Theoretical Study on the Enhancement of the Second

Dec 26, 2014 - (7) The diradical character y has been used for the clarification of the electronic state of the open-shell singlet systems having a fr...
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Theoretical Study on the Enhancement of the Second Hyperpolarizabilities of Si‑, Ge-Disubstituted Quinodimethanes: Synergy Effects of Open-Shell Nature and Intramolecular Charge Transfer Kotaro Fukuda,† Takeshi Nozawa,‡ Hiroko Yotsuyanagi,‡ Masaaki Ichinohe,‡ Akira Sekiguchi,‡ and Masayoshi Nakano*,† †

Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan ‡ Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan S Supporting Information *

ABSTRACT: We have investigated the second hyperpolarizabilities (γ), that is, the third-order nonlinear optical (NLO) properties at the molecular scale, of the realistic Si- and Gedisubstituted para- and meta-quinodimethanes from the viewpoint of synergy effect of the open-shell singlet nature and the donor (D)−π−donor (D) intramolecular charge transfer (ICT). It has been revealed that the disubstituted para isomers exhibit strong D−π−D nature together with the intermediate open-shell singlet nature, which leads to their significantly enhanced γ values. These results well demonstrate the validity of our recent result of the theoretical model study on para-quinodimethane with point charges, and also present a new design strategy based on the concept of open-shell NLO that the replacement of the radical site of the π-conjugated carbon framework with the heavier main group elements induces both the larger open-shell singlet nature and the D−π−D type strong ICT, both of which synergetically contribute to the further enhancement of the γ values. novel class of highly active NLO13,14 and for efficient singlet fission (SF)15,16 molecules based on the diradical character. These molecular design guidelines deduced from the theoretical investigations have been recently confirmed with several experimental observations.17−26 For the realization of these diradical character-based molecular designs, it is essential to clarify how to control the diradical character ranging from closed-shell to pure open-shell singlet states because most of the thermally stable carbon-based π-conjugated molecular frameworks are known to exhibit closed-shell or quite small diradical character. Over the past few years, a series of thermally stable compounds with unique geometric features have been revealed to show intermediate or large diradical character.1−6 para-Quinodimethane framework is one of such open-shell singlet fragments, although paraquinodimethane itself has almost closed-shell nature in the equilibrium geometry.13 This fragment exhibits two resonance structures, quinoid (closed-shell) and benzenoid (diradical) ones, so that the relative contribution of the open-shell resonance structure is expected to characterize the open-shell

1. INTRODUCTION Recently, open-shell singlet systems have attracted much attention from both scientific and engineering points of view because of their unique electronic, optical, and magnetic properties.1−6 Unlike the open-shell systems in the classical sense like monoradicals or the systems in high spin states, these systems exhibit the lowest singlet spin state, while their openshell nature is characterized by a diradical character, which is a chemical index for “instability of chemical bond” or for “electron correlation”.7 The diradical character y has been used for the clarification of the electronic state of the open-shell singlet systems having a fractional value between 0 (closedshell) and 1 (pure open-shell).6−11 This quantity is originally defined as twice the weight of the doubly excited configuration in the ground state, and, in practice, is easily calculated for a molecular system with typical quantum chemical calculation methods like spin-unrestricted Hartree−Fock (UHF), spinunrestricted density functional theory (UDFT), completeactive-space configuration interaction (CAS CI), and so on.7,8,11−13 In the field of open-shell singlet chemistry, we have theoretically found that the excitation energies and properties are fundamentally governed by y value, and that these relations enable us to construct design principles for a © 2014 American Chemical Society

Received: November 18, 2014 Published: December 26, 2014 1188

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original quinodimethanes, Si/Ge-disubstituted quinodimethanes exhibit nonplanar structures because of the difficulty in the formation of sp2 hybridization due to the larger size difference between the valence s and p orbitals of Si and Ge atoms.35 Although this enables us to consider two possible molecular conformations concerned with the relative dihedral angle between the H−X bond of the XH2 group and the plane of the adjacent phenyl ring, we consider only one conformation with less steric hindrance, where two H atoms in both end XH2 groups are located on the mutually opposite side with respect to the phenyl-ring plane. 2.2. Calculation Methods. Geometry optimization was carried out with the spin-flip time-dependent density functional theory method together with the collinear approximation with the BHandHLYP functional, which is known to well reproduce the electronic and geometrical structures of the open-shell singlet systems,36−38 under constraints of symmetry: D2h for 1a, C2h for 2a and 3a, C2v for 1b, and C2 for 2b and 3b. We applied the aug-cc-pVDZ basis set for the geometry optimization. For the estimation of the open-shell singlet nature, we evaluated the diradical character y within the spin-projected UHF (PUHF) scheme as7

singlet nature of the system. Indeed, the elongation of the exocyclic C−C bond length in the para-quinodimethane model, which corresponds to the increase in the weight of the openshell benzenoid resonance structure, is found to increase the diradical character.13 This fact gives us a conceptual idea for the control of the diradical character based on tuning the relative contribution of the quinoid and benzenoid resonance structures.4,5,13,27 On the other hand, in 2011, the synthesis of the Sidisubstituted para- and meta-quinodimethane derivatives was reported.28 It is experimentally found that the para-derivative exhibits singlet ground state together with the smaller bondlength alternation (BLA) of the central benzene ring (0.053 Å) as compared to that of the all-carbon analogue, Thiele’s hydrocarbon (0.103 Å).29 This experimental observation evokes the presence of larger contribution of the open-shell resonance structure in the para-quinodimethane framework for this synthesized system. In addition, it is expected that there exists a large charge transfer from the exocyclic SiH2 region to the central benzene ring in the same manner as in silene.30 Such a large donor (D)−π−donor (D) type intramolecular charge transfer (ICT) has been known to enhance the third-order NLO properties of the closed-shell organic molecules.31−33 More recently, we have performed a model study on the correlation between the two design guidelines, that is, ICT and the open-shell singlet nature, on the second hyperpolarizabilities γ, the third-order NLO properties at the molecular scale, and have found that there exists the synergetic enhancement of γ for the strong ICT systems with intermediate diradical character.34 In this context, the present real Sidisubstituted para-quinodimethane frameworks are predicted to belong to a class of the D−π−D type open-shell singlet systems, which are promising candidates for highly efficient third-order NLO molecules predicted in the previous model study. On the basis of the above background, we here theoretically investigate the replacement effect of the radical site in the quinodimethane frameworks with heavier main group, Si and Ge, atoms on the diradical character, D−π−D nature, and the γ values. The present result shows that the introduction of the heavier main group elements into the radical sites in the carbon framework induces the strong D−π−D nature together with the larger diradical character, which causes the enhancement of γ. Thus, the present approach is demonstrated to be a practical and efficient strategy for realizing the diradical character-based design for highly efficient NLO molecules.

y=1−

2T 1 + T2

(1)

where T indicates the orbital overlap between the highest occupied natural orbital (HONO) and the lowest unoccupied natural orbital (LUNO) and can also be represented by using the occupation numbers (ni) of UHF natural orbitals (UNOs) as n − nLUNO T = HONO (2) 2 We calculated the odd electron density distribution to clarify the spatial distribution of the odd (unpaired) electrons, which are associated with the emergence of the diradical character.11,39 Odd electron density for y at the position r is defined using NOs {ϕi(r)} as11 d(r) = (2 − y)|ϕ HONO(r)|2 + y |ϕ LUNO(r)|2

(3)

To characterize the D−π−D strength of the present systems, following our previous model study,34 we adopt the total natural charge of the central benzene rings (Δq). The natural population analysis was carried out within the UHF level of approximation, which has been revealed to be efficient in comparison with other population analysis schemes and to well reproduce the natural charge calculated using the spinunrestricted coupled cluster singles and doubles (UCCSD) method for the para-quinodimethane with point charges model.34 For the evaluation of the NLO properties of these systems, we calculated the longitudinal component of the static second hyperpolarizabilities γzzzz, which is the dominant component in the present systems, by the finite field approach using the strongly electron-correlated UCCSD with a perturbative inclusion of the triples [UCCSD(T)] method. Further investigation on the spatial contribution of electrons to γ value is carried out with the γ density analysis40 calculated with UCCSD method. Diagonal component of the γ density along the longitudinal z axis is defined as40

2. METHODOLOGY 2.1. Model Systems. We consider six model structures, that is, three para systems 1a (X = C, para-quinodimethane (PQM)), 2a (X = Si), and 3a (X = Ge), as well as three meta systems 1b (X = C, meta-quinodimethane (MQM)), 2b (X = Si), and 3b (X = Ge) (Figure 1a and b). Unlike the planar

(3) ρzzz (r) =

Figure 1. Molecular frameworks of para systems (a) and meta systems (b). 1189

∂ 3ρ(r) ∂Fz3

F=0

(4) DOI: 10.1021/jp511521m J. Phys. Chem. C 2015, 119, 1188−1193

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The Journal of Physical Chemistry C where ρ(r) is the total electron density at the position ρ and Fz is the z component of the external electric field F. This γ density relates to the γ value as40 1 (3) (r) d r γzzzz = − rzρzzz (5) 3!

the other hand, all of the meta systems in the singlet states exhibit quite small BLA and thus nearly pure open-shell nature regardless of atoms X. These differences as well as the facts of the triplet ground state of the meta systems are, as mentioned above, attributed to the absence of the contribution of the quinoid (closed-shell) form in the meta systems. Such a relationship between the open-shell singlet nature and the resonance structures is also exemplified by the spatial distribution of the odd (unpaired) electrons for y (Figure 3).

∫

where a pair of positive and negative γ densities with large amplitudes, separated by a large distance, strongly contribute to the γ values. When the direction from positive to negative γ density coincides with the positive (negative) direction of the coordinate axis, the contribution becomes positive (negative) in sign. For the evaluation of the above several properties, we applied the 6-311+G** basis set except for the X atoms with the LANLDZ(d,p) basis set, which gives reasonable γzzzz values in comparison with the calculation results with all 6-311+G** basis set for all atoms (see Table S7 in the Supporting Information). All of the calculations were carried out using the Gaussian 09 program package41 except for the geometry optimization using the GAMESS program package.42

3. RESULTS AND DISCUSSION 3.1. Open-Shell Singlet Nature. First, we investigate the correlation between the optimized geometries and the openshell nature in the singlet state. Because the open-shell singlet nature is related to the weight of the benzenoid (open-shell) form in the resonance structures, the system with larger y value is expected to exhibit the structural parameters more like the benzenoid form than like the quinoid one. In the present case, para framework exhibits such two resonance structures, quinoid (closed-shell) and benzenoid (open-shell) forms, although meta framework exhibits only the benzenoid (open-shell) form (Figure 2a and b). This difference lets us expect that the para

Figure 3. Odd electron density distributions of 1a−3a and 1b−3b in the singlet state calculated with the spin-projected UHF (PUHF) method (contour value of 0.003 au).

Apparently, all of these systems exhibit a large distribution of the odd electron density around the exocyclic X atoms, and the distribution becomes larger with increasing y. These features also indicate that the systems with larger y values have the larger contribution of the benzenoid (open-shell) form with the radicals on exocyclic X atoms. 3.2. D−π−D Strength. Next, we investigate the amount of the intramolecular charge transfer (ICT) of these systems (Table 1). As shown in the case of X = C, the original Table 1. Sum of the Natural Charge of the Central Benzene Rings Δq Calculated Using the UHF Method

Figure 2. Resonance structures of the para (a) and meta (b) systems in the singlet state.

systems exhibit smaller diradical character than the meta ones, which are predicted to be nearly pure diradical systems. For the evaluation of the geometrical parameters, we examine the BLA of the central benzene ring. Here, BLA is defined as the difference between the longest and the smallest bond length in the central benzene ring for each system, so that the BLA tends to decrease with increasing weight of the open-shell resonance structure. The structural parameters are listed in Table S1 and S2 in the Supporting Information. For the para systems in the singlet states, it is found that BLA decreases as the exocyclic X atoms become heavier (0.102 Å for 1a, 0.035 Å for 2a, and 0.023 Å for 3a), the tendency of which indicates that the weight of the open-shell resonance structure increases in the order: 1a < 2a < 3a. In good agreement with this structural feature, it turns out that the y value increases in the same order and that for 2a and 3a reaches intermediate though the original paraquinodimethane 1a and exhibits almost closed-shell nature. On

spin state

system

Δq [au]

system

Δq [au]

singlet

1a 2a 3a 1a 2a 3a

−0.193 −1.007 −0.934 −0.241 −1.006 −0.991

1b 2b 3b 1b 2b 3b

−0.252 −1.002 −0.988 −0.218 −0.990 −0.972

triplet

quinodimethanes 1a and 1b exhibit relatively small |Δq| values (|Δq| ≈ 0.2 au), which show that the charge distribution of these systems is almost neutral for all over the quinodimethane frameworks regardless of the spin state. On the other hand, all of the disubstituted systems exhibit much larger absolute values for both their singlet and their triplet states (|Δq| ≈ 1.0 au for X = Si and Ge). These strong ICTs are shown to resemble that of the PQM-pc model34 with large negative point charges, which induces the strong D−π−D type charge transfer within the quinodimethane framework. Furthermore, not only the global tendency of the ICT but also the local charge transfer nature are found to be similar to those of the PQM-pc models 1190

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synergetic enhancement of the γ value is further confirmed by the comparison of the PQM model with elongated exocyclic C−C bond length of 1.65 Å. This model system is considered to be an intermediate diradical system without D−π−D nature having diradical character y = 0.660 similar to that of 2a. The comparison of the γ values for these system reveals that the γ value of singlet 2a is even 2.8 times as large as that of the intermediate diradical PQM model (1.65 Å), although the model exhibits the γ value of about 2.7 times as large as that of 1a (see Table S8 in the Supporting Information). These observations strongly indicate that not only the intermediate open-shell singlet nature but also the synergetic effect emerges for 2a and 3a in the singlet state. To further investigate the relationship between the openshell nature and the γ values, we visualize the γ density distributions calculated using the UCCSD method (see Figures 4 and 5). It is found that for the para systems in the singlet

(Supporting Information Table S3). In fact, for 2a in the singlet state, the primary contribution of the D−π−D nature occurs at the exocyclic C−Si bond, and this tendency qualitatively resembles that of the PQM-pc model, whose ICT is dominated with the charge transfer at the exocyclic C−C bond.34 Although there exist some local differences in the natural charge distribution between 2a and the PQM-pc model, that is, the former has the negative charges mainly localized on the C atoms in the exocyclic C−Si bond, while the latter has those spreading over all of the constituting six C atoms, we conclude that the present disubstitution of the radical sites with the main group elements Si presents effects of the natural charge distribution, inducing the strong D−π−D nature, qualitatively similar to those of the PQM-pc models.34 3.3. Second Hyperpolarizabilities. The above section demonstrates that the substitution of the radical sites with the heavier main group elements Si and Ge induces the larger diradical character and the strong D−π−D nature of the quinodimethane molecular framework. To clarify these effects on the third-order NLO properties, we examine the second hyperpolarizabilities γzzzz (referred to as γ hereafter), which are the dominant components in the present systems, using the strongly electron-correlated UCCSD(T) method (Table 2). Table 2. Longitudinal Components of the Second Hyperpolarizabilities γzzzz Calculated Using the UCCSD(T) Method spin state

system

γzzzz [au]

system

γzzzz [au]

singlet

1a 2a 3a 1a 2a 3a

24 800 185 000 175 000 22 300 45 000 45 500

1b 2b 3b 1b 2b 3b

10 600 23 600 24 900 10 300 24 000 26 000

triplet

Figure 4. γzzzz density distributions of 1a−3a and 1b−3b in the singlet state calculated using the UCCSD method (contour value of 200 au).

Comparison of all of the singlet states shows that the disubstituted para systems 2a and 3a exhibit about one-order larger γ values than that of original quinodimethanes (for singlet state, γ(2a)/γ(1a) = 7.5 and γ(3a)/γ(1a) = 7.1) and the meta systems (for singlet state, γ(2a)/γ(2b) = 7.8 and γ(3a)/ γ(3b) = 7.0). Also, it is found that disubstituted meta systems exhibit about 2 times larger γ values than that of the original one (for singlet state, γ(2b)/γ(1b) = 2.2 and γ(3b)/γ(1b) = 2.3). On the other hand, for the triplet systems, the disubstituted para systems 2a and 3a exhibit a larger value than that of the original systems although the increase factor is about 2, which is similar to meta ones (for triplet state, γ(2a)/ γ(1a) = 2.0, γ(3a)/γ(1a) = 2.0, γ(2b)/γ(1b) = 2.3, and γ(3b)/ γ(1b) = 2.5). Such variations of the γ values are explained with the synergetic effects of the open-shell nature and the D−π−D nature. Generally, the introduction of Si or Ge atoms into the molecular frameworks tends to induce the D−π−D nature, and thus for pure open-shell singlet meta and triplet systems, where the open-shell nature is unchanged for the substitution of radical sites, the γ value is predicted to be enhanced by a factor of ∼2 as compared to that of the original quinodimethane counterparts with little ICT. On the other hand, for the singlet para systems, 2a and 3a exhibit not only the D−π−D nature but also the intermediate open-shell singlet nature, and thus the γ value is predicted to be synergetically enhanced with the strong D−π−D nature and the intermediate open-shell singlet nature, as shown in our previous study.34 The present

Figure 5. γzzzz density distributions of 1a−3a and 1b−3b in the triplet state calculated using the UCCSD method (contour value of 200 au).

states, the γ density distribution resembles the odd electron density distribution, especially for the intermediate diradical systems 2a and 3a, where the large γ densities are distributed around the exocyclic X atoms like the odd electron densities. On the other hand, for nearly pure open-shell singlet meta systems, the γ densities are distributed around the aryl−X bond region with small amplitudes, although the large odd electron densities are distributed around the exocyclic X region. These 1191

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(2) Lambert, C. Toward Polycyclic Aromatic Hydrocarbons with a Singlet Open-Shell Ground State. Angew. Chem., Int. Ed. 2011, 50, 1756−1758. (3) Plasser, F.; Pašalić, H.; Gerzabek, M. H.; Libisch, F.; Reiter, R.; Burgörfer, J.; Müller, T.; Shepard, R.; Lischka, H. The Multiradical Character of One- and Two-Dimensional Graphene Nanoribbons. Angew. Chem., Int. Ed. 2013, 52, 2581−2584. (4) Sun, Z.; Wu, J. Open-Shell Polycyclic Aromatic Hydrocarbons. J. Mater. Chem. 2012, 22, 4151−4160. (5) Sun, Z.; Zeng, Z.; Wu, J. Zethrenes, Extended p -Quinodimethanes, and Periacenes with a Singlet Biradical Ground State. Acc. Chem. Res. 2014, 47, 2582−2591. (6) Nakano, M. Excitation Energies and Properties of Open-Shell Singlet Molecules; Springer: New York, 2014. (7) Yamaguchi, K. In Self-Consistent Field: Theory and Applications; Carbo, R., Klobukowski, M., Eds.; Elsevier: Amsterdam, 1990; pp 727−828. (8) 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. (9) Head-Gordon, M. Characterizing Unpaired Electrons from the One-Particle Density Matrix. Chem. Phys. Lett. 2003, 372, 508−511. (10) Kamada, K.; Ohta, K.; Shimizu, A.; Kubo, T.; Nishi, R.; Takahashi, H.; Botek, E.; Champagne, B.; Nakano, M. Singlet Diradical Character from Experiment. J. Phys. Chem. Lett. 2010, 1, 937−940. (11) Nakano, M.; Fukui, H.; Minami, T.; Yoneda, K.; Shigeta, Y.; Kishi, R.; Champagne, B.; Botek, E.; Kubo, T.; Ohta, K.; Kamada, 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. Theor. Chem. Acc. 2011, 130, 725. (12) Nakano, M.; Minami, T.; Fukui, H.; Kishi, R.; Shigeta, Y.; Champagne, B. Full Configuration Interaction Calculations of the Second Hyperpolarizabilities of the H4 Model Compound: Summation-Over-States Analysis and Interplay with Diradical Characters. J. Chem. Phys. 2012, 136, 024315-1−7. (13) Nakano, M.; Kishi, R.; Nitta, T.; Kubo, T.; Nakasuji, K.; Kamada, K.; Ohta, S.; Botek, E.; Champagne, B. Second Hyperpolarizability (γ) of Singlet Diradical Systems: Dependence of γ on the Diradical Character. J. Phys. Chem. A 2005, 109, 885−891. (14) Nakano, M.; Kishi, R.; Ohta, S.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B. Relationship between Third-Order Nonlinear Optical Properties and Magnetic Interactions in Open-Shell Systems: A New Paradigm for Nonlinear Optics. Phys. Rev. Lett. 2007, 99, 033001−1−4. (15) Minami, T.; Nakano, M. Diradical Character View of Singlet Fission. J. Phys. Chem. Lett. 2012, 3, 145−150. (16) Minami, T.; Ito, S.; Nakano, M. Fundamental of Diradical Character Based Molecular Design for Singlet Fission. J. Phys. Chem. Lett. 2013, 4, 2133−2137. (17) Kamada, K.; Ohta, K.; Kubo, T.; Shimizu, A.; Morita, Y.; Nakasuji, K.; Kishi, R.; Ohta, S.; Furukawa, S.; Takahashi, H.; Nakano, M. Strong Two-Photon Absorption of Singlet Diradical Hydrocarbons. Angew. Chem., Int. Ed. 2007, 46, 3544−3546. (18) Kishida, H.; Hibino, K.; Nakamura, A.; Kato, D.; Abe, J. ThirdOrder Nonlinear Optical Properties of a π-Conjugated Biradical Molecule Investigated by Third-Harmonic Generation Spectroscopy. Thin Solid Films 2010, 519, 1028−1030. (19) 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. (20) 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.; Li, Y.; Zeng, W.; Kim, D.; Huang, K.-W.; Webster, R. D.; Casado, J.; Wu, J. Stable Tetrabenzo-Chichibabin’s Hydrocarbons: Tunable Ground State and

observations indicate that the odd electron density significantly contributes to the enhancement of the γ values for the intermediate open-shell systems 2a and 3a in the singlet states, although it gives negligible contribution for the pure open-shell meta systems. This is understood by the fact that the odd electron density indicates the spatial distribution of the unpaired electrons corresponding to y, while the γ density does the field-induced polarization density caused by the virtual electron transfer between the radical sites with the large odd electron densities, and such polarization amplitudes are significantly reduced in nearly closed-shell (y ≈ 0) and pure diradical (y ≈ 1) regions.

4. CONCLUSION In this study, we have clarified the synergy effect of the D−π− D strength and the open-shell singlet nature on the second hyperpolarizabilities of the Si- and Ge-disubstituted quinodimethanes. It is found that the replacement of the radical sites of the originally nearly closed-shell para-quinodimethane framework with the heavier main group elements Si and Ge induces the intermediate open-shell singlet nature together with the strong D−π−D type intramolecular charge transfer (ICT), which causes about one-order enhanced second hyperpolarizabilities as compared to that of the original para-quinodimenthane. These results demonstrate that the Si-/Ge-disubstituted para-quinodimethane framework is one of the realistic examples of open-shell singlet D−π−D systems, and furthermore present a promising design strategy for highly efficient open-shell NLO molecules: the replacement of the radical sites of the carbon molecular frameworks with heavier main group elements induces the ICT and increases the openshell singlet nature, which synergetically contribute to further enhancement of γ as compared to those of closed-shell ICT systems and conventional intermediate diradicaloids without ICT nature.

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ASSOCIATED CONTENT

S Supporting Information *

Details of bond-length alternations (BLAs) for each system, D−π−D strength, and the second hyperpolarizabilities; Cartesian coordinates of each system. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +81-6-6850-6268. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Grant-in-Aid for Scientific Research (A) (no. 25248007), the Grant-in-Aid for Scientific Research on Innovative Areas “Stimuli-Responsive Chemical Species” (no. A24109002a) and “Photosynergetics” (no. A26107004a), MEXT, the Strategic Programs for Innovative Research (SPIRE), and the Computational Materials Science Initiative (CMSI), Japan. Theoretical calculations were partly performed using the Research Center for Computational Science, Okazaki, Japan.

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REFERENCES

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DOI: 10.1021/jp511521m J. Phys. Chem. C 2015, 119, 1188−1193