Supplementary Material to: Electronic Properties of the Coronene Series from Thermally-Assisted-Occupation Density Functional Theory

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Supplementary Material to: Electronic Properties of the Coronene Series from Thermally-Assisted-Occupation Density

Functional Theory

Chia-Nan Yeh,¹ Can Wu,² Haibin Su,^{2, 3, ∗} and Jeng-Da Chai^{1, 4, 5, †}

1Department of Physics, National Taiwan University, Taipei 10617, Taiwan

2School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue,

Singapore 639798, Republic of Singapore

3Department of Chemistry, The Hong Kong University of Science and Technology, Hong Kong, China

4Center for Theoretical Physics, National Taiwan University, Taipei 10617, Taiwan

5Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan

∗ Corresponding author. Electronic mail: [email protected]

† Corresponding author. Electronic mail: [email protected]

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Electronic Supplementary Material (ESI) for RSC Advances.

This journal is © The Royal Society of Chemistry 2018

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LIST OF TABLES

S1 Comparison of the singlet-triplet energy gap E_ST (in kcal/mol) of n-coronene, calculated using spin-unrestricted TAO-LDA with the 6-31G(d) and 6-31G basis sets. . . 3 S2 Singlet-triplet energy gap E_ST (in kcal/mol) of n-coronene, calculated using

spin-unrestricted TAO-LDA, KS-LDA, and KS-B3LYP with the 6-31G basis set. Here, the experimental data is taken from the literature [1]. . . 4 S3 Vertical ionization potential IP_v (in eV), vertical electron affinity EA_v (in eV),

and fundamental gap E_g (in eV) for the lowest singlet state of n-coronene, calculated using spin-unrestricted TAO-LDA with the 6-31G basis set. Here, the experimental data (given in parentheses) are taken from the literature [2–4]. 5 S4 Symmetrized von Neumann entropy S_vN for the lowest singlet state of n-

coronene, calculated using spin-restricted TAO-LDA with the 6-31G basis set. . . 6 S5 Active orbital occupation numbers (HOMO−8, ..., HOMO−1, HOMO,

LUMO, LUMO+1, ..., and LUMO+8) for the lowest singlet state of n- coronene, calculated using spin-restricted TAO-LDA with the 6-31G basis set. For brevity, HOMO is denoted as H, LUMO is denoted as L, and so on. . 7

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TABLE S1. Comparison of the singlet-triplet energy gap EST (in kcal/mol) of n-coronene, calculated using spin-unrestricted TAO-LDA with the 6-31G(d) and 6-31G basis sets.

n 6-31G(d) 6-31G Difference

2 51.31 52.41 -1.10

3 30.05 30.81 -0.76

4 17.68 18.16 -0.48

5 9.96 10.21 -0.25

6 5.49 5.59 -0.10

7 3.18 3.21 -0.03

8 2.02 2.03 -0.01

9 1.41 1.40 0.01

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TABLE S2. Singlet-triplet energy gap EST (in kcal/mol) of n-coronene, calculated using spin- unrestricted TAO-LDA, KS-LDA, and KS-B3LYP with the 6-31G basis set. Here, the experimental data is taken from the literature [1].

n TAO-LDA KS-LDA KS-B3LYP Expt.

2 52.41 60.21 61.10 55.35 [1]

3 30.81 40.77 43.23

4 18.16 28.94 31.35

5 10.21 20.82 22.05

6 5.59 14.86 13.31

7 3.21 10.31 2.91

8 2.03 6.78 -9.06

9 1.40 3.77

10 1.05 0.53

11 0.82 1.34

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TABLE S3. Vertical ionization potential IPv (in eV), vertical electron affinity EAv (in eV), and fundamental gap E_g (in eV) for the lowest singlet state of n-coronene, calculated using spin- unrestricted TAO-LDA with the 6-31G basis set. Here, the experimental data (given in parentheses) are taken from the literature [2–4].

n IPv EAv Eg

2 6.72 (7.29 [2]) 0.58 (0.50 [3, 4]) 6.14 (6.79 [2–4])

3 5.81 1.70 4.11

4 5.30 2.35 2.95

5 4.99 2.77 2.22

6 4.80 3.04 1.76

7 4.68 3.22 1.46

8 4.60 3.35 1.26

9 4.55 3.44 1.11

10 4.51 3.51 0.99

11 4.47 3.57 0.90

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TABLE S4. Symmetrized von Neumann entropy S_vN for the lowest singlet state of n-coronene, calculated using spin-restricted TAO-LDA with the 6-31G basis set.

n S_vN

2 0.01

3 0.15

4 0.54

5 1.29

6 2.39

7 3.77

8 5.30

9 6.93

10 8.65

11 10.44

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TABLE S5. Active orbital occupation numbers (HOMO−8, ..., HOMO−1, HOMO, LUMO, LUMO+1, ..., and LUMO+8) for the lowest singlet state of n-coronene, calculated using spin- restricted TAO-LDA with the 6-31G basis set. For brevity, HOMO is denoted as H, LUMO is denoted as L, and so on.

n 2 3 4 5 6 7 8 9 10 11

H−8 2.000 2.000 2.000 2.000 2.000 1.997 1.990 1.971 1.933 1.870 H−7 2.000 2.000 2.000 1.999 1.996 1.987 1.965 1.927 1.869 1.791 H−6 2.000 2.000 2.000 1.999 1.996 1.987 1.965 1.927 1.868 1.790 H−5 2.000 2.000 2.000 1.999 1.992 1.970 1.917 1.828 1.707 1.574 H−4 2.000 2.000 1.998 1.989 1.964 1.913 1.833 1.728 1.609 1.491 H−3 2.000 2.000 1.998 1.989 1.964 1.913 1.832 1.727 1.608 1.490 H−2 2.000 2.000 1.997 1.975 1.907 1.781 1.624 1.474 1.350 1.257 H−1 1.999 1.988 1.948 1.865 1.743 1.602 1.467 1.353 1.264 1.198 H 1.999 1.988 1.948 1.864 1.742 1.601 1.466 1.352 1.263 1.197 L 0.001 0.012 0.052 0.136 0.262 0.411 0.557 0.685 0.787 0.863 L+1 0.001 0.012 0.052 0.136 0.261 0.409 0.556 0.684 0.786 0.862 L+2 0.000 0.000 0.003 0.025 0.097 0.234 0.408 0.578 0.719 0.823 L+3 0.000 0.000 0.002 0.010 0.032 0.074 0.144 0.241 0.357 0.478 L+4 0.000 0.000 0.002 0.010 0.031 0.074 0.144 0.240 0.356 0.477 L+5 0.000 0.000 0.000 0.001 0.005 0.021 0.061 0.136 0.247 0.378 L+6 0.000 0.000 0.000 0.001 0.004 0.012 0.031 0.065 0.117 0.189 L+7 0.000 0.000 0.000 0.001 0.004 0.012 0.031 0.064 0.117 0.188 L+8 0.000 0.000 0.000 0.000 0.001 0.002 0.007 0.022 0.052 0.104

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