Pati S.K., Enoki T., Rao C.N. R. (eds.) Graphene and Its Fascinating Attributes

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Chapter 3

Singlet Open-Shell Character of Polyperiacenes

Akihiro Shimizu, Akihito Konishi, Yasukazu Hirao

and Takashi Kubo

†

Department of Chemistry, Graduate School of Science, Osaka University,

Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan

y-hirao@chem.sci.osaka-u.ac.jp;

†

kubo@chem.sci.osaka-u.ac.jp

Singlet open-shell character of polyperiacenes has been elucidated by

theoretical analysis based on the Clar’s aromatic sextet valence bond model and

quantum chemical calculations. Anti-ferromagnetic ground state of large

polyperiacenes was relevant to the sufficient stabilization energy derived from

aromatic sextet formation to overcome the energetic penalty associated with

π-bond cleavages. Experimental study on the smallest potential biradicaloid,

2,5,9,12-tetra-tert-butylbisanthene 1, demonstrated no appreciable biradical

character in physical measurements, whereas 1 showed biradicaloid behavior

toward oxygen.

1. Introduction

Graphene, which is a two dimensional sheet consisting of fused six

membered rings of carbon atoms, has zigzag and armchair edges.

STM/STS measurements have revealed the edge-localized electrons at

the zigzag edge,

where a large magnetic moment is suggested by

the tight binding band calculations.

Magnetic and related electronic

properties originating the edge spins are extensively studied theoretically

and experimentally for realization of carbon-based nanoelectronics.

this context, nanographenes as small components of the graphene sheet

have attracted considerable attention recently from synthetic

and

theoretical points of view,

and the theoretical studies using symmetry-

broken DFT calculations on nanographene molecules with zigzag edges

figure out anti-parallel spin orientation between the two edges in the

46 A. Shimizu et al.

ground state instead of the non-magnetic (that is, closed-shell singlet)

ground state predicted simply from their Kekulé structures.

5c,e,i,l

Although the anti-ferromagnetic (that is, open-shell singlet) ground state

would be derived from degeneracy of π and π* bands at the Fermi

level,

easy-understandable guidance for structure–property relationship

is required to simply predict the electronic structures of zigzag-edged

nanographenes including polyperiacenes as well as polyacenes. In this

chapter, we present theoretical consideration on polyperiacenes based on

Clar sextet valence bond model in combination with natural population

and NICS analyses using DFT calculations, and demonstrate that the

anti-ferromagnetic ground state in polyperiacenes a-b is closely related

to formation of the Clar sextets,

6a,b

that is, aromatic stabilization.

Additionally, we describe preparation of the smallest polyperiacenes, a

derivative of bisanthene 3-3, and experimental elucidation of its singlet

open-shell character.

2. Theoretical Consideration on Open-Shell Character

2.1. Clar’s aromatic sextet valence bond model

Open-shell character in seemingly intrinsic closed-shell (Kekulé)

molecules would originate from some kind of extra stabilizations to

compensate the destabilization by π-bond cleavage. In order to consider

Fig. 1. Structure of polyperiacenes a-b.

Singlet Open-Shell Character of Polyperiacenes 47

the relation between the magnetic state and the stabilization balance, we

focus on anthracene 3-1 and phenanthrene, which are minimal units of

zigzag- and armchair-edged nanographenes, respectively. Important extra

stabilization energy expected in aromatic hydrocarbons is aromatization

energy derived from (4n + 2) π cyclic conjugation. One can see two

unpaired electrons on the 9,10-positions in anthracene after pairing

electrons in the π-dot structure of anthracene so as to ensure the maximal

number of the Clar sextet (Fig. 2(a)).

These two unpaired electrons are

located at positions separated each other, and pairing of the two electrons

requires destruction of one sextet (Figs. 2(a)→2(b)). On the other hand,

phenanthrene has two sextets and two unpaired electrons which are

located at the neighboring 9,10-positions (Fig. 2(a')). These two electrons

can participate in a π-bond formation with no destruction of the sextets

(Figs. 2(a')→ 2(b')). Thus, in the Kekulé structures, anthracene is on a

balance between stabilization and destabilization, whereas phenanthrene

contains no unfavorable destabilization. The stabilization balance in

anthracene might lead to its high reactivity at the 9,10-positions.

Fig. 2. Electron pairing process of anthracene 3-1 (upper) and phenanthrene (lower). The

rings drawn in bold lines represent the Clar sextet.

Fig. 3. Electron pairings in bisanthene 3-3.

48 A. Shimizu et al.

Fig. 4. Kekulé and biradical structures of polyacenes and polyperiacenes a-b. The

numeral under each structure represents the number of the Clar sextets.

The consideration for the electronic structure of anthracene could

be adapted to the edge-localization of electrons in polyperiacenes.

Bisanthene 3-3, which is the smallest polyperiacene of anthracene, has

four unpaired electrons in the canonical form having a maximal number

of the sextet (Fig. 3(a)). Two inner neighboring electrons can be paired

with no destruction of the sextets, and consequently this pairing process

is completely favorable in energy (Figs. 3(a)→3(b)). Remaining two

electrons reside on the zigzag-edge regions, and pairing of the two

Singlet Open-Shell Character of Polyperiacenes 49

outer electrons results in decrease of total number of the sextets

(Figs. 3(b)→3(c)). Energy difference between before and after the

pairing of the electrons on the zigzag edges should be smaller in 3-3 than

in 3-1, since the pairing in 3-3 causes the destruction of two sextets;

leading to propensity of electrons to more localize in separated places in

3-3.

For larger polyperiacenes of anthracene such as 3-5 and 3-7, the

difference in the number of the sextet between the biradical and Kekulé

structures increase with increment of molecular size; three for 3-5 and

four for 3-7 (Fig. 4). More sextets in the biradical structures would result

in more dominant contribution of biradical electron configuration to the

ground state. Two unpaired electrons localize at the zigzag-edge regions

so as to gain π-bonding energy in the inner pairs of electrons, as was

seen in Figs. 3(a)→ 3(b).

2.2. Quantum chemical method

The singlet open-shell character was estimated using the index defined

by Yamaguchi

coupled to the symmetry-broken UBHandHLYP/6-31G*

calculation.

The degree of the singlet open-shell character, y

, can

be determined from the following equations: y

= 1 − 2T

/(1 + T

= (n

HOMO–i

– n

LUMO+i

)/2, where n

HOMO–i

and n

LUMO+i

represent natural

orbital occupation numbers of HOMO–i and LUMO+i, respectively.

The index y

which are determined from the HOMO–LUMO pair are

related to a π-bond cleavage and vary continuously from zero to unity.

A perfect biradical molecule has y

of unity. Table 1 shows y

polyacenes and polyperiacenes. The series of polyperinathalene 2-b,

which have been extensively studied by Müllen and co-workers,

has no

appreciable y

, although theoretical calculation for larger systems has

predicted a small HOMO–LUMO energy gap.

Actually even 2-7 shows

high stability. On the other hand, bisanthene 3-3 has a small but non-

negligible value of y

, suggesting that 3-3 is basically classified into a

closed-shell molecule with potential biradical character. High reactivity

toward oxygen of 3-3 supports this idea.

Larger homolog 3-5 and 3-7

give large values of y

, clearly indicating their appreciable biradical

character. It is noteworthy that apparent biradical character is recognized

50 A. Shimizu et al.

in the systems having three or more Clar sextets in the biradical

structures in comparison with the Kekulé structures. Aromatic

stabilization energy (ASE) of benzene based on homodesmic

stabilization energy (HSE) is ca. 90 kJ/mol,

three times of which is

comparable to the C–C π-bonding energy of 272 kJ/mol.

Thus two

unpaired electrons in the biradical structure of 3-3 (the difference of the

Clar sextet is two) prefer electron pairing to form a closed-shell ground

state, whereas 3-5 (the difference of the Clar sextet is three) is subjected

to competition between the pairing of two unpaired electrons and the

aromatization of the six-membered rings.

2.3. Aromaticity of each ring

The nucleus-independent chemical shift (NICS) calculation

16a,b,c,d

informative for an aromatic contribution of each six-membered ring.

We performed the NICS calculation of polyperiacenes a-b with the

GIAO

16e

-B3LYP/6-31G* method. Figure 5 shows the NICS(1) values of

polyacenes and polyperiacenes. Bisanthene 3-3 has the largest aromatic

contribution in the ring B, which suggests a dominant contribution of the

Kekulé structure in Fig. 4 to the ground state.

On the other hand, the

NICS(1) value of the ring B in 3-5 approaches the non-aromatic and a

large aromatic contribution is found in the ring A and D. This finding

clearly indicates decrease and increase of Kekulé and biradical

contributions to the ground state of 3-5, respectively. Larger homolog

3-7 shows more non-aromatic NICS(1) values in the ring B and E,

supporting its more pronounced biradical character.

Table 1. The degrees of open-shell character y

polyacenes and polyperiacenes a-b. In parentheses, spin

contaminations are indicated.

2 3 4

0.00 (0.00) 0.00 (0.00) 0.01 (0.31)

0.00 (0.00) 0.12 (1.01) 0.60 (1.63)

0.01 (0.35) 0.59 (1.66) 0.91 (1.90)

0.05 (0.83) 0.84 (1.83) 0.98 (2.05)

Singlet Open-Shell Character of Polyperiacenes 51

2.4. More extended ring system

Using these findings, one can easily recognize open-shell electronic

structures in polyperiacenes of tetracene (4-b; b = 3, 5, 7). All of these

compounds contain three or more sextets in the biradical structures in

comparison with the Kekulé structures, indicating a large contribution of

the biradical structures to the ground states. Unpaired electrons are prone

Fig. 5. NICS(1) values of polyacenes and polyperiacenes a-b.

52 A. Shimizu et al.

to reside on the zigzag edges to ensure maximal numbers of the Clar

sextets. Large negative NICS(1) values are found at the position where

the sextet can be drawn in the biradical structures of Fig. 4.

3. Experimental Elucidation of the Smallest Polyperiacene

The smallest potential singlet biradical species in the polyperiacenes

would be bisanthene 3-3, which has been isolated as an air-sensitive

crystalline powder.

18a

UV,

18a,b

photoelectron,

18c

fluorescence,

18d

and

vibrational spectra

18e

of this labile compound have been measured,

whereas there has been no direct determination of the experimental

structure so far.

18f

Considering stability in air and solubility in common

organic solvents, we decided to introduce tert-butyl groups on the rings

of 3-3 and prepared a tetra-tert-butyl derivative 1 from commercially

available diphenylmethane in 7 steps (Fig. 6). The structure of 1 was

confirmed by X-ray crystallographic analysis.

3.1. Geometrical consideration

The bond lengths of 1 along with anthracene and phenanthrene are

summarized in Fig. 7. The bond lengths in the ring A and B resemble to

those of anthracene. The central C–C bond (1.451(2) Å) in 1 is quite long

compared to the C–C double bond (1.338(5) Å) in the 9,10-position of

phenanthrene whose structure can be drawn in the biradical resonance

structure. The double bond character of the central C–C bond is

Fig. 6. Synthesis and ORTEP drawing of 1 at the 50% probability level.

Singlet Open-Shell Character of Polyperiacenes 53

estimated to be only 21% according to the Pauling–Brockway

relationship,

which represents C–C bond character as a function of an

experimental bond length. Thus the X-ray data agree with the

consideration of the Kekulé structure as having more importance in the

resonance hybrid of 1.

3.2. Physical properties

Physical properties of 1 also support the geometrical consideration on the

ground state of 1. In general, a small HOMO–LUMO energy gap is an

essential factor for open-shell character of a molecule, because a

HOMO–LUMO gap is closely related to the promotion of electrons from

HOMO to LUMO. A single electron HOMO–LUMO excitation along

with spin inversion leads to the triplet biradical state, whereas admixing

a doubly excited configuration

H,H→ L,L

into a ground state leads to

singlet biradical character of the system. Electronic absorption spectrum

of 1 in a toluene solution gave an intense low-energy band at 662 nm

(ε = 32,500), from which the optical HOMO–LUMO energy gap of 1

(

)

(

)

1.436(2)

(

)

1.423(2)

(

)

1.477(2)

(

)

(

)

1.451(2)

(

)

(

)

1.434(2)

(

)

1.426(3)

(

)

(

)

(

)

(

)

(

)

(

)

1.421(2)

1.431(2)

(

)

(

)

(

)

A B

(

)

1.412(4)

(

)

1.378(4)

(

)

1.454(6)

(

)

(

)

(

)

1.375(4)

(

)

(

)

1.416(4)

(

)

(

)

1.338(5)

Kekulé structure

biradical structure

Fig. 7. (Left) Bond lengths of 1 (at 200 K), anthracene (94 K),

20a

and phenanthrene

(295 K).

20b

(Right) Resonance structure of bisanthene 3-3.