Supporting Information for:

A Comparison of Singlet and Triplet States for One- and Two- Dimensional Graphene Nanoribbons Using Multireference Theory

Shawn Horn  Felix Plasser  Thomas Müller  Florian Libisch  Joachim Burgdörfer  Hans Lischka

Table of Contents

Table S1 Comparison of acene triplet states.p. S-2

Table S2 Comparison of periacene triplet states.p. S-3

Table S3 Singlet-triplet splitting for acenes.p. S-4

Table S4 Singlet-triplet splitting for periacenes.p. S-5

Table S5 Comparison of basis sets and methods for acenes.p. S-6

Table S6 Total number of effectively unpaired electrons for acenes.p. S-7

Table S7 Total number of effectively unpaired electrons for periacenes.p. S-8

Figure S1 HONO/LUNO plot for the1Ag 11-acene. p. S-9

Figure S2 HONO/LUNO plot for the 3B3u 11-acene.p. S-10

Figure S3 HONO/LUNO plot for the1Ag (5a,5z) periacene.p. S-11

Figure S4 HONO/LUNO plot for the 3B3u (5a,5z) periacene.p. S-12

Referencesp. S-13
Table S1 Comparison of the singlet – triplet splitting (eV) of n-acenes (n=2-9) of the four irreducible representations of D2hsymmetry corresponding to singlet and triplet states (see text) for the π-MR-CISD+Q/CAS(8,8)/6-31G calculation.

π-MR-CISD+Q/CAS(8,8)/6-31G
n / ag / b3u / b2u / b1g
2 / 5.46 / 2.92 / 4.14 / 4.36
3 / 4.91 / 2.08 / 3.58 / 3.66
4 / 4.58 / 1.66 / 3.38 / 3.08
5 / 4.10 / 1.09 / 3.04 / 2.50
6 / 3.96 / 0.95 / 3.11 / 2.01
7 / 4.03 / 0.63 / 2.66 / 1.80
8 / 4.00 / 0.60 / 2.17 / 1.49
9 / 3.90 / 0.46 / 2.02 / 1.40

Table S2 Comparison of the singlet – triplet splitting (eV) of (5a,nz) periacenes (n=2-5) of the four irreducible representations of D2h symmetry corresponding to singlet and triplet states for the π-MR-CISD+Q/CAS(8,8)/6-31G calculation.

π-MR-CISD+Q/CAS(8,8)/6-31G
n / ag / b3u / b2u / b1g
2 / 2.82 / 1.68 / 3.82 / 3.47
3 / 4.01 / 0.26 / 2.64 / 2.37
4 / 3.46 / 0.04 / 2.72 / 2.60
5 / 2.62 / 0.07 / 1.94 / 1.91

Table S3 Comparison of the singlet – triplet splitting (eV) for n-acenes (n=2-13) of four different levels of theory with a π-RAS/CAS(4,4)/AUX/6-31G reference space and with experimental data.

Method
n / π-MCSCF / π-MR-CISD / π-MR-CISD+Q / π-MR-AQCC / Experimental
2 / 3.39 / 3.00 / 2.84 / 2.93 / 2.64a
3 / 2.55 / 2.25 / 2.10 / 2.17 / 1.87b
4 / 1.57 / 1.73 / 1.67 / 1.60 / 1.27c
5 / 1.15 / 1.22 / 1.20 / 1.07 / 0.86d
6 / 0.87 / 1.03 / 1.05 / 0.75 / 0.52e
7 / 0.62 / 0.68 / 0.72 / 0.59
8 / 0.58 / 0.58 / 0.57 / 0.52
9 / 0.46 / 0.47 / 0.47 / 0.42
10 / 0.48 / 0.43 / 0.39 / 0.31
11 / 0.44 / 0.40 / 0.38 / 0.26
12 / 0.44 / 0.41 / 0.40
13 / 0.39 / 0.38 / 0.38

a Ref. [1], b Ref. [2], c Ref. [3], d Ref. [4], e Ref. [5]

Table S4 Comparison of the singlet – triplet splitting (eV) for (5a,nz) periacenes (n=2-5) of four different levels of theory with a π-CAS(8,8)/6-31Greference space.

Method
n / π-MCSCF / π-MR-CISD / π-MR-CISD+Q / π-MR-AQCC
2 / 2.31 / 1.95 / 1.68 / 1.10
3 / 0.21 / 0.23 / 0.26 / 0.30
4 / 0.07 / 0.05 / 0.04 / 0.05
5 / 0.21 / 0.14 / 0.07 / 0.05

Table S5 Comparison of singlet-triplet splitting energies (eV) using RAS/CAS(4,4)/AUX MCSCF and MR-AQCC calculations for three different systemsapproaches: π-6-31G, π-6-31G*, and total-6-31G*.

Method
n / MCSCF / MR-AQCC
6-31G* / 6-31G / 6-31G*
(π) / (total) / (π) / (π) / (total)
2 / 3.34 / 3.44 / 2.93 / 3.00 / 3.24
3 / 2.53 / 2.74 / 2.17 / 2.22 / 2.41
4 / 1.62 / 1.92 / 1.60 / 1.61 / 1.73
5 / 1.19 / 1.44 / 1.07 / 1.06 / 1.05
6 / 0.89 / 1.12 / 0.75 / 0.73 / 0.72
7 / 0.62 / 0.86 / 0.59 / 0.60 / 0.65
8 / 0.57 / 0.52 / 0.46
9 / 0.44 / 0.42 / 0.48
10 / 0.31
11 / 0.26

Table S6 Total number of effectively unpaired electrons for the n-acenes (n=2-11) with and without the HONO and LUNO states present for the singlet and triplet states of the π-MR-AQCC/RAS/CAS(4,4)/AUX/6-31G calculation.

State
n / Singlet / Triplet
with HONO/LUNO / without HONO/LUNO / with HONO/LUNO / without HONO/LUNO
2 / 0.32 / 0.17 / 2.42 / 0.61
3 / 0.49 / 0.27 / 2.40 / 0.48
4 / 0.68 / 0.34 / 2.47 / 0.51
5 / 0.92 / 0.43 / 2.59 / 0.64
6 / 1.23 / 0.55 / 2.71 / 0.73
7 / 1.48 / 0.75 / 2.87 / 0.90
8 / 1.94 / 0.90 / 2.99 / 1.01
9 / 2.23 / 1.19 / 3.29 / 1.32
10 / 2.84 / 1.42 / 3.59 / 1.63
11 / 3.88 / 2.03 / 4.40 / 2.47

Table S7 Total number of effectively unpaired electrons for the (5a,nz) periacene series with and without the HONO and LUNO states present for the singlet and triplet states for the π-MR-AQCC/CAS (8,8)/6-31G approach.

State
n / Singlet / Triplet
with HONO/LUNO / without HONO/LUNO / with HONO/LUNO / without HONO/LUNO
2 / 1.07 / 0.69 / 2.93 / 0.94
3 / 2.87 / 1.40 / 3.09 / 1.09
4 / 3.35 / 1.35 / 3.29 / 1.29
5 / 4.00 / 2.00 / 3.86 / 1.86

Figure S1 LUNO (top) and HONO (bottom) plots for the 1Agstate of the 11-acene (isovalue 0.03 a.u.) of the π-MR-AQCC/RAS(6)/CAS(4,4)/AUX(6)/6-31Gcalculation.

Figure S2 LUNO (top) and HONO (bottom) plot for the 3B3u state of the 11-acene (isovalue 0.03a.u.) of the π-MR-AQCC/RAS(6)/CAS(4,4)/AUX(6)/6-31G calculation.

Figure S3 LUNO (left) and HONO (right) plots for the 1Agstate of the (5a,5z) periacene (isovalue 0.03) for the π-MR-AQCC/CAS(8,8)/6-31G calculation.

Figure S4 LUNO (left) and HONO (right) plots for the3B3u state of the (5a,5z) periacene (isovalue 0.03) for the π-MR-AQCC/CAS(8,8)/6-31G calculation.

References

1.Birks J. (1970) Photophysics of Aromatic Molecules. London: Wiley.

2.Schiedt J, and Weinkauf R (1997)Chem Phys Lett 266:201.

3.Sabbatini N, Indelli M, Gandolfi M, and Balzani V (1982)J Phys Chem 86:3585.

4.Burgos J, Pope M, Swendberg C, and Alfano R (1977) Phys Status Solidi B 83:249.

5.Houk K, Lee P, and Nendel M (2001)J Org Chem 66:5517.

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