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Theoretical Study on the Open-Shell Singlet Nature and the Second Hyperpolarizabilities of Corannulene Derivatives with Two Phenoxyl Radicals Yuka Minamida, Hiroshi Matsui, Kotaro Fukuda, Takanori Nagami, Jun-ya Fujiyoshi, Kyohei Yoneda, Shota Takamuku, Ryohei Kishi, Yasutaka Kitagawa, and Masayoshi Nakano J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 11 May 2017 Downloaded from http://pubs.acs.org on May 17, 2017

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The Journal of Physical Chemistry

Theoretical Study on the Open-Shell Singlet Nature and the Second Hyperpolarizabilities of Corannulene Derivatives with Two Phenoxyl Radicals

Yuka Minamida, † Hiroshi Matsui, † Kotaro Fukuda, † Takanori Nagami, † Jun-ya Fujiyoshi,† Kyohei Yoneda,§ Shota Takamuku,† Ryohei Kishi,† Yasutaka Kitagawa,†, ¶ and Masayoshi Nakano†, ¶, *

†

Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka

University, Toyonaka, Osaka 560-8531, Japan §

Department of Chemical Engineering, National Institute of Technology, Nara College, 22

Yata-cho,Yamatokoriyama,Nara, Japan ¶

Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka

University, Toyonaka, Osaka 560-8531, Japan

1 ACS Paragon Plus Environment


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ABSTRACT investigate

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Using the spin-unrestricted density functional theory method, we

the

interplay

between

the

diradical

character

y

and

second

hyperpolarizabilities γ (the third-order nonlinear optical (NLO) properties at the molecular scale) of corannulene derivatives with two phenoxyl radicals.

This

molecule in the singlet state exhibits intermediate y and thus displays a significantly larger γ value than the triplet state and the closed-shell bis-phenol analogue.

We also

examine the planar molecules involving coronene moiety in place of the curved corannulene.

The intermediate y and large γ values of the corannulene systems are

found to originate not from their curved skeleton but from the equilibrium between benzenoid/quinoid resonance forms due to delocalization of the radical electrons of the terminal phenoxyl rings.

The longitudinal γ value of the singlet state is found to be

comparable to that of s-indaceno[1,2,3-cd;5,6,7-c’d’]diphenalene, which is known to be one of the organic molecules with the largest two-photon absorption cross section in this size of pure hydrocarbons.

The present system is thus expected to be a promising

candidate for highly efficient open-shell NLO molecules.


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1. INTRODUCTION Nonlinear optical (NLO) materials of π-conjugated systems have been investigated both theoretically and experimentally because of their unique electronic structures and physicochemical applications such as high-capacity three-dimensional memory,1 ultra-fast optical switching,2 and optical limiting.3

Until now, several design

guidelines for realizing large NLO properties have been presented, for example, π-conjugation extension,4 introduction of donor/acceptor substituents,5–7 and charge state change.8

On the other hand, it has been found theoretically that open-shell

singlet nature, which is quantified by diradical character y,9–13 is strongly correlated to the second hyperpolarizability γ (third-order NLO properties at the molecular scale): open-shell singlet systems with intermediate diradical character exhibit significantly enhanced γ values as compared to closed-shell and pure diradical systems of similar size.14–18

On the basis of this correlation, referred to as “y–γ correlation”, several

practical design guidelines for a new class of open-shell NLO molecular systems have been proposed theoretically and experimentally.19–30 For such a new class of open-shell NLO systems, we have so far explored various

open-shell

singlet

planar

π-conjugated

systems,

for

example,

para-quinodimethane,14 graphene nanoflakes,28 diphenalenyl diradicaloids,18 and zethrenes.29 In particular, it was found that s-indaceno[1,2,3-cd;5,6,7-c’d’]diphenalene (IDPL) and dicyclopenta[b;g]naphthaleno[1,2,3-cd;6,7,8-c’d’]diphenalene (NDPL), which present intermediate diradical character, exhibit gigantic two-photon absorption cross sections as compared to the closed-shell hydrocarbons of similar size.19

On the

other hand, the investigation of NLO properties of curved π-conjugated systems is limited to several fullerenes, some of which are found to exhibit various diradical 3 ACS Paragon Plus Environment


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characters depending on the structures, resulting in a large variation in γ values.30 Under such a situation, in 2010, the synthesis of a corannulene derivative with two phenoxyl radicals was reported,31 where this molecule is found to have highly spin delocalized nature as well as the unique three-dimensional electron network due to its curved π-conjugated nature of corannulene skeleton.

This molecule, which involves a

bowl-shaped corannulene skeleton, is predicted to have an intermediate open-shell singlet nature, which originates from contributions of the benzenoid and quinoid resonance forms in the both-end phenoxyl groups.

This result suggests that the

corannulene derivative with intermediate diradical character has the possibility of exhibiting a large longitudinal γ value.

In this study, therefore, we investigate a

corannulene derivative in order to clarify the relationships between the molecular structure, diradical character, and static γ values using the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method.32–34

To this end, we

also examine two types of molecules of similar size, that is, the bis-phenol analogue, which is predicted to be closed-shell, and planar coronene derivatives, which have coronene skeleton instead of corannulene skeleton.

In addition, in order to clarify spin

state dependence of γ, we investigate the γ values of triplet states of the corrannulene and coronene derivatives involving terminal phenoxyl groups.

The present study will

provide a new class of real open-shell singlet systems, where the open-shell character and γ values are drastically changed by redox reaction, and clarify the effects of curved π-conjugation structures on the diradical characters and the γ values.


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2. METHODOLOGY 2.1. Model Systems. Figure 1a–d show the structures of corannulene derivative with two phenoxyl radicals (1), bis-phenol analogue (2) and the coronene analogues (3 and 4) together with their resonance structures (Figure 1e–h), where molecule 1 (3) is synthesized by oxidizing molecule 2 (4).

The geometries of these systems in their

singlet states were optimized using the RB3LYP/6-311G* method, which is known to well reproduce electronic and geometric structures of conjugated diradical singlet and closed-shell systems.35 Molecule 1, which has Cs symmetry, involves a corannulene skeleton with a small curvature, where the symmetry plane is set to the x-y plane and the both-end phenoxyl groups are twisted in the same direction around the carbon(C)-carbon(C) bond linking the corannulene and phenoxyl group (see Table S1 in the Supporting Information).

Molecule 2 has C1 symmetry, since the two hydrogen

(H) atoms in the both-end OH groups are located on the mutually opposite side with respect to the C–O bond (see Table S2 in the Supporting Information). On the other hand, molecules 3 and 4 involve coronene skeleton instead of corannulene skeleton, and their coronene moieties take planar structures: 3 has Cs symmetry, while 4 has C1 symmetry, since the terminal phenoxyl/phenol rings of 3/4 are twisted in the same direction like 1/2 (see Table S3 and S4 in the Supporting Information).

2.2. Calculation and Analysis Methods.

For the evaluation of the open-shell singlet

nature, we calculate the diradical character (y), which represents the instability of a chemical bond and takes a value between 0 (closed-shell) to 1 (pure diradical).

The

diradical character y is defined by twice the weight of the doubly-excited configuration in the multiconfiguration self-consistent-field (MC-SCF) theory9,10,13 and is formally



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expressed in the single determinant method such as the long-range-corrected (LC-UBLYP) method with a range-separating parameter of µ=0.33 bohr-1 33 :

y = nLUNO = 2 − nHONO ,

(1)

where nLUNO and nHONO represent the occupation numbers of the lowest unoccupied natural orbital (LUNO) and the highest occupied natural orbital (HONO), respectively. The spatial contribution to the diradical character is analyzed using the odd electron density distribution.11

The odd-electron density Dyodd (r) at position r for y is

calculated using the i-th natural orbitals { φi (r) } as13

(

2

2

)

Dyodd (r) = nLUNO φHONO (r) + φLUNO (r) .

(2)

The relationship between diradical character y and Dyodd (r) is expressed by13

y=

1 2

∫ d rD

odd y

The

(r) =

1 2

∫ dr n

LUNO

relationship

(φ

HONO

between

)

2 2 (r) + φ LUNO (r)  . 

diradical

character

(3) and

aromaticity

for

condensed-ring π-conjugated molecular systems has been discussed so far mostly from the viewpoint of structures, the HOMO-LUMO gap, and so on.36–38 Indeed, the diradical character is known to emerge in the case of p-quinodimethane skeleton, which has contributions of two resonance structures, quinoid (closed-shell) and benzenoid (pure diradical) forms, giving anti-aromaticity and aromaticity natures, respectively. In this study, the degree of aromaticity is evaluated with the nucleus-independent chemical shifts (NICSs) at LC-UBLYP(µ=0.33 bohr-1)/6-31+G* level of theory using the gauge-invariant atomic orbital (GIAO) method.39 The negative and positive NICS values indicate aromaticity and antiaromaticity natures, respectively.

We here

calculate the NICS value at the center of mass in the central and terminal rings, that is,


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NICS(0), where a major contribution from π electrons is expected.40 The longitudinal components of electronic static γ, γzzzz, were calculated for corannulene derivative (1), bis-phenol analogue (2), the triplet state of 1, coronene analogues (3 and 4) using the LC-UBLYP (µ=0.33 bohr-1)/6-31+G* method with the finite-field (FF) approach,41 which consists in the fourth-order differentiation of the energy with respect to the external electric field:

γ=

1 [ E(3F) −12E(2F) + 39E(F) − 56E(0) + 39E(−F) −12E(−2F) + E(−3F)] . 36F 4

(4)

This method is found to well reproduce the γ values at highly correlated level of theory, for example, UCCSD(T), for several open-shell organic molecules as well as closed-shell analogues.42 density analysis.43

The spatial contribution of electrons to γ is performed with γ

The γ density along the longitudinal z axis, ρ (3) (r) , is defined by

the third-order derivative of the electron density with respect to the applied field F in the z-direction:

ρ (3) (r) =

∂3ρ (r) ∂F 3 F=0

(5)

which is related to γ value as

γ =−

1 ∫ rρ (3) (r)dr , 3!

(6)

where r is the z component of the electron coordinate.

The positive and negative

ρ (3) (r) values multiplied by F3 correspond, respectively, to the field-induced increase and decrease in the electron density, which induce the third-order polarization in the direction from positive to negative γ density. All the calculations were performed using the Gaussian 09 package.44



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3. RESULTS AND DISCUSSION 3.1. Open-Shell Singlet Nature for Corannulene Derivatives.

It is found that the

diradical characters y of molecule 1 and 2 are 0.841 (intermediate diradical character) and 0.000 (closed-shell), respectively (see Table 1).

As seen from Figure 2, molecule

1 has large odd electron density distributions in the terminal phenoxyl ring regions, while has relatively small distributions in the corannulene skeleton, the feature of which is in agreement with the that of the open-shell forms in the resonance structures (Figure 1e).

This agreement can be explained by the Clar’s sextet rule 45, which ensures the

stability of the resonance forms containing more sextet rings. Indeed, for molecule 1, the closed-shell form has one Clar’s sextet, while the open-shell forms from one to four Clar’s sextets (Figure 3).

The odd electron density distributions are also found to well

accord with the open-shell forms, which tend to have unpaired electrons in their terminal phenoxyl ring regions. In order to clarify the correlation between the open-shell singlet nature and the optimized structures, we first examine the bond-length alternations (BLAs) for 1 and 2 (BLAs for 1 and 2 are shown in Figure 4a–c and Table S5).

As shown in Figure 4c,

in 1, bond r3 has a smaller average bond length [r3 = (r3A + r3B)/2 = 1.357 Å] than average bond lengths r2 (1.467 Å) and r4 (1.441 Å), and the bond length of r1 is 1.231 Å.

The average bond lengths r3 (1.357 Å) and r1 (1.231 Å) in 1 are found to be

slightly larger than the corresponding lengths of quinone (closed-shell), r3' (1.339 Å) and r1' (1.218 Å) (see Figure S1 in the Supporting Information), the tendency of which indicates that the open-shell (benzenoid) forms contribute to 1 in addition to the


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closed-shell (quinoid) form.

On the other hand, in 2, average bond lengths r2, r3 and r4

show more similar values than 1: r2 = 1.396 Å, r3 = 1.389 Å and r4 = 1.403 Å, and the bond length r1 is shown to be 1.365 Å, which is similar to the standard C–O bond length.

Namely, it is found that 2 has a primary contribution of benzenoid

(closed-shell phenol ring) form.

Such different trends in BLAs between 1 and 2 are

also observed in average bond lengths r6, r7 and r8.

As a result, it turns out that the

contribution of both the quinoid and benzenoid forms in the terminal rings in 1 realizes the intermediate y value of 1, while the primary contribution of the benzenoid form in the terminal rings in 2 leads to its closed-shell nature. We next investigate the nucleus-independent chemical shift (NICS(0)) for 1 and 2 (Figure 5a and b) in order to clarify the relationship between the aromaticity and diradical character.

The more negative (positive) the NICS(0) values, the more

aromatic (antiaromatic) the rings are.46

As seen from Figure 5a and b, the NICS(0)

values of both 1 and 2 are negative in the fused six-membered rings and positive in the central five-membered ring, but the negative NICS(0) values for the upper three six-membered rings in the corannulene skeleton of 1 are significantly smaller than those in 2.

This feature is found to correspond to the significant odd electron density

distributions in the corannulene skeleton (Figure 2).

Furthermore, in phenoxyl rings of

1, the positive NICS(0) value (+3.37 ppm), in contrast to the large negative NICS(0) (– 7.96 ppm) in 2, is found to correspond to the large odd electron density distributions in phenoxyl rings in 1 (Figure 2).

The significant decrease of aromaticity in the upper

three six-membered rings in corannulene skeleton and the emergence of antiaromaticity in the terminal rings together with the appearance of odd electron densities in those regions in 1 indicate the contribution of both the quinoid (closed-shell) and benzenoid



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(open-shell singlet) forms, which causes the intermediate open-shell singlet nature of 1. As seen from the resonance structures of 1 and 2 (Figure 1e and f), we also expect the contribution of ionic forms.

To elucidate this feature, we evaluate the

intramolecular charge transfer (ICT) using Hirshfeld charge distribution47 for each atom. Such ionic forms are predicted to have the features i) that since the corannulene skeleton of 1 or 2 is a 20π electron system composed of inner 5π and outer 15π electron rings, ICT occurs from the outer to the inner ring in corannulene region in 1 and 2 based on Hückel rule, and ii) that in the terminal phenoxyl rings of 1, the ICT occurs from the benzene rings to the O atoms due to the large electronegativity of O atom.

Indeed, the

Hirshfeld charge distributions show the ICT features in accordance with the above predictions (see Figure 6a and b), but the longitudinal ICT in the both-end quinone structures of 1 is found to be much larger than the outer–inner ring ICT in the corannulene moieties (see Figure 6a).

This indicates that molecule 1 belongs to

intermediate diradicaloids with acceptor(A)–π–acceptor(A) nature, which is expected to cause larger enhancement of γ than symmetric diradicaloids with no ICT nature.48

3.2. Diradical Character and Spin State Dependences of γ for Corannulene Derivatives. In the preceding sections, we have found that the corannulene derivative 1 exhibits intermediate open-shell singlet nature, which stems from the both-end quinoid and benzenoid resonance forms.

To reveal the impact of the intermediate

diradical character of 1 on the third-order NLO properties, we investigate the longitudinal γ (γzzzz) values of 1 and 2, the latter of which is a closed-shell reference of similar size, using the LC-UBLYP(µ=0.33 bohr-1)/6-31+G* method.

The results are


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listed in Table 1.

It is found that the γ value of 1 is about 16 times enhanced (18.9 x

105 a.u.) as compared to that of 2 (1.15 x 105 a.u.).

This feature is in conformity with

the y–γ correlation.14 Figure 7a and c show the γ density distributions of 1 and 2, respectively, both of which show that the dominant contributions to γ come from π electrons.

The γ densities of 1 are shown to have significantly large amplitudes

delocalized over the whole molecule and to be well-separated positive and negative distributions on the left- and right-hand phenoxyl moieties, respectively, which gives the large positive contribution to γ, though some cancellations between positive and negative contributions are observed in the central corannulene moiety.

In contrast, 2

shows much smaller γ density amplitudes than 1 and mainly localized on the both-end phenol moieties, the feature of which indicates the much smaller positive γ value than 1. It is also found for 1 that the spatial regions (the phenoxyl ring regions) of γ density distributions primarily contributing to γ coincide with those with the primary odd electron density distributions (see Figure 2).

This indicates that the large odd electron

densities distributed on the both-end phenoxyl rings primarily contribute to the enhancement of the γ value for the intermediate open-shell singlet system 1. We next investigate the spin state dependence of γ using molecule 1 in the singlet and triplet states, where the same structure (optimized in the singlet state) is considered in this study in order to clarify the pure spin state effect on the γ.

As seen

from Table 1, in the triplet state, the γ amplitude is about half (9.00 x 105 a.u.) as large as that of singlet state (18.9 x 105 a.u.).

As shown in Figure 7a and b, the γ density

distribution amplitude of triplet state is smaller than that of the singlet state in the whole region and particularly exhibits significant reduction of γ density amplitudes in the



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central corannulene region though the topological feature of the γ distributions on the both-end phenoxyl ring regions is similar to that of the singlet state.

Such small

amplitude and localized nature of γ density distribution in the triplet state are predicted to be caused by the Pauli effect.49

3.3. Comparison between Corannulene and Coronene Derivatives: Curvature Effect on y and γ.

As shown in Figure 1c and d, 3 and 4 are the planar analogues

involving coronene in place of the corannulene, for curved 1 and 2, respectively. resonance structures of 3 and 4 are shown in Figure 1g and h), respectively.

The Their

BLA (Figure S2, Table S5), NICS(0) (Figure 4c and d), ICT (Figure 5c and d) and odd electron density distribution (Figure S3) are shown in the Supporting Information.

It is

found that the diradical characters of 3 and 4 are y = 0.853 (intermediate diradical character) and 0.000 (closed-shell), respectively, whose tendency is similar to that in the corannulene derivatives (see Table 1).

As seen from Figure 2 and S3, molecule 3 also

has large odd electron density distributions in the terminal ring regions like corannulene derivative 1.

In addition, from the analysis of the resonance structures (Figure 1g and

h), BLA, NICS(0) and ICT, the contribution of both the quinoid and benzenoid forms is found to lead to the intermediate open-shell singlet nature of 3, where the relationships between the above quantities show similar trends to those of 1.

Indeed, the coronene

derivatives 3 and 4 are found to display analogous γ features to the corannulene ones, 1 and 2, respectively, though the γ amplitude of 3 is shown to be approximately 40% larger than that of 1.

This is predicted to be caused by the fact that coronene derivative

3 has a larger π-conjugation size along the z-axis than the curved corannulene analogue 1: longitudinal distance between the both-end O atoms is 17.96 Å for 3 and 17.43Å for 12 ACS Paragon Plus Environment

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1.

Namely, we found that there are no significant differences in the y–γ correlation

between the corannulene and coronene derivatives.

On the other hand, as seen from

Figure 5a and c, the phenoxyl rings of 1 have similar NICS(0) values to those of 3 though benzene rings in central π-moiety of 1 have less NICS(0) values than those of 3 due to the curved structure of corannulene. values for 2 and 4 (see Figure 5b and d).

Similar tendency is observed in NICS(0) In addition, as seen from Figure 6a and c,

ICT nature in the phenoxyl rings is still dominant in both 1 and 3, while slight ICT between the outer and inner rings in the central π-moiety in 1 is shown to be larger than that in 3.

This ICT feature in the central π-moiety is understood by Hückel’s rule, that

is, both the inner and outer rings in 3 have 6π and 18π electrons, respectively, while the inner and outer rings in 1 have 5π and 15π electrons, respectively.

Similar tendency is

observed in ICT in the central π-moiety of 2 and 4 (see Figure 6b and d).

In the

present systems, therefore, the origin of the large γ value of corannulene 1 is found not to be the curved structure but to be its intermediate diradical character derived from the both-end phenoxyl ring moeities.

Of course, further investigation is needed to reveal

the relationship between open-shell character and curvature of π-conjugated systems, which is expected to provide another control scheme of physicochemical properties through tuning the open-shell character.50

4. Concluding Remarks In this study, we have investigated the relationships between the diradical character (y) and the second hyperpolarizability (γ) of corannulene derivatives using the spin-unrestricted density functional theory method.

The corannulene π-conjugated

system involving two phenoxyl radicals in the singlet spin state is found to show an 13 ACS Paragon Plus Environment


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intermediate diradical character and to exhibit a significant enhancement of γ value as compared to the closed-shell analogue by a factor of 16 and the triplet state by a factor of 2.

It is also found that the planar coronene analogue shows intermediate diradical

character and a large γ value similar to the curved corannulene derivative.

This

indicates that the significant enhancement of γ for the corannulene system stems not from the curved corannulene skeleton but from the both contributions of benzenoid (diradical) and possible quinoid (closed-shell) forms due to delocalization of the radical electrons in the terminal phenoxyl ring region.

The longitudinal γ value of the singlet

state of the open-shell singlet corannulene derivative is also found to be comparable to that of s-indaceno[1,2,3-cd;5,6,7-c’d’]diphenalene, which is known to be one of the organic molecules with the largest two-photon absorption properties in this size of pure hydrocarbons.

As a result, the present molecule is expected to be a promising

candidate for efficient open-shell singlet third-order NLO molecules.

Furthermore,

judging from the significant redox state and spin state dependences of γ through tuning the diradical character, as well as from the fact that the corannulene derivatives constitute the π-stacking aggregates in a real crystal structure, the present results will contribute to building a design guideline for realistic highly efficient and tunable open-shell NLO materials through the control of the open-shell characters and spin states in a variety of intermolecular packing forms.

These studies are in progress in

our laboratory.

ASSOCIATED CONTENT


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Supporting

Information

Available:

Cartesian

coordinates

of

corannulene

derivatives and coronene derivatives optimized by the (R)B3LYP/6-311G* method; Details of bond-length alternations (BLAs) for corannulene, coronene and quinone systems; Details of calculation results for coronene systems (NICS(0) values, ICT, and odd electron density distribution).

AUTHOR INFORMATION Corresponding Author *Email: [email protected] Telephone number: +81-6-6850-6265 Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS This work is supported by JSPS KAKENHI Grant Number JP25248007 in Scientific Research (A), Grant Number JP24109002 in Scientific Research on Innovative Areas “Stimuli-Responsive Chemical Species”, Grant Numbers JP15H00999 and JP17H05157 in Scientific Research on Innovative Areas “π-System Figuration”, and Grant Number JP26107004 in Scientific Research on Innovative Areas “Photosynergetics”.

H. M.

thanks to JSPS KAKENHI, Research Fellowship for Young Scientists (No. JP15J05489) for financial support.

This is also partly supported by King Khalid 15

ACS Paragon Plus Environment


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University through Grant RCAMS/KKU/001-16 under the Research Center for Advanced Materials Science at King Khalid University, Kingdom of Saudi Arabia.

REFERENCES (1) Pathenopoulos, D. A.; Rentzepis, P. M. Three Dimensional Optical Storage Memory. Science 1989, 245, 843-845. (2) Tao, S.; Miyagoe, T.; Maeda, A.; Matsuzaki, H.; Ohtsu, H.; Hasegawa, M.; Takaishi, S.; Yamashita, M.; Okamoto, H. Ultrafast Optical Switching by Using Nanocrystals of a Halogen-Bridged Nickel-Chain Compound Dispersed in an Optical Polymer. Adv. Mater. 2007, 19, 2707-2710. (3) Zhou, W.; Kuebler, S. M.; Braun, K. L.; Yu, T.; Cammack, J. K.; Ober, C. K.; Perry, J. W.; Marder, S. R. An Efficient Two-Photon-Generated Photoacid Applied to Positive-Tune 3D Microfabrication. Science 2002, 296, 1106-1109. (4) Slepkov, A. D.; Hegmann, F. A.; Eisler, S.; Elliott, E.; Tykwinski, R. R. The Surprising Nonlinear Optical Properties of Conjugated Polyyne Oligomers. J. Chem. Phys. 2004, 120, 6807-6810. (5) Albota, M.; Beljonne, D.; Brédas, J.-L.; Ehrlich, J. E.; Fu, J.-Y.; Heikal, A. A.; Hess, S. E.;Kodej, T.; Levin, M. D.; Marder, S. R. Design of Organic Molecules with Large Two-Photon Absorption Cross Sections. Science 1998, 281, 1653-1656. (6) Rumi, M.; Ehrlich, J. E.; Heikal, A. A.; Perry, J. W. Barlow, S.; Hu, Z.; McCord-Maughon, D.; Paker, T. C.; Röckel, H.; Thayumanavan, S. Structure–Property


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Relationships for Two-Photon Absorbing Chromophores: Bis-Donor Diphenylpolyene and Bis(styryl)benzene Derivatives. J. Am. Chem. Soc. 2000, 122, 9500-9510. (7) Ventelon, L.; Charier, S.; Moreaux, L.; Mertz, J.; Blanchard-Desce, M. Nanoscale Push—Push Dihydrophenanthrene Derivatives as Novel Fluorophores for Two-Photon-Excited Fluorescence. Angew. Chem. Int. Ed. 2001, 40, 2098-2101. (8) Johnston, M. D.; Subbaswamy, K. R.; Senatore, G. Hyperpolarizabilities of Alkali Halide Crystals Using the Local-Density Approximation. Phys. Rev. B 1987, 36, 9202-9211. (9) Hayes, E. F.; Siu, A. K. Q. Electronic Structure of the Open Forms of Three-Membered Rings. J. Am. Chem. Soc. 1971, 93, 2090-2091. (10) Yamaguchi, K. In Self-Consistent Field: Theory and Applications; Carbo, R.; Klobukowski, M., Eds.; Elsevier: Amsterdam, 1990; pp 727-828. (11) Head-Gordon, M. Characterizing Unpaired Electrons from the One-Particle Density Matrix. Chem. Phys. Lett. 2003, 372, 508-511. (12) Kamada, K.; Ohta, K.; Shimizu, A.; Kubo, T.; Kishi, R.; Takahashi, H.; Botek, E.; Champagne, B.; Nakano, M. Singlet Diradical Character from Experiment. J. Phys. Chem. Lett. 2010, 1, 937-940. (13) Nakano, M.; Fukui, H.; Minami, T.; Yoneda, K.; Shigeta, Y.; Kishi, R.; Champagne, B.; Botek, E.; Kubo, T.; Ohta, K. (Hyper)polarizability Density Analysis for Open-Shell Molecular Systems Based on Natural Orbitals and Occupation Numbers. Theor. Chem. Acc. 2011, 130, 711-724; erratum 130, 725-726.



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(20) Kishida, H.; Hibino, K.; Nakamura, A.; Kato, D.; Abe, J. Third-Order Nonlinear Optical Properties of a π-Conjugated Biradical Molecule Investigated by Third-Harmonic Generation Spectroscopy. Thin Solid Films 2010, 519, 1028-1030. (21) Ishida, M.; Shin, J.-Y.; Lim, J. M.; Lee, B. S.; Yoon, M.-C.; Koide, T.; Sessler, J. L.; Osuka, A.; Kim, D. Neutral Radical and Singlet Biradical Forms of Meso-Free, -Keto, and -Diketo Hexaphyrins(1.1.1.1.1.1): Effects on Aromaticity and Photophysical Properties. J. Am. Chem. Soc. 2011, 133, 15533-15544. (22) Li, Y.; Heng, W.-K.; Lee, B. S.; Aratani, N.; Zafra, J. L.; Bao, N.; Lee, R.; Sung, Y. M.; Sun, Z.; Huang, K.-W. et al. Kinetically Blocked Stable Heptazethrene and Octazethrene: Closed-Shell or Open-Shell in the Ground State? J. Am. Chem. Soc. 2012, 134, 14913-14922. (23) Zeng, Z.; Sung, Y. M.; Bao, N.; Tan, D.; Lee, R.; Zafra, J. L.; Lee, B. S.; Ishida, M.; Ding, J.; López Navarrete, J. T. et al. Stable Tetrabenzo-Chichibabin’s Hydrocarbons: Tunable Ground State and Unusual Transition between Their Closed-Shell and Open-Shell Resonance Forms. J. Am. Chem. Soc. 2012, 134, 14513-14525. (24) Kamada, K.; Fuku-en, S.-I.; Minamide, S.; Ohta, K.; Kishi, R.; Nakano, M.; Matsuzaki, M.; Okamoto, H.; Higashikawa, H.; Inoue, K. Impact of Diradical Character on Two-Photon Absorption: Bis(acridine) Dimers Synthesized from an Allenic Precursor. J. Am. Chem. Soc. 2013, 135, 232-241. (25) Zeng, Z.; Ishida, M.; Zafra, J. L.; Zhu, X.; Sung, Y. M.; Bao, N.; Webster, R. D.; Lee, B. S.; Li, R.-W.; Zeng, W. et al. Pushing Extended p-Quinodimethanes to the



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Limit: Stable Tetracyano-oligo(N-annulated perylene)quinodimethanes with Tunable Ground States. J. Am. Chem. Soc. 2013, 135, 6363-6371. (26) Sun, Z.; Lee, S.; Park, K. H.; Zhu, X.; Zhang, W.; Zheng, B.; Hu, P.; Zeng, Z.; Das, S.; Li, Y. et al. Dibenzoheptazethrene Isomers with Different Biradical Characters: An Exercise of Clar’s Aromatic Sextet Rule in Singlet Biradicaloids. J. Am. Chem. Soc. 2013, 135, 18229-18236. (27) Takauji, K.; Suizu, R.; Awaga, K.; Kishida, H.; Nakamura, A. Third-Order Nonlinear Optical Properties and Electroabsorption Spectra of an Organic Biradical, [Naphtho[2,1-d:6,5-d’]bis([1,2,3]dithiazole)]. J. Phys. Chem. C 2014, 118, 4303-4308. (28) Nagai, H.; Nakano, M.; Yoneda, K.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E. Signature of Multiradical Character in Second Hyperpolarizabilities of Rectangular Graphene Nanoflakes. Chem. Phys. Lett. 2010, 489, 212-218. (29) Nakano, M.; Kishi, R.; Takebe, A.; Nate, M.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E. Second Hyperpolarizability of Zethrenes. Computing Letters 2007, 3, 333-338. (30) Muhammad, S.; Fukuda, K.; Minami, T.; Kishi, R.; Shigeta, Y.; Nakano, M. Interplay between the Diradical Character and Third-Order Nonlinear Optical Properties in Fullerene Systems. Chem. Eur. J. 2013, 19, 1677-1685. (31) Ueda, A.; Nishida, S.; Fukui, K.; Ise, T.; Shiomi, D.; Sato, K.; Takui, T.; Nakasuji, K.; Morita, Y. Three-Dimensional Intramolecular Exchange Interaction in a


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Curved and Nonalternant p-Conjugated System: Corannulene with Two Phenoxyl Radicals. Angew. Chem. Int. Ed. 2010, 49, 1678-1682. (32) Stoll, H.; Savin, A. In Density Functional Methods in Physics; Dreizler, R., da Providencia, J., Eds.; Plenum: New York, 1985, pp.177. (33) Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K. A Long-Range Correction Scheme for Generalized-Gradient-Approximation Exchange Functionals. J. Chem. Phys. 2001, 115, 3540-3544. (34) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K.

A

Long-Range-Corrected Time-Dependent Density Functional Theory. J. Chem. Phys. 2004, 120, 8425-8433. (35) Herebian, D.; Wieghardt, K. E.; Neese F. Analysis and Interpretation of Metal-Radical Coupling in a Series of Square Planar Nickel Complexes: Correlated Ab Initio and Density Functional Investigation of [Ni(LISQ)2] (LISQ=3,5-di-tert-butyl-o-diiminobenzosemiquinonate (1-)). J. Am. Chem. Soc. 2003, 125, 10997-11005. (36) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R.; Nucleus-Aromaticity Criterion. Chem. Rev. 2005, 105, 3842-3888. (37) Kertesz, M.; Choi, C. H.; Yang, S. Conjugated Polymers and Aromaticity. Chem. Rev. 2005, 105, 3448-3481.



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(38) Rosenberg, M.; Dahlstrand, C.; Kilså, L.; Ottosson, H. Excited State Aromaticity and Antiaromaticity: Opportunities for Photophysical and Photochemical Rationalizations. Chem. Rev. 2014, 114, 5379-5425. (39) Ruud, L.; Helgaker, T.; Bak, K. L.; Jørgensen, P.; Jensen, H. J. A. Hartree-Fock Limit Magnetizabilities from London Orbitals. J. Chem. Phys. 1993, 99, 3847-3859. (40) Schleyer, P. v. R.; Jiao, H. What is aromaticity? Pure Appl. Chem. 1996, 68, 209-218. (41) Cohen, H. D.; Roothaan, C. C. J. Electric Dipole Polarizability of Atoms by the Hartree-Fock Method. I. Theory for Closed-Shell Systems. J. Chem. Phys. 1965, 43, S34. (42) Kishi, R.; Bonness, S.; Yoneda, K.; Takahashi, H.; Nakano, M.; Botek, E.; Champagne, B.; Kubo, T.; Kamada, K.; Ohta, K. et al. Long-Range Corrected Density Functional Theory Study on Static Second Hyperpolarizabilities of Singlet Diradical Systems. J. Chem. Phys. 2010, 132, 094107-1-11. (43) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. Size-Consistent Approach and Density Analysis of Hyperpolarizability: Second Hyperpolarizabilities of Polymeric Systems with and without Defects. J. Chem. Phys. 1995, 103, 4175−4191. (44) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Peterson, G. A. et al. Gaussian 09, Revision A.02; Gaussian, Inc., Wallingford CT, 2009. (45) Clar, E. The Aromatic Sextet; Wiley: London, 1972.


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(46) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. E. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc. 1996, 118, 6317-6318. (47) Hirshfeld, F. L. Bonded-Atom Fragments for Describing Molecular Charge Densities. Theoret. Chim. Acta 1977, 44, 129-138. (48) Fukuda, K.; Nozawa, T.; Yotsuyanagi, H.; Ichinohe, M.; Sekiguchi, A.; Nakano, M. Theoretical Study on the Enhancement of the Second Hyperpolarizabilities of Si-, Ge-Disubstituted Quinodimethanes: Synergy Effects of Open-Shell Nature and Intramolecular Charge Transfer. J. Phys. Chem. C 2015, 119, 1188-1193. (49) Nakano, M.; Nitta, T.; Yamaguchi, K.; Champagne, B.; Botek, E. Spin Multiplicity Effects on the Second Hyperpolarizability of an Open-Shell Neutral π-Conjugated System. J. Phys. Chem. A 2004, 108, 4105-4111. (50) Fukuda, K.; Fujiyoshi, J.; Minamida, Y.; Nagami, T.; Matsui, M.; Ito, S.; Kishi, R.; Kitagawa, Y.; Nakano, M., Champagne, B. Theoretical Investigation of Curved π-Conjugated Fullerene Flakes: Open-Shell Character, Aromaticity, and Third-Order Nonlinear Optical Property. J. Phys. Org. Chem. 2017, 30, DOI: 10.1002/poc.3581.



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Page 24 of 43

Table 1. Diradical Characters y, and γ Values for Corannulene and Coronene Derivatives Calculated Using the LC-(U)B3LYP/6-31+G* Method γ [x 105 a.u.]

System

y

1 (singlet)

0.841

1 (triplet)

−

9.00

2

0.000

1.15

3

0.853

4

0.000

18.9

26 1.18


Page 25 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure Captions

Figure 1. Molecular frameworks of corannulene derivative with two phenoxyl radicals 1 (a), bis-phenol analogue 2 (b), and the coronene analgues 3 (c) and 4 (d).

Resonance structures of 1 (e), 2 (f), 3 (g), and 4 (h) are also

shown.

Figure 2. Odd

electron

density

distributions

of

1

calculated

using

the

LC-UBLYP(µ=0.33 bohr-1)/6-31+G* method (contour value of 0.0020 a.u.).

Figure 3. Molecular resonance structures of corannulene derivative 1 based on the Clar’s sextet rules.

Red benzene rings indicate the Clar’s sextets.

Figure 4. Labeling of the C–C bonds for corannulene (1 (a) and 2 (b)) systems and comparison of the BLAs in the optimized structures of corannulene derivatives calculated at RB3LYP/6-311G* level of theory (c).

Figure 5. Nucleus-independent chemical shift (NICS(0)) [ppm] for 1 (a), 2 (b), 3 (c) and 4 (d).

Figure 6. Intramolecular charge transfer (ICT) using Hirshfeld charge distribution for 1 (a), 2 (b), 3 (c) and 4 (d). Figure 7. γzzzz density distributions of 1 (singlet (a), triplet (b)) and 2 (singlet (c)) calculated using the LC-UBLYP(µ=0.33 bohr-1)/6-31+G* method.

Yellow

and blue surfaces indicate positive and negative γzzzz densities with contour value of ± 500 a.u., respectively.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 43

Y. Minamida et al. Figure 1 (continued) 26 ACS Paragon Plus Environment

Page 27 of 43

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Y. Minamida et al., Figure 1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 43

1



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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60





1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 43

(a) 7A 3A 4A

2A 1

O

6A 5 6B

4B

7B

8A

9

8B

O

2B 3B

(b) 7A 3A 4A

2A 1

HO

4B 2B

6A 5 6B

7B

8A

9

8B

OH

3B

(c)



Page 31 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60





1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 43



Page 33 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

1(singlet)

(b)

1(triplet) x

(c) y

z

2(singlet)

Y

et al., Figure 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 43

TOC Graphic


Page 35 of 43

(a)

(b) O

O

OH

HO

1

2

(c)

(d)

O

HO

O

OH

4

3 (e) O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

1

...

Closed-shell (neutral)

...

...

Open-shell (ionic)

Open-shell (neutral)

Closed-shell (ionic)

(f) OH

HO

HO

OH

HO

OH

HO

OH

2

x OH

HO

y

z

...

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




Y. Minamida et al. Figure 1 (continued) 26 ACS Paragon Plus Environment


(g) O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

3


...

...

...


Open-shell (neutral)

Open-shell (ionic)

(h) HO

OH

HO

OH

HO

OH

4

x

y

z

...

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 43





Page 37 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1




Three sextets

Four sextets O

O

One sextet

Two sextets O

O

O

O

O

O

1

Open-shell

Open-shell

O

O

O

O

O

O

...

...

...

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 43

Closed-shell O

O

Closed-shell



(a)

Page 39 of 43 The Journal of Physical Chemistry 7A

1 2 3O 4 5 6 7 8 9 10 11 12 13 14 15 HO 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

3A 4A

2A 1

6A 5 6B

4B

7B

8A

9

8B

O

2B 3B

(b) 7A 3A 4A

2A 1

4B 2B

6A 5 6B

7B

8A

9

8B

3B

(c)


OH

(b)

(a)


-3.79 -3.19

1 O2 3 4 5 6 7 (c) 8 9 10 O11 12 13 14 15 16

+3.37

-3.19 +9.33

-5.66

-5.47 +3.37

O

HO

-7.96

-5.66

Page 40 of 43

-5.60 +9.74

-5.76

-5.47 -7.97

OH

-5.78

(d) -8.94

-6.07 +3.56

-5.64

-5.64

+3.56

O

HO

-7.47

0.939

0.475 -8.57

-8.57 -7.52

-8.70

-8.70


-9.04

-9.05 -8.84

-7.47

OH

(a)

Page 41 of 43

1 2 +0.208 O3 4 5 6 7 (c) 8 9 10 11 O12 +0.209 13 14 15 16 17

+0.184

+0.0453

(b)


+0.208

-0.0210

-0.272

O

HO

+0.0387

-0.0577

+0.0387

OH

-0.0809

(d)

+0.117

-0.0328 -0.0221

-0.272 +0.209

O

HO

+0.0421

+0.0421

OH


+0.0102

-0.0075


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 43

(a)

1(singlet)

(b)

1(triplet) x

(c) y

z

2(singlet)



Page 43 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Corannulene + Two Phenoxyl Radicals à Enhance ACS Paragon Plus Environment

γ

Theoretical Study on the Open-Shell Singlet ... - ACS Publications

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