol 10.82 -0.76 11.58

Phenol 9.6 -0.72 10.32

Quinol 9.37 -0.7 10.07

1-Butyne 10.52 -0.77 11.29

Butadine 9.47 -0.83 10.3

1,4-Cyclohexadine 9.3 -0.78 10.08

Benzene 9.86 -0.77 10.63

Naphthalene 8.71 -0.76 9.47

Acridine 8.52 0.31 8.21

Azulene 7.91 0.28 7.63

Furan 9.38 -0.78 10.16

Thiophene 9.57 -0.78 10.35

Pyridine 10.21 -0.67 10.88

Indole 8.41 -0.62 9.03

Quinoline 9.26 -0.41 9.67

Carbazole 8.31 -0.65 8.96

Benzonitrile 10.36 -0.46 10.82

meta Cyano Benzonitrile 10.92 0.35 10.57

TCNE 12.33 2.99 9.34

Fumeronitrile 11.65 0.93 10.72

Benzoquinone 10.69 1.43 9.26

F4- Benzoquinone 11.35 2.18 9.17

Benzaldehyde 10.25 -0.23 10.48

Maleic Anhydride 11.55 0.94 10.61

Pthalimide 10.65 0.32 10.33

Table 9. HOMO, LUMO Energies and their gaps tuned using eq. 5 employing LC-ωPBE//ATZ. (30 compounds).

Compounds -HOMO -LUMO GAP(L-H)

Butyl amine 9.33 -0.75 10.08

Cyclohexyl amine 9.18 -0.73 9.91

Dimethyl amine 8.86 -0.76 9.62

Sec-Butyl amine 9.28 -0.75 10.03

Butanol 10.54 -0.74 11.28

Compounds ω=0.20 ω=0.30 ω=0.40 ω=0.50 ω=0.60

Butyl amine -0.65 -0.73 -0.76 -0.77 -0.77

Cyclohexyl amine -0.64 -0.72 -0.75 -0.76 -0.77

Dimethyl amine -0.67 -0.75 -0.77 -0.79 -0.79

Sec-Butyl amine -0.64 -0.73 -0.76 -0.77 -0.78

Butanol -0.63 -0.71 -0.74 -0.76 -0.76

Ethyleneglycol -0.64 -0.73 -0.76 -0.78 -0.78

Phenol -0.6 -0.69 -0.72 -0.73 -0.74

Quinol -0.58 -0.67 -0.7 -0.71 -0.72

1-Butyne -0.66 -0.74 -0.77 -0.78 -0.79

Butadine -0.39 -0.81 -0.83 -0.83 -0.84

1,4-Cyclohexadine -0.66 -0.75 -0.78 -0.79 -0.79

Benzene -0.67 -0.75 -0.77 -0.78 -0.79

Naphthalene -0.1 -0.55 -0.76 -0.77 -0.77

Acridine 0.93 0.53 0.31 0.17 0.08

Azulene 0.81 0.46 0.28 0.18 0.1

Furan -0.7 -0.76 -0.78 -0.79 -0.79

Thiophene -0.7 -0.76 -0.78 -0.79 -0.79

Pyridine -0.44 -0.65 -0.67 -0.68 -0.68

Indole -0.52 -0.59 -0.62 -0.63 -0.64

Quinoline 0.31 -0.15 -0.41 -0.57 -0.68

Carbazole -0.33 -0.62 -0.65 -0.66 -0.66

Benzonitrile 0.29 -0.2 -0.46 -0.55 -0.55

meta Cyano Benzonitrile 1.08 0.61 0.35 0.21 0.11

TCNE 3.24 3.24 2.99 3.24 3.24

Fumeronitrile 1.84 1.27 0.93 0.73 0.6

Benzoquinone 2.36 1.78 1.43 1.21 1.08

F4- Benzoquinone 3.01 2.49 2.18 1.99 1.87

Benzaldehyde 0.62 0.08 -0.23 -0.42 -0.54

Maleic Anhydride 1.92 1.31 0.94 0.72 0.58

Pthalimide 1.12 0.61 0.32 0.14 0.03

Table 10. Negative LUMO energies at various range separation parameters (0.20, 0.30, 0.40, 0.50, 0.60 bohr-¹) with LC- ωPBE//ATZ. (30 compounds).

Table 11. Default and tuned (ω) based on eq. 5 IP, EA and FG (∆SCF) of LC-BLYP//ATZ. (30 compounds).

Default ω

Tuned ω

IP EA FG IP EA FG

Butyl amine 9.4 -0.66 10.06 9.37 -0.64 10.01

9.8

Table 12. Default and tuned (ω) based on eq. 5 IP, EA and FG (∆SCF) of ωB97XD//ATZ. (30 compounds).

Default ω

Tuned ω

IP EA FG IP EA FG

Butyl amine 9.29 -0.64 9.93 9.41 -0.64 10.05

Cyclohexyl amine 9.12 -0.63 9.75 9.22 -0.63 9.85

Dimethyl amine 8.82 -0.69 9.51 9.72 -0.6 10.32

Sec-Butyl amine 9.17 -0.65 9.82 9.27 -0.65 9.92

Butanol 10.51 -0.63 11.14 10.64 -0.62 11.26

Ethyleneglycol 10.57 -0.69 11.26 11.28 -0.69 11.97

Phenol 9.01 -0.59 9.6 9.06 -0.59 9.65

Quinol 8.78 -0.7 9.48 8.83 -0.63 9.46

1-Butyne 10.11 -0.65 10.76 10.25 -0.65 10.9

Butadine 8.92 -0.99 9.91 9.02 -0.98 10

1,4-Cyclohexadine 8.72 -0.71 9.43 8.88 -0.7 9.58

Benzene 9.28 -0.83 10.11 9.34 -0.69 10.03

Naphthalene 8.06 -0.5 8.56 8.08 -0.49 8.57

Acridine 7.81 0.67 7.14 7.79 0.66 7.13

Azulene 7.28 0.54 6.74 7.27 0.52 6.75

Furan 8.88 -0.68 9.56 8.98 -0.68 9.66

Thiophene 9.34 -0.68 10.02 9.45 -0.67 10.12

Pyridine 9.56 -1.01 10.57 9.62 -0.54 10.16

Indole 7.8 -0.44 8.24 7.86 -0.44 8.3

Quinoline 9.27 -0.1 9.37 9.5 -0.53 10.03

Carbazole 7.61 -0.63 8.24 7.59 -0.64 8.23

Benzonitrile 9.72 -0.2 9.92 9.78 -0.18 9.96

meta Cyano Benzonitrile 10.22 0.67 9.55 10.27 0.68 9.59

TCNE 11.61 3.25 8.36 11.76 3.3 8.46

Fumeronitrile 11.1 1.15 9.95 11.31 1.19 10.12

Benzoquinone 10.24 1.69 8.55 10.72 1.71 9.01

F4- Benzoquinone 10.7 2.35 8.35 10.87 2.39 8.48

Benzaldehyde 9.87 0.06 9.81 9.68 0.08 9.6

Maleic Anhydride 11.2 1.11 10.09 11.72 1.17 10.55

Pthalimide 10.1 0.63 9.47 10.15 0.64 9.51