Theoretical investigation on the photoswitchable second-order nonlinear optical properties of a series of B(C6F5)2-coordinated dithienylethene derivatives

Journal of Photochemistry and Photobiology A: Chemistry 335 (2017) 155–164

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Theoretical investigation on the photoswitchable second-order nonlinear optical properties of a series of B(C6F5)2-coordinated dithienylethene derivatives Xian-He Liu, Zeng-Xia Zhao* , Jian Wang, Wei Zhang, Hong-Xing Zhang* International Joint Research Laboratory of Nano-Micro Architecture Chemistry, Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, 130023 Changchun, China

A R T I C L E I N F O

Article history: Received 29 July 2016 Received in revised form 25 November 2016 Accepted 28 November 2016 Available online 29 November 2016 Keywords: B(C6F5)2-coordinated dithienylethene derivatives Second-order NLO properties Absorption spectra DFT

A B S T R A C T

The photoswitchable second-order nonlinear optical (NLO) properties of a series of B(C6F5)2-coordinated dithienylethene derivatives have been investigated by density functional theory (DFT) method. The calculations showed that static first hyperpolarizabilities (btot) of ring-opening and ring-closed systems dramatically increased by introducing the appropriate substituents. Moreover, the calculated btot values of ring-closed systems were larger than those of the corresponding ring-opening systems, it is mainly attributed to the forming of a larger p-conjugation in the ring-closed systems. The ring-closed form 5c owned the largest btot values (7361.4
1030 esu), which are 29.8 times larger than that of the corresponding ring-opening form 5o. Besides, to better describe the NLO behaviors of the studied dithienylethene derivatives, the absorption spectra and relative frontier molecular orbitals were calculated by time-dependent density functional theory (TDDFT) method. At last, we also demonstrated that the dispersions have barely influence on the frequency-dependent first hyperpolarizabilities (btot (v)) at the low-frequency region v (0.000–0.030 a.u.). Thus, these theoretical calculations predicted the possible role of the studied systems as effective photoswitchable second-order NLO materials. We hope that this current work will pave the way for further theoretical and experimental design of efficient NLO materials. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Photochromic materials [1] have drawn growing interests because of their extensive utilizations in the field of emerging optoelectronic devices over the past decades. Among them, photoswitchable nonlinear optical (NLO) materials play a vital role for basic research and practical applications, such as biological imaging, optical molecular switches and optical memory devices [2–6]. Accordingly, design and synthesis of the excellent secondorder NLO materials displaying large first hyperpolarizabilities have been the focus of intensive investigations. In recent years, photochromic molecules, including diarylethene [7–9], azobenzene [10,11] and fulgide [12–14], have been widely investigated as photoswitchable units for various photo-responsive NLO materials. Among these photochromic materials, organic diarylethene

* Corresponding authors. E-mail addresses: [email protected] (Z.-X. Zhao), [email protected] (H.-X. Zhang). http://dx.doi.org/10.1016/j.jphotochem.2016.11.029 1010-6030/© 2016 Elsevier B.V. All rights reserved.

derivatives, especially for dithienylethene (DTE), have been one of the most representative and promising candidate for NLO applications due to its excellent fatigue resistant and high thermal irreversibility [15,16], and the DTE unit can proceed a reversible transformation between the ring-opening form and ring-closed form by irradiation with appropriate absorption wavelength. This reversible photochromic behavior often gives rise to some obvious variations of geometry structures or other photophysical properties, such as absorption spectrum, luminescence efficiency or NLO properties, and so on. Hence, the DTE-based derivatives are hopeful to act as a potential candidate for multi-functional NLO materials. Recently, to improve the stability of photochromic compounds and regulate their photochromic reactivity, many DTE derivatives coordinated with metal centers have been substantially reported and some of them NLO properties have been investigated [17–22]. Actually, apart from coordinating with metals, a new class of boron-coordinated DTE complexes have been synthesized and reported [23–26] due to the boron (III) center exhibits lots of attractive photophysical properties and strong electron-

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Scheme 1. Photoisomerization between ring-opening forms (left) and ring-closed forms (right) of BR2-coordinated dithienylethene derivatives (Ar = phenyl (Ph), thienyl (Th), and 4, 5-dimeththylthiophen-3-yl) (thiophen-2-yl (DTE-Th)).

withdrawing ability. In previous studies, quantum chemical methods have been used to investigate the second-order nonlinear optical responses of boron-containing organic complexes by Qiu et al. [27]. Padilha and co-workers [28] also investigated the effect of different substituents on the linear and nonlinear optical spectroscopy of fluoroalkylated boron dipyrromethene dyes. These nonlinear optical studies revealed that different substituents have a great influence on their excited state absorption properties. However, in the past few years, Yam and co-workers [29] also have successfully synthesized a series of DTE-containing boron (III) compounds, they noticed that the combination of boron center shifts the absorption wavelength to near-infrared (NIR) region. This research opens up a new thread for the development of photochromic materials. In 2013, they further designed and synthesized a series of BR2-coordinated (R = F, C6F5, and Ph) DTEcontaining b-diketonate complexes [30] (Scheme 1): 1-Thienyl-3aryl-propane-1,3-diones (aryl = phenyl (Ph), thienyl (Th), and 4,5dimeththylthiophen-3-yl)thiophen-2-yl (DTE-Th)). It is noteworthy that the incorporation of boron center has a significant effect on their photophysical and photochromic properties. These structural modifications may provide new insights into the design

of photoswitched photochromic materials. Despite considerable efforts have concentrated on the studies of photochromic properties of boron-coordinated DTE complexes and the synthesis and development of novel photochromic materials. However, it is very little known about their second-order NLO properties. Therefore, theoretical tools are indispensable to provide a rational strategy for the design of highly efficient NLO materials. In this paper, we initially calculated the btot values of nine BR2coordinated DTE derivatives, which have been synthesized by experimental methods (Scheme 1). Based on the analysis of btot values, several design strategies were proposed to improve the NLO responses of the studied systems. First, we proposed a strategy of structural modifications by introducing a simple ligand (N¼N-ph) at the 3-position of the b-diketonate based on the original structure of 2-B(C6F5)2. Second, we further discussed the influence of different substituents on the second-order NLO properties. Finally, we obtained five B(C6F5)2-coordinated DTE derivatives (Scheme 2). The electronic structures, absorption and second-order NLO properties for all of these designed molecules were calculated by DFT and TDDFT methods. In addition, we also considered the influence of dispersions on the btot (v) at the

Scheme 2. Molecular structures of the B(C6F5)2-coordinated dithienylethene derivatives 1  5.

X.-H. Liu et al. / Journal of Photochemistry and Photobiology A: Chemistry 335 (2017) 155–164 Table 1 The optimized geometrical parameters for ring-opening forms of the studied complexes 1–5 at ground state. The sign o stands for ring-opening form and c stands for ring-closed forms, and the relative atomic labels are exhibited in Fig. S2. 1o

2o

3o

4o

5o

Bond Length [Å] B-O1 B-O2 B-C1 B-C2 C3-C4

1.507 1.510 1.615 1.632 1.396

1.512 1.516 1.612 1.629 1.398

1.514 1.517 1.611 1.628 1.399

1.511 1.515 1.612 1.629 1.399

1.513 1.517 1.611 1.628 1.400

Bond Angle [ ] C1-B-O2 C2-B-O1 C1-B-C2 O1-B-O2 C1-B-O1 C2-B-O2

111.1 111.4 112.3 107.3 106.8 107.8

111.2 111.3 112.6 107.0 106.8 107.8

110.9 111.3 113.0 106.7 107.0 107.8

111.2 111.4 112.6 107.0 106.7 107.8

110.9 111.3 112.9 106.8 107.0 107.8

Dihedral Angle [ ] C3-C4-C5-C6 47.9 C4-C3-C7-C8 51.2

47.2 51.2

47.0 50.7

45.6 50.3

45.4 49.7

frequency region v (0.000  0.065 a.u.). It is expected that these studied systems possessing switchable NLO properties could provide a thread for the design of efficient NLO materials.

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between computational efficiency and accuracy, the PBE0 functional was chosen in our discussions. And the calculations of absorption properties were performed in benzene solution using the polarizable continuum model (PCM). In addition, all the optimized structures were verified as the minima of potential energy surface by vibrational frequency analysis. On the basis of geometrical optimization, the static first hyperpolarizabilities (btot) were also calculated at the DFT level of theory. It should be noted that the selection of functionals is pivotal to obtain credible NLO data. In general, conventional DFT methods often lead to a great overestimation of the btot values, which can be ascribed to its improper asymptotic behavior as well as poor charge transfer description [37–39]. However, the range-separated exchange functionals with correct asymptotic behavior often give reliable results in assessing the btot for the similar systems [40,41]. Therefore, to have an accurate description of their photoswitchable NLO behaviors, we chose the traditional PBE0 functional and three range-separated exchange functionals with different percentage of Hartree-Fock (HF) exchange (PBE0 [32] (25%), CAM-B3LYP [34,35] (19%  65%), vB97XD [42] (22.2%  100%) and vB97X [42] (15.77%  100%)) as comparison in this study. The 6–31 + G(d) basis set was employed for all atoms. At last, the calculations of frequencydependent first hyperpolarizabilities (btot (v)) were carried out by the coupled perturbed density functional theory (CPDFT) at CAMB3LYP/6–31 + G(d) level.

2. Computational details All calculations were implemented with Gaussian 09 program package [31]. In our calculations, the geometries of all ground-state molecules were fully optimized without any symmetry restriction (C1 symmetry) at the DFT level by using PBE0 [32] hybrid exchange-correlation functional and the standard 6–31G(d) basis set, this functional and basis set have been confirmed that it is appropriate to evaluate the ground state and excited state properties for the similar systems by Yam et al. [30]. Besides, in order to avoid the possible shortcomings of the TD-PBE0 method in simulating the absorption properties, several other functionals (B3LYP [33], CAM-B3LYP [34,35], M06 [36] and M06-2X [36]) were employed as supplements for the studied systems, and the corresponding absorption data and simulated absorption spectra are provided in Table S1 and Fig. S1. As a desired compromise

Table 2 The optimized geometrical parameters for ring-closed forms of the studied complexes 1  5 at ground state. 1c

2c

3c

4c

5c

Bond Length [Å] B-O1 B-O2 B-C1 B-C2 C3-C4

1.508 1.509 1.615 1.632 1.460

1.513 1.515 1.613 1.630 1.459

1.514 1.511 1.612 1.631 1.457

1.508 1.507 1.616 1.634 1.456

1.510 1.504 1.616 1.636 1.451

Bond Angle [ ] C1-B-O2 C2-B-O1 C1-B-C2 O1-B-O2 C1-B-O1 C2-B-O2

111.1 111.3 112.4 107.4 106.7 107.8

111.1 111.2 112.7 107.2 106.8 107.8

111.2 110.9 112.7 107.4 106.9 107.8

111.3 111.1 112.1 108.1 106.7 107.5

111.2 110.8 112.1 108.0 106.7 107.9

Dihedral Angle [ ] C3-C4-C5-C6 C4-C3-C7-C8

7.1 9.7

7.0 9.8

7.4 10.5

7.3 10.9

8.0 11.7

Fig. 1. Comparison of static first hyperpolarizabilities (btot) for the (a) ring-opening forms and (b) ring-closed forms of the studied complexes 1–5 with four different functionals.

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Table 3 The calculated static first hyperpolarizabilities btot (1030 esu) with four different functionals in benzene solution for the studied complexes 1–5, and the corresponding molecular structures are shown in Scheme 2. Functional

Complex

1

2

3

4

5

PBE0

Closed Open D-value Q-value Closed Open D-value Q-value Closed Open D-value Q-value Closed Open D-value Q-value

1587.5 226.9 1360.6 7.0 600.7 108.4 492.3 5.5 472.4 92.5 379.9 5.1 353.1 74.6 278.5 4.7

2248.9 360.1 1888.8 6.2 952.9 168.6 784.3 5.7 718.9 142.3 576.6 5.1 513.2 112.3 400.9 4.6

2174.9 621.0 1553.9 3.5 2161.1 207.0 1954.1 10.4 1706.0 168.7 1537.3 10.1 1187.1 128.5 1058.6 9.2

4025.3 459.3 3566 8.8 3663.7 201.6 3462.1 18.2 2213.5 171.4 2042.1 12.9 1208.1 133.2 1074.9 9.1

2439.1 844.3 1594.8 2.9 7361.4 247.2 7114.2 29.8 7771.0 202.0 7569 38.5 5074.7 151.7 4923.0 33.5

CAM-B3LYP

vB97XD

vB97X

The static first hyperpolarizability btot is computed by Eq. (1) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ btot ¼ bx 2 þ by 2 þ bz 2

In which the bi is defined by Eq. (2)

bi ¼ biii þ bijj þ bikk ; i; j; k ¼ x; y; z The frequency-dependent first hyperpolarizability b computed by Eq. (3)

btot ðvÞ ¼

ð2Þ

tot

(v) is

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bx 2 ðvÞ þ by 2 ðvÞ þ bz 2 ðvÞ

ð3Þ

Fig. 2. Comparison of static first hyperpolarizabilities (btot) and the relative parameters from the two-level model between (a) ring-opening forms and (b) ringclosed forms of the studied complexes 1–5.

In order to gain an in-depth understanding on the NLO properties, time-dependent density functional theory [43,44] with PBE0/6-31G(d) was employed to analyze the electronic excited state properties for ring-opening and ring-closed systems of the studied complexes as they are verified to give reliable results. To consider the solvent effect and to be consistent with the experimental conditions, the most usual benzene has been used as solvent in the calculations of absorption properties and hyperpolarizabilities depending on the polarizable continuum model [45].

and bond angles around the boron atom haven't obvious changes between the ring-opening and ring-closed forms. The main structural variations are from DTE part, the bond length of C3C4 has a relatively obvious change (around 0.06 Å) from ringopening to ring-closed forms. The following variation comes from the dihedral angles among different thiophene rings of DTE unit. For the ring-opening systems, molecular structures are nonplanar and the dihedral angles are about 50 . When the DTE moiety is closed, the dihedral angles (C3-C4-C5-C6 and C4-C3-C7-C8) significantly decrease by  40 , it can be mainly ascribed to the reversible photochromic behavior between the ring-opening and ring-closed forms. In addition, the cyclization of DTE part effectively enhance the p-conjugation and almost exhibit a coplanar structure for the ring-closed systems. It is noteworthy that these large changes of geometrical structures will inevitably influence the NLO properties of the studied five DTE derivatives.

3. Results and discussion

3.2. Photoswitchable second-order NLO properties

3.1. Ground state geometries

To theoretically explore the photoswitched second-order NLO properties of the studied five complexes (Scheme 2), we calculated the static first hyperpolarizabilities at the DFT level of theory by using four functionals with different percentage of HF exchange, including PBE0, CAM-B3LYP, vB97XD and vB97X. Comparisons of btot with four different functionals are described in Fig. 1. The results indicate that most of the traditional hybrid functional (PBE0) calculated btot values are larger than the corresponding range separated functionals, and three range-separated

In which the bi (v) is defined by Eq. (4)

bi ðvÞ ¼ biii ðvÞ þ

1X ðb ðvÞ þ bjij ðvÞ þ bjji ðvÞÞ; i; j ¼ x; y; z 3 j6¼i ijj

ð4Þ

The ground state geometrical structures of the B(C6F5)2coordinated DTE derivatives 1  5 (Scheme 2) are fully optimized at the PBE0/6-31G(d) level of theory. The main geometrical parameters of ring-opening and ring-closed systems are collected in Tables 1 and 2, respectively. The sign o denotes ring-opening form and c denotes ring-closed form, and the relative atomic labels are marked in Fig. S2. As shown in Tables 1 and 2, the bond lengths

X.-H. Liu et al. / Journal of Photochemistry and Photobiology A: Chemistry 335 (2017) 155–164 Table 4 The calculated vertical excitation energies (nm), oscillator strength (a.u.) and dipole moments (debye) for the studied complexes 1–5 at the PBE0/6-31G(d) level. Complex

Eeg

fos

mgg

mee

Dmge

Ta

Ta
Dmge

btotb

1o 2o 3o 4o 5o 1c 2c 3c 4c 5c

2.24 2.06 1.91 1.77 1.61 1.12 1.00 0.78 0.92 0.82

0.33 0.23 0.17 0.09 0.08 0.22 0.25 0.40 0.39 0.59

11.32 10.71 10.75 12.05 12.24 12.96 12.95 15.43 18.73 23.95

12.30 11.64 11.65 13.07 13.24 14.63 14.86 18.49 22.51 30.78

0.98 0.93 0.90 1.02 1.00 1.67 1.91 3.06 3.78 6.83

0.029 0.026 0.024 0.016 0.019 0.16 0.25 0.84 0.50 1.07

0.029 0.024 0.022 0.017 0.019 0.26 0.48 2.58 1.89 7.31

108.4 168.6 207.0 201.6 247.2 600.7 952.9 2161.1 3663.7 7361.4

a b

T = fos/Eeg3. The btot values are calculated using the CAM-B3LYP functional.

functionals show a consistent trend for the calculated btot values, and the results of btot are also in well accordance with the aforementioned prediction of molecular structures in the ground state. Besides, the btot values of synthesized experimentally nine complexes (Scheme 1) are calculated at CAM-B3LYP/6–31 + G(d) level and the btot data are summarized in Table S2. By the analysis and comparison of btot values for the nine complexes, the 2-B (C6F5)2 complex (62.5
1030 esu for ring-opening form and 222.4
1030 esu for ring-closed form, respectively) exhibits a great potential toward the photoswitchable NLO applications, which can be interpreted by stronger electron-accepting ability of

159

 C6F5 group, making boron center more electron-deficient and thus increasing the interaction of B-O. Based on the original structure of 2-B(C6F5)2, we introduced a simple ligand (N¼N-ph) by the substitution of thiophene ring at the 3-position of the b-diketonate, the molecular structure of complex 1 is shown in Scheme 2, the calculated btot values of complex 1 is 108.4
1030 esu for ring-opening form and 600.7
1030 esu for ring-closed form, respectively. Then, we also further investigated the effect of different electron-withdrawing groups (CF3, NO2) in the R2 position of benzene ring and electron-donating groups (CH3, NH2) in the R1 position of thiophene ring on the second-order NLO properties. Finally, we obtained five B(C6F5)2-coordinated DTE derivatives. For brevity, we only took CAM-B3LYP as an example to qualitatively assess the second-order NLO behaviors of the studied five complexes. 3.2.1. Static first hyperpolarizabilities of ring-opening and ring-closed systems We calculated the btot values of ring-opening and ring-closed systems with four different functionals in benzene solution and the relative parameters of btot for the ring-opening and ring-closed systems are summarized in Table 3, the D-value represents the difference of btot between the ring-opening and ring-closed systems, and the Q-value is defined as the quotient of btot between the ring-opening and ring-closed systems, respectively. These factors are closely linked to the NLO properties of the studied systems. The direct comparisons of btot values are described in Fig. 1. Here, all calculated btot values of ring-opening and ring-

Table 5 The calculated absorption data and relative frontier molecular orbitals (isovalue = 0.02) for the ring-opening forms of the studied complexes 1  5 in benzene solution by TDPBE0 method. Complex

Main state

E (eV)

l (nm)

f

Transitiona (coefficient)

1o

S1

2.243

553

0.3336

H ! L (0.70)

2o

S1

2.060

602

0.2326

H ! L (0.70)

3o

S1

1.906

651

0.1714

H ! L (0.70)

4o

S2

1.774

699

0.0940

H–1 ! L (0.70)

5o

S2

1.614

768

0.0808

H–1 ! L (0.69)

a

H and L represent HOMO and LUMO, respectively.

Occupied orbital

Unoccupied orbital

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Table 6 The calculated absorption data and relative frontier molecular orbitals (isovalue = 0.02) for the ring-closed forms of the studied complexes 1–5 in benzene solution by TDPBE0 method. Complex

Main state

E (eV)

l (nm)

f

Transitiona (coefficient)

1c

S1

1.117

1110

0.2238

H ! L (0.71)

2c

S1

1.000

1240

0.2462

H ! L (0.71)

3c

S1

0.775

1600

0.3994

H ! L (0.73)

4c

S1

0.924

1342

0.3862

H ! L (0.72)

5c

S1

0.824

1504

0.5922

H ! L (0.75)

a

Occupied orbital

Unoccupied orbital

H and L represent HOMO and LUMO, respectively.

closed systems are discussed at the CAM-B3LYP/6–31 + G(d) level of theory. For the ring-opening systems 1o, 2o and 3o, as described in Table 3 and Fig. 1(a), the btot values gradually increase with the enhancement of electron-withdrawing ability of substituents (H, CF3, NO2), and 3o exhibits the largest btot values of 207.0
1030 esu contrast with the ring-opening forms 1o and 2o, the D-value is 1954.1
1030 esu and the Q-value is 10.4, all of these factors related with btot show an increasing trend. Analogously, for the ring-opening forms 4o and 5o, the 5o owns the largest btot values (247.2
1030 esu) in contrast to the corresponding ring-opening forms 1o  4o. Similarly, for the ring-opening systems 2o, 4o and 3o, 5o, the btot values also greatly increase with the enhancement of electron-donating ability of substituents. The order of btot for the ring-opening systems is as follows: btot (5o) > btot (3o) > btot (4o) > btot (2o) > btot (1o). Therefore, we come to a conclusion that the btot values of ring-opening systems can be significantly improved with the strengthening of electron-withdrawing and electron-donating ability of substituents in the R2 and R1 positions, respectively. For the ring-closed systems 1c, 2c and 3c, as described in Table 3 and Fig. 1(b), the btot values greatly improve with the strengthening of electron-withdrawing ability of substituents (R = H, CF3, NO2), especially for 3c, it possesses the largest btot values (2161.1
1030 esu) contrast with 1c and 2c, which is 3.6 and 2.3 times of 1c and 2c, respectively. Moreover, the D-value and Qvalue also show an increasing trend with the strengthening of electron-withdrawing ability. The similar situation is observed for 4c and 5c, and 5c exhibits the highest btot value (7361.4
1030 esu), the D-value and Q-value also are the highest in comparison to

other four ring-closed forms. Furthermore, by the comparison of 2c, 4c and 3c, 5c, we notice that the btot values obviously increase with the enhancement of electron-donating ability of substituents (CH3, NH2), the order of btot values for ring-closed systems is as follows: btot (5c) > btot (4c) > btot (3c) > btot (2c) > btot (1c). The results indicate that the btot values of ring-closed systems have an evident increase with the enhancement of electron-withdrawing and electron-donating ability of substituents in the R2 and R1 positions, respectively. On the whole, the results of btot calculation for the ring-opening and ring-closed systems are in good agreement with the analysis of geometrical structures, in other words, the btot values of ringclosed systems are larger than those of the corresponding ringopening systems. In general, the excellent NLO materials should own not only large btot values, but also large D-values and Q-value. Surprisingly, the designed complex 5 exhibits the largest btot values, D-value and Q-value in comparison to the corresponding complexes 1  4, so the complex 5 is hopeful to act as an potential candidate toward effective NLO applications. In summary, different electron-withdrawing and electron-donating groups play an important role in the design of high-efficiency NLO materials. The electronic absorption characters are closely associated with the molecular NLO behaviors. Therefore, the btot can be interpreted from the standpoint of electronic absorption by a two-level model proposed by Oudar and Chemla [46,47],

b / ðmee  mgg Þ

f os

Eeg 3

ð5Þ

X.-H. Liu et al. / Journal of Photochemistry and Photobiology A: Chemistry 335 (2017) 155–164

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of the Eeg is inversely proportional to the btot and the fos is proportional to the btot. Thus, we predict that the large btot values are intimately related to the strong oscillator strength and small vertical excitation energies. To gain an intuitive understanding of this relationship between btot and the relative parameters from the two-level model, we map a chart graph in Fig. 2 for the ringopening and ring-closed systems and the relative parameters (Eeg, fos, Dmge, T
Dmge, btot) are collected in Table 4. The parameter Dmge stands for the difference between mee and mgg, and the symbol T is equivalent to fos/Eeg3. For the ring-opening systems 1o  3o, as seen in Table 4 and Fig. 2(a), the parameter T
Dmge exhibits a slight decreasing trend, which may be mainly attributed to its large vertical excitation energies and small oscillator strength. However, in terms of the ring-opening forms 4o and 5o, the T
Dmge values are proportional to the btot values. For the ring-closed systems 1c  5c, the small transition energies are more favorable to obtain the large btot values. In other words, the btot values of ring-closed systems are larger than those of the corresponding ring-opening systems. As described in Table 4 and Fig. 2(b), the relative parameters of the two-level model (Dmge, T, T
Dmge) are proportional to the btot values, and the T
Dmge values of ring-closed systems are also higher than those of the corresponding ring-opening systems, which is in accordance with the expression (5) from the two-level model.

Fig. 3. Simulated absorption curves for (a) ring-opening forms and (b) ring-closed forms of the studied complexes 1–5 by TD-PBE0 method in benzene solution.

where mee and mgg represent the dipole moments of excited state and ground state, respectively. fos represents the oscillator strength and Eeg represents vertical excitation energy of the studied excited state. In this two-level model expression, we observe that the cubic

3.2.2. Absorption spectra and frontier molecular orbitals analysis To obtain a more profound understanding on the NLO responses of the studied systems, the frontier molecular orbitals (FMOs) and absorption properties were analyzed with TD-PBE0 method in benzene solution. The main absorption data including crucial transition state (Sn), vertical excitation energies (E), absorption wavelength (l), oscillator strength (f) and relative transition molecular orbitals with maximum contribution coefficient are summarized in Tables 5 and 6, respectively. The simulated absorption spectra of ring-opening forms 1o  5o and ring-closed forms 1c  5c are shown in Fig. 3, and the energy level diagrams of partial FMOs are presented in Fig. 4. It can be observed in Fig. 3(a) that the absorption wavelength of the ring-opening forms are in the range of 553 nm to 768 nm (the order of absorption

Fig. 4. Energy level diagrams of relative frontier molecular orbitals for the ring-opening and ring-closed forms of the studied complexes 1–5, the blue and red lines represent the transition of HOMO to LUMO, and the black lines represent the transition of HOMO  1 to LUMO. (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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Fig. 5. Electron density difference maps (isovalue = 0.0005 a.u.) between the ground states and excited states at the PBE0/6-31G(d) level for the studied complexes 1–5. Purple (blue) regions represent positive (negative) values, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

wavelength: 5o > 4o > 3o > 2o > 1o), which exhibit an obvious red shift compared with the available experimental values (475 nm) of 2-B(C6F5)2 complex [30]. The red shift of absorption bands mainly depends on the electron-withdrawing and electron-donating ability of substituents. More specially, the absorption spectra of ring-opening forms show an obvious red shift with the enhancement of electron-withdrawing and electron-donating ability of substituents. Besides, as presented in Fig. 4, the changes of

absorption spectra are also in good agreement with the reduction of energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbitals (LUMO). The relative FMOs of ring-opening forms are plotted in Table 5. In terms of the ring-opening systems 1o  5o, the main excitations of S0 ! S1 and S0 ! S2 state originate from the transition of HOMO to LUMO and HOMO  1 to LUMO, and the occupied molecular orbitals (HOMO and HOMO-1) and unoccupied molecular orbitals

Fig. 6. Simulated varying curves of frequency-dependent first hyperpolarizabilities b (-v; v, 0) and b (-2v; v, v) in benzene solution for the ring-opening forms of the studied complexes 1o–5o.

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(LUMO) present a similar electron density distribution. That is, the HOMO and HOMO  1 mostly locate on the left DTE part. Whereas, the LUMO mainly distribute in cyclopentene of DTE units, center b-diketonate moiety and right N¼N-ph ligand. In other words, the DTE moiety plays the role of electron donor in the studied systems. Based on the topologies analysis of HOMO, HOMO  1 and LUMO, these excitations of ring-opening systems are primarily attributed to the p ! p* transition. Similarly, for the ring-closed systems 1c  5c, the absorption wavelengths in Fig. 3(b) are in the range of 1100 nm to 1600 nm, which also show an pronounced red shift (the order of absorption wavelength: 3c > 5c > 4c > 2c > 1c) and extend to NIR region contrast with the corresponding experimental data (863 nm) of 2-B(C6F5)2 complex [30]. It is assigned to the coordination of boron center as well as the enhancement of electron-withdrawing and electron-donating ability of substituents. The relative FMOs of ring-closed forms are provided in Table 6. The primary electronic transition of S0 ! S1 state comes from HOMO to LUMO. The FMOs in Table 6 also exhibit a similar distribution except for 5c. Specially, the HOMO are mainly centered on left DTE moiety, center b-diketonate moiety and right azo moiety (N¼N-), and the LUMO spreads over the whole systems except for B(C6F5)2 part and partial thiophene ring of DTE units. But, the ring-closed form 5c almost delocalizes over the whole molecule for the HOMO and LUMO. Owing to the large superposition between HOMO and LUMO for the ring-closed form 5c, it is benefit to the electron transfer, and it is also in good agreement with its large absorption wavelength and high btot values. By the analysis of FMOs of ring-closed systems, the lowestenergy absorption of the ring-closed forms are assigned as p ! p* transition. In conclusion, we find that different substituents can significantly influence the absorption properties and energy levels of FMOs, and the decrease of energy gaps of ring-closed systems are in well accordance with the enhancement of btot values. Specially, the smaller HOMO-LUMO energy gap can give rise to the larger btot values. We hope that the discussions of absorption properties can provide a guidance for the subsequent computational and experimental NLO investigations. To describe the charge transfer situations in detail and obtain a visual view of the studied five complexes, we map the electron density difference maps (EDDMs) of ring-opening and ring-closed systems in Fig. 5. The purple region stands for a gain in electronic density and blue region stands for a decrease in electronic density, it explicitly indicates the scope of the charge transfer for the studied molecules. As displayed in Fig. 5, the direction of charge transfer is mainly from blue region to purple region. The DTE part mainly acts as an electron donor in this system and the btot values can be altered by introducing different substituents. The EDDMs of ring-opening systems show that the changes of electron density almost spread over the whole systems. The variations of electron density in DTE fragment are mainly negative and in N¼N-ph part is mainly positive, and the degree of charge transfer exhibits an increasing trend with the enhancement of electron-withdrawing and electron-donating ability of substituents. However, for the ring-closed systems, the variations of electron density have a decreasing trend with the strengthening of electron-withdrawing and electron-donating ability of substituents, particularly to the center b-diketonate moiety and right N¼N-ph ligand. However, with regard to the left DTE moiety, the changes of electron density show a slight increase with the enhancement of electronwithdrawing and electron-donating ability of substituents. 3.3. Frequency-dependent first hyperpolarizabilities In order to fully take into account the influence of dispersions for the studied complexes 1–5, we calculated the btot (v) in benzene solution by employing the CPDFT method at the CAM-

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B3LYP/6–31 + G(d) level of theory. The obtained data of b (-v; v, 0) and b (-2v; v, v) at the frequency range from 0.000  0.065 a.u. are summarized in Table S3 and Table S4, respectively. Here, we analyzed the effect of dispersions on the frequency-dependent first hyperpolarizabilities of the ring-opening forms 1o  5o. The relationships between b (-v; v, 0) and b (-2v; v, v) are clearly presented in Fig. 6. As depicted in Fig. 6, the values of b (-2v; v, v) show different varying trend compared with the corresponding b (-v; v, 0) values. With regard to the ring-opening forms 1o  5o, the values of b (-v; v, 0) slightly increase with the expansion of frequency range from 0.000 to 0.065 a.u. However, the values of b (-2v; v, v) initially exhibit a slow enhancement in the range of 0.000 to 0.0400 a.u., then it markedly raise and reach a maximum in the range of 0.040 to 0.060 a.u., which can be ascribed to the effect of resonance or dispersion at 553 nm to 768 nm based on the analysis of TDDFT calculations. Hence, to avoid the interference of resonance or dispersions on the frequency-dependent first hyperpolarizabilities of the studied five complexes, we suggest that the low-frequency region v (0.000  0.003 a.u.) will be worthwhile to consider in the experiments for the design of effective NLO materials. 4. Conclusions In summary, we have performed a systematical DFT calculation to probe the electronic structures and second-order NLO properties of a series of B(C6F5)2-coordinated DTE derivatives. The optimized geometries indicated that ring-closed forms of the DTE unit almost presented a coplanar structure, which brought about the forming of a larger p-conjugation compared with the corresponding ring-opening forms. It may account for its large btot values. Moreover, our DFT calculations also showed that the reversible photochromic process of DTE units dramatically changed its static first hyperpolarizabilities. Specially, the btot values of ring-closed forms are 5.5  29.8 times larger than those of the corresponding ring-opening forms. Furthermore, the btot values of ring-opening and ring-closed systems markedly improved by bearing strong electron-donating and electron-withdrawing groups at the R1 and R2 position of B(C6F5)2-coordinated DTE derivatives. Besides, the electronic excited state properties were analyzed by TDDFT method. In the end, we considered the influence of dispersions on the btot (v) at the frequency region v (0.000–0.065 a.u.). We hope that this work will provide a new strategy to design efficient photoswitchable NLO materials for the subsequent experiments. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 21173096) and the State Key Development Program for Basic Research of China (Grant No. 2013CB834801). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. jphotochem.2016.11.029. References [1] H. Rau, H. Durr, H. Bouas-Laurent, Photochromism: molecules and systems, photochromism, Molecules Syst. (1990) 165–192. [2] L.R. Dalton, A.W. Harper, R. Ghosn, W.H. Steier, M. Ziari, H. Fetterman, Y. Shi, R. Mustacich, A.-Y. Jen, K.J. Shea, Synthesis and processing of improved organic second-order nonlinear optical materials for applications in photonics, Chem. Mater. 7 (1995) 1060–1081.

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