Polarizability and first-order hyperpolarizability of cyclic imides

Journal of Molecular Structure: THEOCHEM 910 (2009) 56–60

Contents lists available at ScienceDirect

Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem

Polarizability and first-order hyperpolarizability of cyclic imides M. Asghari-Khiavi a,b, P. Hojati-Talemi a, F. Safinejad a,* a b

School of Chemistry, Monash University, Vic. 3800, Australia Department of Chemistry, McGill University, Montreal, Canada H3A 2K6

a r t i c l e

i n f o

Article history: Received 14 February 2009 Received in revised form 8 June 2009 Accepted 12 June 2009 Available online 21 June 2009 Keywords: Cyclic imides Polarizability First hyperpolarizability

a b s t r a c t Dipole moment, polarizability, and first-order hyperpolarizability of cyclic imides (maleimide, succinimide, phthalimide and some of their derivatives) have been investigated using ab initio and density functional theory calculations. It is found that 4,5-dichloro-, and 3,4,5,6-tetrachlorophthalimide have highest mean polarizabilities and total hyperpolarizabilities among the studied molecules. Furthermore, polarized continuum model has been employed to investigate solvent effects on the nonlinear optical (NLO) properties of succinimide; results indicate that solvent polarity has considerable influence on the NLO response of the molecules. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Cyclic imides can be used in the synthesis of nonlinear optical (NLO) materials such as tetrabenzporphyrins, N-(3-nitrophenyl) phthalimide, NLO crystal of N-bromosuccinimide, and polyimides [1–4]. Nonlinear optical polyimides and cyclic imide copolymers have attracted great interest in recent years [4–8]; these compounds are important for the development of high-speed optical modulators and switches. Great effort have been made in the synthesis and characterization of NLO polymers based on cyclic imides, for instance, radical copolymerization of N-(substituted phenyl) maleimide or N-(azo dye) maleimide and styrene was performed by Sung et al. [9] and according to their experimental results a stable second-order optical nonlinearity was observed for the copolymer with azo dye; using potassium phthalimide, Huang and coworkers synthesized oligomers with nonlinear optical property [5], (the prepared oligomers were then characterized by 1H NMR, 13C NMR, IR, and UV–visible spectroscopy); direct synthesis of functionalized polyimides using the nitro-displacement reaction between an alkanediol monomer and a diimide monomer without thermal curing step was represented by another research group where, the resulting polymers showed considerable second-order nonlinearity [4]. Considering the significance and influence of cyclic imides in NLO materials, in this paper, we study the linear and nonlinear optical properties of maleimide, succinimide, phthalimide, and some of their derivatives using ab initio and density functional theory (DFT) calculations; the assessment of conventional density * Corresponding author. E-mail address: fsafi[email protected] (F. Safinejad). 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.06.015

functional theory methods for predicting electric properties has been presented in Ref. [10]. Moreover, polarized continuum model (PCM) [11] is employed to investigate the effect of solvent on dipole moment, polarizability (a) and first hyperpolarizability (b) of succinimide. To the best of our knowledge, the optical properties of succinimide in the reaction field have not yet been investigated. In the following, we first introduce the theoretical and computational procedure applied in this paper (Section 2); then the dipole moments, polarizabilities and first hyperpolarizabilities of the studied molecules are presented in Section 3.

2. Computational procedure Calculations were performed at several levels of theory to determine the static polarizability and first hyperpolarizability of the molecules. Furthermore, several dielectric media including argon e ¼ 1:43, carbon tetrachloride e ¼ 2:228, diethyl ether e ¼ 4:335, and water e ¼ 78:39 were considered in the context of the polarized continuum model to investigate solvation effects on succinimide. Dipole moment, polarizability, and first hyperpolarizability can be determined as the derivatives of the energy W; using the Taylor series expansion,

1 1 W ¼ W 0  l0a Ea  a0ab Ea Eb  b0abc Ea Eb Ec 2 6 in which W 0 , l0a , a0ab , and b0abc are, respectively, energy, dipole moment, polarizability, and hyperpolarizability of the molecule in the absence of field and Ea is the final electric field along a axis. Having the calculated a and b components the linear and nonlinear optical properties can be determined as follows (calculations were carried out using Gaussian 03 software package [12]):

57

M. Asghari-Khiavi et al. / Journal of Molecular Structure: THEOCHEM 910 (2009) 56–60

Table 1 Calculated dipole moments (Debye), polarizabilities (a.u.), and first hyperpolarizabilities (1033 esu) of the studied cyclic imides based on HF/6-311++G(d,p), B3LYP/6311++G(d,p), and BHandHLYP/cc-pVDZ levels of theory: maleimide (1), succinimide (5), and phthalimide (8). No.

Structure

1

O

O

N H

Cl 2

O Br

3

O H3C

4

O

O

O

N H

O

O

N H

O

2.02 1.72 1.56

51.68 57.47 46.81

503.14 558.59 566.25

838.57 930.98 943.75

HF B3LYP BHandHLYP

0.05 0.18 0.09

73.97 83.53 67.47

454.03 1403.75 930.77

756.72 2339.59 1551.29

HF B3LYP BHandHLYP

0.40 0.56 0.30

87.08 98.08 78.42

107.59 1172.04 1024.06

179.31 1953.40 1706.77

HF B3LYP BHandHLYP

2.72 2.55 2.20

74.59 83.14 70.14

64.00 459.55 112.47

106.67 765.91 187.45

HF B3LYP BHandHLYP

2.57 2.22 1.99

50.96 57.95 47.80

559.44 567.01 645.26

932.40 945.02 1075.44

HF B3LYP BHandHLYP

3.81 3.44 3.26

61.81 70.76 57.85

589.33 788.59 928.81

982.22 1314.31 1548.01

HF B3LYP BHandHLYP

3.30 2.97 2.80

68.07 77.94 63.12

61.84 130.91 506.86

103.06 218.18 844.76

HF B3LYP BHandHLYP

3.39 3.11 2.80

92.40 102.29 85.52

260.78 336.36 42.26

434.63 560.60 70.43

HF B3LYP BHandHLYP

4.79 4.45 4.22

104.55 117.04 97.28

267.60 622.51 515.62

445.99 1037.51 859.37

HF B3LYP BHandHLYP

4.26 3.95 3.71

111.27 124.83 103.03

412.78 424.95 40.79

687.96 708.25 67.99

HF B3LYP BHandHLYP

0.49 0.68 0.27

116.49 131.79 109.01

1604.25 4405.50 2743.44

2673.76 7342.50 4572.41

HF B3LYP BHandHLYP

0.58 0.81 0.46

139.38 158.34 130.61

1481.79 4314.01 2659.43

2469.66 7190.01 4432.39

bl

btot

CH3 O

N

O

N

O

N Cl

7

HF B3LYP BHandHLYP

a

Br

H

6

l

Cl

H

5

Method

O

N Br

O NH

8

O O N Cl

9

O O N Br

10

O Cl

O NH

11

Cl

O Cl

Cl

O NH

12

Cl Cl

O

58

M. Asghari-Khiavi et al. / Journal of Molecular Structure: THEOCHEM 910 (2009) 56–60

 and the anisotropy of the polarizabilThe mean polarizability a ity Da can be written as [13]

1 3

a ¼ ðaxx þ ayy þ azz Þ h ðaxx  ayy Þ2 þ ðayy  azz Þ2 þ ðazz  axx Þ2  . i1=2 2 þ6 a2xy þ a2yz þ a2zx

Da ¼

For the first hyperpolarizability, the vector component along the dipole moment direction is

P 3 bl ¼ 5

i

li b i i ¼ x; y; z

jlj

where

bi ¼ biii þ

1X ðb þ bjij þ bjji Þ i; j ¼ x; y; z 3 j–i ijj

Considering Kleinman symmetry in the static limit we have,

bi ¼

X

bijj

i; j ¼ x; y; z

j

Another quantity of interest is the total intrinsic quadratic hyperpolarizability (or simply the total hyperpolarizability) btot which has the form

btot ¼ ðb2x þ b2y þ b2z Þ1=2 3. Results and discussion 3.1. Electric properties The calculated dipole moments, polarizabilities, and first hyperpolarizabilities of the studied cyclic imides are shown in Table 1.

The difference between the l values of the original molecules (maleimide, succinimide, and phthalimide) and the derivatives can be easily explained by considering the permanent dipole moment direction in the studied cyclic imides. According to BHandHLYP/cc-pVDZ calculations, the dipole moment of maleimide, 2,3-dichloromaleimide, and 2,3-dibromomaleimide are respectively, 1.56, 0.09, and 0.30 Debye; and the dipole moment of succinimide, N-chlorosuccinimide, and N-bromosuccinimide are determined to be 1.99, 3.26, and 2.80 Debye, respectively. Based on the same level of theory, the dipole moment of phthalimide, N-chlorophthalimide, and 4,5-dichlorophthalimide are evaluated to be 2.80, 4.22, and 0.27 Debye, respectively.  are also included in Table 1 (moleThe mean polarizabilities a cules are in the xy plane). It is observed that the B3LYP/6 in comparison to 311++G(d,p) level of theory leads to higher a other applied methods. Moreover, addition of halogen atom or methyl group to the original molecules increases the mean polarizability; this is because the molecular charge distribution in the case of derivatives can be distorted more easily by an external electric field in comparison with the original molecules. Using B3LYP,  value increases from 57.47 a.u. for maleimide to 83.53, the a 98.08, and 83.14 a.u. for 2,3-dichloro-, 2,3-dibromo-, and 2,3-dim values for succinimide, N-chloethylmaleimide, respectively. The a rosuccinimide, and N-bromosuccinimide are found to be 57.95, 70.76, and 77.94 a.u., respectively. Additionally, the anisotropy of the polarizability Da of maleimide has been determined using ab initio and DFT methods; the calculated values are 41.98, 47.11, and 43.98 a.u. using HF/6-311++G(d,p), B3LYP/6-311++G(d,p), and BHandHLYP/cc-pVDZ, respectively. The electric properties of maleimide, 2,3-dichloromaleimide, 2,3-dibromomaleimide, and phthalimide have also been studied at MP2/cc-pVDZ level of theory where the mean polarizabilities are found to be, respectively, 48.20, 68.55, 79.10, and 88.76 a.u. According to HF results the btot of maleimide, 2,3-dichloromaleimide, 2,3-dibromomaleimide, and 2,3-dimethylmaleimide are calculated to be 838.57  1033, 756.72  1033, 179.31  1033, and 106.67  1033 esu, respectively. In the case of succinimide,

Table 2 Experimental and theoretical dipole moments (Debye) and average molecular polarizabilities (in both a.u. and Å3) of several cyclic imides.

a (a.u.)

a (Å3)

2.02 1.72 1.56 1.69 1.38

51.68 57.47 46.81 52.34

7.66 8.52 6.94 7.76 7.84

Vacuum Vacuum Vacuum Dioxane Dioxane

2.57 2.22 1.99 2.14 1.68

50.96 57.95 47.80 52.60

7.55 8.59 7.08 7.79 9.15

HF/6-311++G(d,p) B3LYP/6-311++G(d,p) BHandHLYP/cc-pVDZ BHandHLYP/cc-pVDZ expa

Vacuum Vacuum Vacuum Dioxane Dioxane

3.81 3.44 3.26 3.66 2.87

61.81 70.76 57.85 63.67

9.16 10.49 8.57 9.43 11.67

N-bromosuccinimide

HF/6-311++G(d,p) B3LYP/6-311++G(d,p) BHandHLYP/cc-pVDZ BHandHLYP/cc-pVDZ expa

Vacuum Vacuum Vacuum Dioxane Dioxane

3.30 2.97 2.80 3.14 2.05

68.07 77.94 63.12 69.72

10.09 11.55 9.35 10.33 13.20

Phthalimide

HF/6-311++G(d,p) B3LYP/6-311++G(d,p) BHandHLYP/cc-pVDZ BHandHLYP/cc-pVDZ expa

Vacuum Vacuum Vacuum Dioxane Dioxane

3.39 3.11 2.80 3.12 2.11

92.40 102.29 85.52 97.43

13.69 15.16 12.67 14.44 14.53

Molecule

Method

Medium

l

Maleimide

HF/6-311++G(d,p) B3LYP/6-311++G(d,p) BHandHLYP/cc-pVDZ BHandHLYP/cc-pVDZ expa

Vacuum Vacuum Vacuum Dioxane Dioxane

Succinimide

HF/6-311++G(d,p) B3LYP/6-311++G(d,p) BHandHLYP/cc-pVDZ BHandHLYP/cc-pVDZ exp

N-chlorosuccinimide

a

From Ref. [14].

59

M. Asghari-Khiavi et al. / Journal of Molecular Structure: THEOCHEM 910 (2009) 56–60

Table 3 Calculated energy (a.u.), dipole moment (Debye), polarizability (a.u.), and first hyperpolarizability (in both a.u. and 1033 esu) of succinimide in several dielectric media based on HF/6-311++G(d,p) level of theory and PCM procedure. Medium

Energy

l

a

bl (a.u.)

btot (a.u.)

bl (1033 esu)

btot (1033 esu)

Vacuum e ¼ 1:43 e ¼ 2:228 e ¼ 4:335 e ¼ 78:39

358.702 358.707 358.712 358.719 358.727

2.57 2.69 2.81 2.94 3.07

50.96 53.65 56.65 60.14 65.11

64.62 75.15 88.27 105.51 133.61

107.70 125.25 147.12 175.86 222.68

559.43 650.60 764.19 913.44 1156.64

932.39 1084.34 1273.66 1522.40 1927.74

N-chlorosuccinimide, and N-bromosuccinimide the total hyperpolarizability values are, respectively, 932.40  1033, 982.22  1033, and 103.06  1033 esu. The btot for phthalimide, N-chlorophthalimide, N-bromophthalimide, 4,5-dichlorophthalimide, and 3,4,5,6-tetrachlorophthalimide are evaluated to be 434.63  1033, 445.99  1033, 687.96  1033, 2673.76  1033, and 2469.66  1033 esu, respectively. A comparison between the btot values of the studied molecules using HF, B3LYP, and BHandHLYP methods indicates that 4,5-dichloro-, and 3,4,5,6-tetrachlorophthalimide have highest mean polarizabilities and total hyperpolarizabilities. Table 2 presents the experimental and theoretical dipole moments and average molecular polarizabilities of several cyclic imides (maleimide, succinimide, N-chlorosuccinimide, N-bromosuccinimide, and phthalimide). As can be seen, a reasonable agreement is found between the experimental and calculated values in dioxane. 3.2. Solvent effects We have considered polarized continuum model to investigate solvent effects on the NLO properties of cyclic imides. Table 3 presents the molecular properties of succinimide in several dielectric media (argon e ¼ 1:43, carbon tetrachloride e ¼ 2:228, diethyl ether e ¼ 4:335, and water e ¼ 78:39). Due to the polarization of the molecule, it is expected that energy decreases and dipole moment increases with the reaction field. The ab initio-calculated energy of the molecule decreases from 358.702 a.u. in vacuum to 358.727 a.u. in dielectric medium e ¼ 78:39. Moreover, the molecular dipole moment is found to be 2.57 Debye for the isolated molecule. This quantity increases to 3.07 Debye in water. Based on PCM, the mean polarizability of succinimide is 1.3 times higher in water compared with the corresponding value in the gas phase.

The first hyperpolarizability bl of succinimide in vacuum is evaluated to be 559.43  1033 esu. This value increases to 764.19  1033 esu in carbon tetrachloride and 1156.64  1033 esu in water. In other words, bl is found to be ca. 1.4 and 2.1 times higher in carbon tetrachloride and water, respectively, compared with the related values in the vacuum. These results demonstrate a considerable dependency of NLO properties on the solvent polarity; see Fig. 1. The total intrinsic quadratic hyperpolarizability btot is another quantity of interest that enhances with dielectric medium; results are shown in Table 3. 4. Summary The linear and nonlinear optical properties of maleimide, succinimide, phthalimide, and some of their derivatives have been investigated using quantum chemical computations at HF/6311++G(d,p), B3LYP/6-311++G(d,p), and BHandHLYP/cc-pVDZ levels of theory. It is observed that 4,5-dichloro-, and 3,4,5,6-tetrachlorophthalimide have highest mean polarizabilities and total hyperpolarizabilities among the studied molecules. Moreover, a reasonable agreement has been found between the experimental and calculated dipole moments l and average molecular polariz of several cyclic imides. abilities a Furthermore, PCM procedure has been employed to study solvent effects on the NLO responses of succinimide. Results demonstrate a considerable dependency of NLO properties on the solvent polarity. Acknowledgments Support from Monash e-Research Centre and ITS-Research Services for the use of Monash Sun Grid cluster is appreciated. M. Asghari-Khiavi acknowledges the support from Monash University scholarships (MGS and MFRS). References

2500

first hyperpolarizability

βμ Series1 2000

Series2 βtot

1500 1000 500 0

0

0.11

0.23

0.34

0.49

k Fig. 1. First hyperpolarizability bl (1033 esu) and total hyperpolarizability btot of succinimide in several dielectric media; k ¼ ðe  1Þ=ð2e þ 1Þ.

[1] J.B. Carlson, P. Vouros, J. Mass. Spectrom. 31 (1996) 1403. [2] H.J. Ravindra, M.R. Suresh Kumar, C. Rai, S.M. Dharmaprakash, J. Cryst. Growth 294 (2006) 318. [3] T. Kanagasekaran, P. Mythili, P. Srinivasan, S.N. Sharma, R. Gopalakrishnan, Mater. Lett. 62 (2008) 2486. [4] Y.-B. Lee, H.Y. Woo, C.-B. Yoon, H.-K. Shim, J. Mater. Chem. 9 (1999) 2345. [5] D. Huang, C. Zhang, L.R. Dalton, W.P. Weber, J. Polym. Sci. Polym. Chem. 38 (2000) 546. [6] C. Samyn, T. Verbiest, E. Kesters, K. Van den Broeck, M. Van Beylen, A. Persoons, Polymer 41 (2000) 6049. [7] C. Samyn, W. Ballet, T. Verbiest, M. Van Beylen, A. Persoons, Polymer 42 (2001) 8511. [8] K.R. Yoon, H. Lee, B.K. Rhee, C. Jung, Macromol. Res. 12 (2004) 581. [9] P.-H. Sung, C.-Y. Chen, S.-Y. Wu, J.Y. Huang, J. Polym. Sci. Polym. Chem. 34 (1996) 2189. [10] B. Champagne, E.A. Perpte, D. Jacquemin, S.J.A. van Gisbergen, E.-J. Baerends, C. Soubra-Ghaoui, K.A. Robins, B. Kirtman, J. Phys. Chem. A 104 (2000) 4755. [11] J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev. 105 (2005) 2999. [12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox,

60

M. Asghari-Khiavi et al. / Journal of Molecular Structure: THEOCHEM 910 (2009) 56–60 H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L.

Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W.G. ill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Gaussian, Inc., Pittsburgh PA, 2003. [13] G. Maroulis, C. Pouchan, Phys. Chem. Chem. Phys. 5 (2003) 1992. [14] B.A. Arbuzov, L.K. Novikova, A.N. Vereshchagin, Russ. Chem. Bull. 27 (1978) 1679.