Nonlinear optical properties of dihydrobenzothiazolylidene and dihydroquinoinylidene compounds

Optical Materials 36 (2013) 437–443

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Nonlinear optical properties of dihydrobenzothiazolylidene and dihydroquinoinylidene compounds Yuanzuo Li a,⇑, Jing Li b, Runzhou Su a, Jingang Cui a a b

College of Science, Northeast Forestry University, Harbin 150040, China Departamento de Química, Universidade de Coimbra, 3004-535 Coimbra, Portugal

a r t i c l e

i n f o

Article history: Received 26 August 2013 Accepted 3 October 2013 Available online 28 October 2013 Keywords: Benzothiazolylidene (BTZ) 4-Quinolinylidene (QUIN) Density functional theory Nonlinear optical materials

a b s t r a c t The geometrical parameters, absorption spectra and first hyperpolarizability of BTZ (12a, 12c) and QUIN (13a, 13c) compounds have been studied with quantum chemistry methods. The hyperpolarizability b and transition energy were determined by density functional theory (DFT) and time-dependent DFT (TD-DFT). Electric field was considered to study the dependence of transition energy on electric field and to fit state-to-state dipole moment. DFT calculation and visualized methods (charge different density and molecular orbital analysis) provided an insight into the relationship between structure and first hyperpolarizability. In addition, two-photon absorption character of them has been firstly studied with the response theory approach. Results demonstrated that 12c and 13c with same electron-withdrawing substitution display obvious nonlinear optical response, and larger value of two-photon absorption sections suggest that they are good candidates for NLO materials. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Nonlinear optical (NLO) properties of materials have been widely investigated due to potential utility in the field of data storage, telecommunication, optical computing, and dynamic image processing [1–4]. Donor (D)–acceptor (A) substituted organic molecules with large second-order nonlinear optical (NLO) properties have been the focus of sizeable research efforts. Compared with conventional inorganic crystals, organic compounds have some merits: (a) optical damage threshold, and lower dielectric constant; (b) fast response time (10–14 s); (c) they are low-priced to produce; and (d) optical properties of compounds can be tunable by using chemical modification. Therefore, the compounds with D–A configuration are the archetypal molecules for quadratic hyperpolarizability, which were also found to exhibit two- or three-photon absorption cross-sections. Since intramolecular charge-transfer interactions during photoexcitation, such molecules are considered as promising candidates for designing organic solar cell [5]. It is important to understand the structure–NLO property relationship of D–A molecules for finding strategies to enhance NLO response. Much calculated methods have been used to insight into structure–property relationship of NLO materials. Zhang et al. [6] used time-dependent density functional theory and analyzed resorting to the summation-over-states scheme to study the first ⇑ Corresponding author. Tel.: +86 451 82192245 8211. E-mail address: [email protected] (Y. Li). 0925-3467/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optmat.2013.10.006

hyperpolarizability of metal–organic chromophore systems. They demonstrate that the metal-to-ligand charge transfer state is responsible for the larger b response. Coe et al. [7] studied the structure-activity relationships in diquaternized 2,20 -bipyridyl (diquat) derivatives, in which DFT, TDDFT and the finite field (FF) were used to calculate the optical parameters and first hyperpolarizability. They point out a relatively high multiplicity of visible ICT transitions for the disubstituted species. Sundaraganesan et al. [8] studied energies, geometrical structure, vibrational wave numbers and first-order molecular hyperpolarizabilities of ferulic acid. Effect of p conjugation spacer and structure substitution on first hyperpolarizabilities [9], as well as the linear, and second-order nonlinear optical (NLO) properties of chiral mononucles [10] and imidazole derivatives [11], have been investigated in the frame of DFT method. Experimental researches focus on regulating structural parameter [12,13], such as the conjugation length, donor and acceptor strength, and planarity of the conjugated bridged center, to improve the photosensitivity. Among much synthesis experiments, Kay et al. [14] recently reported a series of chromophores containing dihydrobenzothiazolylidene (BTZ) and dihydroquinoiny-lidene (QUIN) donors with an azo linker, and they confirm that the use of pro-aromatic donors results in compounds with higher nonlinear optical responses and larger value of first hyperpolarizability. To reveal the structure–NLO property relationship, we performed a detailed calculation on the push–pull molecules containing BTZ and QUIN. Firstly, the geometry, electronic and optical response properties of the subjected chromophores was studied

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by using quantum chemical method. Secondly, the photoinduced charge transfer under external field was visualized by using the developed 3D cube representations of charge different density. Recently, 3D cube representations have been used to study the charge transfer and excited states properties of organic molecules during one-photon [15–17] and two-photon absorption [18], to reveal the charge transfer mechanism of mixed dimer system [19] as well as the chemical mechanism study of the Surface Enhancement Raman Spectroscopy [20]. Current research not only discuses the relation between structure and first hyperpolarizability, but also firstly investigate two-photon absorption (TPA) character of them to develop its potential application on TPA materials. 2. Methods The equilibrium geometries of the BTZ compounds (12a and 12b) and QUIN compounds (13a and 13c) in the ground state were optimized with DFT [21] at the Beck three parameter hybrid functional using the Lee–Yang–Parr correlation functional (B3LYP) [22]/ 6-31G(d) level, followed by the calculations of the first hyperpolarizabilities. The total static first hyperpolarizability can be written as followed,

bTol ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2x þ b2y þ b2z

ð1Þ

Individual static components in the above equation is calculated from,

bi ¼ biii þ 1=3

X ðbijj þ bjij þ bjji Þ

ð2Þ

i–j

where bijk (i, j, k = x, y, z) are tensor components of hyperpolarizability. Due to the Kleinman symmetry [23], one finally obtains the equation that has been employed:

btot ¼ ½ðbxxx þ bxyy þ bxzz Þ2 þ ðbyyy þ byzz þ byxx Þ2 þ ðbzzz þ bzxx þ bzyy Þ2 

1=2

ð3Þ The excitation energies and oscillator strengths for the four compounds were obtained in the framework of TD-DFT [24] calculations with the 6-31G(d) basis sets. Solvent effect was considered in both the ground state optimization and excitation energies calculation, and the polarizable continuum model (PCM) [25] was adopted for THF. Above quantum chemistry calculations were carried out with the Gaussian09 program package [26]. Two-photon absorption (TPA) was performed with the response theory approach at DFT level with Dalton code [27]. To clearly understand excited state properties of three dyes, the 3D real space analysis of CDD has been applied, which indicates the electronic redistribution involving in the whole structure during excitation [15–18]. 3. Results and discussion Compounds 12a, 12c, 13a and 13c, have similar conjugated bridge spacer and different donor and acceptor, in which Series 12 and 13, benzothiazolylidene (BTZ) and 4-quinolinylidene (QUIN) act as donor unit, respectively. The geometry optimization of four compounds was performed by the B3LYP with the basis set 6-31G(d). Fig. 1 shows the chemical structures of the above compounds, and selected structural parameters are listed in Table 1. It is seen in Fig. 1 that for 12a, 12c and 13a, 13c there is a conplaner structure along molecular skeleton; for an example, dihedral angle of C1–C2–N3–N4, N3–N4–C5–C13, C14–C6–C7–C8, near close to 180 degree. The conjugated length of 12a and 12c is 9.44089 Å (LC1–C8) and 14.33418 Å (LC1–C11), and LC1–C8 of 13a and LC1–C11 of 13c is 9.87615 Å and 14.32348 Å, respectively. It means that the conjugated length of 12c and 13c is longer than that of 12a and 13a, respectively. One also calculated the structural parameters

Fig. 1. Chemical structure of the four compounds.

439

7577.50683 22470.88124 3129.834668 26897.71318

Btol(vec) B11 Bxzz Byyz Bxyz Byyy

where Dleg represents the difference of dipole moment between the ground and excited state, Eeg and feg is the transition energy and oscillator strength, respectively. The electronic transition factors controlling first hyperpolarization can be obtained with TDDFT. The transition energy, oscillator strength and electronic transition configuration were provided in Table 3. As seen from Table 3 that the one photon absorption of 12 serial compounds shows a peak at the first excited state about 440–490 nm, which are composed of HOMO–LUMO electronic transition. In order to insight into the charge transfer properties, molecular orbital of four compounds (including HOMOs and LUMOs) were shown in Fig. 2. As shown, electron density of HOMO for 12a is primarily located in BTZ unit and p conjugated bridge, and electron density of LUMO resides in p conjugated bridge and TCF unit. Therefore, the S1 state of 12a is a charge transfer (CT) state, with considerable charge transfers from donor to acceptor. Similar, the first state of 12c is a CT state, and CT takes place between donor and acceptor. Due to the enhanced conjugated length, CT degree of 12c is larger than that of 12a, and then the absorption spectra of 12c make red-shifted about 50 nm. It is seem from Table 3 that for 13c, there are two absorption peaks, located at 545.18 nm (f = 2.242) and 367.20 nm (f = 0.22), respectively, and their oscillator strengths are stronger than those of 13a. When considering the red-shifted absorption and

Bxxz

ð4Þ

Bxyy

E3eg

Bxxy

Dleg feg

Table 2 Hyperpolarisabilities of four dyes (in a.u.).

b1

Byzz

of compound 14 to compare with experimental value, as shown in Supporting material (Table S1). As one can find from Table S1 that the calculated N–N, C–N, C–S, and C–C bond lengths show a good agreement with the experimental values, while with a difference about 0.04 Å for bond lengths of C–O and S–C, which may therefore rationalized as follows: one carried out the calculations in the gas phase but the experimental values are obtained from the crystal. After the geometry optimization, the components and final total hyper-polarizabilities for all the compounds were calculated, as shown in Table 2. The magnitude of the first hyperpolarization for 12a and 13a is substantially lower than the same serials compounds. For 12 serial, 12c with an acceptor (4,4,5-trimethyl-3-cyano-2(5H)-furanylidenepropanedinitrile, TCF) displays the largest first hyperpolarization, and 13C with the same acceptor (TCF) also presents the largest first hyper-polarization. It is well established that there is a trend between the total hyperpolarizabilities and the donor and or acceptor character: larger hyperpolarizabilities may be attributed to the stronger electronic interaction between donor and acceptor by enhancing charge transfer characteristics coupling [7–10]. According to the two-level model [28], the relationship between hyperpolarizabilities and electronic transition parameters can be written as:

4157.3923493 13882.3135306 8175.713585 20219.1779853

Bzzz

14.32348

73.9685698 140.1487766 0.0069819 4.2297508

9.87615 14.33418

Bxxx

9.44089

6141.458161 18289.1152624 7770.4503638 22981.5211608

180.00000 0.01142

24.5109692 23.3776348 60.9301936 56.6903215

0.00270 0.14095

110.9223387 201.4814673 0.0237102 5.1161186

1.3971 1.3480 1.2956 1.3926 1.4398 1.3713 180.00

8496.296671 23592.5328398 7534.3899476 24667.0343161

13c

1.3939 1.3515 1.2930 1.3939 1.4405 1.3742 180.00

0.3671721 0.5685832 0.0059906 0.0357198

13a

1.3815 1.3536 1.2865 1.3978 1.4435 1.3683 179.8459 179.21154 179.69255

16.0593057 11.2818613 6.6779849 3.0337661

12c

1.3820 1.3530 1.2862 1.3990 1.4423 1.3731 179.8067 178.84444 179.90931

161.252909 275.36523 0.0011097 5.8696497

12a

10655.5166857 29687.6683075 6980.5726885 24202.3590196

C1–C2 C2–N3 N3–N4 N4–C5 C6–C7 C7–C8 C1–C2–N3–N4 N3–N4–C5–C13 C14–C6–C7–C8 C6–C7–C8–C9 C8–N9–C10–C11 L(C1–C8) L(C1–C11)

12a 12c 13a 13c

Table 1 Calculated bond lengths (Å) and dihedral angle (degree) for four compounds, respectively.

21033.08886 48837.64685 21507.84331 65082.39708

Y. Li et al. / Optical Materials 36 (2013) 437–443

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Y. Li et al. / Optical Materials 36 (2013) 437–443

Table 3 Calculated transition energy and oscillator strength of four compounds. State

Transition energy

CI coefficients

Oscillator (f)

12a

S1 S2 S3

441.00 430.53 293.44

(0.66688)93 -> 94 (0.49451)91 -> 94 (0.59144)93 -> 95

1.4601 0.0708 0.2595

12c

S1 S2

492.89 430.29

2.1580 0.0018

S3

351.97

(0.65740)128 -> 129 (0.48986)126 -> 129 (0.47881)126 -> 130 (0.63178)127 -> 129

13a

S1 S2 S3

488.33 461.46 320.08

(0.69306)92 -> 93 (0.63568)91 -> 93 (0.67460)92 -> 94

1.8085 0.0000 0.0345

13c

S1 S2 S3

545.18 461.28 367.20

(0.67031)127 -> 128 (0.54313)125 -> 128 (0.54896)127 -> 129

2.2420 0.0000 0.2200

0.0646

Fig. 2. Contour surface plots of HOMO and LUMO of the four compounds, where green and red correspond to the different phases of the molecular wave functions for the HOMOs and LUMOs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

stronger oscillator strengths, it can be understandable that the value of f/E for 13c is larger than that of 13a. For the first state of 13c, it is a CT state since the state comes from electronic transition from HOMO to LUMO (electronic density of HOMO is located in donor and bridge, and LUMO is located in acceptor). Due to the enhanced conjugated size, 13c displays an obvi-

ous CT character and the larger first hyper polarization (see Tables 1 and 2). Meanwhile, for the second absorption peak of 12c and 13c, their transitions are mainly originated from HOMO–LUMO+1. LUMO+1 and LUMO sharing similar distribution of electronic density, and thus the two states are both CT states.

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Y. Li et al. / Optical Materials 36 (2013) 437–443

As aim to obtain the dipole moment transition between the ground and excited state, one calculated Dleg by using the HellmanneFeynman theorem, as the analytical derivative of the excited-state energy with respect to an applied electric field. The transition energy dependent on the static electric field F can be expressed as [29],

1 Eexc ðFÞ ¼ Eexc ð0Þ  DlF  DaF 2 2

ð5Þ

where Eexc(0) is the excitation energy at zero field, Da is the change in polarizability. One calculated transitions energy and oscillator strengths of the four compounds under the electric field (F), 1  103, 2  103 and 3  103 a.u., respectively, which was listed in Table 4. Value of Dleg fitted according to Eq. (5), is 2.324 a.u. for 12a and 3.7825 a.u. for 12c, respectively, and significant changes are an important factor in controlling NLO properties. The Btol(vec) of 12c is larger than that of 12a, and the reason is bigger dipole moment variation and low transition energy under similar oscillator strength. With increasing electric field, there is a performance of redshifted absorption about 50 nm for 12a and about 60 nm for 12c; when F = 3  103 a.u., 12c absorption is 572 nm. One tries to use charge difference density to study the charge transfer process alone the increasing electric field, as shown in Fig. 3. When absorption peak of 12c is at 451 nm, photo-induced electron transfer from donor, benzothiazolylidene unit, to forepart five-member rings of TCF, which is a charge transfer process. One also found that there is a litter hole stayed at bank-end TCF, which means there is also a charge transfer occurring on TCF. Therefore, CT occurs from the both sides of 12c molecular to middle area. When electric field was increased into be 3  103, ample single direction of CT take

place. One can find in Fig. 3 that electrons move to TCF and green hole left on QUIN unit. It seems that electric field great affect absorption of 13 serial, in which 13c have an absorption peak at 621 nm. Therefore, it is found that absorption spectra of BTZ and QUIN dyes have a dependence of electric field. From the calculated first hyperpolarization (see Table 2), Btol(vec) of 13c is three times as big as 13a, and reason is that dipole moment difference (Dleg) of 13c increases about 2-fold under decreasing transition energy and similar oscillator strength in comparison with 13a. So from the viewpoint of molecule, the introduction of TCF indeed increases electron delocation and improve first hyperpolarization. Transition energy and the first hyperpolarizabilities of four compounds were calculated in solvent phase since solvent polarity can play a significant role on absorption spectra and the first hyperpolarizabilities of push–pull molecular system [30]. One used DFT approach with polarizable continuum model (PCM) for simulating solvent condition (THF), and calculated transition energy and first hyper polarizabilities were listed in Table 5. Calculated absorption peak of 12a and 13a show a good agreement with experimental data, while absorption peak of 12c and 13c with spectral red-shifted or blue-shifted due to the solute-solvent intermolecular hydrogen bonding interaction [31]. Comparing 12a with 12c, absorption wavelength and oscillator strength of 12c increase in varying degrees, and its first hyperpolarizabilities is obviously increased. Considering the studies of acceptor–donor configurations with ICT character, it is expected that these complexes might provide some new interesting opportunities to nonlinear optical (NLO) materials. Table 6 shows the TPA cross sections referring to three lowest states, and the strongest TPA cross section of four compounds all occur at the third excited state. Due to the relationship

Table 4 Transition energy and oscillator strength under the electric field as well as dipole moment difference. Field (  104 au)

10 20 30 Dleg

12a

12c

13a

13c

E (nm)

OSC

E (nm)

OSC

E (nm)

OSC

E (nm)

OSC

451.72 464.23 478.24 2.324

1.5005 1.5039 1.5024

514.55 541.60 572.91 3.7825

2.0959 2.0408 2.0048

497.64 508.30 519.78 1.704

1.8184 1.8287 1.8394

567.44 593.57 621.01 3.324

2.2277 2.2224 2.2368

Fig. 3. The charge difference densities (CDD) of the 12c under the electric field (green and red colour represents the hole and electron, respectively). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Y. Li et al. / Optical Materials 36 (2013) 437–443

Table 5 Calculated transition energy, oscillator strength and value of Btol  1030 (esu) in solvent phase. 12a

Cal. Exp* *

12c

13a

13c

TE (nm)

OSC

Btol

TE (nm)

OSC

Btol

TE (nm)

OSC

Btol

TE (nm)

OS

Btol

484.38 477

1.6579

661.53

540.03 637

2.2399

2085.96

542.37 539

1.9562

768.23

605.38 572

2.3540

2419.30

Experimental data come from Ref. [14].

Table 6 Calculated TPA cross-section (r, 1050 cm4 s photon1) and the excited energy E (eV) with B3LYP functionals. State

E (eV)

r

State

E (eV)

r

12a

S1 S2 S3

2.51 2.53 3.36

49.86 54.88 652.82

12c

S1 S2 S3

2.13 2.45 2.63

250.71 0.38 1667.81

13a

S1 S2 S3

2.24 2.30 3.00

0.054 10.27 501.95

13c

S1 S2 S3

1.970 2.19 2.43

37.25 0.12 1306.94

between the two-photon absorptions probability (dtp) and the two-photon matrix element (Sij), dtp ¼ 6ðSxx þ Syy þ Szz Þ2 þ 8ðS2xy þ S2xz þ S2yz  Sxx Syy  Sxx Szz  Syy Szz Þ, one estimates Sij to study microscopic mechanism of the enhanced TPA by means of four-state model: h a i h a i h0jl j1ih1jlb j3i h0jlb j1ih1jla j3i h0jl j2ih2jlb j3i h0jlb j2ih2jla j3i Sab ¼ þ . The þ þ DE1 DE1 DE2 DE2 value of l02 is proportional to the oscillator strength of second excited state, which is very small (see Table 3), thus, h a i b lb j3i la j3i Sab 1 h0jl j1ih1j . Table S2 listed the components of þ h0jl j1ih1j DE1 DE1

l01 and l13. There are smallest transition moment values of l01 and l13 for 13a, which yields the smallest value of Sab. Among four compounds, 12c presents largest transition dipole moment of l01 and l13. Calculated results indicates that a large transition moment results in a larger two-photon matrix and in turn a larger TPA section, and calculated TPA cross section obtains such a ordering 13a < 12a < 13c < 12c. We previously investigated the symmetrically charged molecules, selenopyrylium- and bis(dioxaborine)terminated polymethine dyes (called SE-7C and DOB-9C). The maximal TPA cross-sections for symmetrical system are 2697.75  1050 cm4 s photon1 (SE-7C) and 1248.87  1050 cm4 s photon1 (DOB-9C) [19], respectively. Currently calculated TPA cross section is 501.95  1050 cm4 s photon1 for 13a, 652.82  1050 cm4 s photon1 for 12a, 1306.94  1050 4 1 cm s photon for 13c, and the largest TPA section is 1667.81  1050 cm4 s photon1 for 12c. So we can propose that among the BTZ and QUIN compounds, 12 and 13 compounds could be good candidates as the optoelectronic materials with large NLO response by altering the donors and/or acceptors in comparison with the others. 4. Conclusions One have reported a theoretical study of nonlinear optical properties of four donor–bridge–acceptor compounds containing dihydrobenzothiazolylidene and dihydroquinoinylidene by using quantum chemistry methods. The geometries of the compounds all show a coplanar structure, and conjugated length is in the order 12a < 12c and 13a < 13c. Based on two-level model, hyperpolarizability b was determined. Our calculations show donor units (BTZ and QUIN) can form a very effective push–pull system with acceptor (TCF) in donor–bridge–acceptor system, leading to larger dipole moment variation and low transition energy, which can be the root of larger first hyperpolarizabilities. Furthermore, external environment (such as field and solvent) was considered, which make

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