Rational Design Using Dewar's Rules for Enhancing the First

Dec 1, 2010 - We study the effect of various electron-donating and -withdrawing groups ... The accuracy and validity of the two-state model are discus...
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J. Phys. Chem. C 2010, 114, 22284–22288

Rational Design Using Dewar’s Rules for Enhancing the First Hyperpolarizability of Nonlinear Optical Chromophores Jane Hung,† Wenkel Liang,† Jingdong Luo,‡ Zhengwei Shi,‡ Alex K.-Y. Jen,‡ and Xiaosong Li*,† Department of Chemistry, UniVersity of Washington, Seattle, Washington 98195-1700, United States, and Department of Materials Science and Engineering, UniVersity of Washington, Seattle, Washington 98195-2120, United States ReceiVed: August 17, 2010; ReVised Manuscript ReceiVed: October 18, 2010

A rational material design based on Dewar’s predictions is introduced in this paper. A number of conjugationbridge-modified phenylpolyene chromophores were proposed as candidates for nonlinear optical chromophores. Hyperpolarizabilities of these candidates were calculated using density functional theory with a two-state model and finite-field methods. Significant enhancement with up to 72% increase in the first hyperpolarizability was observed. Another design mechanism using the bond length alternation analysis was proposed and supported by the study. In addition to the strength of the acceptor and donor, and the positions modifying the electron delocalization pathway, the density of lower lying excited states is shown to play an important role in the molecular hyperpolarizability. Increasing the density of lower lying excited states can be an effective approach in the design of highly nonlinear chromophores. I. Introduction The research of highly efficient organic electro-optic (E-O) materials is continuously driven by the potential applications in optical telecommunications, signal processing, data storage, image reconstruction, logic technologies, and optical computing.1-5 In principle, large molecular hyperpolarizability (β) of a π-conjugated donor-acceptor (D-A) chromophore usually leads to large bulk E-O response of a material. It is known that the β value is primarily associated with the intramolecular chargetransfer (ICT) transition, which depends on the strength of the donor and acceptor moieties, and on the electronic characteristics of the π-conjugated bridge through which they interact.6,7 Considerable progress has been made on the development of large β chromophores with newly exploited donors and acceptors.8-10 However, due to the complexity of the problem, relatively little success has been reported for directional π-electron delocalization from electron donors to electron acceptors along the π-conjugated bridge. For example, polyenic spacers constitute one of the most efficient conjugated bridges and displays large β arising from the energetically favored ICT electron relay. However, the flexibility for further modification is very limited.11,12 Classical theories, such as Dewar’s rules,13 have been used to optimize the molecular design for efficient and stable chromophores.14-16 According to Dewar’s rules, a π-conjugated bridge in a D-A chromophore (e.g., the phenylpolyene base chromophore in Figure 1) exhibits alternating electronegativities along the charge-transfer direction. This behavior can be used to predict the relationships of molecular energy levels with substitution positions and the nature of substitution groups (Figure 2), based on perturbational molecular orbital theory. For example, the substitution of an electron-withdrawing group at an unstarred position (i.e., 1 and 7 in Figure 1) would decrease * Corresponding author, [email protected]. † Department of Chemistry. ‡ Department of Materials Science and Engineering.

Figure 1. Depiction of phenylpolyene base chromophore. Substitution positions on the conjugated backbone are divided into starred (2*, 4*, 6*, 8*) and unstarred (1, 7) groups according to Dewar’s convention. Note that substitutions on the site chain are considered starred positions (3* 5*).

the energy level of the lowest unoccupied molecular orbital (LUMO). Similarly, an electron-donating group at a starred position (i.e., 2*, 4*, 6*, and 8* in Figure 1) would increase the energy level of the highest occupied molecular orbital (HOMO). In both cases, there is a bathochromic shift of the absorption spectra. On the other hand, substitution of an electron-withdrawing group at a starred position would lead to a lower energy level of the HOMO; substitution of an electrondonating group at an unstarred position would lead to a higher energy level of the lowest unoccupied molecular orbital (LUMO), and both substitutions would result in a hypsochromic shift of the absorption spectrum. In a previous experimental study guided by Dewar’s rules, a mild electron-withdrawing group, sulfur,16 and an electron-

10.1021/jp107803q  2010 American Chemical Society Published on Web 12/01/2010

Nonlinear Optical Chromophores

Figure 2. A schematic description of Dewar’s rules.

donating group, oxygen,17 were introduced into the starred position of the π-conjugated bridge, respectively. A dramatic increase of molecular hyperpolarizability and enhanced chemical and photochemical stability was observed experimentally. These results support predictions of Dewar’s rules and thus support the use of Dewar’s rules as a rational design concept for molecular engineering of dipolar push-pull phenyltetraenebased chromophores. Recently, Chafin and Lindsay have used density functional theory (DFT) calculations to study a polyene dye scaffold. In their study, the end groups and bridge length were maintained but the pattern of electron-donating and electron-withdrawing substituents along the polyene bridge was varied.18 Their results indicated that the basic pattern leading to an increase of the first hyperpolarizability was electron-withdrawing substituents on even-numbered methine carbons and donating substituents on odd-numbered methines. These theoretical and experimental investigations suggest that substituent groups play a critical role in affecting the nonlinearity and stability of push-pull polyene chromophores, which could provide a general tool to guide the future molecular design of highly efficient nonlinear optical (NLO) chromophores. In this contribution, we present a systematic computational study to search for molecular candidates that are associated with large hyperpolarizabilities. We study the effect of various electron-donating and -withdrawing groups substituted on the π-conjugated bridge based on Dewar’s rules. Both a two-state model and finite-field methods are used to compute the hyperpolarizabilities. The accuracy and validity of the two-state model are discussed and compared to the finite-field method, and the importance of lower lying excited states in addition to HOMO f LUMO transition will be illustrated. II. Methodology All chromophore structures were optimized using the development version of the GAUSSIAN series of programs19 with the hybrid generalized gradient density functional, B3LYP,20 and 6-31G(2df) basis set. Excited state properties were obtained using the linear response time-dependent density functional theory (TDDFT).21 Excitation energies, transition dipoles, and ground and excited state dipole moments were calculated using the optimized ground state geometry. Although there are general concerns regarding the accuracy of the B3LYP method for dipole moments and hyperpolarizabilities for large pull-push systems,29,30 a recent study has shown that the B3LYP method is reliable for chromophores with fewer than six single-double bond paris28 and has also shown consistent assessment of relative properties of similar chromophore systems.18,28 In addition, a basis set with diffuse functions is recommended for studies of

J. Phys. Chem. C, Vol. 114, No. 50, 2010 22285 nonlinear optical properties. For a select set of chromophores presented herein, the hyperpolarizabilities computed using a basis set with diffuse functions, 6-31+G(2p,2d), are only 6-10% larger than the those calculated with the 6-31G(2p,2d) basis set, though at a much larger computational cost. A dipolar push-pull phenylpolyene-based model chromophore (Figure 1) is used as the conjugation backbone structure in this study. To investigate the effect of the modified conjugation bridge on the optical properties of the chromophore, a number of electron-donating (-OCH3, phenoxide, -NH2, and -N(CH3)2) and -withdrawing (-SCH3, -COCH3, and -CN, and -F) group substitutions at different positions along the conjugation bridge are studied. Possible substitution positions are divided into starred and unstarred groups following Dewar’s convention. In this article, we use two different methods to compute the first-order hyperpolarizability. The first method is based on the sum-over-states (SOS) approach22 and simplified to the twostate model,23,24 assuming a single excited state dominates the linear and nonlinear molecular optical responses. In the twostate model, the static molecular-axis (x-axis) component of the first-order hyperpolarizability can be estimated as

βxxx

2 3 µx,ge(µx,e - µx,g) ) 2 E2

(1)

ge

where Ege is the excitation energy, µge is the transition dipole, µe is the excited state dipole, and µg is the ground state dipole. We also compute the first-order hyperpolarizability using the coupled-perturbed density functional theory (CP-DFT) approach with a finite field.25-27 The purpose of using finite-field calculations is to illustrate mechanisms governing high β values that are beyond the simple description of the two-state model. Direct finite field calculations are performed here with a small field strength of 0.0003 au applied along the (x, (y, and (z directions. The static first hyperpolarizability β in the direction of the molecular dipole moment can be calculated by18,28

∑

βµ ) βi )

∑

µiβi

i)x,y,z

|µ|

1 (β + βjij + βjji) 3 j)x,y,z ijj

(2a)

(2b)

Note that if the molecular axis is defined along the x direction, the βxxx in the two-state model of eq 1 becomes the dominant term in eq 2a. The above two methods will be used to evaluate the first hyperpolarizabilities in conjugation-bridge-modified chromophores. III. Results and Discussion Figure 3 shows the HOMO and LUMO of the phenylpolyene base chromophore (Figure 1). The HOMO f LUMO transition has the characteristics of intramolecular charge transfer from donor to acceptor. Such a transition is usually associated with large transition dipole moment and significantly contributes to molecular susceptibilities. To investigate how a chemically modified conjugation backbone affects first hyperpolarizabilities, different positions on the polyene backbone were substituted by the widely used electron-donating group OCH3 and -with-

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Hung et al. TABLE 2: Calculated Dipole Moments, Excitation Energy, and β Strength of Single Substitutions with Select Electron-Donating and -Withdrawing Groups on Optimal Starred/Unstarred Positions βxxxa βxxxb βµb µge |µe - µg| Ege groups position (D) (eV) (×10-30 esu) (×10-30 esu) (×10-30 esu) (D) base OCH3 NH2 O-C6H5 N(CH3)2 F CdOCH3 SCH3 CN

2* 2* 2* 2* 2* 7 7 7

17.06 16.28 15.41 16.58 14.75 16.49 12.56 13.54 15.96

9.22 10.79 9.12 9.16 9.93 10.28 17.76 15.41 9.00

1.99 1.92 1.74 1.95 1.81 1.92 1.84 1.87 1.82

1021 1160 1075 993 990 1141 1247 1212 1036

968 1115 1342 977 1254 1145 1219 1155 1142

898 1040 1265 963 1186 1052 1161 1142 1138

a Calculated using the two-state model (eq 1). b Calculated using the finite field method (eq 2a).

Figure 3. HOMO and LUMO of the phenylpolyene base chromophore.

TABLE 1: Calculated Dipole Moments, Excitation Energy, and β Strength of Single Substitutions on Conjugated Backbone with Electron Donor (OCH3) and Electron Acceptor (CdOCH3) βxxxa βxxxb βµb µge |µe - µg| Ege groups position (D) (D) (eV) (×10-30 esu) (×10-30 esu) (×10-30 esu) base OCH3

CdOCH3

1 2* 3* 4* 5* 6* 7 8* 1 2* 3* 4* 5* 6* 7 8*

17.06 15.87 16.28 17.34 16.61 16.63 17.23 14.61 17.12 14.73 15.99 16.95 16.94 16.76 17.27 12.56 17.46

9.22 11.20 10.79 8.04 9.48 9.55 8.34 12.55 9.12 13.42 12.50 9.05 9.35 8.67 8.62 17.76 8.08

1.99 2.04 1.92 1.97 1.93 1.94 1.95 2.05 1.96 1.94 1.99 1.98 1.97 1.92 1.97 1.84 1.98

1021 1019 1160 934 1057 1058 980 955 1047 1166 1214 995 1037 995 990 1247 944

968 774 1115 927 1062 1064 994 843 1012 959 1022 931 990 1025 963 1219 925

898 710 1040 871 984 993 925 751 953 903 941 865 910 941 892 1161 865

occurs at the starred position 2* closest to the electron donor terminal. Similarly, with an electron-withdrawing group, substitution at the unstarred position 7 closest to the acceptor terminal leads to the strongest red shift. Both the two-state model (eq 1) and perturbative calculations (eq 2b) predicted these phenomena although the detailed values vary from case to case. This observation suggests that the most important contribution to the first hyperpolarizability is the charge-transfer transition to the first excited state, which has dominant character of HOMO f LUMO transition. The observed increases in the first hyperpolarizability are from the enhanced charge transfer transitions by increasing electron-donating or -accepting abilities of the terminal groups, as indicated by the large change in dipole moment between the ground and first excited state. A set of characteristic electron-donating/withdrawing groups was also analyzed, and the optimal positions for the largest β value are listed in Table 2. For all electron-donating groups considered herein, the optimal position for the largest β value is the starred position nearest to the donor terminal. Note that the fluorine is a π-donating group in the case considered here. Among various electron-donating groups, the -NH2 and -N(CH3)2 groups lead to the largest increase in β value, associated with lower excitation energy. This observation can be approximately correlated with the Hammett’s substitution constant σ (σ ) -0.27 for OCH3, σ ) -0.66 for NH22, σ ) -0.83 for N(CH3)2)31 as the more negative σ indicates stronger

a Calculated using the two-state model (eq 1). b Calculated using the finite field method (eq 2a).

drawing group COCH3. Table 1 lists calculated excitation energies, Ege, of the first excited state computed with the linear response TDDFT. We also include transition dipoles, µge, from TDDFT calculations and the difference in static dipole moments, |µe - µg|, between the ground and first excited electronic states for calculations of hyperpolarizabilities using the two-state model in eq 1. Static dipole moments are calculated using selfconsistent-field converged electron densities for both the ground and first excited states. For electron-donating group (OCH3) substituted structures, absorption spectra (excitation energy) are red-shifted at starred substitution positions (2*, 3*, 4*, 5*, 6*, 8*), and blue-shifted at unstarred positions (1, 7), in excellent agreement with the Dewar’s rules. Note that substitution positions 3 and 5 are equivalent to starred positions, although they are not directly on the conjugation backbone. These positions are considered herein because they provide additional possibilities to modify electronic structures with desired morphology. With an electrondonating substituent group, the largest absorption spectrum shift

Figure 4. Calculated hyperpolarizabilities from the two-state model (βxxxt) and the finite field method (βxxxf) plotted as a function of first excitation energy. A polynomial fitting provides guides to the eye.

Nonlinear Optical Chromophores

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Figure 5. Calculated absorption spectra for -CN, -NH2, and -O-C6H5 substituted chromophores. Gaussian broadening of 0.12 is applied to theoretical absorption peaks.

electron-donating properties. For electron-withdrawing groups, substitutions at the unstarred position closest to the acceptor lead to the largest increase in β value. The finite-field method calculated βxxx value exhibits a strong correlation with the excitation energy (Figure 4). On the other hand, βxxx values calculated using the two-state model do not agree with results from finite-field calculations. This suggests that other lower lying excited states also contribute to the hyperpolarizability, although the dominant contribution is from the lowest excited state. Figure 5 compares the absorption spectra for -CN, -NH2, and -O-C6H5 substituted chromophores. The lowest excited state in the -O-C6H5 substituted molecule displays a single dominant absorption peak, while there are multiple lower lying absorption peaks in -CN or -NH2

substituted cases. As a result, the lowest excited state in -O-C6H5 substituted chromophore contributes most to the optical properties, and the two-state model predicts reasonably accurate hyperpolarizability. In contrast, other lower lying excited states in -CN or -NH2 substituted chromophores have significant contributions to the absorption spectra. With such broad excited state energy profiles, the simple approximation in the two-state model is expected to miss important effects and mechanisms from other electronic excitations beyond the first excited state. Analysis above suggests that hyperpolarizabilities can be significantly enhanced by modifying the conjugation backbone with either electron-donating or -accepting groups. The optimal position to enhance β strength for electron-donating groups is the starred position 2* closest to the donor terminal and for electron-withdrawing groups is the unstarred position 7 nearest to the acceptor terminal. An intuitive thought is to introduce a pair of electron-donating and -withdrawing groups to create an even larger hyperpolarizability. We investigated a number of double substitution schemes with both donating and withdrawing groups added to the conjugated carbon bridge at their optimal positions, and the calculation results are listed in Table 3. With double substitutions, the β value can be further enhanced compared to that in single substitution cases. The largest hyperpolarizability is observed in the -CN and -NH2 doubly substituted chromophore, with a 72% increase in β value compared to that of the unmodified case. As discussed previously, this large enhancement arises from additional contributions from large density of states of lower lying excited states induced by both -CN and -NH2 groups. To better understand the effectiveness of single and double substitutions with various electron-donating/withdrawing groups on the enhancement of chromophore hyperpolarizability, we correlate the polarization results with bond length alternation (BLA) measurements. The BLA is the difference between the average bond lengths of odd- and even-numbered carbon-carbon bonds on the conjugation bridge. The BLA measurement is often considered a major factor in describing the electronic structure and charge transport properties of π-conjugated polymers.15,32,33 Figure 6 shows the finite-field method calculated hyperpolarizabilities as a function of BLA. A strong correlation is observed between the calculated β strength and BLA for all chromophores considered herein. This observation suggests that the classical properties of conjugated systems, such as the BLA, can be directly used to predict the strength of hyperpolarizabilities. IV. Conclusion In this study, we have investigated the effect of perturbational substitutions on the conjugation bridge of phenylpolyene-based

TABLE 3: Calculated Dipole Moments, Excitation Energy and β Strength of Double Substitutions with Select Electron-Donating and -Withdrawing Groups on Starred/Unstarred Positions groups

position/ type

µge (D)

|µe - µg| (D)

Ege (eV)

βxxxa (×10-30 esu)

βxxxb (×10-30 esu)

βµb (×10-30 esu)

base OCH3 + CdOCH3 OCH3 + CdOCH3 OCH3 + CdOCH3 OCH3 + CdOCH3 OCH3 + CN OC6H5 + CdOCH3 OC6H5 + CN N(CH3)2 + CdOCH3 NH2 + CdOCH3 NH2 + CN

(2*, 1) (2*, 7) (4*, 1) (4*, 7) (2*, 7) (2*, 7) (2*, 7) (2*, 7) (2*, 7) (2*, 7)

17.06 6.79 11.63 14.11 11.91 15.25 11.70 15.27 11.18 10.04 13.58

9.22 33.96 20.05 14.53 19.02 10.08 20.55 10.38 18.64 22.33 10.50

1.99 1.64 1.76 1.88 1.77 1.75 1.80 1.77 1.66 1.57 1.56

1021 875 1315 1230 1287 1146 1302 1160 1267 1364 1190

968 886 1337 1067 1306 1305 1282 1295 1435 1553 1586

898 809 1257 1010 1242 1277 1218 1276 1346 1422 1545

a

Calculated using the two-state model (eq 1). b Calculated using the finite field method (eq 2a).

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Figure 6. Calculated hyperpolarizabilities (βµ) from the finite-field method plotted as a function of bond length alternation. A polynomial fitting provides guides to the eye.

NLO chromophores with electron-donating and -withdrawing groups. Single substitutions of electron-donating (withdrawing) groups on the starred (unstarred) position closest to the donor (acceptor) terminal can result in a significant increase in the β value. Double substitutions on the conjugation polyene bridge can further enhance β compared to that of single-substituted cases. The best performing double-substituted chromophores exhibit large β strength with up to ∼72% increase compared to the base structure. The strong correlation between the β value and the bond length alternation measurement can be used to predict the strength of hyperpolarizabilities. In comparison to finite-field calculations, the simple twostate model can correctly predict the hyperpolarizabilities only when the low-energy excitations are strongly dominated by a single state. In addition to the strength of acceptor and donor, and positions for modifying the electron delocalization pathway, the density of lower lying excited state is shown to play an important role in the strength of molecular hyperpolarizability. This observation can lead to a new design concept by increasing the density of lower lying excited states for increased hyperpolarizability. Acknowledgment. This work was supported by the National Science Foundation under CHE-CAREER 0844999 to X.L. and NSFSTC program under Agreement Number DMR-0120967. J. Hung thanks the Mary Gates Foundation, NASA Space Grant Consortium, and Washington Research Foundation for research scholarships. Additional support from Gaussian, Inc., and the University of Washington Student Technology Fund is gratefully acknowledged. Alex K.-Y. Jen thanks the Boeing-Johnson Foundation for its support. References and Notes (1) Chang, C. C.; Chen, C. P.; Chou, C. C.; Kuo, W. J.; Jeng, R. J. J. Macromol. Sci., Polym. ReV. 2005, C45, 125. (2) Hochberg, M.; Baehr-Jones, T.; Wang, G.; Shearn, M.; Harvard, K.; Luo, J.; Chen, B.; Shi, Z.; Lawson, R.; Sullivan, P.; Jen, A. K. Y.; Dalton, L.; Scherer, A. Nat. Mater. 2006, 5, 703.

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