Large Nonlinear Optical Responses of Dimers Bearing a Donor and

Article pubs.acs.org/JPCC

Large Nonlinear Optical Responses of Dimers Bearing a Donor and Acceptor: Long, Intradimer Multicenter Bonding Wen-Yong Wang,† Yu-He Kan,*,‡ Li Wang,† Shi-Ling Sun,† and Yong-Qing Qiu*,† †

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun 130024, People’s Republic of China ‡ Jiangsu Key Laboratory for Chemistry of Low-Dimensional Materials, School of Chemistry and Chemical Engineering, Huaiyin Normal University, Huai’an 223300, People’s Republic of China S Supporting Information *

ABSTRACT: Unusual long, multicenter dimers bearing a large electron donor and acceptor have been the subject of great interest over the last decades due to their better conducting, superconducting, magnetic, or other physical properties. Twoelectron, multicenter bonding between two interplanar fragments has been recently recognized as a novel and important bonding interaction. Herein, the [TTF][TCNE], [TTF][TCNQ], [TTF][TCNP], and [TTF][TCNB] dimeric species have been studied by quantum mechanics methods with the view of assessing their interactions and first hyperpolarizabilities. It is found that the stabilities of the dimers primarily originate from the electrostatic bonding component. Although to a lesser extent, long, multicenter interactions due to the overlap of the molecular orbitals of the monomers are important also in the stability of these systems. Significantly, a severe hyperpolarizability decrease with changing the acceptor monomers of the dimeric species is qualitatively explained in terms of change in their charge transfer patterns. It indicates that the first hyperpolarizabilities of these dimers can be optimized by controlling their relative acceptor monomers. We believe that these results shall provide important information for further exploration of long, multicenter dimers with versatile and fascinating nonlinear optical properties.

1. INSTRUCTION

Chart 1. Highest Occupied Molecular Orbital (HOMO) and MO Diagram for [TCNE]22−

It is evident that over the past several years, incredible progress has been made in terms of identifying long, multicenter bonding that was first introduced to describe the structure, electronic and magnetic properties of [TCNE]22− dimer (TCNE = tetracyanoethylene).1−3 The [TCNE]22− dimer, resulting from the dimerization of two [TCNE]•‑ anions, represents an unusual class of organic compounds that possess exceptionally long intradimer carbon−carbon (C−C) bond distance (that is, 2.9 A°) involving two electrons and fourcenter carbon atoms.4−6 This long C−C bond has the similar electronic property as conventional covalent bond, excepting that its distance is much longer than that for the conventional covalent C−C bond ( [TTF][TCNQ] > [TTF][TCNP] > [TTF][TCNB]. And this holds for all the corresponding projection of β on dipole moment vector (βvec) values we considered here. The hyperpolarizability magnitudes listed in Table 3 are found comparable to those of long, multicenter bonding molecules previously studied by Zhong et al.80 and ferrocene-based complexes studied by us.26,81 Moreover, βvec match well with βtot, since the dipole moment has no vanished.82 Also, when the charge transfer is unidirectional and parallel to the molecular dipole moment, the βvec should be very identical to βtot. What makes these results more increasing to rationalize is the fact that, for all dimers, the sign of βvec is defined by βy. Another interesting point that bearing mention is that the evidenced hyperpolarizability variations (with the exception of [TTF][TCNQ]) show obvious connection with the respective HOMO−LUMO gaps (Figure 4). Further, a severe hyperpolarizability decreases with the change of the acceptor monomers, indicating that such motifs may offer considerable flexibility in optimizing their NLO properties by controlling the relative acceptor monomers. Since hyperpolarizabilities are derivatives of the molecular energy with respect to the strength of the applied electric field, thus their theoretically calculated values may be sensitive to basis-set feature. Hence, the problem of basis-set incompleteness and superposition error appears. We now turn our attention to the hyperpolarizability of [TTF][TCNE] calculated at various basis sets (Table 4). [TTF][TCNE] was Table 4. First Hyperpolarizabilities (10−30 esu) of [TTF][TCNE] Calculated at the CAM-B3LYP Level Using Various Basis Sets basis set

βx

βy

βz

βtot

βvec

6-31G(d) 6-31G(d,p) 6-31G(2d,p) 6-31+G(d) 6-31+G(d,p) 6-31++G(d,p) 6-311G(d) 6-311+G(d,p) 6-311+G(2df,2pd) 6-311++G(3df,2pd)

−9.6 −9.6 −9.2 −10.4 −10.4 −10.4 −10.7 −10.6 −10.5 −10.2

85.2 85.1 78.4 81.5 81.4 81.3 88.5 82.2 79.1 77.5

−20.2 −20.2 −19.0 −20.5 −20.4 −20.4 −31.1 −20.6 −20.0 −19.7

88.1 88.0 81.2 84.7 84.6 84.4 91.6 85.4 82.2 80.6

87.9 87.8 81.0 84.5 84.5 84.3 91.3 85.2 82.1 80.5

selected as an ideal case because this dimer provides the larger hyperpolarizability. It is worth noticing that the 6-31+G(d,p)

Table 5. Excited Transition Energies (ΔE, eV), Oscillator Strengths (fos), and Major Molecular Orbital Contributions of the Dimers Calculated at the CAM-B3LYP/6-31+G(d) Level molecule

ΔE

f

MO transition

[TTF][TCNE] [TTF][TCNQ] [TTF][TCNP] [TTF][TCNB]

1.52 3.14 1.55 5.80

0.1117 0.7457 0.0085 0.5184

HOMO → LUMO(100%) HOMO−1 → LUMO (94%) HOMO → LUMO+1 (100%) HOMO−4 → LUMO+1 (39%) HOMO → LUMO+12 (27%) HOMO−5 → LUMO (17%)

G

dx.doi.org/10.1021/jp506681k | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

contribute to their overall hyperpolarizability values. The crucial transition contributions of [TTF][TCNE], [TTF][TCNQ] and [TTF][TCNP] represent at least 60% of overall hyperpolarizability with exception of [TTF][TCNB] closed to 50%, rendering it possible to use two-level model to qualitative analysis of these dimers. The ΔE values at the crucial transition states that contribute the most to the hyperpolarizabilities are listed in Table 5. The ΔE values increase in the order of [TTF][TCNE] (1.52 eV) < [TTF][TCNP] (1.55 eV) < [TTF][TCNQ] (3.14 eV) < [TTF][TCNB] (5.80 eV). However, instead of the ΔE value of [TTF][TCNQ] falling between those of [TTF][TCNE] and [TTF][TCNP], the ΔE value of [TTF][TCNQ] is larger than those of [TTF][TCNP], indicating that the sequence of βtot values could not be determined only in terms of ΔE values. For this reason, we focus on the other controlling factors of βtot values, i.e., oscillator strength. What is intriguing here is that the oscillator strength of [TTF][TCNP] is particularly small, which is mainly attributed to the small overlap between the orbitals of HOMO and LUMO+1 (because the CT at this state arises from HOMO to LUMO+1). What’s more, the monotonic dependence of the first hyperpolarizability on the f/ΔE3 is shown in Figure 5.

Figure 6. 3D contour plots of the MOs involved in the crucial electronic transitions of the dimers.

Figure 7. EDDM corresponding to the crucial electronic transitions of the dimers. Green and yellow colors indicate depletion and accumulation of electron density, respectively.

Figure 5. Relationship between the βtot values (green square) and the corresponding f/ΔE3 values (orange circle) for the four dimers.

TTF and TCNB fragments coupled with intramolecular CT within the TCNB moiety. And the transition pattern is also confirmed by the EDDM (Figure 7). Over all, the results show some important changes in the CT pattern that are accompanied by significant differences on the corresponding first hyperpolarizability properties.

To further understand the origin of the transition property, we focused on the molecular orbitals of the crucial transition states of the four dimers. As shown in Table 5, the electronic transition of [TTF][TCNE] arises from the HOMO → LUMO excitation. Taking into account the shape of the MOs (Figure 6) and relevant electron density difference maps (EDDM) (Figure 7), this transition could be assigned as intramolecular CT transition from TTF to TCNE fragments, since the electronic distribution of HOMO is mainly located at the TTF moiety while the LUMO is mainly concentrated on the TCNE moiety. Similar to electronic transition of [TTF][TCNE], the electronic transition of [TTF][TCNP] is ascribed as TTF to TCNE transition. Compound [TTF][TCNQ], however, exhibits a remarkably different charge transfer transition. This transition from HOMO−1 → LUMO corresponds to the local transitions occurred within the TCNQ fragment, which is also essentially reflected by the TDM in the Figure S5 of the Supporting Information. As seen, the coherence between atoms in TCNQ fragment is very strong. Contrary, for [TTF][TCNB], the complexity of the CT transition increases, indicating that the CT is the mixture of interlayer CT between

4. CONCLUSION In this work, the interactions of the long, intradimer multicenter [TTF][TCNE], [TTF][TCNQ], [TTF][TCNP], and [TTF][TCNB] dimers have been systematically investigated by quantum mechanics methods. The long, multicenter bonding has five, eight, 10, and eight BCPs, respectively, and thus always involves two electrons with 10, 16, and 17, and 16 bonding atoms for these dimers, respectively. Our computational work has demonstrated that the large electrostatic interactions stabilize the long-bond formation, while the SOMO−SOMO overlap plays also an important role in the stabilities of the dimers, which thus significantly different from the typical long, multicenter bonds of [TTF] 22+ and [TCNE]22−. The long, multicenter bonding in [TTF][TCNP] and [TTF][TCNB] dimers result from the dominant electroH

dx.doi.org/10.1021/jp506681k | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

A Unified Description of Multicenter, Long Bonds. J. Am. Chem. Soc. 2009, 131, 7699−7707. (8) Garcia-Yoldi, I.; Miller, J. S.; Novoa, J. J. [Cyanil]22‑ Dimers Possess Long, Two-electron Ten-center (2e−/10c) Multicenter Bonding. Phys. Chem. Chem. Phys. 2008, 10, 4106−4109. (9) Willi, C.; Reis, A. H.; Gebert, E.; Miller, J. S. Crystal and Molecular Structure of the 1:2 Charge-transfer Salt of Trimethyleneferrocene and 7,7,8,8-tetracyano-p-quinodimethane: [Fe(C5H4)2(CH2)3+·][(TCNQ)2‑·]. Inorg. Chem. 1981, 20, 313−318. (10) Goldberg, S. Z.; Spivack, B.; Stanley, G.; Eisenberg, R.; Braitsch, D. M.; Miller, J. S.; Abkowitz, M. Synthesis, Structure, and Physical Properties of the Bis(7,7,8,8-tetracyano-p-quinodimethane) Salt of the Paramagnetic Cluster Tris[(di-.mu.-chloro)(hexamethylbenzene)niobium], [Nb3(μ-Cl)6(C6Me6)3]2+(TCNQ)22. J. Am. Chem. Soc. 1977, 99, 110−117. (11) Teresa Azcondo, M.; Ballester, L.; Golhen, S.; Gutierrez, A.; Ouahab, L.; Yartsev, S.; Delhaes, P. Structural, Magnetic, Electrical and Optical Characterization of Systems Built from [M([9]aneN3)2]2+ (M = CuII or NiII) and TCNQ or TCNQF4. J. Mater. Chem. 1999, 9, 1237−1244. (12) Bagnato, J. D.; Shum, W. W.; Strohmeier, M.; Grant, D. M.; Arif, A. M.; Miller, J. S. The Structure of Fractionally Charged Tetracyanobenzenenn− Present in [TCNB]32−. Angew. Chem., Int. Ed. 2006, 45, 5322−5326. (13) Taliaferro, M. L.; Thorum, M. S.; Miller, J. S. RoomTemperature Organic-Based Magnet (Tc ≈ 50 °C) Containing Tetracyanobenzene and Hexacarbonylvanadate(−I). Angew. Chem., Int. Ed. 2006, 45, 5326−5331. (14) Vickers, E. B.; Selby, T. D.; Miller, J. S. Magnetically Ordered (Tc = 200 K) Bis(tetracyanopyrazine)vanadium, V[TCNP]2·yCH2Cl2. J. Am. Chem. Soc. 2004, 126, 3716−3717. (15) Scott, B. A.; La Placa, S. J.; Torrance, J. B.; Silverman, B. D.; Welber, B. The Crystal Chemistry of Organic Metals. Composition, Structure, and Stability in the Tetrathiafulvalinium-halide Systems. J. Am. Chem. Soc. 1977, 99, 6631−6639. (16) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakusi, K.; Ouyang, J. A Stable Neutral Hydrocarbon Radical: Synthesis, Crystal Structure, and Physical Properties of 2,5,8-Tri-tert-butyl-phenalenyl. J. Am. Chem. Soc. 1999, 121, 1619−1620. (17) Morita, Y.; Kawai, J.; Fukui, K.; Nakazawa, S.; Sato, K.; Shiomi, D.; Takui, T.; Nakasuji, K. Topological Symmetry Control in Spin Density Distribution: Spin Chemistry of Phenalenyl-Based Neutral Monoradical Systems. Org. Lett. 2003, 5, 3289−3291. (18) Zhong, R. L.; Xu, H. L.; Sun, S. L.; Qiu, Y. Q.; Zhao, L.; Su, Z. M. Theoretical Investigation on the 2e/12c Bond and Second Hyperpolarizability of Azaphenalenyl Radical Dimers: Strength and Effect of Dimerization. J. Chem. Phys. 2013, 139, 124314(1−6). (19) García-Yoldi, I.; Mota, F.; Novoa, J. J. The Origin of the Twoelectron/four-centers C C Bond in π-TCNE22− dimers: Electrostatic or Dispersion? J. Comput. Chem. 2007, 28, 326−334. (20) Clemente, D. A.; Marzotto, A. Structure of Two Polymorphs of the TTF-TCNE Charge-transfer Complex and the Degree of Ionicity. J. Mater. Chem. 1996, 6, 941−946. (21) Meneghetti, M.; Pecile, C. TTF−TCNE A Charge Transfer π− molecular Crystal with Partial Ionic Ground State: Optical Properties and Electron-Molecular Vibrations Interaction. J. Chem. Phys. 1996, 105, 397−407. (22) Capdevila-Cortada, M.; Novoa, J. J.; Bell, J. D.; Moore, C. E.; Rheingold, A. L.; Miller, J. S. Unusually Long, Multicenter, Cationδ+··· Anionδ− Bonding Observed for Several Polymorphs of [TTF][TCNE]. Chem.−Eur. J. 2011, 17, 9326−9341. (23) Das, A.; Ghosh, S. Supramolecular Assemblies by ChargeTransfer Interactions between Donor and Acceptor Chromophores. Angew. Chem., Int. Ed. 2014, 53, 2038−2054. (24) Xu, H. L.; Li, Z. R.; Wu, D.; Wang, B. Q.; Li, Y.; Gu, F. L.; Aoki, Y. Structures and Large NLO Responses of New Electrides: Li-Doped Fluorocarbon Chain. J. Am. Chem. Soc. 2007, 129, 2967−2970.

static component that enable the fragments to approach each other so that their molecular geometries substantially change. Interestingly, the first hyperpolarizabilities are significantly dependent on the acceptor monomers, indicating that the NLO properties of these dimers can be optimized by controlling their relative acceptor monomers. These differences on the first hyperpolarizabilities are found due to the changes in the CT pattern. Furthermore, it was established that these dimers possess notable hyperpolarizabilities, particularly [TTF][TCNE], which display obvious charge transfer transition from TTF to TCNE. It obviously that these long, multicenter bonding molecules are promising materials with highly efficient NLO properties.

■

ASSOCIATED CONTENT

S Supporting Information *

Figures and tables giving the stretching monomer−monomer vibrational frequencies and modes, NBO and AIM charge, properties of the BCPs, molecular orbital energy, orbital compositions, density of states, tensorial components, dipolar and octupolar contributions to the first hyperpolarizabilities, position of the intermolecular BCPs, molecular orbitals of bonding character, convergent behavior of βtot values of the dimers dependent on the first 40 states, and the transition density matrix. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*(Y.-Q.Q.) E-mail: [email protected]. Telephone: +86 431 85099291. *(Y.-H.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 21173035).

■

REFERENCES

(1) Del Sesto, R. E.; Miller, J. S.; Lafuente, P.; Novoa, J. J. Exceptionally Long (≥2.9 Å) CC Bonding Interactions in π[TCNE]22− Dimers: Two-Electron Four-Center Cation-Mediated CC Bonding Interactions Involving π* Electrons. Chem.−Eur. J. 2002, 8, 4894−4908. (2) Miller, J. S. Four-Center Carbon−Carbon Bonding. Acc. Chem. Res. 2007, 40, 189−196. (3) Novoa, J. J.; Lafuente, P.; Del Sesto, R. E.; Miller, J. S. Exceptionally Long (≥2.9 Å) C−C Bonds between [TCNE]− Ions: Two-Electron, Four-Center π*−π* C−C Bonding in π-[TCNE]22−. Angew. Chem., Int. Ed. 2001, 40, 2540−2545. (4) Lü, J. M.; Rosokha, S. V.; Kochi, J. K. Stable (Long-Bonded) Dimers via the Quantitative Self-Association of Different Cationic, Anionic, and Uncharged π-Radicals: Structures, Energetics, and Optical Transitions. J. Am. Chem. Soc. 2003, 125, 12161−12171. (5) Jakowski, J.; Simons, J. Theoretical Analysis of the Electronic Structure and Bonding Stability of the TCNE Dimer Dianion (TCNE)22. J. Am. Chem. Soc. 2003, 125, 16089−16096. (6) Jung, Y.; Head-Gordon, M. What Is the Nature of the Long Bond in the TCNE22‑ π-dimer? Phys. Chem. Chem. Phys. 2004, 6, 2008− 2011. (7) Mota, F.; Miller, J. S.; Novoa, J. J. Comparative Analysis of the Multicenter, Long Bond in [TCNE]·− and Phenalenyl Radical Dimers: I

dx.doi.org/10.1021/jp506681k | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

(25) Song, H. J.; Zhang, M. Y.; Sun, X. X.; Sun, S. L.; Qiu, Y. Q. Nonlinear Optical Properties of a Series of 6,12-Diethynylindeno[1,2b]fluorene Derivatives. Acta. Phys. Chim. Sin. 2012, 28, 2839−2844. (26) Wang, W. Y.; Ma, N. N.; Sun, S. L.; Qiu, Y. Q. Redox Control of Ferrocene-Based Complexes with Systematically Extended π-conjugated Connectors: Switchable and Tailorable Second Order Nonlinear Optics. Phys. Chem. Chem. Phys. 2014, 16, 4900−4910. (27) Wang, W. Y.; Du, X. F.; Ma, N. N.; Sun, S. L.; Qiu, Y. Q. Theoretical Investigation on Switchable Second-order Nonlinear Optical (NLO) Properties of Novel Cyclopentadienylcobalt Linear [4]phenylene Complexes. J. Mol. Model 2013, 19, 1779−1787. (28) Wang, W. Y.; Ma, N. N.; Wang, C. H.; Zhang, M. Y.; Sun, S. L.; Qiu, Y. Q. Enhancement of Second-order Nonlinear Optical Response in Boron Nitride Nanocone: Li-doped Effect. J. Mol. Graphics Modell. 2014, 48, 28−35. (29) Qiu, Y. Q.; Wang, W. Y.; Ma, N. N.; Wang, C. H.; Zhang, M. Y.; Zou, H. Y.; Liu, P. J. Computational Investigation on Redox-switchable Nonlinear Optical Properties of a Series of Polycyclic p-quinodimethane Molecules. J. Mol. Model 2013, 19, 5479−5487. (30) Ma, N. N.; Yan, L. K.; Guan, W.; Qiu, Y. Q.; Su, Z. M. Theoretical Investigation on Electronic Structure and Second-order Nonlinear Optical Properties of Novel Hexamolybdate-organoimido(car)borane Hybrid. Phys. Chem. Chem. Phys. 2012, 14, 5605−5612. (31) Ma, N. N.; Li, S. J.; Yan, L. K.; Qiu, Y. Q.; Su, Z. M. Switchable NLO Response Induced by Rotation of Metallacarboranes [NiIII/ IV(C2B9H11)2]−/0 and C-,B-functionalized derivatives. Dalton. Trans. 2014, 43, 5069−5075. (32) Č ížek, J. On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods. J. Chem. Phys. 1966, 45, 4256−4266. (33) Waller, M. P.; Kruse, H.; Muck-Lichtenfeld, C.; Grimme, S. Investigating Inclusion Complexes Using Quantum Chemical Methods. Chem. Soc. Rev. 2012, 41, 3119−3128. (34) Hobza, P. Calculations on Noncovalent Interactions and Databases of Benchmark Interaction Energies. Acc. Chem. Res. 2012, 45, 663−672. (35) Riley, K. E.; Pitoňaḱ , M.; Jurečka, P.; Hobza, P. Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories. Chem. Rev. 2010, 110, 5023−5063. (36) Grimme, S. Semiempirical Hybrid Density Functional with Perturbative Second-order Correlation. J. Chem. Phys. 2006, 124, 034108(1−16). (37) Schwabe, T.; Grimme, S. Towards Chemical Accuracy for the Thermodynamics of Large Molecules: New Hybrid Density Functionals Including Non-local Correlation Effects. Phys. Chem. Chem. Phys. 2006, 8, 4398−4401. (38) Goerigk, L.; Grimme, S. A Thorough Benchmark of Density Functional Methods for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions. Phys. Chem. Chem. Phys. 2011, 13, 6670−6688. (39) Goerigk, L.; Grimme, S. Efficient and Accurate Double-HybridMeta-GGA Density FunctionalsEvaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions. J. Chem. Theory Comput. 2010, 7, 291−309. (40) Chai, J. D.; Head-Gordon, M. Long-range Corrected Doublehybrid Ddensity Functionals. J. Chem. Phys. 2009, 131, 174105 (1− 13). (41) Biegler-könig, F. W.; Bader, R. F. W.; Tang, T. H. Calculation of the Average Properties of Atoms in Molecules. II. J. Comput. Chem. 1982, 3, 317−328. (42) Sanville1, E.; Kenny1, S. D.; Smith1, R.; Henkelman, G. Improved Grid-based Algorithm for Bader Charge Allocation. J. Comput. Chem. 2007, 28, 899−908. (43) Biegler-König, F. Calculation of Atomic Integration Data. J. Comput. Chem. 2000, 21, 1040−1048.

(44) Lu, T.; Chen, F. W. Comparison of Computational Methods for Atomic Charges. Acta Phys. Chim. Sin. 2012, 28, 1−18. (45) Glendening, E. D.; Landis, C. R.; Weinhold, F. Natural Bond Orbital Methods. WIREs Comput. Mol. Sci. 2012, 2, 1−42. (46) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. mol. Phys. 1970, 19, 553−566. (47) ADF 2012.01 SCM; Theoretical Chemistry, Vrije Universiteit: Amsterdam, http://www.scm.com. (48) Chen, W.; Li, Z. R.; Wu, D.; Li, R. Y.; Sun, C. C. Theoretical Investigation of the Large Nonlinear Optical Properties of (HCN)n Clusters with Li Atom. J. Phys. Chem. B 2004, 109, 601−608. (49) Champagne, B.; Perpète, E. A.; Jacquemin, D.; van Gisbergen, S. J. A.; Baerends, E.-J.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density Functional Schemes for Computing the Dipole Moment and (Hyper)polarizabilities of Push−Pull π-Conjugated Systems†. J. Phys. Chem. A 2000, 104, 4755−4763. (50) Champagne, B. t.; Perpète, E. A.; van Gisbergen, S. J. A.; Baerends, E.-J.; Snijders, J. G.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density Functional Schemes for Computing the Polarizabilities and Hyperpolarizabilities of Conjugated Oligomers: An ab initio Investigation of Polyacetylene Chains. J. Chem. Phys. 1998, 109, 10489−10498. (51) van Gisbergen, S. J. A.; Schipper, P. R. T.; Gritsenko, O. V.; Baerends, E. J.; Snijders, J. G.; Champagne, B.; Kirtman, B. Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains. Phys. Rev. Lett. 1999, 83, 694−697. (52) Torrent-Sucarrat, M.; Anglada, J. M.; Luis, J. M. Evaluation of the Nonlinear Optical Properties for Annulenes with Hückel and Möbius Topologies. J. Chem. Theory Comput. 2011, 7, 3935−3943. (53) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. A Long-range-corrected Time-dependent Density Functional Theory. J. Chem. Phys. 2004, 120, 8425−8433. (54) Limacher, P. A.; Mikkelsen, K. V.; Lüthi, H. P. On the Accurate Calculation of Polarizabilities and Second Hyperpolarizabilities of Polyacetylene Oligomer Chains Using the CAM-B3LYP Density Functional. J. Chem. Phys. 2009, 130, 194114(1−7). (55) Chopra, P.; Carlacci, L.; King, H. F.; Prasad, P. N. Ab initio Calculations of Polarizabilities and Second Hyperpolarizabilities in Organic Molecules with Extended π-electron Conjugation. J. Phys. Chem. 1989, 93, 7120−7130. (56) Stratmann, R. E.; Scuseria, G. E.; Frisch, M. J. An Efficient Implementation of Time-dependent Density-functional Theory for the Calculation of Excitation Energies of Large Molecules. J. Chem. Phys. 1998, 109, 8218−8224. (57) Hirata, S.; Head-Gordon, M. Time-dependent Density Functional Theory for Radicals: An Improved Description of Excited States with Substantial Double Excitation Character. Chem. Phys. Lett. 1999, 302, 375−382. (58) 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. et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (59) Lu, T.; Chen, F. W. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580−592. (60) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (61) Pendás, A. M.; Francisco, E.; Blanco, M. A.; Gatti, C. Bond Paths as Privileged Exchange Channels. Chem.Eur. J. 2007, 13, 9362−9371. (62) Garcia-Yoldi, I.; Miller, J. S.; Novoa, J. J. Structure and Stability of the [TCNE]22‑ Dimers in Dichloromethane Solution: A Computational Study. J. Phys. Chem. A 2007, 111, 8020−8027. (63) Steinmann, S. N.; Piemontesi, C.; Delachat, A.; Corminboeuf, C. Why are the Interaction Energies of Charge-Transfer Complexes Challenging for DFT? J. Chem. Theory Comput. 2012, 8, 1629−1640. (64) Capdevila-Cortada, M.; Ribas-Arino, J.; Novoa, J. J. Assessing the Performance of CASPT2 and DFT Methods for the Description of J

dx.doi.org/10.1021/jp506681k | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Long, Multicenter Bonding in Dimers between Radical Ions. J. Chem. Theory Comput. 2014, 10, 650−658. (65) Steinmann, S. N.; Corminboeuf, C. Exploring the Limits of Density Functional Approximations for Interaction Energies of Molecular Precursors to Organic Electronics. J. Chem. Theory Comput. 2012, 8, 4305−4316. (66) Grimme, S. Density Functional Theory with London Dispersion Corrections. WIREs: Comput. Mol. Sci. 2011, 1, 211−228. (67) Lu, T.; Chen, F. W. Revealing the Nature of Intermolecular Interaction and Configurational Preference of the Nonpolar Molecular Dimers (H2)2, (N2)2, and (H2)(N2). J. Mol. Model. 2013, 19, 5387− 5395. (68) Morokuma, K. Molecular Orbital Studies of Hydrogen Bonds. III. CO···H−O Hydrogen Bond in H2CO···H2O and H2CO··· 2H2O. J. Chem. Phys. 1971, 55, 1236−1244. (69) Szalewicz, K. Symmetry-adapted Perturbation Theory of Intermolecular Forces. WIREs Comput. Mol. Sci. 2012, 2, 254−272. (70) Liu, Z. Chemical Bonding in Silicon-Carbene Complexes. J. Phys. Chem. A 2009, 113, 6410−6414. (71) Krapp, A.; Bickelhaupt, F. M.; Frenking, G. Orbital Overlap and Chemical Bonding. Chem.Eur. J. 2006, 12, 9196−9216. (72) Garcia-Yoldi, I.; Miller, J. S.; Novoa, J. J. Theoretical Study of the Electronic Structure of [Tetrathiafulvalene]22+ Dimers and Their Long, Intradimer Multicenter Bonding in Solution and the Solid State. J. Phys. Chem. A 2008, 113, 484−492. (73) Karamanis, P.; Maroulis, G. An ab Initio Study of CX3substitution (X = H, F, Cl, Br, I) Effects on the Static Electric Polarizability and Hyperpolarizability of Diacetylene. J. Phys. Org. Chem. 2011, 24, 588−599. (74) Maroulis, G.; Karamanis, P.; Pouchan, C. Hyperpolarizability of GaAs Dimer is not Negative. J. Chem. Phys. 2007, 126, 154316(1−5). (75) Karamanis, P.; Otero, N.; Pouchan, C. Unleashing the Quadratic Nonlinear Optical Responses of Graphene by Confining WhiteGraphene (h-BN) Sections in Its Framework. J. Am. Chem. Soc. 2014, 136, 7464−7473. (76) Karamanis, P.; Pouchan, C. Second-Hyperpolarizability (γ) Enhancement in Metal-Decorated Zigzag Graphene Flakes and Ribbons: The Size Effect. J. Phys. Chem. C 2013, 117, 3134−3140. (77) Mendes, P. J.; Silva, T. J. L.; Helena Garcia, M.; Prates Ramalho, J. P.; Palace Carvalho, A. J. J. Chem. Inf. Model. 2012, 52, 1970−1983. (78) Oteroa, N.; Alsenoy, C. V.; Karamanis, P.; Pouchan, C. Electric Response Properties of Neutral and Charged Al13X (X = Li, Na, K) Magic Clusters. A Comprehensive Ab Initio and Density Functional Comparative Study. Compu. Theor. Chem. 2013, 1021, 114−123. (79) Karamanis, P.; Otero, N.; Pouchan, C.; Torres, J. J.; Tiznado, W.; Avramopoulos, A.; Papadopoulos, M. G. Significant Nonlinearoptical Switching Capacity in Atomic Clusters Built from Silicon and Lithium: A Combined Ab Initio and Density Functional Study. J. Comput. Chem. 2014, 35, 829−838. (80) Zhong, R. L.; Zhang, J.; Muhammad, S.; Hu, Y. Y.; Xu, H. L.; Su, Z. M. Boron/Nitrogen Substitution of the Central Carbon Atoms of the Biphenalenyl Diradical π Dimer: A Novel 2e−12c Bond and Large NLO Responses. Chem.−Eur. J. 2011, 17, 11773−11779. (81) Wang, W. Y.; Ma, N. N.; Sun, S. L.; Qiu, Y. Q. Impact of Redox Stimuli on the Ferrocene-buckybowl Complexes: Switchable Optoelectronic and Nonlinear Optical Properties. Organometallics 2014, 33, 3341−3352. (82) Karamanis, P.; Pouchan, C. Fullerene−C60 in Contact with Alkali Metal Clusters: Prototype Nano-Objects of Enhanced First Hyperpolarizabilities. J. Phys. Chem. C 2012, 116, 11808−11819. (83) Kenawi, I. M.; Kamel, A. H.; Hilal, R. H. BSSE Effects on the Static Dipole Polarizability and First Dipole Hyperpolarizability of Diclofenac Sodium. J. Mol. Struct.-THEOCHEM 2008, 851, 46−53. (84) Oudar, J. L. Optical Nonlinearities of Conjugated Molecules. Stilbene Derivatives and Highly Polar Aromatic Compounds. J. Chem. Phys. 1977, 67, 446−457. (85) Oudar, J. L.; Chemla, D. S. Hyperpolarizabilities of the Nitroanilines and Their Relations to the Excited State Dipole Moment. J. Chem. Phys. 1977, 66, 2664−2668. K

dx.doi.org/10.1021/jp506681k | J. Phys. Chem. C XXXX, XXX, XXX−XXX