Multiple Molecular Recognition Host System using Charge-Transfer

Crystal Growth & Design .... Publication Date (Web): August 4, 2009 ... This CT host system exhibits multiple molecular recognition property (selectiv...
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DOI: 10.1021/cg9003388

Multiple Molecular Recognition Host System using Charge-Transfer Complex of 3,30 -Disubstituted-1,10 -bi-2-naphthol and Methylviologen

2009, Vol. 9 4096–4101

Yoshitane Imai,*,† Kensaku Kamon,† Takafumi Kinuta,† Nobuo Tajima,‡ Tomohiro Sato,§ Reiko Kuroda,§,^ and Yoshio Matsubara*,† †

Department of Applied Chemistry, Faculty of Science and Engineering, Kinki University, 3-4-1 Kowakae, Higashi-Osaka, Osaka 577-8502, Japan, ‡First-Principles Simulation Group, Computational Materials Science Center, NIMS, Sengen, Tsukuba, Ibaraki 305-0047, Japan, § JST ERATO-SORST Kuroda Chiromorphology Team, 4-7-6, Komaba, Meguro-ku, Tokyo 153-0041, Japan, and ^Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan Received March 25, 2009; Revised Manuscript Received July 11, 2009

ABSTRACT: A charge-transfer (CT) complex composed of rac-3,30 -dibromo-1,10 -bi-2-naphthol as an electron donor and 1,10 -dimethyl-4,40 -bipyridinium dichloride as an electron acceptor serves as a host system. This CT host system exhibits multiple molecular recognition property (selective inclusion behavior, change in color, and diffuse reflectance spectra of inclusion complex depending on the included guest).

Introduction Although the synthesis of many supramolecular host compounds that include guest molecules has been reported,1 in particular, a supramolecular host system composed of two or more organic molecules has attracted much attention. We have been conducting studies on donor-acceptor interactions; these are intermolecular forces that play an important role in the construction and control of a supramolecular complex. Recently, it has been reported that charge-transfer (CT) host complexes composed of 1,10 -bi-2-naphthol derivatives as electron donors and p-benzoquinone derivatives as electron acceptors serve as excellent visual indicators for guest molecules.2 Furthermore, in addition to the p-benzoquinone derivatives, we have also reported the formation of a CT complex composed of rac-1,10 -bi-2-naphthol (rac-1a) and 1,10 -dimethyl-4,40 -bipyridinium dichloride (methylviologen, MVCl2) that act as an electron donor and an electron acceptor, respectively.3 However, this CT complex cannot include guest molecules. Therefore, we have developed a CT host complex composed of rac-3,30 -dibromo-1,10 -bi-2naphthol and MVCl2 that can include guest molecules.4 This CT host complex selectively includes benzenediol molecules. In addition, the color of this CT complex is sensitive to the structure of the included benzenediol molecules. In this study, we analyze the multiple molecular recognition properties (selective inclusion behavior and molecular recognition visualization of guest benzeneol derivatives) of a CT complex composed of rac-1,10 -bi-2-naphthol derivatives as an electron donor and MVCl2 as an electron acceptor. Since this system is supramolecular, that is, it is composed of two molecules and not one, the host complex can be easily modified by changing the combination of the system components. Therefore, rac-1,10 -bi-2-naphthol derivatives can be replaced with rac-3,30 -dimethyl-1,10 -bi-2-naphthol (rac-1b) and rac-3,30 -dibromo-1,10 -bi-2-naphthol (rac-1c). In addition, *To whom correspondence should be addressed. (Y.I.) E-mail: y-imai@ apch.kindai.ac.jp. Fax: þ81-6-6727-2024. Tel: þ1-6-6730-5880 (Ext. 5241). (Y.M.) E-mail: [email protected]. pubs.acs.org/crystal

Published on Web 08/04/2009

the formation of the CT complex without the substituents of rac-1a was attempted. The effect of the use of three benzeneol derivatives with different numbers of hydroxyl groups, such as phenol (2), 1,3-benzenediol (3), and 1,3,5-benzenetriol (4), in this CT host system was also analyzed (Chart 1). Chart 1

Experimental Section General Methods. All reagents were used directly as obtained commercially. Component molecules 1, 3, 4, and MVCl2 were purchased from Tokyo Kasei Kogyo Co., Ltd. Component molecule 2 and EtOH were purchased from Wako Pure Chemical Industry. Selective Inclusion Behavior of CT Host System. rac-1 (2.25  10-2 mmol), MVCl2 (5.8 mg, 2.25  10-2 mmol), 2 (2.2 mg, 2.34  10-2 mmol), 3 (2.6 mg, 2.36  10-2 mmol), and 4 (2.9 mg, 2.30  10-2 mmol) were dissolved in EtOH (3 mL) under heat and left to stand at room temperature. In the case of the rac-1c/MVCl2 system, after a few days, colored crystals (7.1 mg) were deposited and collected. The weight of crystals is defined as the total weight of the obtained crystals in one batch. An inclusion ratio of guest molecules in the obtained crystals was determined by 1H NMR analyses using a Varian Mercury M300 spectrometer in acetone-d6. Formation of CT Complexes Including Each Guest Molecule. rac1 (2.25  10-2 mmol), MVCl2 (5.8 mg, 2.25  10-2 mmol), and each guest molecule (2.25  10-2 mmol) were dissolved in EtOH (3 mL) r 2009 American Chemical Society

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under heat and left to stand at room temperature. When the rac-1cMVCl2 host system was used, after a few days, colored crystals [crystal I (7.0 mg), crystal II (8.6 mg), and crystal III (8.5 mg)] were deposited and collected. The weight of the crystals is defined as the total weight of obtained crystals in one batch. Measurement of DRS of CT Complex. The DRS of the crystals were measured using a HITACHI U-4000 spectrometer. X-ray Crystallographic Study of Crystal I. The X-ray diffraction data for single crystals were collected using Bruker Apex. The crystal structures were solved by the direct method5 and refined by fullmatrix least-squares using SHELX97.6 The diagrams were drawn using PLATON.7 The absorption corrections were performed using SADABS.8 The non-hydrogen atoms were refined with anisotropic displacement parameters, and the hydrogen atoms were included in the models at their calculated positions in the riding-model approximation. Crystallographic data of I: 0.5C12H14N2Cl2 3 0.5C6H6O 3 C20H12O2Br2 3 C2H6O, red prism crystal, crystal size=0.45  0.25  0.20, M = 665.81, triclinic, space group P1, a = 10.2111(8), b = 10.7567(9), c = 13.841(1) A˚, R = 106.981(1), β = 90.440(1), γ = 112.164(1), V=1334.6(2) A˚3, Z=2, Dc=1.657 g cm-3, μ(Mo KR) =3.175 mm-1, 11 544 reflections measured, 5925 unique, final R(F2) =0.0324 using 5112 reflections with I>2.0σ(I), R(all data)=0.0395, T=115(2) K. CCDC 644047. Crystallographic data can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cambridge Crystallographic Data Centre, 12, Union Road, Cambridge CB21EZ, UK; fax: (þ44)1223-336-033; deposit@ccdc. cam.ac.uk). X-ray Crystallographic Study of Crystal II. Crystallographic data of II: 0.5C12H14N2Cl2 3 0.5C6H6O2 3 C20H12O2Br2 3 C2H6O, orange plate crystal, crystal size=0.35  0.25  0.15, M=673.81, triclinic, space group P1, a=10.437(1), b=10.711(1), c=13.740(1) A˚, R= 104.967(2), β=91.731(2), γ=112.771(2), V=1353.5(3) A˚3, Z=2, Dc = 1.653 g cm-3, μ(Mo KR) = 3.133 mm-1, 11 740 reflections measured, 6016 unique, final R(F2) = 0.0662 using 4928 reflections with I >2.0σ(I), R(all data)= 0.0803, T =100(2) K. CCDC 644049.4 X-ray Crystallographic Study of Crystal III. Crystallographic data of III: 0.5C12H14N2Cl2 3 0.5C6H6O3 3 C20H12O2Br2 3 C2H6O, orange plate crystal, crystal size = 0.25  0.20  0.10, M = 680.3, triclinic, space group P1, a=10.245(1), b=10.794(1), c=14.149(1) A˚, R=106.993(2), β=91.265(2), γ=112.231(2) , V=1369.5(2) A˚3, Z=2, Dc=1.653 gcm-3, μ(Mo KR)=3.099 mm-1, 12 154 reflections measured, 6134 unique, final R(F2) = 0.0420 using 4958 reflec tions with I >2.0σ(I), R(all data)= 0.0561, T =120(2) K, CCDC 699185. Method of Calculation. The low-lying excited states of the CT chromophores in their X-ray structures were examined theoretically using the ZINDO method.9 The calculated chromophores are molecular clusters consisting of a viologen ion (MV2þ), two binaphthol molecules (1c), two guest molecules (2, 3, or 4), and two counteranions (Figure 5), where the bromine atoms and the chlorine atoms in the original X-ray structures have been replaced with fluorine atoms to calculate the excited states by the ZINDO method. The guest molecules of crystal I-III are disordered in the X-ray structures. We therefore picked up a set of carbons atoms for molecular skeleton from the disordered data, and attached the peripheral atom groups (i.e., hydroxyl groups and hydrogen atoms) to fit the molecular skeleton. The atomic coordinates for these peripheral atoms groups, the fluorine atoms to substitute the bromine and chlorine atoms, and all hydrogen atoms were optimized by the PM3 method10 prior to the excited state calculations. All these calculations were performed using the GAUSSIAN 03 program.11

Results and Discussion The selective inclusion behavior of this CT host system under the coexistence of 2, 3, and 4 as guest molecules was studied. rac-1a, MVCl2, 2, 3, and 4 were dissolved in ethanol (EtOH) under heat and left to stand at room temperature. After a few days, colored crystals were found to be deposited and these were collected. However, the obtained colored crystals were the previously reported 1a/MVCl2 complex

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without guest molecules.3 Then, the selective inclusion of a guest molecule was attempted using the rac-1b/MVCl2 and rac-1c/MVCl2 host systems under the same conditions. As a result, when the rac-1c/MVCl2 host system was used, although colored inclusion crystals were not obtained from the rac-1b/MVCl2 host system, colored inclusion crystals composed of rac-1c and MVCl2 were obtained. It is interesting to note that this host system exhibited the ability to selectively include a guest molecule. Crystals that included 2 were not obtained. On the other hand, both crystals that included 3 and 4 were obtained; however, crystals that included 4 were obtained as the major product (63%/37%=crystals including 4/crystals including 3). Although the selective formation of CT crystals with a substituted aromatic hydrocarbon as the donor molecule had been reported previously, it was believed that the molecular recognition of aromatic molecules containing hydroxyl groups using CT host systems is rare. In order to study the selective inclusion mechanism of guest molecules, we attempted the formation of a CT complex that includes each of the above-mentioned guest molecules and carried out X-ray crystallographic analysis. First, the inclusion behavior of the rac-1b/MVCl2 host system was studied. Similarly, the formation of an inclusion CT complex that includes 2 was attempted by crystallization from the EtOH solution containing rac-1b, MVCl2, and 2. However, in this case too, an inclusion CT complex was not obtained. Then, the formation of a rac-1c/MVCl2 CT complex that includes 2 was attempted under the same conditions. After a few days, several red crystals (I) were obtained. X-ray analysis was carried out to investigate the structure of these crystals; the structure is shown in Figure 1. The stoichiometry of complex I is expressed as (R)-1c/(S)1c/MVCl2/EtOH/2=1:1:1:2:1, and the space group is P1. (R)1c [or (S)-1c] is connected by a hydrogen bond through disordered EtOH and a chloride anion (ball-shaped structures in Figure 1), and it forms a 1D-structure unit along the b-axis (Figure 1a). In addition, a 1D-layered structure unit is formed as a result of CT interactions between two 1D-structure units (solid circle in Figure 1b) and the MV2þ (1,10 -dimethyl-4,40 bipyridinium) ion. Characteristically, 1D cavities are formed along the b-axis by the self-assembly of this 1D-layered structure (Figure 1c). These cavities are maintained by naphthalene-naphthalene edge-to-face interactions (Figure 1c, indicated by arrows marked as A, 2.91 A˚)12 between the 7-CH of the naphthol ring in 1c and the naphthol ring of another 1c. In these cavities, 2 (Figure 1c, shown in the form of a spacefill model) is one-dimensionally trapped by two interactions. One is the naphthalene-benzene edge-to-face interaction (Figure 1c, indicated by arrows marked as B, 2.88 A˚) between the 4-CH of the naphthol ring in 1c and the benzene ring of 2. The other is a hydrogen bond between the hydroxyl group of 2 and the chloride anion (O 3 3 3 Cl, 3.09 A˚). When the rac-1b/MVCl2 host system was used, 2 was not included. The reason for this can be explained as follows. The methyl group is bulkier than the bromide group; therefore, the bulky methyl groups, which exist near the hydroxyl group in 1b, interfere with the formation of a hydrogen bond and the construction of a 1D-structure unit. In addition, the inclusion behaviors of benzenediol, 3, and benzenetriol, 4, were analyzed. Inclusions of 3 and 4 were also attempted by crystallization from the EtOH solution containing rac-1c, MVCl2, and either 3 or 4. Each solution was left to stand at room temperature for a few days. As a result, orangecolored inclusion crystals II and III were obtained for 3 and 4,

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Figure 1. Crystal structure of CT complex I. Chloride ions are indicated as balls. (a) 1D-structure unit parallel to the b-axis. (b) 1D-layered structure observed along the b-axis. Solid circle indicates the 1D-structure unit. (c) 1D cavity formed by self-assembly of 1D-layered structure observed along the b-axis. Solid arrows A and B indicate naphthalene-naphthalene and naphthalene-benzene edge-to-face interactions, respectively.

respectively. X-ray analysis was carried out to investigate the structure of these crystals. The structure of II is shown in Figure 2.4 The stoichiometry and space group of complex II are the same as that of I; that is, (R)-1c/(S)-1c/MVCl2/EtOH/3 = 1:1:1:2:1, and the space group is P1. Complex II also has the same 1D-structure unit containing (R)-1c [or (S)-1c] and a 1Dlayered structure formed by CT interactions between two 1D-structure units (solid circle in Figure 2b) and the MV2þ (Figure 2a,b). 1D cavities are formed along the b-axis by selfassembly of these 1D-layered structures by the same naphthalene-naphthalene edge-to-face interactions (Figure 2c, indicated by arrows marked as A, 2.82 A˚) as those in crystal I (Figure 2c). In these 1D cavities, 3 (Figure 2, shown in the form of a spacefill model) is included. One 3 molecule exists very close to the center of symmetry, which generates another one of a different orientation. These two orientations are related to the positional disorder of the chlorine atom. Figure 2 shows only one of the two orientations of the 3 molecules. 3 is trapped by the following three interactions: (1) a naphthalene-benzene edge-to-face interaction (Figure 2, indicated by arrows marked as B, 2.91 A˚) between the 4-CH of the naphthol ring in 1c and the benzene ring of 3, (2) a hydrogen

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Figure 2. Crystal structure of CT complex II. Chloride ions are indicated as balls. (a) 1D-structure unit parallel to the b-axis. (b) 1D-layered structure observed along the b-axis. Solid circle indicates the 1D-structure unit. (c) 1D cavity formed by self-assembly of the 1D-layered structure observed along the b-axis. Solid arrows A and B indicate naphthalene-naphthalene and naphthalenebenzene edge-to-face interactions, respectively.

bond with the chloride ion (ball-shaped structures in Figure 2), and (3) a hydrogen bond with EtOH (O 3 3 3 O, 2.65 A˚). The structure of complex III is shown in Figure 3. The stoichiometry and space group of III is the same as those of I and II; that is, the stoichiometry is (R)-1c/(S)-1c/ MVCl2/EtOH/4 = 1:1:1:2:1, and the space group is P1. In contrast to I and II, (R)-1c [or (S)-1c] is connected by a hydrogen bond through EtOH, a chloride anion (ball-shaped structures in Figure 3), and 4, and it forms a 1D-structure unit along the b-axis, although 4 is disordered (Figure 3a). In addition, a 1D-layered structure unit is formed as a result of CT interactions between two 1D-structure units (solid circle in Figure 3b) and MV2þ (Figure 3b). 1D cavities are formed along the b-axis by the self-assembly of these 1D-layered structures by the same naphthalene-naphthalene edge-toface interactions (Figure 3c, indicated by arrows marked as A, 2.88 A˚) as those in I and II (Figure 3c). In these 1D cavities, 4 (Figure 3c, shown in the form of a spacefill model) is included; it is trapped by the following four interactions: (1) a naphthalene-benzene edge-to-face interaction (Figure 3, indicated by arrows marked as B, 2.96 A˚) between the 4-CH of the naphthol ring in 1c and the benzene ring of 4, (2) a hydrogen bond with the chloride ion (O 3 3 3 Cl, 3.00 A˚),12 (3)

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Figure 4. Diffuse reflectance spectra of crystals I (black line), II (gray line), and III (narrow black line).

Figure 5. Chromophore clusters obtained from the X-ray structures of crystals I-III. Cl and Br atoms in the original X-ray structures are replaced by F atoms for performing ZINDO calculations. Figure 3. Crystal structure of CT complex III. Chloride ions are indicated as balls. (a) 1D-structure unit parallel to the b-axis. (b) 1Dlayered structure observed along the b-axis. Solid circle indicates the 1D-structure unit. (c) 1D cavity formed by self-assembly of the 1Dlayered structure observed along the b-axis. Solid arrows A and B indicate naphthalene-naphthalene and naphthalene-benzene edge-to-face interactions, respectively.

a hydrogen bond with the hydroxyl group of 1c (O 3 3 3 O, 2.74 A˚),12 and (4) a hydrogen bond with EtOH (O 3 3 3 O, 2.70 A˚).12 Characteristically, in the rac-1c/MVCl2 host system, a CT complex could not be obtained by crystallization without the presence of 2-4. In the case of I-III, the packing styles of component molecules as well as each guest molecule are the same (Figures 1c, 2c, and 3c). In other words, the structures of these complexes are isostructural, and their structural motifs are identical. With a change in the guest molecule from 2 to 3, the distance between the 1D-layered structures along the a-axis (C, Figures 1c and 2c) decreases from 8.42 to 8.17 A˚, while that along the c-axis (D, Figures 1c and 2c) increases from 9.16 to

9.44 A˚. On the other hand, with a change in the guest molecule from 3 to 4, the distance between the 1D-layered structures along the a-axis (C, Figures 2c and 3c) increases from 8.17 to 8.57 A˚, while that along the c-axis (D, Figures 2c and 3c) decreases from 9.44 to 9.34 A˚. This shows that by slightly changing the packing style of the 1D-layered structure, the CT host system can accommodate these guest alcohols. By observing the selective inclusion behavior of this system, it can be inferred that the guest inclusion selectivity of the rac1c/MVCl2 host system increases with the number of hydroxyl groups as the guest molecules used changes from 2 to 3 to 4. The results of the X-ray crystallographic analyses reveal that the interactions between the guest molecule and the molecule of the host component increase and become stronger with the number of hydroxyl groups as the guest molecule used changes from 2 to 3 to 4 (Figures 1c, 2c, and 3c). Therefore, in the case of this host system, since 4 is included more easily than 2 and 3, complex III containing 4 is obtained as the major product. This host system is constructed by means of donor-acceptor interactions. Therefore, it was expected that the color of

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Table 1. Calculated Excited States for the Molecular Clustersa I

S1 S2 S3 S4 S5 S6 a

II

III

characterb

Ec/eV

fc

characterb

Ec/eV

fc

characterb

Ec/eV

fc

1cfMV2þ 1cfMV2þ 1cfMV2þ 2fMV2þ 1cfMV2þ 2fMV2þ

2.27 2.30 2.87 2.90 2.91 2.94

0.000 0.022 0.040 0.000 0.012 0.009

1cfMV2þ 1cfMV2þ 3fMV2þ 3fMV2þ 1cfMV2þ 1cfMV2þ

2.47 2.50 2.97 2.97 3.17 3.17

0.000 0.013 0.005 0.000 0.013 0.000

1cfMV2þ 1cfMV2þ 1cfMV2þ 1cfMV2þ 4fMV2þ 4fMV2þ

2.25 2.26 2.44 2.44 2.70 2.71

0.000 0.017 0.000 0.003 0.013 0.000

Calculated by the ZINDO method. b Electronic transition from the ground state is given. c Excitation energies (E ) and oscillator strength ( f ). Table 2. The Intermolecular Distances in Clusters I-IIIa MV

I II III

2þ

3 3 3 1c 3.346 3.484 3.395

MV2þ 3 3 3 2(3,4) 5.106 5.087 5.122

Cl- 3 3 3 MV2þ 3.828 3.358 4.031

Cl- 3 3 3 1c 3.695 3.944 3.724

Cl- 3 3 3 2(3,4) 3.572 2.910 2.850

a The distances given are the center-plane distances for MV2þ 3 3 3 1c, the center-center distances for MV2þ 3 3 3 2(3,4) and the smallest interatonuc (non-hydrogen) distances for Cl- 3 3 3 MV2þ,Cl- 3 3 3 1c, Cl- 3 3 3 2(3,4), in A˚.

the inclusion crystal would be sensitive to the structure of the guest molecules. As expected, the color of this CT host system depends on the included guest molecule; that is, inclusion crystals I containing 2 are red in color, whereas both inclusion crystals II containing 3 and III containing 4 have similar orange colors. Diffuse reflectance spectra (DRS) of I-III are shown in Figure 4. The solid-state DRS of I, II, and III differ significantly from each other, with absorption edges located at ca. 380, 380, and 490 nm, respectively. Although the absorption edges of II and III are almost the same, III exhibits long wavelength absorption. The above-mentioned colors of these complexes are unique to the solid state, while highly concentrated solutions of these crystals exhibit a light yellow color. This suggests that the rac-1c/MVCl2 host system can be used not only as a selective inclusion host system but also as visual and DRS indicators for molecular recognition. The DRS indicate that the electronic absorptions of I-III differ from each other. To understand the origins of these lowenergy absorptions, the excited states of the CT chromophores in their X-ray structures were examined theoretically. The theoretically calculated chromophores are molecular clusters consisting of MV2þ, two binaphthol molecules (1c), two guest molecules (2, 3, or 4), and two counteranions, as shown in Figure 5.13 The least energy excited states of these molecular clusters are listed in Table 1. The calculated data suggest that experimentally observed absorptions at the lowest energy side originate from the electronic transitions from 1c to MV2þ (excitations to S1 and S2). Therefore, it is hypothesized that electronic transitions from the guest molecules to MV2þ are not responsible for the formation of the guest-dependent absorption edge of the DRS. Excitation energies of these lowest states in clusters I and III are comparable and are smaller than those in cluster II. The ordering of excitation energies of these three clusters is consistent with the DRS: Absorptions of I and III extend toward a lower energy side (larger wavelength side) than that of II. The difference between the excitation energies of the three clusters is related to the relative locations of the counteranions Cl- to the molecules because the arrangement of molecules except Cl- is similar in the three clusters (see Figure 5, and Table 2 for the intermolecular distances). It is most probable

that the larger excitation energies of cluster II are related to the smaller Cl 3 3 3 MV distance than those of other clusters. (Note that a small Cl 3 3 3 MV distance stabilizes the ground state (Cl- 3 3 3 MV2þ) more than the excited states (where Cl- 3 3 3 MV1þ), leading to the formation of a large excitation energy). Conclusions We developed a multiple molecular recognition system using CT host complexes composed of rac-1c and MVCl2. This CT host system selectively includes an aromatic molecule having a hydroxyl group as the guest. In addition, the color and DRS of this inclusion crystal are sensitive to the structure of the included guest molecules. This further enhances the functionality of these CT host systems; these systems may prove to be useful as selective host systems and sensitive visual indicators for molecular recognition. Acknowledgment. This work was supported by a Grantin-Aid for Scientific Research (No. 20750115) from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and a research grant from The Mazda Foundation. Supporting Information Available: X-ray crystallographic reports (CIF) of complexes I and III. This information is available free of charge via the Internet at http://pubs.acs.org.

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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, 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.; and Pople, J. A.; Gaussian, Inc.: Wallingford CT, 2004. (12) It is an average distance. (13) The excitation energies of the three systems should be calculated evenly correctly for comparison. From this reason, the molecular clusters are selected so that they have mutually corresponding intermolecular interactions.