ARTICLE pubs.acs.org/JPCC
Shape Effect of Graphene Quantum Dots on Enhancing Second-Order Nonlinear Optical Response and Spin Multiplicity in NH2GQDNO2 Systems Zhong-Jun Zhou, Zhen-Bo Liu, Zhi-Ru Li,* Xu-Ri Huang,* and Chia-Chung Sun State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, People's Republic of China ABSTRACT: In the donorbridgeacceptor [NH2graphene quantum dot (GQD)NO2] system, we found that, for GQDs with the same number of carbon atoms, changing the shape of the GQDs not only effectively enhances the first hyperpolarizability (β0) but also changes the spin multiplicity of the systems, which is useful to designing the smaller nanoscale spin and optical device. Here, special shaped species with a singlet diradical or multiradical character exhibit a very large β0 value, up to 1.7 105 au. Interestingly, it is found that the large β0 value is not presented in the highspin trapezoidal 3-1 (3A) and triangle 3-2 (5A), but in the low-spin 3-1 (1A) and 3-2 (1A), which are unusual cases.
1. INTRODUCTION Graphene nanoribbons (GNRs) have attracted great attention from theoretical and experimental chemists and physicists since graphene—a one-atom-thick carbon sheet—can be experimentally realized.1 More and more attention is being paid to potential applications of GNRs,2 such as ballistic electronic transport,3 magnetic properties,410 quasirelativistic behavior,1114 and band-gap engineering capabilities.1518 Another basic element of graphene derivatives is a graphene quantum dot (GQD).19 It is a nanometer-scale disklike material that has a closed edge. GQDs can be constructed by connecting several benzenes. More recently, Yan et al. have successfully synthesized graphene quantum dots with various shapes and tunable sizes, exhibiting efficient photovoltaic properties.2023 For GQDs, several theoretical calculations have shown that different shaped GQDs have different electronic properties. These properties render the GQD as the building block for nanodevices, such as spin memory, transistors, solid-state qubits, and perhaps optoelectronics applications.2430 On the other hand, both CNTs (carbon nanotubes) and GNRs functioning as conjugated bridges have been introduced into the donorconjugated bridgeacceptor (DBA) framework, which has been a successful motif for designing organic nonlinear optical (NLO) materials.3139 Recently, our group has reported that NH2GNRNO2 displays prominent NLO properties in frequency doubling applications.40 On the basis of our previous work, in this paper, we introduce different shaped graphene quantum dots functioning as a conjugated bridge into the DBA framework. However, unlike the previous studies, our aim is mainly to improve the NLO response at the smaller nanometer scale. We r 2011 American Chemical Society
found that the shape effect of GQDs has an important role in enhancing the NLO response. This work enriches NLO studies based on graphene and will provide a theoretical guide for experimental synthesis of smaller and higher-performance NLO nanophotonic devices.
2. COMPUTATIONAL DETAILS We study a set of disubstituted graphene quantum dots (GQDs) with hydrogen atoms passivating the edges, H2NGQDNO2, in which GQD consists of 46 carbon atoms. This medium-sized GQD not only provides different structures of GQD but also reduces the computational cost. In previous investigation,40 it is shown that the longer the conjugated bridge between a donor and an accepotor, the larger the first hyperpolarizability. Thus, we fix the position of NH2 and NO2 groups on the end of the GQD as far as possible. To describe well the shape effect of the GQDs on the second-order NLO response, we choose some representive structures (see Figure 1). All the H2NGQDNO2 species were investigated at the spin-unrestricted (U) B3LYP/6-31G* level.41,42 With regard to the calculation of the first hyperpolarizability, choosing a proper method is very important. The B3LYP method has been reported to overestimate the hyperpolarizabilities for the large DπA systems.43 The MP2 method is more reliable than B3LYP in the hyperpolarizability calculations, but it is very costly for larger systems. A new density functional, the Coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP),44,45 Received: March 6, 2011 Revised: June 24, 2011 Published: July 04, 2011 16282
dx.doi.org/10.1021/jp202129b | J. Phys. Chem. C 2011, 115, 16282–16286
The Journal of Physical Chemistry C
ARTICLE
Table 1. Static First Hyperpolarizability (β0) at the Different Levels, Such as M06-2X, BHandHLYP, LC-BLYP, HF, CAMB3LYP, and MP2, for the Medium-Sized H2NGQDNO2 (C30H18N2O2) System β0
methods
error (%)
BHandHLYP
5981
40.8
M06-2X
5222
22.9
LC-BLYP
3313
22.0
HF
3420
19.5
CAM-B3LYP
5032
18.5
MP2
4248
0.00
When a system is in a weak and stable applied electric field, its energy can be written as 1 1 E ¼ E0 μR FR RRβ FR Fβ βRβγ FR Fβ Fγ ::: 2 6
ð1Þ
where E0 is the molecular energy without the electric field and FR is an electric field component along the R direction; μ, RRβ, and βRβγ are the dipole moment, polarizability, and first hyperpolarizability, respectively. In this paper, we mainly focus on the β0 value. The first hyperpolarizability is defined as β0 ¼ ðβ2x þ β2y þ β2z Þ1=2 Figure 1. Structures of disubstituted GQDs. The light green, dark blue, red, and pink balls denote C, N, O, and H atoms, respectively.
Figure 2. Structure of the medium-sized disubstituted GQDs (C30H18N2O2) to test which method is more suitable to the computation of first hyperpolarizability. The light green, dark blue, red, and pink balls denote C, N, O, and H atoms, respectively.
where βx ¼
3 ðβ þ βxyy þ βxzz Þ 5 xxx
βy ¼
3 ðβ þ βyxx þ βyzz Þ 5 yyy
βz ¼
3 ðβ þ βzxx þ βzyy Þ 5 zzz
We employ Nakano’s method41,42 to obtain the diradical character yi (related to the HOMO i and LUMO + i) defined by twice the weight of the doubly excited configuration in the multiconfigurational self-consistent-field theory. In the case of the spin-projected UHF (PUHF) theory, it is formally expressed as50,51 yi ¼ 1
has recently been developed specifically to overcome these limitations of the traditional density functional, and it has been shown to properly predict the molecular properties of charge-transfer processes.4649 We choose the medium-sized H2NGQDNO2 (see Figure 2) as an example to test the reliance of CAM-B3LYP. Different methods are used to calculate the first hyperpolarizability for the medium-sized H2NGQDNO2, and results are listed in Table 1. From Table 1, we see that the β0 value calculated by the CAM-B3LYP method is closer to that by the MP2 method than others. The CAM-B3LYP method is, therefore, employed to calculate the first hyperpolarizabilities by a finite field approach in the present study. The basis sets employed are 6-31G(d) for all the atoms. The magnitude of the applied electric field is chosen as 0.001 au for the calculation of the hyperpolarizability, which is proven to be the proper value for the present systems.40
ð2Þ
2T i 1 þ T 2i
ð3Þ
where Ti is the orbital overlap between the corresponding orbital pair. It can also be expressed in terms of the occupation numbers [nj (j = HOMO i, LUMO + i)] of UHF natural orbitals (UNOs): Ti ¼
ðnHOMOi nLUMOi Þ 2
ð4Þ
The singlet diradical character yi obtained from the UNO occupation numbers takes a value between 0 and 1, which corresponds to closedshell and pure singlet multiradical states, respectively. The present scheme using the UNOs is the simplest, but it can well reproduce the singlet multiradical characters calculated by other methods, such as the ab initio configuration interaction (CI) method.52 The y0 value is diradical character, and y1 is tetraradical character. All of these calculations are performed with the Gaussian 09 program packages.53 16283
dx.doi.org/10.1021/jp202129b |J. Phys. Chem. C 2011, 115, 16282–16286
The Journal of Physical Chemistry C
ARTICLE
Table 2. Static Polarizability (au), First Hyperpolarizability β0 (au), Transition Energy ΔE (eV), Oscillator Strength f0, Crucial Transition (H d HOMO, L = LUMO), and ΔEr (kcal/mol)a species
R0
β0
ΔE
f0
4
CT
ΔEr
1-1 ( A)
913
1.2 10
0.755
0.0324
HfL
1-2 (1A)
759
6.9 103
2.857
0.1931
H 1f L
1-3 (1A)
716
6.2 103
2.975
0.2210
HfL
2-1 (1A)
954
5.0 104
1.029
0.3103
HfL
2-2 (1A)
882
1.5 104
1.813
1.3656
HfL
2-3 (1A)
989
2.0 104
1.714
1.8319
HfL
3-1 (3A) 3-1 (1A)
667 1116
9.8 103 5.6 104
2.386 1.708
0.6517 0.3135
HfL H1fL
3-2 (5A)
622
2.7 103
2.493
0.0296
HfL+2
0.00
1097
1.7 105
0.556
0.1066
HfL
9.53
1
1
3-2 ( A)
0.00 3.94
a Note that ΔEr includes the zero-point vibration energy (ZPVE) at the B3LYP/6-31G* level.
3. RESULTS AND DISCUSSION 3.1. Geometries and Spin State of H2NGQDNO2. To facilitate discussion, H2NGQDNO2 is divided into three groups (see Figure 1): The first group (C46H26N2O2) contains a row of fused benzene rings (11 hollows), that is, the linear species 1-1, the Z-type species 1-2, and the trifurcate species 1-3. The second (C46H20N2O2) contains two rows of fused benzene rings (14 hollows), that is, the linear species 2-1, the L-type species 22, and the Z-type species 2-3. The third (C46H18N2O2) is multiple rows of fused benzene rings (15 hollows), that is, the trapezoidal species 3-1 and the triangle species 3-2. From the above, we see that increase a hollow and just reduce two hydrogen atoms, which indicates that the conjugated degree is increased. In addition, from Table 2, we can see that, in the first group, the linear species 1-1 is an open-shell singlet ground-state system with an almost pure diradical character (y0 = 0.945). However, when 1-1 is formally evolved into the species 1-2 and 1-3, the system becomes an intermediate diradical character (y0 = 0.310) and a closed-shell system, respectively; the original pure diradical character disappears. Like the first group, the linear species 2-1 in the second group is also an open-shell singlet ground-state system with an almost pure diradical character (y0 = 0.821). However, when 2-1 is formally changed into the L-shaped species 2-2 and Z-shaped species 2-3, respectively, the system becomes a closed-shell singlet ground-state system and the diradical character also disappears. However, unlike the first and second groups, for the third group, the trapezoidal 3-1 and the triangle 3-2 are triplet and pentet ground states, respectively, while the open-shell singlet state with diradical (y0 = 1.0) and teraradical character (y0 = 1.0, y1 = 1.0) correspond to their excited states. Although all the molecules have the same number of carbon atoms, different shaped molecules display different spin states. The shape effect of GQDs will be helpful to designing different spin devices. 3.2. Shape Effect on Polarizability and First Hyperpolarizability. The static polarizabilities (R0) and first hyperpolarizabilities (β0) of H2NGQDNO2 systems at the CAM-B3LYP level are listed in Table 2. From Table 2, for the former two groups, the range of R0 values of the three groups is 716989 au. It is shown that the shape effect of GQDs has a small effect on the polarizability.
On first hyperpolarizability (β0), for the first group (C46H26N2O2) with 11 fused benzene rings, the β0 value of the linear species 1-1 (y0 = 0.946) is 1.2 104 au. However, when 1-1 (y0 = 0.946) is formally curved into the nonlinear species 1-2 (y0 = 0.310), the β0 value is decreased to 6.9 103 au. Moreover, when the GQD of 1-1 is changed into the trifurcate type 1-3 (y0 = 0.00), its β0 is decreased to 6.2 103 au and is smaller than that of 1-2. For the first group, the linear species 1-1 with an almost pure diradical character exhibits the largest β0 (1.2 104 au). For the second group (C46H20N2O2) with 14 fused benzene rings, the β0 value of the linear 2-1 (y0 = 0.821) is 5.0 104 au. When it is formally bended into the L-shaped species 22 (y0 = 0.0), the β0 value falls to 2.5 104 au, and when it is further bended into the Z-type species 2-3 (y0 = 0.0), the β0 value is decreased to 2.0 104au, respectively. Like the first group, the linear species 2-1 with an almost pure diradical character displays the largest β0 value in the second group. Differing from the first and second groups, in the third group (C46H20N2O2) with 15 fused rings, the trapezoidal 3-1 and the triangle 3-2 are high-spin ground states. Their β0 values are 9.8 103 and 2.7 103 au, respectively. For comparison, we also investigate their β0 values of the low-spin singlet excited state. Their β0 values are 5.6 104 and 1.7 105 au, respectively. In previous investigations,5456 the NLO response of the high-spin state is larger than that of the low-spin state. However, both the trapezoidal 3-1 and the triangle 3-2 with the high-spin states exhibit small β0 values. This is an unusual case. From the above part, we know that the molecule with singlet diradical character has a large β0 value. In the singlet 3-1 and 3-2 molecules, we also found the pure diradical and tetraradical characters, respectively, and they thus exhibit very large β0 values. In addition, the singlet excited state 3-1 and 3-2 are only 3.94 and 9.53 kcal/mol higher than those of the triplet ground state 3-1 and the pentet ground state 3-2, respectively. This indicates that the excited states are also stable in thermodynamic. Furthermore, the case of polarizability is similar to that of hyperpolarizabiliy for 3-1 and 3-2. To rationalize the origin of the hyperpolarizability (β0), Oudar and Chemla57,58 established a simple link between β0 and a low-lying charge-transfer transition by the two-level model for dipolar organic molecules.3140 For our systems, the physical quantities in the twolevel model may be helpful to qualitatively understand the variation of β0. In the two-level expression, the third power of the transition energy is inversely proportional to the β0 value, while the first power of the oscillator strength f0 is proportional to the β0 value. Obviously, for H2NGQDNO2 dipolar molecules, the low transition energy is a decisive factor in the large first hyperpolarizability. The TD-DFT/CAM-B3LYP method is carried out to estimate the crucial excited states of H2NGQDsNO2. The transition energy (ΔE) is listed in Table 2. In the first group, the linear species 1-1 with the largest β0 (1.2 104) has the smallest ΔE (0.755 eV). The nonlinear species 1-2 and 1-3 with the smaller β0 values (6.9 103 and 6.2 103 au) have the larger ΔE values (2.857 and 2.975 eV). Likewise, in the second group, the linear 2-1 with the largest β0 value (5.0 104 au) has the smallest ΔE (1.029 eV). The nonlinear species 2-2 and 23 with the smaller β0 values (2.5 104 and 2.0 104) possess the larger ΔE values (1.813 and 1.714 eV). In the third group, the β0 value (9.8 103 for 3-1 and 2.7 103 for 3-2) of the ground state is much smaller than that (5.6 104 for 3-1 and 1.7 105 for 3-2) of the excited state. The ΔE value (1.706 for 3-1 and 0.556 for 3-2) of the ground state is much more than that (2.384 for 3-1 and 2.493 for 3-2) of the excited state, which is well in agreement with the two-level model and explains 16284
dx.doi.org/10.1021/jp202129b |J. Phys. Chem. C 2011, 115, 16282–16286
The Journal of Physical Chemistry C why the NLO response of the high-spin state is larger than that of the low-spin state.
4. CONCLUSIONS In this paper, we have studied the shape effect of graphene quantum dots (GQDs) on the first hyperpolarizability in H2NGQDNO2 systems. On the basis of the same number of carbon atoms of the conjugated bridge GQD, different shaped GQDs are designed to serve as a conjugated bridge in the donorconjugated bridgeacceptor framework. It is found that the shape effect and singlet diradical or mutiradical character of GQDs have a key role in enlarging β0. This work may provide a theoretical guide to design smaller and high-performance nanophotonic devices in the future. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (Z.-R.L.),
[email protected] (X.-R.H.).
’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Nos. 20773046, 20773048, and 21073075). ’ REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Gregorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) Hod, O.; Barone, V. ; Scuseria, G. E. Phys. Rev. B 2008, 77, 035411. (3) Berger, C.; Song, Z.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; De Heer, W. A. Science 2006, 312, 1191. (4) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. J. Phys. Soc. Jpn. 1996, 65, 1920. (5) Wakabayashi, K.; Sigrist, M.; Fujita, M. J. Phys. Soc. Jpn. 1998, 67, 2089. (6) Wakabayashi, K.; Fujita, M.; Ajiki, H.; Sigrist, M. Phys. Rev. B 1999, 59, 8271. (7) Kusakabe, K.; Maruyama, M. Phys. Rev. B 2003, 67, 092406. (8) Yamashiro, A.; Shimoi, Y.; Harigaya, K.; Wakabayashi, K. Phys. Rev. B 2003, 68, 193410. (9) Lee, H.; Son, Y.-W.; Park, N.; Han, S.; Yu, J. Phys. Rev. B 2005, 72, 174431. (10) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature (London) 2006, 444, 347. (11) Zhang, Y.; Tan, Y.; Stormer, H.; Kim, P. Nature 2005, 438, 201. (12) Peres, N. M. R.; Castro Neto, A. H.; Guinea, F. Phys. Rev. B 2006, 73, 195411. (13) Peres, N. M. R.; Castro Neto, A. H.; Guinea, F. Phys. Rev. B 2006, 73, 241403(R). (14) Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Science 2007, 315, 1379. (15) Ezawa, M. Phys. Rev. B 2006, 73, 045432. (16) Barone, V.; Hod, O.; Scuseria, G. E. Nano Lett. 2006, 6, 2748. (17) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. € (18) Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805. (19) Ezawa, M. Phys. Status Solidi C 2007, 4, 489. (20) Yan, X.; Cui, X.; Li, B.; Li, L.-S. Nano Lett. 2010, 10, 1869. (21) Yan, X.; Cui, X.; Li, L.-S. J. Am. Chem. Soc. 2010, 132, 5944. (22) Li, L. S.; Yan, X. J. Phys. Chem. Lett. 2010, 1, 2572.
ARTICLE
(23) (a) Du, A.; Smith, S. C. J. Phys. Chem. Lett. 2011, 2, 73. (b) Kastler, M.; Schmidt, J.; Pisula, W.; Sebastiani, D.; M€ullen, K. J. Am. Chem. Soc. 2006, 128, 9526. (24) Yang, X.; Dou, X.; Rouhanipour, A.; Zhi, L.; R€ader, H. J.; M€ullen, K. J. Am. Chem. Soc. 2008, 130, 4216. (25) Ezawa, M. Phys. Rev. B 2007, 76, 245415. (26) Wang, W. L.; Meng, S.; Kaxiras, E. Nano Lett. 2008, 8, 241–245. (27) G€u)c l€u, A. D.; Potasz, P.; Voznyy, O.; Korkusinski, M.; Hawrylak, P. Phys. Rev. Lett. 2009, 103, 246805. (28) Wang, W. L.; Yazyev, O. V.; Meng, S.; Kaxiras, E. Phys. Rev. Lett. 2009, 102, 157201. (29) Recher, P.; Trauzettel, B. Nanotechnology 2010, 21, 302001. (30) Yu, S. S.; Zheng, W. T.; Wang, C.; Jiang, Q. ACS Nano 2010, 4, 7619. (31) Marder, S. R. Chem. Commun. 2006, 131. (32) Priyadarshy, S.; Therien, M. J.; Beratan, D. N. J. Am. Chem. Soc. 1996, 118, 1504. (33) Marder, S. R.; Beratan, D. N.; Cheng, L.-T. Science 1991, 252, 103. (34) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; John Wiley & Sons: New York, 1991. (35) Bishop, D. M.; Champagne, B.; Kirtman, B. J. Chem. Phys. 1998, 109, 9987. (36) Bulat, F. A.; Toro-Labbe, A.; Champagne, B.; Kirtman, B.; Yang, W. J. Chem. Phys. 2005, 123, 014319. (37) Blanchard-Desce, M.; Alain, V.; Bedworth, P. V.; Marder, S. R.; Fort, A.; Runser, C.; Barzoukas, M.; Lebus, S.; Wortmann, R. Chem.— Eur. J. 1997, 3, 1091. (38) Champagne, B.; Perpete, E.; Jacquemin, D.; Van Gisbergen, S.; Baerends, E.; Soubra-Ghaoui, C.; Robins, K.; Kirtman, B. J. Phys. Chem. A 2000, 104, 4755. (39) Nakano, M.; Ohta, S.; Kamada, K.; Kishi, R.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E.; Takahashi, H. Chem. Phys. Lett. 2007, 443, 95. (40) Zhou, Z. J.; Li, X. P.; Liu, Z. B.; Ma, F.; Li, Z. R.; Huang, X. R.; Sun, C. C. Chem.—Eur. J. 2011, 17, 2414. (41) Nakano, M.; Nagai, H.; Fukui, H.; Yoneda, K.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; et al. Chem. Phys. Lett. 2008, 467, 120. (42) Nagai, H.; Nakano, M.; Yoneda, K.; Fukui, H.; Minami, T.; Boness, S.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; et al. Chem. Phys. Lett. 2009, 477, 355. (43) Champagne, B.; Perpete, E. A.; Jacquenmin, D.; van Gisbergen, S. J. A.; Baerends, E.-J.; Soubra-Ghaoui, C.; Robins, K. A. J. Phys. Chem. A 2000, 104, 4755. (44) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. J. Chem. Phys. 2004, 120, 8425. (45) Yanai, T.; Tew, D. P.; Handy, N. C. Chem. Phys. Lett. 2004, 393, 51. (46) Peach, M. J. G.; Helgaker, T.; Salek, P.; Keal, T. W.; Lutnaes, O. B.; Tozer, D. J.; Handy, N. C. Phys. Chem. Chem. Phys. 2006, 8, 558. (47) Kobayashi, R.; Amos, R. D. Chem. Phys. Lett. 2006, 420, 106. (48) Cai, Z. L.; Crossley, M. J.; Reimers, J. R.; Kobayashi, R.; Amos, R. D. J. Phys. Chem. B 2006, 110, 15624. (49) Ma, F.; Li, Z. R.; Zhou, Z. J.; Wu, D.; Li, Y.; Wang, Y. F.; Li, Z. S. J. Phys. Chem. C 2010, 114, 11242. (50) Yamaguchi, K. In Carbo, R., Klobukowski, M., Eds.; SelfConsistent Field:Theory and Applications; Elsevier: Amsterdam, 1990; p 727. (51) Yamanaka, S.; Okumura, M.; Nakano, M.; Yamaguchi, K. J. Mol. Struct. 1994, 310, 205. (52) Herebian, D.; Wieghardt, K. E.; Neese, F. J. Am. Chem. Soc. 2003, 125, 10997. (53) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, 16285
dx.doi.org/10.1021/jp202129b |J. Phys. Chem. C 2011, 115, 16282–16286
The Journal of Physical Chemistry C
ARTICLE
T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; 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.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (54) Nakano, M.; Nitta, T.; Yamaguchi, K.; Champagne, B.; Botek, E. J. Phys. Chem. A 2004, 108, 4105. (55) 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. (56) Dirk, C. W.; Kuzyk, M. G. Phys. Rev. A 1989, 39, 1219. (57) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (58) Oudar, J. L. J. Chem. Phys. 1977, 67, 446.
16286
dx.doi.org/10.1021/jp202129b |J. Phys. Chem. C 2011, 115, 16282–16286
