Enhancement of Second Hyperpolarizabilities in Open-Shell Singlet

ARTICLE pubs.acs.org/JPCA

Enhancement of Second Hyperpolarizabilities in Open-Shell Singlet Slipped-Stack Dimers Composed of Square Planar Nickel Complexes Involving o-Semiquinonato Type Ligands Hitoshi Fukui, Yasuteru Shigeta, and Masayoshi Nakano* Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

Takashi Kubo Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Kenji Kamada and Koji Ohta Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan

Benoît Champagne and Edith Botek Laboratoire de Chimie Theorique, Facultes Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, B-5000 Namur, Belgium

bS Supporting Information ABSTRACT: Using the spin-unrestricted hybrid density functional theory method, we have investigated the intermolecular interaction effects on the longitudinal static second hyperpolarizability (γ) of open-shell singlet slipped-stack dimers composed of singlet diradical square planar nickel complexes involving o-semiquinonato type ligands, Ni(o-C6H4X2)2 (where X = O, NH, S, Se, PH). For comparison, we have also examined the γ values of a closed-shell singlet slipped-stack dimer composed of closed-shell monomers Ni[o-C6H4S(NH2)]2. It is found that for interplanar distance ranging between 3.0 and 5.0 Å the slipped-stack dimers with intermediate monomer diradical characters exhibit larger γ values per monomer (γdimer/2) than those with large monomer diradical characters or than the closed-shell dimer. These results extend the domain of validity of the relationship found between γ and the diradical character for individual molecules. It also turns out that the ratio R = (γdimer/2)/γmonomer increases upon decreasing the interplanar distance and that this increase is larger for intermediate diradical character than for the other cases. These phenomena have been analyzed by considering the γ density distributions of the dimers, demonstrating a significant field-induced third-order charge transfer between the monomers in the case of intermediate diradical character. The present results indicate that open-shell singlet slipped-stack aggregates composed of monomers with intermediate diradical characters constitute another mean for achieving highly efficient and tunable third-order nonlinear optical materials.

1. INTRODUCTION Many kinds of organic compounds exhibiting highly efficient nonlinear optical (NLO) properties have been intensively studied due to their potential applications in photonic devices such as optical switching, three-dimensional memory, optical limiting, and photodynamic therapy.1-3 In particular, the third-order NLO properties (at the molecular level, the second hyperpolarizabilities γ) r 2011 American Chemical Society

of organic π-conjugated compounds have been investigated because of their larger and faster responses as well as due to the lower driving voltage, more flexible molecular design, and potentially lower Received: August 5, 2010 Revised: December 21, 2010 Published: January 19, 2011 1117

dx.doi.org/10.1021/jp1073895 | J. Phys. Chem. A 2011, 115, 1117–1124

The Journal of Physical Chemistry A

ARTICLE

Figure 1. Structures of the singlet diradical monomers Ni(o-C6H4X2)2, where X = O (1), NH (2), S (3), Se (4), and PH (5), and of a closed-shell monomer Ni[o-C6H4S(NH2)]2 (6) (a) and their slipped-stack dimers (b). Coordinate axes are also shown.

processing cost than for their inorganic analogs. Although experimental and theoretical studies on such third-order NLO systems have revealed several tuning parameters for the amplitude and sign of γ, e.g., the π-conjugation length, the bond length alternation, the strength of donor/acceptor substituents, and the charge,4-8 most of these studies have focused on closed-shell systems. Recently, we have theoretically investigated open-shell compounds as a novel class of NLO systems and have revealed their structure-property relationship: singlet diradical systems with intermediate diradical characters tend to exhibit larger γ values than pure diradical systems and conventional closed-shell systems.9-13 The mechanism underlying the diradical character dependence of the static/dynamic γ has been theoretically clarified on the basis of the analytical expressions of the static γ and of the two photon absorption cross section for a two-site system using the valence configuration interaction method.14 This has also been substantiated by computational and experimental studies on several model and real open-shell molecular systems.9-12,15 Other types of open-shell molecules have also been investigated experimentally and theoretically from the viewpoint of their NLO properties.16-18 In a previous study,12a we have investigated the γ values as well as the diradical characters of singlet square planar nickel complexes involving o-semiquinonato type ligands, Ni(o-C6H4X2)2 (where X = O, NH, S, Se, PH), and of closed-shell nickel complexes, Ni(o-C6H4XY)2 [where (X, Y) = (NH, NH2) and (S, NH2)]. This study has shown that the diradical character of these complexes varies from 0.0 to 0.884 as a function of the donor atoms and that the γ variation follows the bell-shape relationship.14 Moreover, the NLO responses depend on the molecular environment and, in crystals, on the type of crystal packing.19a This is particularly true for radical species that can exhibit specific π-interactions. So, Kubo et al. have reported a one-dimensional (1D) chain of polycyclic diphenalenyl diradicals (IDPL) with a slipped-stacking arrangement, which exhibits an unusually small interplanar distance of 3.137 Å, a large conductivity as well as an absorption peak shifted extraordinarily to the low-energy region.19b These phenomena originate from intra- and intermolecular interactions of the unpaired electrons. Owing to a significant field-induced third-order charge transfer between the monomers, these intermolecular interactions also lead to a significant enhancement of the γ value per IDPL monomer, in contrast to the situation encountered in the closed-shell pyrene

dimer (PY2) when the same interplanar distance of 3.137 Å is imposed. In a subsequent work, the relationship between the strength of these two-electron multicenter bonds and the chemical structure of organic radicals has been studied, showing the interplay with substitutions in R and β positions of phenalenyl.19c In this paper, we extend these studies on the intermolecular interaction effects by considering the open-shell singlet slippedstack dimers built from Ni(o-C6H4X2)2 (where X = O, NH, S, Se, PH) and by assessing the relationships between the interplanar distance, the diradical character, and the γ per monomer. Some preliminary results recently reported20 have demonstrated a substantial enhancement of γ per monomer. Since the Ni(o-C6H4X2)2 monomers display a wide diradical character range (0.342-0.884) as a function of the ligands, their dimers are appropriate models for the present study. This study is achieved by employing the density functional theory (DFT) method and a hybrid exchange-correlation functional including 50% of Hartree-Fock exchange, the BHandHLYP functional.21 Spin density and γ density distributions are employed to clarify the intra/ intermolecular interaction effects on the open-shell character and on the interaction-induced γ values of these dimers. These results are then analyzed from the viewpoint of the design of the third-order NLO materials built from slipped-stack aggregates of open-shell singlet monomers.

2. THEORETICAL AND COMPUTATIONAL ASPECTS 2.1. Model Systems and Diradical Character. Figure 1a shows the structures of the singlet diradical monomers Ni(o-C6H4X2)2 [where X = O (1), NH (2), S (3), Se (4), PH (5)] and of a closed-shell monomer Ni[o-C6H4S(NH2)]2 (6). The structures of monomers 1-5 belong to the D2h point group, while that of monomer 6 to the C2h. In each monomer, the longitudinal (x) axis is defined by the line passing through the midpoints between C3 and C4 and between C9 and C10. In the slipped-stack dimers, characterized by an interplanar distance (D), the phenyl rings of the monomers face to each other (see Figure 1b). To build these dimer structures, we employed the monomer geometries optimized by the UB3LYP method for monomers 1 and 2, and by the RB3LYP method for monomers 3-612a using the SDD basis set22 for the forth-row atoms, Ni and Se, and the 6-31G* basis set for the other atoms. This combination of the basis sets is referred to as “SDDþ6-31G*” in this paper. 1118

dx.doi.org/10.1021/jp1073895 |J. Phys. Chem. A 2011, 115, 1117–1124


ARTICLE

The diradical character is obtained from spin-unrestricted Hartree-Fock (UHF) calculations. The diradical character yi related to the HOMO-i and LUMOþi is defined by the weight of the doubly excited configuration in the multiconfigurational (MC)-SCF theory and is formally expressed in the case of the spin-projected UHF (PUHF) theory as23,24 yi ¼ 1 -

2Ti 1 þ Ti 2

ð1Þ

where Ti, the orbital overlap between the corresponding orbital pairs23,24 (χHOMO-i and ηHOMO-i), can also be represented using the occupation numbers (nj) of UHF natural orbitals (UNOs): nHOMO - i - nLUMO þ i Ti ¼ ð2Þ 2 The diradical character yi takes a value between 0 and 1, which corresponds to the closed-shell and pure diradical systems, respectively. The present calculation scheme using the UNOs is the simplest, but it can well reproduce the diradical character calculated by other methods such as the ab initio configuration interaction (CI) method.25 In this study, we examine the γ values of the dimers, which are expected to display some tetra-radical nature, as a function of monomer diradical character y0. 2.2. Evaluation and Analysis of the Static Second Hyperpolarizability. We calculate the longitudinal tensor component γxxxx (γ) because it dominates the third-order response of these systems (γxxxx = 3473 103, γyyyy = 45 103, and γzzzz = -514 103 au for dimer 3 with D = 3.0 Å) and it is therefore sufficient for revealing the relationship between the open-shell character and the third-order NLO properties. As seen from our previous studies on organic compounds,9a,10d-10f the UBHandHLYP method provides reliable γ for diradical systems with intermediate and large diradical characters, while the RBHandHLYP method does for closed-shell systems. This was later confirmed for Ni-dithiolene compounds by SerranoAndres and co-workers.17a We therefore employed the UBHandHLYP and RBHandHLYP methods to calculate γ of dimers 1-5 and dimer 6, respectively. Since extended basis sets are known to be necessary for obtaining quantitative γ values for small and medium-size π-conjugated systems,26 the effect of adding diffuse functions to the 6-31G* basis set was assessed by considering the γ of monomer 3 and its dimer with D = 3.0 Å. These calculations were performed at the UBHandHLYP level of approximation with the 6-31G*þp basis set (ζp = 0.0523 for C and 0.0402 for S) and compared with the 6-31G* data. For the monomer, the 6-31G* and 6-31G*þp basis sets give γ values of 677 103 and 753 103 au, while for the dimer they amount to 3473 103 and 3750 103 au, respectively. Thus, the set of diffuse p functions increases γ values by 11% for the monomer and 8% for the dimer. Subsequently, the interaction-induced ratio [R = (γdimer/2)/γmonomer, vide infra] attains 2.57 with the 6-31G* basis set and is only slightly smaller (2.49) using the 6-31G*þp one. On this basis, we employed the standard 6-31G* basis set, except for the Ni and Se atoms. For Ni and Se, we employ the SDD basis set, which has shown to reproduce the γ of monomer 2 calculated with Huzinaga’s all-electron basis set MIDIþpdf (ζp,d,f = 0.088).12a The γ values are calculated using the finite-field (FF) approach,27 which consists of a fourth-order differentiation of the energy with respect to the applied external electric field. The power series expansion convention (called B convention28) is

chosen for defining γ and the following fourth-order numerical differentiation formula is employed: 1 fEð3FÞ - 12Eð2FÞ þ 39EðFÞ - 56Eð0Þ γ ¼ 36F 4 þ 39Eð - FÞ - 12Eð - 2FÞ þ Eð - 3FÞg ð3Þ E(F) indicates the total energy in the presence of the static electric field F in x-direction. We used F values ranging from 0.0010 to 0.0035 au to obtain numerically stable γ values. Moreover, an ultrafine integration grid21 and a tight convergence threshold of 10-10 au on the energy are adopted to obtain sufficiently precise γ values. The γ values are given in atomic units (au): 1.0 au of γ is equal to 6.235377 10-65 C4 m4 J-3 and 5.0367 10-40 esu. All calculations are performed with the Gaussian 03 program package.21 The spatial electronic contribution to γ is described by the γ density analysis.8c,29 This method is based on the expression Z 1 rFð3Þ ðrÞ d3 r ð4Þ γ ¼ 3! where the γ density F(3)(r) is determined by the third-order derivative of the electron density with respect to the applied electric field: ∂3 FðrÞ ð3Þ ð5Þ F ðrÞ ¼ ∂F 3 F¼0

The positive and negative values of F(3)(r) multiplied by F3 represent, respectively, the field-induced increase and decrease of the charge density in proportion to F3 and are thus at the origin of the third-order dipole moment (third-order polarization) in the direction from positive to negative γ densities. The γ densities are numerically evaluated for a grid of points from the third-order differentiation of the electron densities calculated by the Gaussian 03 program. The box dimensions (-15 e x e 15 Å, -6.0 e y e 6.0 Å, and -7.0 e z e 7.0 Å) ensure that the γ values obtained by integration coincide with the FF values within an error of 1%. The relationship between γ and F(3)(r) is explained by considering the example of a pair of localized γ densities with positive and negative values: the sign of their contribution to the total γ is positive when the direction from positive to negative γ densities coincides with the direction of the applied electric field and vice versa. Moreover, the magnitude of the contribution associated with this pair of γ densities is proportional to the distance between them. To illuminate the intermolecular interaction effect on γ, we examine the difference between the γ density of the interacting system [F(3) int (r)] and that of noninteracting system [F(3) nonint(r) composed of the densities of noninteracting monomers]: ð3Þ

ð3Þ

ð3Þ

Fdiff ðrÞ ¼ Fint ðrÞ - Fnonint ðrÞ

ð6Þ

Therefore, the γ contribution induced by intermolecular interactions reads Z 1 ð3Þ rFdiff ðrÞ d3 r Δγ ¼ ð7Þ 3!

3. RESULTS AND DISCUSSION 3.1. Relationship between the Diradical Character of the Monomer and γ of the Dimer as a Function of the Interplanar distances. Figure 2 shows the relationship between y0 1119



ARTICLE

Table 1. Diradical Characters (y0) and γ Values (γmonomer) for Monomers 1-6, γ Values per Monomer (γdimer/2), and Interaction-Induced Ratios (R) for Dimers 1-6 with an Interplanar Distance of 3.0 Å O (1) NH (2) S (3) Se (4) PH (5) S, NH2 (6) y0a

0.884

γmonomerb [103 au] 176

0.718

0.595 0.556

0.342

0.0

612

677

819

14.2

807

γdimer/2b [103 au] 285

1058

1737

2354

1885

21.6

R

1.73

2.57

2.92

2.30

1.52

1.62

a

The y0 values are calculated from UNO/SDDþ6-31G* occupation numbers. b The γmonomer and γdimer/2 values are calculated by the (U)BHandHLYP/SDDþ6-31G* method. Figure 2. Relationship between the monomer diradical character (y0) and γ per monomer (γdimer/2) [au] for dimers with interplanar distances (D) of 3.0, 4.0, and 5.0 Å as well as with γmonomer of the isolated monomers.

Figure 3. Dependence of the intermolecular interaction-induced γ ratio (R) as a function of the interplanar distance (D) for dimers 1-6.

and γdimer/2 for interplanar distances (D) of 3.0, 4.0, and 5.0 Å in comparison with the γmonomer values (which correspond to γdimer/2 for D f ¥). The interaction-induced effects are further characterized by the ratio R = (γdimer/2)/γmonomer, in such a way that an enhancement of γ by intermolecular interactions is described by R > 1. The relationship between R and D is shown in Figure 3 whereas the corresponding data are listed in Table 1 as well as in Supporting Information. It is found that for any interplanar distance, the dimers with intermediate monomer diradical characters (3-5) exhibit larger γdimer/2 values than those with large monomer diradical characters (1, 2) and the closed-shell dimer (6), e.g., at D = 3.0 Å, γdimer/2 = 285 103 au for 1, γdimer/2 = 2354 103 au for 4, and γdimer/2 = 21.6 103 au for 6. This extends the domain of validity of the γ/y structure-property relationship to the slipped-stack dimers. For a large D value, the γdimer/2 versus y0 evolution follows the relationship between γmonomer and y0, demonstrating that these dimers behave almost like isolated monomers. On the other hand, for small D, the γdimer/2 enhancement is larger in the intermediate y0 region. Indeed, for D = 3.0 Å, the γdimer/2 value (2354 103 au) of dimer 4 having intermediate y0 (0.556) is about 8 times as large as that (285 103 au) of dimer 1 having large y0 (0.884), and more than 100 times as large as that (21.6 103 au) of the closed-shell dimer 6. Taking Figure 3, R decreases

Figure 4. Schematic representation of the intra- and intermolecular covalent interactions between the unpaired electrons in a dimer composed of singlet diradical compounds having an intermediate diradical character when the interplanar distance is large (a) and small (b). Horizontal and vertical dotted lines represent the intra- and intermolecular covalent interactions, respectively.

asymptotically as a function of the interplanar distance and the variations in R are larger for compounds with intermediate y0 values. So, the R values of dimers 3 and 4 rapidly increase in the small D region (D < ∼3.2 Å), which is predicted to originate from intra- and intermolecular covalent interactions of the unpaired electrons. As sketched in Figure 4a, for large D, the unpaired electrons are predicted to covalently interact only within each monomer while, for small D, the unpaired electrons interact not only within each monomer but also between monomers (Figure 4b). If so, the two cofacial phenyl rings in the dimer can be regarded as a singlet diradical moiety with its own intermediate diradical character, while each monomer presents also an intermediate diradical character. Consequently, the unpaired electrons can be easily transferred from one monomer to the other by an external electric field due to the comparable intermediate intra- and intermonomer diradical characters. This explains the large R values for dimers 3 (R = 2.57) and 4 (R = 2.92) at D = 3.0 Å. Note that the coexistence of intra- and intermolecular covalent interactions between unpaired electrons has also been theoretically and experimentally predicted in slipped-stack 1D chains of singlet diradical IDPL by Huang and Kertesz30 and Shimizu et al.31 1120



ARTICLE

Figure 5. Distributions of the Mulliken spin densities obtained by the UBHandHLYP/SDDþ6-31G* method for monomers 1 and 4 (a) and for dimers 1 and 4 with the interplanar distances (D) of 5.0 and 3.0 Å (b). The white and black circles represent R and β spin densities, respectively. The values are the sums of the spin densities in each ligand delimited by a dotted circle.

The unpaired electrons on the cofacial phenyl rings of dimers 1 and 2 are also expected to interact covalently with each other as in the case of dimers 3 and 4. However, these intermolecular interactions are stronger than those in dimers 3 and 4 since the unpaired electrons are more localized on both end ligands (larger diradical character). This feature leads to an attenuation of the field-induced polarization between monomers 1 and 2 in small D region and a corresponding moderate R values in small D region: R = 1.62 and 1.73 for dimers 1 and 2 at D = 3.0 Å. To confirm these predictions on the relationship between the intra/intermolecular covalent interactions in a dimer and the monomer diradical character, we examined the Mulliken spin density distributions in dimers 1 (y0 = 0.884) and 4 (y0 = 0.556) at D = 3.0 and 5.0 Å as well as those of their monomers (see Figure 5), in which the positive and negative values represent the sums of the spin densities in each ligand. We recall that the R/β spin polarization originates from the broken-symmetry solution obtained using an unrestricted approach, that this polarization is not observed in real systems but that it is much helpful to analyze the spatial correlation between the R and β spins. For dimer 1 at D = 5.0 Å as well as for the monomer 1, in agreement with the large y0 value, the spin densities are close to (1 on all moieties, demonstrating very small intra/intermolecular interactions. At D = 3.0 Å, the sums of spin densities in the cofacial ligands somewhat (4%) decrease ((0.952), while those in the both end ligands of the dimer hardly change, as compared to those at D = 5.0 Å. This indicates the covalent-like interaction between the cofacial phenyl rings, while such interaction is localized in the cofacial region and does not have an impact on the both end

unpaired electrons. As a result, the intramolecular diradical character is predicted to remain as large as the monomer diradical character. For dimer 4 at D = 5.0 Å, the spin density distributions on the cofacial ligands ((0.837) and on both end ligands ((0.836) are almost the same as those on the both side ligands of its isolated monomer ((0.837) as in the case of dimer 1. Going to D = 3.0 Å, the spin densities slightly decrease and increase (∼1%) in the cofacial and both end ligands, respectively. The reason for the smaller changes in the spin densities for dimer 4 than for dimer 1 at D = 3.0 Å comes from the stronger (weaker) intramolecular (intermolecular) covalent interactions of the unpaired electrons for dimer 4 than for dimer 1, as shown by y0(1) > y0(4). As a result, both the intra- and intermolecular diradical characters of dimer 4 lie in the intermediate region similar to the diradical character of its isolated monomer, the feature of which is also exemplified by the similarity of their spin density distributions. Dimer 6 also gives moderate variation in R since the monomers are closed-shell and therefore cannot interact through unpaired electrons. So, for D = 3.0 Å, dimer 6 exhibits the smallest R = 1.52 value among compounds 1-6. These results indicate that γ of slipped-stack aggregates of singlet diradical molecules with intermediate diradical characters are significantly enhanced when they have very small interplanar distances ( 1.52 (dimer 1) at D = 3.0 Å]. In contrast, for dimer 4, the regions with large F(3) diff (r) amplitudes cover both end phenyl rings, whereas the F(3) diff (r) on the central phenyl rings is very small. This explains the significant γ enhancement by the intermolecular interactions [R(dimer 4) = 2.92]. Thus, when diradical compounds with intermediate diradical characters are dimerized in a slipped-stack arrangement, a strong field-induced intermonomer third-order charge transfer appears and the γ density amplitudes are enhanced on the both end regions, leading to an increase of the interaction-induced ratio of γ (R).

Figure 6. Distributions of the γ density difference [F(3) diff (r)] (side view) for dimers 1, 4, and 6 with an interplanar distance of 3.0 Å calculated by the (U)BHandHLYP/SDDþ6-31G* method. The yellow and blue surfaces, respectively, represent positive and negative values with contour values of (100 au for dimer 1, (1000 au for dimer 4, and (10 au for dimer 6. The monomer diradical characters (y0) and the intermolecular interaction-induced γ ratios (R) are also shown.

the unpaired electrons in open-shell singlet molecular aggregates like the 1D crystal of IDPL.19,30,31 We now turn to the discussion of the role of effective exchange (J) on this γ enhancement, since J is often used to monitor magnetic interactions. In a previous study,14a we have elucidated the relationships between the diradical character, rJ (=2J/U), rK (=2K/U), and the dimensionless γ (γND) (J, effective exchange; U, effective Coulomb repulsion; K, direct exchange) using the static γ analytical expression derived from the valence configuration interaction method with a two-site model, and we have found that the dependence of γND on rJ corresponds to that on y (Figure 3 in ref 14a). Moreover, although the enhancement of γND can be completely scrutinized on the y-rJ plane, the diradical character can be practically used to control γND as compared to the effective exchange because the rJ value giving the maximum γND depends on rK, while the y value associated with this maximum is found to be almost constant (y ≈ 0.4). Therefore, we have investigated here the enhancement of γ from the viewpoint of the variation in the diradical character. 3.2. γ Density Analysis. To understand the dependence of R on the monomer structure (at the same interplanar distance), we investigated the spatial distributions of γ density difference [F(3) diff (r)]. In the present case, the positive (negative) values of F(3) diff (r) represent the increase (decrease) in the γ density induced by the dimerization (intermolecular interaction). As shown in Figure 6, the (U)BHandHLYP/SDDþ6-31G* F(3) diff(r) for dimers 1, 4, and

4. FURTHER DISCUSSION AND CONCLUSIONS Using the UBHandHLYP method, we have theoretically investigated the intermolecular interaction effects on γ in openshell singlet slipped-stack dimers composed of singlet diradical o-semiquinonato nickel complexes as well as closed-shell analogues. The relationship between the monomer diradical character and the γ values per monomer of the dimer (γdimer/2) is similar to that between the diradical character and γ of the isolated monomer (γmonomer): the dimers with intermediate monomer diradical characters exhibit larger γdimer/2 values than the closedshell and the nearly pure open-shell dimers. For all the studied dimers, the γdimer/2 values are enhanced by the intermolecular interactions. Moreover, the smaller the interplanar distance, the larger the γdimer/2 enhancement. The degree of enhancement depends on the diradical character of the monomer: the dimers composed of complexes with intermediate diradical characters show a significant enhancement of γ when their interplanar distances are less than 3.2 Å. This γ enhancement is understood by the degree of intra- and intermolecular covalent interactions between the unpaired electrons. It is interesting to make a link with the results on the IDPL and PY2 dimers (D = 3.147 Å) for which the R = γdimer/2γmonomer value amounts to 1.99 and 1.15, respectively.32 Although other structural and electronic parameters have an impact on γ and therefore on R, there is some consistency with the present results since y0 of IDPL is 0.770 whereas PY2 is closed-shell. The present results indicate that γ values of singlet diradical compounds with intermediate diradical characters could be strongly enhanced if they form crystals with slipped-stack arrangement as well as with an interplanar distance smaller than 3.4 Å (van der Waals radius), which is expected to be realized in singlet diradical compounds due to the intermolecular covalent interactions of unpaired electrons.19c Since singlet diradical compounds do not always form crystals with the slipped-stack arrangement, chemical modifications on the monomers, e.g., appropriate substitutions to the monomers, could be needed to realize such stacking. 1122



’ ASSOCIATED CONTENT

bS

Supporting Information. γdimer/2 values and R for dimers 1-6 with interplanar distances of 3.2, 3.5, 4.0, 4.5, and 5.0 Å. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Fax: þ81-6-6850-6268. E-mail: [email protected].

’ ACKNOWLEDGMENT This work is supported by Grants-in-Aid for Scientific Research (Nos. 21350011 and 20655003) and the “Japan-Belgium Cooperative Program” (J091102006) by the Japan Society for the Promotion of Science (JSPS) and the global COE (center of excellence) program “Global Education and Research Center for Bio-Environmental Chemistry” of Osaka University. H.F. expresses his special thanks for a JSPS Research Fellowship for Young Scientists. E.B. thanks the IUAP program No. P6-27 for her postdoctoral grant. This work has also been supported by the Academy Louvain (ARC “Extended π-Conjugated Molecular Tinkertoys for Optoelectronics, and Spintronics”) and by the Belgian Government (IUAP program No. P06-27 “Functional Supramolecular Systems”). ’ REFERENCES (1) Pathenopoulos, D. A.; Rentzepis, P. M. Science 1989, 245, 893. (2) Zhou, W.; Kuebler, S. M.; Braun, K. L.; Yu, T.; Cammack, J. K.; Ober, C. K.; Perry, J. W.; Marder, S. R. Science 2002, 296, 1106. (3) Frederiksen, P. K.; Jørgensen, M.; Ogilby, P. R. J. Am. Chem. Soc. 2001, 123, 1215. (4) Heflin, J. R.; Wong, K. Y.; Zamani-Khamiri, O; Garito, A. F. Phys. Rev. B 1988, 38, 1573. (5) (a) Beljonne, D.; Shuai, Z.; Bredas, J. L. J. Chem. Phys. 1993, 98, 8819. (b) Tykwinski, R. R.; et al. J. Phys. Chem. B 1998, 102, 4451. (c) Toto, J. L.; Toto, T. T.; de Melo, C. P.; Kirtman, B.; Robins, K. J. Chem. Phys. 1996, 104, 8586. (d) Tretiak, S.; Chernyak, V.; Mukamel, S. Phys. Rev. Lett. 1996, 77, 4656. (e) Loboda, O.; Zalesny, R.; Avramopoulos, A.; Luis, J. M.; Kirtman, B.; Tagmatarchis, N.; Reis, H.; Papadopoulos, M. G. J. Phys. Chem. A 2009, 113, 1159. (f) Bruschi, M.; Limacher, P. A.; Hutter, J.; L€uthi, H. P. J. Chem. Theor. Comput. 2009, 5, 506. (6) (a) Nakano, M.; Yamaguchi, K.; Fueno, T. Chem. Phys. Lett. 1991, 185, 550. (b) Meyers, F.; Marder, S. R.; Pierce, B. M.; Bredas, J. L. J. Am. Chem. Soc. 1994, 116, 10703. (c) Ferrighi, L.; Frediani, L.; Cappelli, C.; Salek, P.; Ågren, H.; Helgaker, T.; Ruud, K. Chem. Phys. Lett. 2006, 425, 267. (7) (a) Nakano, M.; Fujita, H.; Takahata, M.; Yamaguchi, K. J. Am. Chem. Soc. 2002, 124, 9648. (b) Bulat, F. A.; Toro-Labbe, A.; Champagne, B.; Kirtman, B.; Yang, W. J. Chem. Phys. 2005, 123, 014319. (c) Chen, W.; Yu, G. T.; Gu, F. L.; Aoki, Y. J. Phys. Chem. C 2009, 113, 8447. (8) (a) de Melo, C. P.; Silbey, R. J. Chem. Phys. 1988, 88, 2567. (b) Villesuzanne, A.; Hoarau, J.; Ducasse, L.; Olmedo, L.; Hourquebie, P. J. Chem. Phys. 1992, 96, 495. (c) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. J. Chem. Phys. 1995, 103, 4175. (d) Champagne, B.; Spassova, M.; Jadin, J. B.; Kirtman, B. J. Chem. Phys. 2002, 116, 3935. (e) Oliveira, L. N.; Amaral, O. A. V.; Castro, M. A.; Fonseca, T. L. Chem. Phys. 2003, 289, 221. (9) (a) Nakano, M.; Kishi, R.; Nitta, T.; Kubo, T.; Nakasuji, K.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E.; Yamaguchi, K. J. Phys. Chem. A 2005, 109, 885. (b) Nakano, M.; Kishi, R.; Ohta, S.; Takebe, A.; Takahashi, H.; Furukawa, S.; Kubo, T.; Morita, Y.; Nakasuji, K.;

ARTICLE

Yamaguchi, K.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E. J. Chem. Phys. 2006, 125, 74113. (10) (a) Nakano, M.; Kubo, T.; Kamada, K.; Ohta, K.; Kishi, R.; Ohta, S.; Nakagawa, N.; Takahashi, H.; Furukawa, S.; Morita, Y.; Nakasuji, K.; Yamaguchi, K. Chem. Phys. Lett. 2006, 418, 142. (b) Nakano, M.; Nakagawa, N.; Kishi, R.; Ohta, S.; Nate, M.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E.; Morita, Y.; Nakasuji, K.; Yamaguchi, K. J. Phys. Chem. A 2007, 111, 9102. (c) Ohta, S.; Nakano, M.; Kubo, T.; Kamada, K.; Ohta, K.; Kishi, R.; Nakagawa, N.; Champagne, B.; Botek, E.; Takebe, A.; Umezaki, S.; Nate, M.; Takahashi, H.; Furukawa, S.; Morita, Y.; Nakasuji, K.; Yamaguchi, K. J. Phys. Chem. A 2007, 111, 3633. (d) Nakano, M.; Kishi, R.; Nakagawa, N.; Ohta, S.; Takahashi, H.; Furukawa, S.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E.; Yamada, S.; Yamaguchi, K. J. Phys. Chem. A 2006, 110, 4238. (e) Kishi, R.; Bonness, S.; Yoneda, K.; Takahashi, H.; Nakano, M.; Botek, E.; Champagne, B.; Kubo, T.; Kamada, K.; Ohta, K.; Tsuneda, T. J. Chem. Phys. 2010, 132, 094107. (f) Bonness, S.; Fukui, H.; Yoneda, K.; Kishi, R.; Champagne, B.; Botek, E.; Nakano, M. Chem. Phys. Lett. 2010, 493, 195. (11) Nakano, M.; Nagai, H.; Fukui, H.; Yoneda, K.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E. Chem. Phys. Lett. 2008, 467, 120. (12) (a) Fukui, H.; Kishi, R.; Minami, T.; Nagai, H.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, Koji.; Champagne, B.; Botek, E.; Nakano, M. J. Phys. Chem. A 2008, 112, 8423. (b) Fukui, H.; Nagai, H.; Kishi, R.; Minami, T.; Takahashi, H.; Kubo, T.; Nakano, M. Synth. Met. 2009, 159, 2416. (13) (a) Champagne, B.; Botek, E.; Nakano, M.; Nitta, T.; Yamaguchi, K. J. Chem. Phys. 2005, 122, 114315. (b) Champagne, B.; Botek, E.; Quinet, O.; Nakano, M.; Kishi, R.; Nitta, T.; Yamaguchi, K. Chem. Phys. Lett. 2005, 407, 372. (14) (a) Nakano, M.; Kishi, R.; Ohta, S.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B. Phys. Rev. Lett. 2007, 99, 033001–1. (b) Nakano, M.; Yoneda, K.; Kishi, R.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B. J. Chem. Phys. 2009, 131, 114316–1. (15) Kamada, K.; Ohta, K.; Kubo, T.; Shimizu, A.; Morita, Y.; Nakasuji, K.; Kishi, R.; Ohta, S.; Furukawa, S; Takahashi, H.; Nakano, M. Angew. Chem., Int. Ed. 2007, 46, 3544. (16) (a) Qiu, Y. Q.; Fan, H. L.; Sun, S. L.; Liu, C. G.; Su, Z. M. J. Phys. Chem. A 2008, 112, 83. (b) Li, Z. J.; Wang, F. F.; Li, Z. R.; Xu, H. L.; Huang, X. R.; Wu, D.; Chen, W.; Yu, G. T.; Gu, F. L.; Aoki, Y. Phys. Chem. Chem. Phys. 2009, 11, 402. (c) Jha, P. C.; Rinkevicius, Z.; Ågren, H. ChemPhysChem 2009, 10, 817. (17) (a) Serrano-Andres, L.; Avramopoulos, A.; Li, J.; Labeguerie, P.; Begue, D.; Kell€o, V.; Papadopoulos, M. G. J. Chem. Phys. 2009, 131, 134312. (b) Soras, G.; Psaroudakis, N.; Mousdis, G. A.; Manos, M. J.; Tasiopoulos, A. J.; Aloukos, P.; Couris, S.; Labeguerie, P.; Lipinski, J.; Avramopoulos, A.; Papadopoulos, M. G. Chem. Phys. 2010, 372, 33. (18) Cho, S.; Lim, J. M.; Hiroto, S.; Kim, P.; Shinokubo, H.; Osuka, A.; Kim, D. J. Am. Chem. Soc. 2009, 131, 6412. (19) (a) Champagne, B.; Bishop, D. M. Adv. Chem. Phys. 2003, 126, 41. (b) Kubo, T.; Shimizu, A.; Sakamoto, M.; Uruichi, M.; Yakushi, K.; Nakano, M.; Shiomi, D.; Sato, K.; Takui, T.; Morita, Y.; Nakasuji, K. Angew. Chem., Int. Ed. 2005, 44, 6564. (c) Tian, Y. H.; Kertesz, M. J. Am. Chem. Soc. 2010, 132, 10648. (20) Fukui, H.; Yoneda, K.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B.; Nakano, M. AIP Conf. Proc. 2011, in press. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, 1123



ARTICLE

V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (22) (a) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866. (b) Bergner, A.; Dolg, M.; K€uchle, W.; Stoll, H.; Preuss, H. Mol. Phys. 1993, 80, 1431. (23) Yamaguchi, K. Self-Consistent Field: Theory and Applications; Carbo, R., Klobukowski, M., Eds.; Elsevier: Amsterdam, 1990; p 727. (24) Yamanaka, S.; Okumura, M.; Nakano, M.; Yamaguchi, K. J. Mol. Struct. (THEOCHEM) 1994, 310, 205. (25) Herebian, D.; Wieghardt, K. E.; Neese, F. J. Am. Chem. Soc. 2003, 125, 10997. (26) (a) Maroulis, G. J. Chem. Phys. 1999, 111, 583. (b) Maroulis, G.; Xenides, D.; Hohm, U.; Loose, A. J. Chem. Phys. 2001, 115, 7957. (27) Cohen, H. D.; Roothaan, C. C. J. J. Chem. Phys. 1965, 43, S34. (28) Willetts, A.; Rice, J. E.; Burland, D. M.; Shelton, D. P. J. Chem. Phys. 1992, 97, 7590. (29) (a) Nakano, M.; Yamaguchi, K.; Fueno, T. Chem. Phys. Lett. 1991, 185, 550. (b) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. J. Chem. Phys. 1995, 103, 4175. (c) Nakano, M.; Fujita, H.; Takahata, M.; Yamaguchi, K. Chem. Phys. Lett. 2002, 356, 462. (30) Huang, J.; Kertesz, M. J. Am. Chem. Soc. 2007, 129, 1634. (31) Shimizu, A.; Uruichi, M.; Yakushi, K.; Matsuzaki, H.; Okamoto, H.; Nakano, M.; Hirao, Y.; Matsumoto, K.; Kurata, H.; Kubo, T. Angew. Chem., Int. Ed. 2009, 48, 5482. (32) Nakano, M.; Takebe, A.; Kishi, R.; Fukui, H.; Minami, T.; Kubota, K.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E. Chem. Phys. Lett. 2008, 454, 97.

1124


Enhancement of Second Hyperpolarizabilities in Open-Shell Singlet

Recommend Documents