Supplementary Material to: Electronic Properties of Cyclacenes from TAO-DFT

20  Download (0)

Full text

(1)

Supplementary Material to: Electronic Properties of Cyclacenes from TAO-DFT

Chun-Shian Wu,1, 2, Pei-Yin Lee,1, and Jeng-Da Chai1, 3,

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

2Department of Chemistry, National Taiwan University, Taipei 10617, Taiwan

3Center for Theoretical Sciences and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan

These authors contributed equally to this work.

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

(2)

LIST OF TABLES

S1 Singlet-triplet energy gap (in kcal/mol) of n-cyclacene as a function of the number of benzene rings, calculated using TAO-LDA and KS-LDA. For com- parison, the CASPT2, KS-M06L, and KS-B3LYP data are taken from the literature [1]. . . 3 S2 Singlet-triplet energy gap (in kcal/mol) of n-cyclacene/n-acene as a function

of the number of benzene rings, calculated using TAO-LDA. . . 3 S3 Vertical ionization potential (in eV) for the lowest singlet state of n-cyclacene/n-

acene as a function of the number of benzene rings, calculated using TAO-LDA. 7 S4 Vertical electron affinity (in eV) for the lowest singlet state of n-cyclacene/n-

acene as a function of the number of benzene rings, calculated using TAO-LDA. 10 S5 Fundamental gap (in eV) for the lowest singlet state of n-cyclacene/n-acene

as a function of the number of benzene rings, calculated using TAO-LDA. . . . 14 S6 Symmetrized von Neumann entropy for the lowest singlet state of n-cyclacene/n-

acene as a function of the number of benzene rings, calculated using TAO-LDA. 17

(3)

[1] Sadowsky, D., McNeill, K. & Cramer, C. J. Electronic structures of [n]-cyclacenes (n = 6-12) and short, hydrogen-capped, carbon nanotubes. Farad. Discuss, 145, 507–521 (2010).

TABLES

TABLE S1. Singlet-triplet energy gap (in kcal/mol) of n-cyclacene as a function of the number of benzene rings, calculated using TAO-LDA and KS-LDA. For comparison, the CASPT2, KS-M06L, and KS-B3LYP data are taken from the literature [1].

n TAO-LDA KS-LDA CASPT2 KS-M06L KS-B3LYP

4 36.72 40.93

5 6.01 7.52

6 9.96 8.95 12.00 12.31 15.97

7 6.10 10.45 12.00 7.70 9.87

8 11.14 10.02 14.51 13.10 21.85

9 2.84 3.32 8.01 4.59 6.93

10 9.02 10.78 11.40 13.60 54.76

11 2.49 2.64 7.50 3.80 6.67

12 6.35 11.31 13.77 10.99

13 2.77 2.74

14 4.28 10.81

15 3.04 3.43

16 3.09 8.13

17 3.06 4.69

18 2.52 4.51

19 2.83 6.16

20 2.25 2.86

(4)

TABLE S2. Singlet-triplet energy gap (in kcal/mol) of n-cyclacene/n-acene as a function of the number of benzene rings, calculated using TAO-LDA.

n n-cyclacene n-acene

4 36.72 29.01

5 6.01 19.60

6 9.96 13.55

7 6.10 9.91

8 11.14 7.85

9 2.84 6.66

10 9.02 5.91

11 2.49 5.32

12 6.35 4.82

13 2.77 4.38

14 4.28 3.98

15 3.04 3.65

16 3.09 3.37

17 3.06 3.14

18 2.52 2.94

19 2.83 2.77

20 2.25 2.62

21 2.51 2.49

22 2.11 2.37

23 2.21 2.25

24 2.00 2.15

25 1.97 2.06

26 1.89 1.98

27 1.80 1.90

28 1.77 1.83

29 1.67 1.76

30 1.65 1.70

(5)

31 1.57 1.64

32 1.54 1.59

33 1.48 1.54

34 1.44 1.49

35 1.40 1.45

36 1.36 1.40

37 1.32 1.36

38 1.28 1.33

39 1.25 1.29

40 1.22 1.26

41 1.19 1.23

42 1.16 1.20

43 1.14 1.17

44 1.11 1.14

45 1.09 1.11

46 1.06 1.09

47 1.04 1.07

48 1.02 1.04

49 1.00 1.02

50 0.98 1.00

51 0.96 0.98

52 0.93 0.96

53 0.92 0.94

54 0.90 0.92

55 0.89 0.91

56 0.87 0.89

57 0.86 0.87

58 0.84 0.86

59 0.83 0.84

60 0.81 0.83

(6)

61 0.80 0.82

62 0.79 0.80

63 0.77 0.79

64 0.76 0.78

65 0.75 0.76

66 0.74 0.75

67 0.73 0.74

68 0.72 0.73

69 0.71 0.72

70 0.70 0.71

71 0.69 0.70

72 0.68 0.69

73 0.67 0.68

74 0.66 0.67

75 0.65 0.66

76 0.64 0.65

77 0.63 0.64

78 0.63 0.64

79 0.62 0.63

80 0.61 0.62

81 0.60 0.61

82 0.60 0.60

83 0.59 0.60

84 0.58 0.59

85 0.57 0.58

86 0.57 0.58

87 0.56 0.57

88 0.55 0.56

89 0.55 0.56

90 0.54 0.55

(7)

91 0.54 0.54

92 0.53 0.54

93 0.52 0.53

94 0.52 0.53

95 0.51 0.52

96 0.51 0.51

97 0.50 0.51

98 0.50 0.50

99 0.49 0.50

100 0.49 0.49

TABLE S3. Vertical ionization potential (in eV) for the lowest singlet state of n-cyclacene/n-acene as a function of the number of benzene rings, calculated using TAO-LDA.

n n-cyclacene n-acene

4 6.99 6.46

5 5.95 6.07

6 5.73 5.79

7 5.53 5.59

8 5.59 5.44

9 5.33 5.33

10 5.41 5.23

11 5.21 5.15

12 5.24 5.08

13 5.12 5.01

14 5.10 4.96

15 5.04 4.91

16 4.99 4.86

17 4.96 4.82

18 4.91 4.78

(8)

19 4.89 4.75

20 4.84 4.71

21 4.82 4.68

22 4.78 4.66

23 4.76 4.63

24 4.73 4.61

25 4.71 4.59

26 4.69 4.57

27 4.67 4.55

28 4.65 4.53

29 4.63 4.51

30 4.61 4.50

31 4.59 4.48

32 4.57 4.47

33 4.56 4.45

34 4.54 4.44

35 4.53 4.43

36 4.52 4.42

37 4.50 4.40

38 4.49 4.39

39 4.48 4.38

40 4.47 4.37

41 4.45 4.36

42 4.44 4.35

43 4.43 4.35

44 4.42 4.34

45 4.41 4.33

46 4.40 4.32

47 4.40 4.31

48 4.39 4.31

(9)

49 4.38 4.30

50 4.37 4.29

51 4.36 4.29

52 4.36 4.28

53 4.35 4.27

54 4.34 4.27

55 4.33 4.26

56 4.33 4.26

57 4.32 4.25

58 4.32 4.24

59 4.31 4.24

60 4.30 4.23

61 4.30 4.23

62 4.29 4.23

63 4.29 4.22

64 4.28 4.22

65 4.28 4.21

66 4.27 4.21

67 4.27 4.20

68 4.26 4.20

69 4.26 4.20

70 4.25 4.19

71 4.25 4.19

72 4.24 4.18

73 4.24 4.18

74 4.23 4.18

75 4.23 4.17

76 4.23 4.17

77 4.22 4.17

78 4.22 4.16

(10)

79 4.22 4.16

80 4.21 4.16

81 4.21 4.15

82 4.20 4.15

83 4.20 4.15

84 4.20 4.15

85 4.19 4.14

86 4.19 4.14

87 4.19 4.14

88 4.18 4.14

89 4.18 4.13

90 4.18 4.13

91 4.18 4.13

92 4.17 4.13

93 4.17 4.12

94 4.17 4.12

95 4.16 4.12

96 4.16 4.12

97 4.16 4.11

98 4.16 4.11

99 4.15 4.11

100 4.15 4.11

TABLE S4. Vertical electron affinity (in eV) for the lowest singlet state of n-cyclacene/n-acene as a function of the number of benzene rings, calculated using TAO-LDA.

n n-cyclacene n-acene

4 0.19 0.90

5 1.23 1.34

6 1.17 1.66

7 1.45 1.89

(11)

8 1.53 2.06

9 1.88 2.19

10 1.88 2.30

11 2.14 2.39

12 2.15 2.48

13 2.33 2.55

14 2.36 2.61

15 2.47 2.67

16 2.52 2.72

17 2.58 2.77

18 2.64 2.81

19 2.68 2.85

20 2.73 2.89

21 2.77 2.92

22 2.81 2.95

23 2.84 2.98

24 2.88 3.00

25 2.90 3.03

26 2.93 3.05

27 2.96 3.07

28 2.98 3.09

29 3.01 3.11

30 3.03 3.13

31 3.05 3.15

32 3.07 3.16

33 3.09 3.18

34 3.11 3.19

35 3.12 3.21

36 3.14 3.22

37 3.15 3.23

(12)

38 3.17 3.25

39 3.18 3.26

40 3.19 3.27

41 3.21 3.28

42 3.22 3.29

43 3.23 3.30

44 3.24 3.31

45 3.25 3.32

46 3.26 3.33

47 3.27 3.33

48 3.28 3.34

49 3.29 3.35

50 3.30 3.36

51 3.31 3.36

52 3.32 3.37

53 3.32 3.38

54 3.33 3.39

55 3.34 3.39

56 3.35 3.40

57 3.35 3.40

58 3.36 3.41

59 3.37 3.42

60 3.37 3.42

61 3.38 3.43

62 3.39 3.43

63 3.39 3.44

64 3.40 3.44

65 3.40 3.45

66 3.41 3.45

67 3.41 3.46

(13)

68 3.42 3.46

69 3.42 3.46

70 3.43 3.47

71 3.43 3.47

72 3.44 3.48

73 3.44 3.48

74 3.45 3.48

75 3.45 3.49

76 3.46 3.49

77 3.46 3.50

78 3.46 3.50

79 3.47 3.50

80 3.47 3.51

81 3.48 3.51

82 3.48 3.51

83 3.48 3.52

84 3.49 3.52

85 3.49 3.52

86 3.49 3.52

87 3.50 3.53

88 3.50 3.53

89 3.50 3.53

90 3.51 3.54

91 3.51 3.54

92 3.51 3.54

93 3.52 3.54

94 3.52 3.55

95 3.52 3.55

96 3.52 3.55

97 3.53 3.55

(14)

98 3.53 3.56

99 3.53 3.56

100 3.53 3.56

TABLE S5. Fundamental gap (in eV) for the lowest singlet state of n-cyclacene/n-acene as a function of the number of benzene rings, calculated using TAO-LDA.

n n-cyclacene n-acene

4 6.81 5.56

5 4.72 4.73

6 4.56 4.13

7 4.08 3.69

8 4.06 3.38

9 3.45 3.13

10 3.53 2.93

11 3.07 2.76

12 3.09 2.60

13 2.79 2.46

14 2.74 2.34

15 2.57 2.23

16 2.47 2.13

17 2.38 2.05

18 2.27 1.97

19 2.21 1.89

20 2.11 1.83

21 2.05 1.76

22 1.97 1.71

23 1.92 1.65

24 1.86 1.60

25 1.81 1.56

26 1.75 1.52

(15)

27 1.71 1.47

28 1.66 1.44

29 1.62 1.40

30 1.58 1.37

31 1.54 1.33

32 1.50 1.30

33 1.47 1.27

34 1.44 1.25

35 1.41 1.22

36 1.38 1.20

37 1.35 1.17

38 1.32 1.15

39 1.30 1.13

40 1.27 1.11

41 1.25 1.09

42 1.22 1.07

43 1.20 1.05

44 1.18 1.03

45 1.16 1.01

46 1.14 1.00

47 1.12 0.98

48 1.11 0.96

49 1.09 0.95

50 1.07 0.94

51 1.05 0.92

52 1.04 0.91

53 1.02 0.89

54 1.01 0.88

55 0.99 0.87

56 0.98 0.86

(16)

57 0.97 0.85

58 0.95 0.84

59 0.94 0.82

60 0.93 0.81

61 0.92 0.80

62 0.91 0.79

63 0.89 0.78

64 0.88 0.77

65 0.87 0.77

66 0.86 0.76

67 0.85 0.75

68 0.84 0.74

69 0.83 0.73

70 0.82 0.72

71 0.81 0.72

72 0.80 0.71

73 0.80 0.70

74 0.79 0.69

75 0.78 0.69

76 0.77 0.68

77 0.76 0.67

78 0.75 0.67

79 0.75 0.66

80 0.74 0.65

81 0.73 0.65

82 0.72 0.64

83 0.72 0.63

84 0.71 0.63

85 0.70 0.62

86 0.70 0.62

(17)

87 0.69 0.61

88 0.69 0.61

89 0.68 0.60

90 0.67 0.59

91 0.67 0.59

92 0.66 0.58

93 0.66 0.58

94 0.65 0.58

95 0.64 0.57

96 0.64 0.57

97 0.63 0.56

98 0.63 0.56

99 0.62 0.55

100 0.62 0.55

TABLE S6. Symmetrized von Neumann entropy for the lowest singlet state of n-cyclacene/n-acene as a function of the number of benzene rings, calculated using TAO-LDA.

n n-cyclacene n-acene

4 0.04 0.15

5 1.51 0.40

6 1.03 0.75

7 1.53 1.08

8 0.99 1.34

9 2.50 1.52

10 1.23 1.67

11 2.80 1.82

12 1.74 1.98

13 2.83 2.16

14 2.42 2.36

15 2.90 2.55

(18)

16 3.06 2.75

17 3.10 2.94

18 3.55 3.13

19 3.43 3.31

20 3.92 3.50

21 3.85 3.69

22 4.24 3.88

23 4.29 4.07

24 4.55 4.26

25 4.72 4.44

26 4.90 4.63

27 5.11 4.82

28 5.26 5.01

29 5.49 5.20

30 5.64 5.39

31 5.86 5.58

32 6.03 5.77

33 6.23 5.95

34 6.41 6.14

35 6.60 6.33

36 6.79 6.52

37 6.98 6.71

38 7.17 6.90

39 7.36 7.09

40 7.55 7.27

41 7.73 7.46

42 7.92 7.65

43 8.11 7.84

44 8.30 8.03

45 8.49 8.22

(19)

46 8.68 8.41

47 8.87 8.59

48 9.06 8.78

49 9.24 8.97

50 9.43 9.16

51 9.62 9.35

52 9.81 9.54

53 10.00 9.73

54 10.19 9.92

55 10.38 10.10

56 10.56 10.29

57 10.75 10.48

58 10.94 10.67

59 11.13 10.86

60 11.32 11.05

61 11.51 11.23

62 11.70 11.42

63 11.89 11.61

64 12.07 11.80

65 12.26 11.99

66 12.45 12.18

67 12.64 12.37

68 12.83 12.56

69 13.02 12.74

70 13.21 12.93

71 13.39 13.12

72 13.58 13.31

73 13.77 13.50

74 13.96 13.69

75 14.15 13.88

(20)

76 14.34 14.06

77 14.53 14.25

78 14.71 14.44

79 14.90 14.63

80 15.09 14.82

81 15.28 15.01

82 15.47 15.20

83 15.66 15.38

84 15.85 15.57

85 16.04 15.76

86 16.22 15.95

87 16.41 16.14

88 16.60 16.33

89 16.79 16.52

90 16.98 16.70

91 17.17 16.89

92 17.36 17.08

93 17.54 17.27

94 17.73 17.46

95 17.92 17.65

96 18.11 17.84

97 18.30 18.02

98 18.49 18.21

99 18.68 18.40

100 18.86 18.59

Figure

Updating...

References

Related subjects :