Rational Design Using Dewar’s Rules for Enhancing the First Hyperpolarizability of NLO...

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Rational Design Using Dewars Rules for Enhancing the First Hyperpolarizability of

Nonlinear Optical Chromophores

Jane Hung, Wenkel Liang, Jingdong Luo, Zhengwei Shi, Alex K.-Y. Jen, andXiaosong Li*,

Department of Chemistry, UniVersity of Washington, Seattle, Washington 98195-1700, United States, andDepartment 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 Dewars predictions is introduced in this paper. A number of conjugation-

bridge-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 () o f a-conjugated donor-acceptor (D-A) chromophore usually leadsto large bulk E-O response of a material. It is known that the value is primarily associated with the intramolecular charge-

transfer (ICT) transition, which depends on the strength of the

donor and acceptor moieties, and on the electronic characteristicsof the -conjugated bridge through which they interact.6,7

Considerable progress has been made on the development of

large chromophores with newly exploited donors andacceptors.8-10 However, due to the complexity of the problem,

relatively little success has been reported for directional

-electron delocalization from electron donors to electronacceptors along the -conjugated bridge. For example, polyenicspacers constitute one of the most efficient conjugated bridges

and displays large arising from the energetically favored ICTelectron relay. However, the flexibility for further modification

is very limited.11,12

Classical theories, such as Dewars rules,13 have been used

to optimize the molecular design for efficient and stablechromophores.14-16 According to Dewars rules, a -conjugatedbridge 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

the energy level of the lowest unoccupied molecular orbital

(LUMO). Similarly, an electron-donating group at a starredposition (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 electron-

donating 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 Dewars rules, a

mild electron-withdrawing group, sulfur,16 and an electron-

* Corresponding author, [email protected]. Department of Chemistry. Department of Materials Science and Engineering.

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

J. Phys. Chem. C2010, 114, 222842228822284

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donating group, oxygen,17 were introduced into the starred

position of the -conjugated bridge, respectively. A dramaticincrease of molecular hyperpolarizability and enhanced chemical

and photochemical stability was observed experimentally. These

results support predictions of Dewars rules and thus support

the use of Dewars rules as a rational design concept for

molecular engineering of dipolar push-pull phenyltetraene-

based 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

-conjugated bridge based on Dewars rules. Both a two-statemodel 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 devel-

opment 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, abasis set with diffuse functions is recommended for studies of

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 chro-

mophore (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 Dewars

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 two-

state model,23,24 assuming a single excited state dominates the

linear and nonlinear molecular optical responses. In the two-

state model, the static molecular-axis (x-axis) component of the

first-order hyperpolarizability can be estimated as

where Ege is the excitation energy, ge is the transition dipole,e is the excited state dipole, and g 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 valuesthat 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 (zdirections. The static first hyperpolarizability in the directionof the molecular dipole moment can be calculated by18,28

Note that if the molecular axis is defined along the x direction,

the xxx in the two-state model of eq 1 becomes the dominantterm 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 substitutedby the widely used electron-donating group OCH3 and -with-

Figure 2. A schematic description of Dewars rules.

xxx )3

2

x,ge2

(x,e - x,g)

Ege2

(1)

)

i)x,y,z

ii

||(2a)

i )1

3

j)x,y,z

(ijj + jij + jji) (2b)

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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, ge, from

TDDFT calculations and the difference in static dipole moments,|e - g|, between the ground and first excited electronic statesfor calculations of hyperpolarizabilities using the two-state

model in eq 1. Static dipole moments are calculated using self-

consistent-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

Dewars 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 electron-donating substituent group, the largest absorption spectrum shift

occurs at the starred position 2* closest to the electron donor

terminal. Similarly, with an electron-withdrawing group, sub-

stitution 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 value are listed in Table 2. For all electron-donating groups

considered herein, the optimal position for the largest valueis the starred position nearest to the donor terminal. Note that

the fluorine is a -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 value,associated with lower excitation energy. This observation can

be approximately correlated with the Hammetts substitution

constant () -0.27 for OCH3, ) -0.66 for NH22, )-0.83 for N(CH3)2)

31 as the more negative indicates stronger

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

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

TABLE 1: Calculated Dipole Moments, Excitation Energy,and Strength of Single Substitutions on ConjugatedBackbone with Electron Donor (OCH3) and ElectronAcceptor (CdOCH3)

groups positionge(D)

|e - g|(D)

Ege(eV)

xxxa

(10-30 esu)

xxxb

(10-30 esu)

b

(10-30 esu)

base 17.06 9.22 1.99 1021 968 898

OCH3 1 15.87 11.20 2.04 1019 774 710

2* 16.28 10. 79 1.92 1160 1115 1040

3* 17.34 8.04 1.97 934 927 871

4* 16.61 9.48 1.93 1057 1062 984

5* 16.63 9.55 1.94 1058 1064 993

6* 17.23 8.34 1.95 980 994 925

7 14.61 12.55 2.05 955 843 751

8* 17.12 9.12 1.96 1047 1012 953CdOCH3 1 14.73 13.42 1.94 1166 959 903

2* 15.99 12.50 1.99 1214 1022 941

3* 16.95 9.05 1.98 995 931 865

4* 16.94 9.35 1.97 1037 990 910

5* 16.76 8.67 1.92 995 1025 941

6* 17.27 8.62 1.97 990 963 892

7 12.56 17.76 1.84 1247 1219 1161

8* 17.46 8.08 1.98 944 925 865

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

TABLE 2: Calculated Dipole Moments, Excitation Energy,and Strength of Single Substitutions with SelectElectron-Donating and -Withdrawing Groups on OptimalStarred/Unstarred Positions

groups positionge(D)

|e - g|(D)

Ege(eV)

xxxa

(10-30 esu)

xxxb

(10-30 esu)

b

(10-30 esu)

base 17.06 9.22 1.99 1021 968 898

OCH3 2* 16.28 10.79 1.92 1160 1115 1040

NH2 2* 15.41 9.12 1.74 1075 1342 1265

O-C6H5 2* 16.58 9.16 1.95 993 977 963

N(CH3)2 2* 14.75 9.93 1.81 990 1254 1186F 2* 16.49 10.28 1.92 1141 1145 1052

CdOCH3 7 12.56 17.76 1.84 1247 1219 1161

SCH3 7 13.54 15.41 1.87 1212 1155 1142

CN 7 15.96 9.00 1.82 1036 1142 1138

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

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electron-donating properties. For electron-withdrawing groups,

substitutions at the unstarred position closest to the acceptorlead to the largest increase in value.

The finite-field method calculated xxx value exhibits a strongcorrelation with the excitation energy (Figure 4). On the other

hand, xxx values calculated using the two-state model do notagree 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 chro-

mophores. 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 strength for electron-donating groups isthe 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 value can be further enhancedcompared to that in single substitution cases. The largest

hyperpolarizability is observed in the -CN and -NH2 doubly

substituted chromophore, with a 72% increase in valuecompared to that of the unmodified case. As discussed previ-

ously, this large enhancement arises from additional contribu-

tions 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 oftenconsidered a major factor in describing the electronic structure

and charge transport properties of-conjugated polymers.15,32,33

Figure 6 shows the finite-field method calculated hyperpolar-

izabilities as a function of BLA. A strong correlation is observed

between the calculated strength and BLA for all chromophoresconsidered 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

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

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

groupsposition/

typege(D)

|e - g|(D) Ege (eV)

xxxa

(10-30 esu)xxx

b

(10-30 esu)

b

(10-30 esu)

base 17.06 9.22 1.99 1021 968 898OCH3 + CdOCH3 (2*, 1) 6.79 33.96 1.64 875 886 809OCH3 + CdOCH3 (2*, 7) 11.63 20.05 1.76 1315 1337 1257OCH3 + CdOCH3 (4*, 1) 14.11 14.53 1.88 1230 1067 1010OCH3 + CdOCH3 (4*, 7) 11.91 19.02 1.77 1287 1306 1242OCH3 + CN (2*, 7) 15.25 10.08 1.75 1146 1305 1277OC6H5 + CdOCH3 (2*, 7) 11.70 20.55 1.80 1302 1282 1218OC6H5 + CN (2*, 7) 15.27 10.38 1.77 1160 1295 1276N(CH3)2 + CdOCH3 (2*, 7) 11.18 18.64 1.66 1267 1435 1346NH2 + CdOCH3 (2*, 7) 10.04 22.33 1.57 1364 1553 1422

NH2 + CN (2*, 7) 13.58 10.50 1.56 1190 1586 1545a Calculated using the two-state model (eq 1). b Calculated using the finite field method (eq 2a).

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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 value. Double substitutions on the conjugation polyene bridge

can further enhance compared to that of single-substitutedcases. The best performing double-substituted chromophores

exhibit large strength with up to 72% increase compared tothe base structure. The strong correlation between the valueand the bond length alternation measurement can be used to

predict the strength of hyperpolarizabilities.

In comparison to finite-field calculations, the simple two-

state 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 hyper-

polarizability.

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 gratefullyacknowledged. Alex K.-Y. Jen thanks the Boeing-Johnson

Foundation for its support.

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JP107803Q

Figure 6. Calculated hyperpolarizabilities () from the finite-fieldmethod plotted as a function of bond length alternation. A polynomialfitting provides guides to the eye.

22288 J. Phys. Chem. C, Vol. 114, No. 50, 2010 Hung et al.
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