Computational Study on Second-Order Nonlinear Response of a

J. Phys. Chem. C 2008, 112, 7021-7028

7021

Computational Study on Second-Order Nonlinear Response of a Series of Two-Dimensional Carbazole-Cored Chromophores Chun-Guang Liu, Yong-Qing Qiu,* Zhong-Min Su, Guo-Chun Yang, and Shi-Ling Sun Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal UniVersity, Changchun 130024, P. R. China ReceiVed: August 5, 2007; In Final Form: January 18, 2008

The static second-order nonlinear optical (NLO) properties on a series of two-dimensional A-π-D-π-A carbazole-cored chromophores were investigated by density functional theory (DFT). The carbazole heterocycles can be viewed as auxiliary donors in these compounds. It is found that the first hyperpolarizabilities of these two-dimensional NLO molecules are sensitive to the changing of heterocycles on the donor. Moreover, the orientation of the thiophene ring in the chromophore significantly affects the second-order NLO properties. According to the time-dependent DFT calculations, the low transition energy and strong charge transfer are the key factors to determine the first hyperpolarizability, and an auxiliary donor provides an intrinsic enhancement of the NLO response in set III.

1. Introduction Organic nonlinear optical (NLO) materials are currently attracting considerable attention because of their advantages,1-3 such as reduced production cost, lower dielectric constants, and higher photoelectric coefficients. The donor-(π electron bridge)acceptor (D-π-A) one-dimensional (1D) structure,4 as a simple molecular scheme, has been successfully used in the development of second-order organic NLO materials. However, the 1D chromophores tend to align in antiparallel fashion, diminishing the macroscopic NLO responses.5 Various approaches, including electric field poling,6 Langmuir-Blodgett techniques,7 and vapor-phase self-assembly,8 have been employed to induce the molecular noncentrosymmetry arrangements. But the improvements of these approaches do not hold for some dipole molecules. On the other hand, phase-matching conditions also need to be considered,9 and an optimal molecular orientation in the crystal should obtain efficient phase-matched second harmonic generation (SHG). However, the orientation of 1D chromophores only allows for the recovery of fewer macroscopic NLO responses because of the one charge transfer (CT) axis.10 Moreover, for higher symmetry crystals, the effective phasematched nonlinearities are even smaller. Thus, the chromophores with large off-diagonal β tensor components have been proposed because they can offer large macroscopic NLO responses. When compared with 1D chromophores, the two-dimensional (2D) chromophores with large off-diagonal β tensor components displayed better phase matching.11,12 The 2D Λ-shaped molecules have been regarded as a candidate due to significant NLO responses.13-15 These Λ-shaped molecules can form transparent and phase-matched noncentrosymmetric crystal structures and exhibited large second-order NLO responses because of large off-diagonal β tensor components.16 Moreover, the theoretical studies indicated that the relative magnitudes between the diagonal and off-diagonal β tensor components of Λ-shaped molecules are strongly related to the angle between two D-A branches.9 The C2V 2D Λ-shaped molecules display significant off-diagonal β components because the electron transition dipole * Corresponding author. E-mail: [email protected].

moment between two states is perpendicular to the C2 axis and offers new possibilities for achieving phase-matched SHG. Furthermore, the C2V 2D molecule can enhance the second-order NLO responses without undesirable visible transparency losses.17 Coe and co-workers found that two- and three-dimensional ruthenium (II) or iron (II) complexes display good two- and three-dimensional second-order NLO properties because of the metal-to-ligand charge-transfer transition.18,19 Moreover, a series of 2D NLO molecular materials have been synthesized, and their second-order NLO properties have been measured by using electric field-induced second harmonic generation and hyperRayleigh scattering (HRS) technologies.20-24 It suggested that these 2D compounds have potential application in NLO material fields. There are several principles to enhance β value, such as the planar D-π-A model, the bond length alternation theory, and auxiliary donors and acceptors model of heterocycle, concerning the electron-rich ring (auxiliary donor) and the electron-deficient ring (auxiliary acceptor), and their relative orientations lead to substantial increases in β values. Directed by these strategies, the large second-order NLO responses have been observed by using polyene and multiple thiophene rings as π-conjugated bridges.25 Thus, heterocyclic compounds have attracted considerable interest due to their good linear and nonlinear optical properties. In the past decade, considerable efforts have been focused on the development of 1D NLO materials with heterocycles as auxiliary electron donor/acceptors. Earlier studies of heterocyclic systems with 1D stilbene structures have supported the following points.26-29 First, it is well-known that the charge transfer from a donor to an acceptor across a π-electron bridge would disrupt the aromaticity of the bridge. Thus, the decreases of the aromatic delocalization energy by introduction of a heterocycle would lead the charge-transfer state to dominate the exited state and enhance the second-order NLO responses. Second, the electron-excessive/deficient heterocyclic bridges act as an auxiliary donor/acceptor, significantly enhancing the second-order NLO response. Third, the relative orientation of the thiazole compounds with 1D stilbene structures significantly affects the second-order NLO responses, and the

10.1021/jp0762673 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/08/2008

7022 J. Phys. Chem. C, Vol. 112, No. 17, 2008

Liu et al.

Figure 1. Structural formulas for all compounds.

matched structures of thiazole compounds produces very large hyperpolarizabilities. However, 2D NLO materials with the heterocycles acting as auxiliary electron donors/acceptors are rare. Moreover, a detailed understanding of the structureproperty relationship for the 2D heterocyclic system is lacking. In the present paper, the relationship between structure and second-order NLO properties of the 2D carbazole-cored A-πD-π-A chromophores was calculated by density functional theory (DFT) combined with finite field (FF) and timedependent (TD)DFT sum-over-state (SOS) methods. The heterocyclic derivatives sets I∼III were designed to understand the role of the heterocyclic replacements on the donor or acceptor end and their relative orientation producing the NLO responses. Sets I∼III represent structures that show a trend in second-order NLO properties of three different heterocycles as the auxiliary donors. The chromophores in every set represent the structures that show second-order NLO properties of the various heterocycles as auxiliary acceptors. Moreover, the orientations of auxiliary acceptors also have been considered. A chromophore in every set was chosen as the reference benzenoid system (Ia

in set I, IIa in set II, and IIIa in set III). All of the molecular structures are shown in Figure 1. 2. Computational Details For a molecule of C2V symmetry, there are only three nonzero β tensor components. However, in the present paper, the molecular symmetry is broken by the out-of-plane methyl group. As a result, some β tensor components become nonzero. But these nonzero components are so small that the following discussion is only concerned with theβxxx, βxyy, and βxzz. In addition, the molecules lie in the XY plane, and the βxxx and βxyy components are larger than the corresponding βxzz values. Therefore, all compounds have the following first hyperpolarizability tensor βvec which is described by eq 1.

βvec ≈ βxxx + βxyy

(1)

The geometries of all compounds were optimized at the B3LYP/ 6-31g(d) level. To obtain a more intuitive description of the trends on the nonlinear optical behavior of the studied com-

Two-Dimensional Carbazole-Cored Chromophores

J. Phys. Chem. C, Vol. 112, No. 17, 2008 7023

TABLE 1: First Hyperpolarizability Tensors (× 10-30 esu) and Dipole Moments (Debye) of All Compounds (B3LYP/6-31g(d)) compd

βxxx (SOS)

βxyy (SOS)

βxzz (SOS)

Ia Ib Ic Id Ie If Ig Ih Ii

-27.893 -20.758 -13.299 -38.153 -26.392 -72.281 -22.457 -25.137 -28.722

-32.277 -35.695 -19.108 -42.119 -37.905 -67.840 -39.859 -38.530 -37.642

-0.004 -0.010 -0.004 -0.006 -0.011 -0.004 -0.005 -0.005 -0.009

IIa IIb IIc IId IIf

-46.883 -34.245 -81.522 -36.821 -69.560

-43.011 -44.637 -58.224 -56.173 -46.734

-0.037 -0.030 -0.044 -0.030 -0.022

IIIa IIIb IIIc IIId IIIe IIIf IIIg IIIh

-64.398 -131.870 -51.316 -123.964 -70.309 -84.551 -45.518 -117.110

-188.193 -324.384 -199.201 -342.451 -331.926 -351.193 -156.939 -535.259

-0.012 -0.017 -0.010 -0.022 -0.017 -0.173 -0.074 -0.628

pounds, TDDFT methods were used to investigate the molecular electronic structures. All of the calculations in this work were carried out by the Gaussian 03 program package.30 The static first hyperpolarizability tensors of all compounds were calculated by the FF method and TDDFT-SOS formalism at the B3LYP/6-31g(d) level. The FF method was broadly applied to investigate NLO because this methodology can be used in concert with the electronic structure method to compute β.31-33 When a molecule is subjected to a static electric field (F), the energy (E) of the molecule is expressed by eq 2

1 1 E ) E(0) - µiFi - RijFiFj - βijkFiFjFk 2 6 1 γ F F F F - ‚‚‚ (2) 24 ijkl i j k l where E(0) is the energy of molecule in the absence of an electronic field; µi is the components of the dipole moment vector; R is the linear polarizability tensor; β and γ are the second- and third-order polarizability tensor, respectively; and i, j, and k label the x, y, and z components, respectively. The molecular Hamiltonian includes a term (-µ j ‚F h ) describing the interaction between the external uniform static field and the molecule. µ is the total dipole moment. It is clear that the values of µ, R, β, and γ can be obtained by differentiating E with respect to F. For the FF calculations, the energy convergence criteria and strength of field are the important factors. In this present paper, the first hyperpolarizability β was calculated by using the field frequency of 0.0010 a.u., the default convergence criteria in the Gaussian 03 program package were used. The first hyperpolarizabilities were calculated by the SOS formula. For the framework of SOS perturbation theory, the electronic states are created by the perturbing laser field (ω), which is treated as an infinite expansion over a complete set of unperturbed ψn and ψn′ particle-hole excited states. Thus, the individual tensor components of the molecular first hyperpolarizabilities, βijk, are exactly related to all the excited states of the molecule in terms of the difference, pω, between excitedand ground-state energies; dipole moment matrix elements; (µi)gn

βxxx/βxyy (SOS)

βvec (SOS)

βvec (FF)

µtot

1.2 1.7 1.4 1.1 1.4 0.9 1.8 1.5 1.3

-60.173 -56.462 -32.492 -80.277 -64.308 -140.125 -62.321 -53.670 -66.370

-123.317 -115.939 -170.027 -123.721 -119.173 -164.340 -161.996 -55.203 -65.751

10.527 9.340 5.198 10.512 10.870 14.946 6.980 12.464 13.797

0.9 1.3 0.7 1.5 0.7

-89.931 -78.911 -137.790 -93.023 -116.316

-117.872 -115.449 -129.197 -107.656 -115.343

9.961 14.015 17.108 12.812 15.193

2.9 2.5 3.9 2.8 4.7 4.2 3.4 4.6

-256.603 -456.272 -250.529 -466.432 -402.257 -435.928 -202.531 -652.997

-553.446 -601.187 -575.916 -541.313 -549.741 -619.697 -647.073 -751.883

10.506 13.489 6.963 12.270 10.100 16.414 7.077 14.069

Set I

Set II

Set III

and (µi)mn between unperturbed ground and excited states; and between two excited states, respectively; and the dipole moment difference, (µ j j)mn ) (µj)mn - (µj)gg. The first hyperpolarizabilities tensor can be described in the following,

βijk )

1 4p2

P(i,j,k; -ωσ,ωI,ω2)

[

∑ ∑×

m*g n*g

(µi)gm(µ j j)mn(µk)gn

(ωmg - ωσ - iγmg)(ωng - ωI - iγng)

]

(3)

where ωσ ) ω1 + ω2 is the polarization response frequency; P(i,j,k; -ωσ,ωI,ω2) indicates all permutations of ω2, ω1, and ωσ along with associated indices i, j, and k; and γmg is the damping factor. On the basis of Gaussian 03 calculations and the sum-over-states formula, the self-compiled program was used to obtain the first hyperpolarizabilities, and we have used this method to investigate a series of compounds.34-37 The TDDFT-SOS method considers the ground and excited-state molecular structures because of (µi)gm and (µ j j)ng in the TDDFTSOS formalism. When compared with the FF method, the calculated results of the TDDFT-SOS method are more sensitive to the changing of the molecular structures and can obtain more reliable results. An amount equal to 40 excited states is enough according to the converge curves of SOS method in this work 3. Results and Discussion 3.1. Static Second-Order NLO Properties. Carbazole heterocycles on donor end and various five/six-member heterocycles on acceptor ends are set I (see Figure 1). The first hyperpolarizabilities of all compounds in set I were calculated by the FF and TDDFT-SOS methods at the B3LYP/6-31g(d) level and are shown in Table 1. The results show that the β values are sensitive to the replacement of heterocycles on the acceptor end in comparison with reference compound Ia. Compound If with a thiophene ring on the acceptor end displays a large β value and dipole moment in set I. Introduction of a

7024 J. Phys. Chem. C, Vol. 112, No. 17, 2008

Figure 2. Addition of the dipole moment vectors.

thiophene ring in set I enhances second-order NLO properties; moreover, the second-order NLO properties of these compounds (If and Ig) are related to the changing of their orientation according to TDDFT-SOS calculations. Although compound Ii (thiazole ring on acceptor end) also has a large dipole moment, its β value is smaller than that of reference compound Ia. Breitung et al. reported that the thiazole ring displays a good second-order NLO property in 1D structures,29 but it does not give the large β values in 2D structures in this work, and the matched structure of thiazole in 1D structures does not produce a good second-order NLO property (see Ie). Moreover, the other possible orientation of the thiazole ring has been considered (see Ih and Ii), but the thiazole ring does not display good second-order NLO response in our studies here. The relative orientation of the thiazole ring in set I does not significantly affect second-order NLO response and dipole moment. As mentioned above, compounds If and Ig (with the thiophene ring on the acceptor end) give interesting results. First, the relative orientation of the thiophene ring on the acceptor end significantly affected the dipole moment values. The dipole moment in compound If is larger than that of Ig. How does it display a large dipole moment for compound If? It is wellknown that the dipole moment of D-π-A-like molecules is determined by the D-A strength. The D-A strength of two D-A branches in compound If (see Figure 2) is similar. The angle, ω, between the two dipole moment vectors of D-A branches in If is related to the orientation of the thiophene ring. When compared with compound Ig, the angle ω decreased because of the orientation of the thiophene ring in If. According to the addition of dipole moment vectors, the decrease in angle ω might increase the total dipole moment value of If (see Figure 2). Second, the related orientation of the thiophene ring also affected the β values of compounds If and Ig. According to TDDFT-SOS calculations, compound If displays a large β value, 2.25 times as large as that of compound Ig. Set II (See Figure 1) was obtained by the replacement of the heterocycles on the donor end of set I, which carbazole heterocycles contain three heteroatom atoms. When compared with set I, the β values of analogous structural compounds in set II do not significantly change (such as Ia vs IIa). According to FF and TDDFT-SOS calculations at the B3LYP/6-31G(d) level, compound IIc, which contains the thiophene ring, displays a large second-order NLO response in set II, but the β value of IIc is smaller than that of relevant compound If. When compared with the reference compound IIa, the β values of set II are not sensitive to the replacement of heterocycles on the acceptor end. The orientation of the thiophene ring also affects the dipole moment and β values in set II. Compound IIc displays a large dipole moment and β value according to the TDDFT-SOS calculations. The introduction of two nitrogen atoms in set II does not gain a strong electron auxiliary donor. Set III (see Figure 1) was obtained by introducing four heteroatoms (two nitrogen atoms and two sulfur atoms) into carbazole heterocycles as auxiliary donors and various five/sixmember heterocycles as auxiliary acceptors. The first hyperpolarizabilities of all compounds of set III are shown in Table 1. The results show that the β values in set III are significantly larger than that of sets I and II. The β value of reference

Liu et al. compound IIIa calculated by FF and TDDFT-SOS methods is ∼4 times as large as that of reference compounds Ia and IIa. For reference compound IIIa, the enhancement of the β value is mainly due to the replacement of the heterocycles on the donor end. The carbazole heterocycle containing two nitrogen atoms and two sulfur atoms displays a good second-order NLO response. In set III, in comparison with reference compound IIIa, the replacement of the heterocycles on the acceptor also affected the second-order NLO responses, but the enhancement of second-order NLO properties are weaker than that of replacement of the heterocycle on the donor end according to the FF and TDDFT-SOS calculations at the B3LYP/6-31G(d) level. The β value of compound IIIh with six-member heterocycles on the acceptor end is 1.36 and 2.55 times as large as that of reference compound IIIa by FF and TDDFT-SOS calculations, respectively. The orientation of the thiophene and the pyridazine ring affects the second-order NLO properties and dipole moments of compounds IIIb, IIIc, IIIf, and IIIg in set III, but the orientation of the thiazole ring does not affect the secondorder NLO properties and dipole moments of compounds IIId and IIIe. A large off-diagonal β tensor component of these compounds is an important factor in determining 2D NLO properties. As mentioned above, the βxxx and βxyy components are larger than the corresponding βxzz because of the molecular Cartesian coordinates (see Table 1). The βxxx and βxyy components are comparable in magnitude for each molecule, which can display their 2D NLO properties. The results indicate that the absolute values of βxyy are much larger than that of βxxx for the molecules in set III. The largest βxxx/βxyy value in set III is 4.7 (IIIe), whereas βxxx/βxyy values in sets I and II are smaller than that of set III according to TDDFT-SOS calculations (see Table 1). For these compounds with the same auxiliary electron acceptor in sets I, II, and III, their molecular structures are not significantly changed, and the angle between the two charge transfer axes is not largely changed. But the βxxx/βxyy values significantly changed; for example, the reference compounds in every set, in which the βxxx/βxyy values of IIIa, IIa, and Ia are 3.9, 0.9, and 1.2 respectively. Obviously, the enhancement of βxxx/βxyy values in set III is related to the changing of the electronic auxiliary donor; thus, the carbazole heterocycle containing two nitrogen atoms and two sulfur atoms also displays a good 2D second-order NLO response, which generated a large off-diagonal β tensor component in the relevant compound. 3.2. Consideration of the Related Orientation of the Thiophene Ring. As mentioned above, the changing of orientation of the thiophene ring would affect the dipole moment of the related compound. Compounds If, IIc, and IIIb display large dipole moments and second-order NLO properties, respectively. Moreover, the two planar conformations of thiophene compounds in each set will interchange rapidly in solution at room temperature by rotating the C-N bond (such as If and Ig, see Figure 3). Our calculations show that the dipole moment and absorption character between the two compounds are different and that the transition energy and oscillator strength of maximal absorption of If are smaller than that of Ig. It is well-known that the measurement of UV-visible absorption spectrum only probes an average of these conformations under room temperature. Thus, our TDDFT calculations can separately probe the electronic spectra of these two configurations.38 On the basis of the complex SOS expression, Oudar and Chemla established a simple link between β and a low-lying

Two-Dimensional Carbazole-Cored Chromophores

J. Phys. Chem. C, Vol. 112, No. 17, 2008 7025

Figure 3. TDDFT and single-point energy results at theB3LYP/6-31g(d) level for planar conformations of compounds If and Ig in the gas phase.

TABLE 3: Results of TDDFT Calculations at B3LYP/ 6-31g(d) Level for the Electron Transitions of All Compounds excited state

Ege(eV)

µge(a.u.)

Ia Ib Ic Id Ie If Ig Ih Ii

S3 S3 S3 S3 S3 S1 S1 S7 S3

2.893 2.752 2.618 2.811 2.751 2.412 2.455 3.213 2.751

Set I -3.7450 HOMO f LUMO(100%) -4.0561 HOMO f LUMO(100%) -3.9185 HOMO f LUMO(100%) -4.3712 HOMO f LUMO(100%) -3.8862 HOMO f LUMO(100%) -3.9677 HOMO f LUMO(100%) -4.3647 HOMO f LUMO(92.4%) -3.4488 HOMO f LUMO(100%) -3.7110 HOMO f LUMO(100%)

1.676 2.172 2.240 2.418 1.996 2.706 3.161 1.152 1.820

IIa IIb IIc IId IIf

S3 S3 S3 S3 S3

2.853 2.591 2.558 2.622 2.572

Set II -3.5258 HOMO f LUMO(100%) -3.9291 HOMO f LUMO(100%) -3.4140 HOMO f LUMO(100%) -3.8970 HOMO f LUMO(100%) -3.2834 HOMO f LUMO(100%)

1.527 2.300 1.781 2.209 1.630

IIIa IIIb IIIc IIId IIIe IIIf IIIg IIIh

S1 S1 S1 S1 S1 S1 S1 S1

0.7595 0.6502 0.6317 0.5366 0.5478 0.6450 0.6075 0.4167

Set III -2.5109 HOMO f LUMO(92.1%) -2.5338 HOMO f LUMO(90.6%) -2.6608 HOMO f LUMO(90.5%) -2.5278 HOMO f LUMO(92.8%) -2.3132 HOMO f LUMO(92.8%) -2.3368 HOMO f LUMO(91%) -2.4179 HOMO f LUMO(90.9%) -2.1739 HOMO f LUMO(91.6%)

10.930 15.186 17.742 22.191 17.831 13.126 15.841 27.216

compd

Figure 4. Frontier molecular orbital energies of all compounds: set I (9), set II (O), and set III (f).

TABLE 2: Mulliken Charge of Carbazole Heterocycles Donor and Nitryl Acceptor Moieties in Gas Phase and Acetonitrile donor

acceptor

compd

gas

acetonitrile

gas

acetonitrile

IIIa IIIb IIIc IIId IIIe IIIf IIIg IIIh

0.461 0.496 0.503 0.567 0.595 0.509 0.531 0.680

0.493 0.593 0.572 0.714 0.772 0.660 0.642 0.940

-0.400 -0.384 -0.393 -0.382 -0.377 -0.331 -0.331 -0.281

-0.458 -0.462 -0.468 -0.451 -0.451 -0.387 -0.387 -0.349

charge-transfer transition through the two-level model.39,40 The static first hyperpolarizability is expressed by the following expression:41

β ∝ (µee - µgg)

µ2ge E 2ge

(4)

where µgg and µee are the ground and excited-state dipole moments, µge is the transition dipole, and Ege is the transition energy. Hence, as a guideline, the two-level model requires wellperforming NLO chromophores that possess a low-energy CT excited state with large oscillator strength.42 Three factors (µee - µgg, Ege, and µge) are all intimately correlated and are

major contributions

µge2/Ege2

controlled by the electronic properties of the D/A and the length of conjugate bridge.43 For example, increasing the conjugation bridge length, in general, results in an increase in the magnitude of the ground-to-excited-state change in dipole moment, which concomitantly diminishes the square of the dipole matrix element and decreases the square of the CT transition energy. Thus, the optimal combination of the factors will provide the maximal β value. On the other hand, the simplified two-level picture can be used to understand the sign of the β value.44 If the two-level model holds a negative β value, only the µee µgg term can afford a negative value. The sign of the β values of all compounds is negative, and the ground-state dipole moments of all compounds are positive in set I∼III. If the excited-state dipole moment is aligned in the same direction as the ground-state dipole moment, the excited-state dipole moment must be smaller than that of the ground state. The solvatochromic azobenzene bridging units are powerful acceptors and have been successfully used in development of NLO molecular materials because of the charge asymmetry.45,46 Solvatochromic compounds can be described by two extreme resonance contributing structures: one form is quinoidal,

7026 J. Phys. Chem. C, Vol. 112, No. 17, 2008

Liu et al.

Figure 5. Frontier molecular orbital of reference compounds (Ia, IIa, IIIa).

nonpolarized, and formally nonaromatic; the other is zwitterionic, polarized, and fully aromatic. The UV-visible absorption spectra of some compounds (Ia, Ib, Ic, Id) in this work are measured.47 The results show that the absorption bands at 350700 nm are attributed to the πfπ* transition of the azo conjugated unit. The effect of different polar solvents on the position, shape, or intensity of absorption bands of a molecule has been determined according to the UV-visible spectrum, and the result suggests that the absorptions show blue-shifted (negative solvatochromism) in different polar solvents. The negative solvatochromic phenomena of these compounds provided strong evidence that these compounds can be viewed as the zwitterions, and the zwitterionic resonance states would dominate the molecular ground states. In order to confirm the zwitterionic structures of set III, the geometrical structures and Mulliken charge of these compounds of set III in acetonitrile have been calculated by using the polarized continuum model (PCM) in the Gaussian 03 program package at the B3LYP/6-31G(d) level. The values obtained for the Mulliken charges in carbazole heterocycle donor and nitryl acceptor moieties are shown in Table 2. The results show that the Mulliken charge absolute values of the donor or acceptor in solution are larger than that of gas-phase structures. Consequently, the zwitterionic character of these compounds is expected on increasing in the polar medium.2 Thus, the results confirmed the zwitterionic assumption. For the zwitterionic

structures, the polar ground state is determined by the zwitterion with a greater dipole moment. The neutral excited state would give a smaller dipole moment, which would give a negative β value. Considering the magnitude of µee - µgg, the large groundstated dipole moment would be favorable to give a larger negative µee - µgg value, and enhance β value. Thus, changing of orientation of the thiophene ring generates a larger groundstated dipole moment and enhances the second-order NLO responses of related compounds. 3.3. The TD-DFT Studies. The TD-DFT calculations were carried out to obtain the excited states of all compounds at the B3LYP/6-31G(d) level. The crucial excited states that significantly contribute to the first hyperpolarizabilities are shown in Table 3. The results show that the order of µge2/Ege2 values is set III > set I ≈ set II, which is in agreement with β values calculated with FF and TDDFT-SOS methods (see Table 3). The µge2/Ege2 values in set III are ∼10 times as large as that of sets I and II. It should be noted that the µge values of set III are smaller than that of sets I and II, but the µge2/Ege2 values of set III are larger than that of set I and set II. Thus, the lower transition energies of set III are the decisive factors and lead to a considerably larger β value of set III. The small transition energies of set III are related to their molecular structures; that is, the carbazole heterocycle containing five heteroatoms is a good auxiliary electron donor. It can be seen that the electron transition in every case included a HOMO f LUMO transition,

Two-Dimensional Carbazole-Cored Chromophores and these transitions (HOMO f LUMO) in every set would be associated with the second-order NLO properties. Figure 4 displays the energies of the HOMO and LUMO of all compounds. Obviously, the energy gaps between HOMO and LUMO (∆EH-L) of set III are lower than that of sets I and II. It is well-known that the decrease of ∆EH-L would enhance the second-order NLO properties. Thus, the compounds in set III display large second-order NLO properties. The question we are now concerned with is the orbital transition properties associated with the crucial exited states. The TDDFT calculations show that these crucial excited states are mainly composed of HOMO f LUMO transitions (see Table 3). We used only reference compounds (Ia, IIa, IIIa) as examples to analyze the role of heterocycles on the donor in the CT process. The HOMO and LUMO of the reference compounds in every set are shown in Figure 5. As expected, HOMO and LUMO are π-orbitals. It can be seen that the electron densities in the HOMOs and LUMOs of reference compounds Ia and IIa are located on the whole molecules. Moreover, the electron densities in the HOMOs of reference compounds Ia and IIa are largely located on the heterocycles on the donor, and the electron densities in the LUMO of reference compounds Ia and IIa are heavily located toward the acceptor and phenylene ring attached to the acceptor. It can be seen that the electron densities in the HOMO of reference compound IIIa are significantly different from that of reference compounds Ia and IIa; that is, the electron densities in the HOMO of reference compound IIIa are wholly located on the heterocyclic donor end, but the electron densities in the LUMO of reference compound IIIa display the same character as that of reference compounds Ia and IIa. Clearly, these excitations mostly consist of CT from the heterocycles on the donor to the phenylene and acceptor. Thus, the structure of reference compound IIIa would enhance the CT extent and displays large second-order NLO properties. The electron densities in the HOMO and LUMO of the other molecules in every set have been analyzed, and the replacement of the heterocycles on the acceptor did not largely affect the electron densities in the HOMO and LUMO. The transitions between occupied and unoccupied orbitals, which contributed to the crucial excited state, are found to have the same feature throughout every set studied here. Thus, the structures of set III enhance the CT extent and generate a large second-order NLO response. 4. Conclusions In this study, we report the first hyperpolarizabilities of a series of 2D carbazole-cored chromophores. The first hyperpolarizabilities of all compounds have been analyzed according to FF and TDDFT-SOS calculations at the B3LYP/6-31G(d) level. The results indicate that a large first hyperpolarizability has been obtained in set III. The low transition energy and large CT extent are the decisive factors to cause a large first hyperpolarizability in set III. The orientation of the thiophene ring has been probed according to the two-level model. The ground and excited-stated structures of zwitterions are the key factors in determining β values. The main conclusion of this study is that carbazole heterocycles containing five heteroatoms are a strong auxiliary electron donor in 2D structures. Acknowledgment. This work was supported by the Program for Changjiang Scholars and Innovative Research Team in

J. Phys. Chem. C, Vol. 112, No. 17, 2008 7027 University, the foundation of Jilin provincial Excellent Youth (Grant No. 20050107) and the Youth Science Foundation of Northeast Normal University (Grant No. 20060314). Supporting Information Available: Converge curves of the SOS method for all compounds in this work. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Geskin, V. M.; Lambert, C.; Bredas, J. L. J. Am. Chem. Soc. 2003, 125, 15651. (2) Andreu, R.; Blesa, M. J.; Carrasquer, L.; Garin, J.; Orduna, J.; Villacampa, B.; Alcala, R.; Casado, J.; Delgado, M. C. R.; Navarrete, J. T. L.; Allain, M. J. Am. Chem. Soc. 2005, 127, 8835. (3) Humphrey, J. L.; Lott, K. M.; Wright, M. E.; Duciauskas, D. J. Phys. Chem. B 2005, 109, 21497. (4) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Organic Molecules and Polymers; Wiley: New York, 1991. (5) Liao, Y.; Eichinger, B. E.; Firestone, K. A.; Haller, M.; Luo, J.D.; Kaminsky, W.; Benedict, J. B.; Reid, P. J.; Alex, K.-Y.; Dalton, L. R.; Robinson, B. H. J. Am. Chem. Soc. 2005, 127, 2758. (6) Dalton, L. R. AdV. Polym. Sci. 2002, 158, 1. (7) Saadeh, H.; Wang, L.; Yu, L. J. Am. Chem. Soc. 2000, 122, 546. (8) Zhu, P.; Kang, H.; Facchetti, A.; Evmenenko, G.; Dutta, P.; Marks, T. J. J. Am. Chem. Soc. 2003, 125, 11496. (9) Yang, M. L.; Champagne, B. J. Phys. Chem. A 2003, 107, 3942. (10) Zyss, J.; Oudar, J. L. Phys. ReV. A: At., Mol., Opt. Phys. 1982, 26, 2028. (11) Kou, W. J.; Hsiue, G. H.; Jeng, R. J. Macromolecules 2001, 34, 2373. (12) Yamamoto, H.; Datogi, S.; Watanabe, T.; Sato, H.; Miyata, S.; Hosomi, T. Appl. Phys. Lett. 1992, 60, 935. (13) Srinivas, K.; Sitha, S.; Rao, V. J.; Bhanuprakash, K. Opt. Mater. 2006, 28, 1006. (14) Moylan, C. R.; Ermer, S.; Lovejoy, S. M.; McComb, I.-H.; Leung, D. S.; Wortmann, R.; Krdmer, P.; Twieg, R. J. J. Am. Chem. Soc. 1996, 118, 12950. (15) Liu, Y. J.; Liu, Y.; Zhang, D. J.; Hu, H. Q.; Liu, C. B. J. Mol. Struct. 2001, 570, 43. (16) Moylan, C. R.; Twieg, R. G.; Lee, V. Y.; Swanson, S. A.; Betterton, K. M.; Miller, R. D. J. Am. Chem. Soc. 1993, 115, 12599. (17) Coe, B. J. Acc. Chem. Res. 2006, 39, 383. (18) Coe, B. J.; Harris, J. A.; Jones, L. A.; Brunschwig, B. S.; Song, K.; Clays, K.; Garin, J.; Orduna, J.; Coles, S. J.; Hursthouse, M. B. J. Am. Chem. Soc. 2005, 127, 4845. (19) Coe, B. J.; Harris, J. A.; Brunschwig, B. S.; Asselberghs, I.; Clays, K.; Garin, J.; Orduna, J. J. Am. Chem. Soc. 2005, 127, 13399. (20) Wolff, J. J.; Langle, D.; Hillenbrand, D.; Wortmann, R.; Matschiner, R.; Glania, C.; Kriirner, P. AdV. Mater. 1997, 9, 138. (21) Cui, Y. Z.; Qi, F.; Huang, Z. L.; Xue, G.; Yu, W. T.; Lei, H. Opt. Mater. 2005, 27, 1571. (22) Ostroverkhov, V.; Petschek, R. G.; Singer, K. D.; Twieg, R. J. Chem. Phys. Lett. 2001, 340, 109. (23) Di Bella, S.; Fragala, I.; Ledoux, I.; Diaz-Garcia, M. A.; Marks, T. J. J. Am. Chem. Soc. 1997, 119, 9550. (24) Di Bella, S.; Fragala, I.; Ledoux, I.; Zyss, J. Chem.sEur. J. 2001, 7, 3738. (25) Shi, Y. Q.; Zhang, C.; Zhang, H.; Bechtel, J. H.; Dalton, L. R.; Robinson, B. H.; Steier, W. H. Science. 2000, 288, 119. (26) Varanasi, P. R.; Jen, A. K.-Y.; Chandrasekhar, J.; Namboothiri, I. N. N.; Rathna, A. J. Am. Chem. Soc. 1996, 118, 12443. (27) Albert, I. D. L.; Marks, T. J.; Ratner, M. A. J. Am. Chem. Soc. 1997, 119, 6575. (28) Albert, I. D. L.; Marks, T. J.; Ratner, M. A. Chem. Mater. 1998, 10, 753. (29) Breitung, E. M.; Shu, C. F.; McMahon, R. J. J. Am. Chem. Soc. 2000, 122, 1154. (30) 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, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D.

7028 J. Phys. Chem. C, Vol. 112, No. 17, 2008 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. (31) Sim, F.; Chin, S.; Dupuis, M.; Rice, J. E. J. Phys. Chem. 1993, 97, 1158. (32) Dehu, C.; Meyers, F.; Bredas, J. L. J. Am. Chem. Soc. 1993, 115, 6198. (33) Matsuzawa, N.; Dixon, D. Int. Quant. Chem. 1992, 44, 497. (34) Yang, G. C.; Fang, L.; Tan, K.; Shi, S. Q.; Su, Z. M.; Wang, R. S. Organometallics 2007, 26, 2082. (35) Yang, G. C.; Su, Z. M.; Qin, C. S. J. Phys. Chem. A 2006, 110, 4817. (36) Guan, W.; Yang, G. C.; Yan, L. K.; Su, Z. M. Inorg. Chem. 2006, 45, 7864. (37) Yan, L. K.; Yang, G. C.; Guan, W.; Su, Z. M.; Wang, R. S. J. Phys. Chem. B 2005, 109, 22332.

Liu et al. (38) Coe, B. J.; Harris, J. A.; Hall, J. J.; Brunschwig, B. S.; Hung, S. T.; Libaers, W.; Clays, K.; Coles, S. J.; Horton, P. N.; Light, M. E.; Hursthouse, M. B.; Garin, J.; Orduna, J. Chem. Mater. 2006, 18, 5907. (39) Oudar, J. L. J. Chem. Phys. 1977, 67, 446. (40) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (41) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. ReV. 1994, 94, 195. (42) Kanis, D. R.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 1992, 114, 10338. (43) Zhang, T. G.; Zhao, Y.; Asselberghs, I.; Persoons, A.; Clays, K.; Therien, M. J. J. Am. Chem. Soc. 2005, 127, 9710. (44) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. ReV. 1994, 94, 217. (45) Gibson, H. W. Tetrahedron 1977, 77, 6789. (46) Buncel, E.; Rajagopal, S. Acc. Chem. Res. 1990, 23, 226. (47) Qian, Y.; Xiao, G. M.; Wang, G.; Sun, Y. M.; Cui, Y. P.; Yuan, C. W. Dyes Pigm. 2006, 71, 109.