Tailoring the Linear and Second-Order Nonlinear Optical Responses

Subscriber access provided by YORK UNIV

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Tailoring the Linear and Second-Order Nonlinear Optical Responses of the Titanium-MIL-125 Metal-Organic Framework through Ligand Functionalization: A First Principles Study Bilian Ni, Xu Cai, Jing Lin, Yi Li, Shuping Huang, Zhaohui Li, and Yongfan Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08008 • Publication Date (Web): 13 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Tailoring the Linear and Second-Order Nonlinear Optical Responses of the Titanium-MIL-125 Metal-Organic Framework through Ligand Functionalization: A First Principles Study Bilian Ni,†,‡ Xu Cai,† Jing Lin,† Yi Li,,†,§ Shuping Huang,† Zhaohui Li,† and Yongfan Zhang*,†,§ †State Key Laboratory of Photocatalysis on Energy and Environment, College of Chemistry, Fuzhou University, Fuzhou, Fujian, 350116, China ‡Department of Basic Chemistry, College of Pharmacy, Fujian Medical University, Fuzhou, Fujian 350004, China §Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen, Fujian, 361005, China

Abstract Density functional theory calculations have been performed to investigate the linear and second order nonlinear optical (NLO) properties of titanium-based MIL-125 metal-organic frameworks in crystalline form, in which the 1,4-benzene-dicarboxylate (BDC) linkers are modified by introducing different functional groups or by extending BDC ligand to contain two (MIL-126) and three (MIL-127) benzene rings. Our results reveal that the functionalization of BDC linker tends to increase the dielectric constants and the magnitude of birefringence of MIL-125, especially for the aminated derivatives. Correspondingly, the incorporation of substituent group will improve the phase matching performance of MIL-125. As for the second harmonic generation (SHG) susceptibility, the SHG activity of the pristine MIL-125 is comparable to KDP, which can be attributed mostly to the contributions of TiO5(OH) octahedra. It is noted that after introducing substituent group into BDC linker, the organic part will have a remarkable influence on the SHG intensity. However, the specific effect on the NLO response is dependent on the type of functional group incorporated into BDC ligand, and only the inclusion of amine group that is strongly electron-donating can obviously enhance the SHG activity of MIL-125. In addition, MIL-126 and MIL-127 with longer aromatic linking unit are not suitable to act as NLO materials due to their poor phase matching abilities, but they are the promising candidates for the low dielectric constant materials. The present study can provide theoretical insights to design new second-order NLO materials based on MIL-125.



Corresponding authors. E-mail address: [email protected]; [email protected] 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 31

1. INTRODUCTION Metal-organic frameworks (MOFs) are a new type of crystal with hybrid networks consisting of inorganic metal nodes and organic linkers. The major advantage of MOF materials is that their properties can be regulated in a controlled way at the molecular level by simply altering their composition and topology.1 Due to their tunable crystalline structures, MOFs have shown many promising potential applications in very diverse fields such as gas separation and storage, catalysis, biochemistry, etc. It is noted that for those polar MOFs with noncentrosymmetric structure, they also have potential applications as ferroelectric and second-order nonlinear optical (NLO) materials.2–4 With respect to the traditional inorganic and organic molecular NLO crystals, the modular feature of MOFs allows that the noncentrosymmetric structure can be designed purposely by taking advantage of the strong and highly directional nature of metal-ligand coordination bonds, which makes MOFs as a particularly interesting family of NLO materials.5,6 In addition, as a class of inorganic-organic hybrid material, besides having strong second-harmonic generation (SHG) signal that is comparable to commercial inorganic crystals such as KH2PO4 (KDP), the organic nature of MOFs results in other advantages including the ultrashort response times and biocompatibility.6 During past two decades extensive investigations have been carried out to study the unique chemical properties of MOFs, however little attention is paid to understand the sources of the SHG responses of polar MOFs, especially how the organic linkers affect the second-order NLO performances still remains unclearly.4 The sensitive relationship between the strength of SHG susceptibility and the configuration of the organic linker units has been observed in a recent study on a zeolitic imidazolate framework, ZIF-8.6 Therefore, theoretical investigations on MOF-derived

2


Page 3 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


NLO crystals are highly expected.4 Considering that the titanium-based MOFs are one of the most appealing classes of MOFs reported to date owing to their potential applications in photocatalysis and optoelectronics,7 the NLO properties of the crystalline titanium carboxylate MOF, MIL-125,8 and its derivatives are focused on the present work. As the most widely investigated member of the Ti-MOFs, MIL-125 crystallizes in a quasi-cubic tetragonal lattice, and its framework is constructed by cyclic octamers of edge and corner sharing TiO5(OH) octahedra that connect to each other through 1,4-benzenedicarboxylate (BDC) linkers. To control the optical response of MIL-125, the functionalization of the organic linking unit of MIL-125 has been attracted attention recent years, and different functional groups such as -NH2, and -OH have been introduced into the BDC linkers to tuning the optical responses of MOFs.9–13 Although the electronic structures of MIL-125 and its derivatives have been reported,10,14,15 the theoretical investigations of the second-order NLO properties of these materials have not been performed. Moreover, due to the large size of the unit cell, there are few theoretical studies on the SHG properties of MOFs. Zhang et al. performed the first theoretical treatment on the NLO response of MOF, in which a Zn-based MOF is simulated by adopting cluster model.16 Similar approach was used to study the SHG activity of ZIF-8.6 In two other recent works,17,18 the second-order NLO susceptibilities of PEB-Zn/Cd and MIL-53 MOFs have been evaluated by employing the combined local field theory/charge embedding method. Considering that the optical properties of a crystal material are dependent on the band structure, from the theoretical point of view, it would be interesting to study the NLO property on the periodic three-dimensional MOF structure by adopting band structure approach. According to our knowledge, the present work may be the first time for directly evaluating the SHG responses of MOF materials by using band structure approach.

3



Page 4 of 31

In here, via first principle calculations, we perform a careful evaluation on the linear and second-order NLO properties of MIL-125 and its different derivatives with monoaminated and diaminated BDC linkers, as well as the cases that BDC ligands are modified by other functional groups including -OH and -NO2. Additionally, to study the influences of the length of the linkers, we also consider the situations that the BDC linkers are replaced by 4,4-biphenyl-dicarboxylate (BPDC) and terphenyl dicarboxylate (TPDC) ligands. Our results reveal that the optical properties of MIL-125 can be tuned by introducing functional groups into BDC linker or by extending the length of aromatic ring. The chemical modifications of BDC tend to increase the dielectric constants and the magnitude of birefringence of MIL-125 at the low energy region, especially for two aminated derivatives. For the second-order NLO susceptibility, the SHG response is sensitive to the type of functional group incorporated into BDC ligand. As a strong electron-donating substituent, the inclusion of amino group can enhance the SHG activity of MIL-125, while the addition of -NO2 group that is strongly electron-withdrawing leads to a weakening of SHG effect. Moreover, the derivatives with BPDC and TPDC ligands are not suitable to act as NLO materials due to their poor phase matching performances, but they may be promising candidates for the low dielectric constant materials required for future electronics. The present work can provide important information for developing new NLO materials with good performances based on titanium-MIL-125 MOF.

2. COMPUTATIONAL DETAILS All density functional theory (DFT) calculations were performed by using the Vienna ab initio simulation package (VASP) and the projected augmented wave (PAW) method.19–21 The generalized

gradient

approximation

Perdew-Burke-Ernzerhof

(PBE)

exchange-correlation

4


Page 5 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


functional was employed, and the kinetic cut-off energy for the plane-wave expansion was set to 500 eV. The influences of van der Waals interactions were taken into account by using the dispersion corrected vdW-DF2 functional.22 During the structural optimizations, only  point was involved in the Brillouin zone integration, and the convergence thresholds of the energy change and the maximum force were set to 10-5 eV and 0.03 eV/ Å, respectively. After the structural optimizations, the optical properties of MIL-125 and its derivatives were evaluated in the next step. The linear optical response is directly related to the complex dielectric function  ( )   1 ( )  i 2 ( ) , and the imaginary part of the dielectric function,  2 ( ) can be calculated by following equation,23

 2ab ( ) 

4 2 V

 f nm

nm , k

a b rnm rmn  nm  

(1)

where superscripts, a and b indicate Cartesians components; n and m represent the energy bands;

f nm  f n  f m is the difference of the Fermi distribution functions; nm  n  m is the frequency difference between the energy bands n and m at the same k point; V is the volume of the unit cell. a The rnm is the matrix element of the position operator,

a  rnm

a  ip nm

 nm

(2)

where pnm is the momentum matrix element. The real part of the dielectric function was yielded from  2 ( ) by a Kramer-Kronig transformation. From the dielectric function, all other linear optical properties, such as the refractive index (n) and the birefringence (n), can be derived. In the present work, the so-called length-gauge formalism derived by Aversa and Sipe,24 was employed to calculate the SHG coefficients of MOFs, and at a zero-frequency limit the second-order nonlinear susceptibility  abc (2 ,  ,  ) can be expressed as,

5



 abc (2 ,  ,  ) 

1 V

i 4V

a rnm {rmlb rlnc }



nml , k

nm , k

[n f ml  m f ln  l f nm ] 

nm

f nm



mlln

Page 6 of 31

2 mn

a b c b a c c a b [rnm (rmn ;c  rmn ;b )  rnm ( rmn ;c  rmn ; a )  rnm ( rmn ;b  rmn ; a )]

(3)

b where rmn ; a is the generalized derivative of the coordinate operator in k space.

b rmn ;a 

a b rnm bmn  rnm amn

 nm



i

 nm

 (

r r   nl rnlb rlma )

a b lm nl lm

(4)

l

a a where amn  ( p nn  p mm ) / m is the difference between the electronic velocities at the energy

bands n and m. While for the frequency-dependent SHG susceptibility (i.e.,  > 0),

 i 2V

abc

f

nm , k

1



1 (2 ,  ,  )  V

2 mn

(

nm

[

a rnm {rmlb rlnc } 2 f nm f ml f ln [ ]    ln   ml   nml , k (ln  ml ) mn  2

2

mn (mn  2 )

a b c rnm (rnm ;c  rmn ;b ) 

1

mn (mn   )

a b a c (rnm ;c rmn  rnm ;b rmn ) 

1 4 1 a b c b c c b  )rnm (rmn  cmn  rmn  bmn )  (rnm ; a rmn  rnm ; a rmn )] mn   mn  2 2mn (mn   )

(5)

To obtain reliable results of the linear and nonlinear optical properties, a dense k-point mesh and many empty energy bands were required. After carefully examining the convergences of the optical properties as functions of the size of k-point mesh and the number of empty bands, our results showed that when the sizes of k-point meshes of systems with BDC, BPDC and TPDC linkers were set to (7 × 7 × 7), (6 × 6 × 6) and (5 × 5 × 5), respectively, and 2000, 4000, and 5000 energy bands were involved in the calculations, the good convergences of the SHG coefficients were achieved. Due to the insufficient cancellation of the self-interaction correction inherent in the pure DFT method, the PBE functional tends to underestimate the band gap of semiconductor with respect to the experimental value. Therefore, the hybrid HSE06 functional was used to determine the band gap of different derivatives based on MIL-125, which has been shown to be suitable to

6


Page 7 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


describe the electronic structures of MOFs.10,14,25 In the following sections, the d-tensor defined as

dij 

 abc 2

was used to denote the second-order NLO susceptibility, in which Voigt notation

indices were introduced to simplify second rank tensors. Previous theoretical works indicated that the above method was suitable for predicting the SHG responses of different solids including both inorganic materials (such as AgGaS2)26,27 and organic molecular crystals (such as DAST and DSTMS).28 (see Table S1 in the Supporting Information (SI) for the comparisons between the theoretical and experimental results).

3. RESULTS AND DISCUSSION 3.1 Structures of MIL-125 and its Derivatives Total seven MOFs derived from MIL-125 are taken into account in this work. Figure 1a shows the structure of pristine MIL-125 which contains 120 atoms (Ti8O36C48H28) in the primitive cell. To investigate the impacts of functional group on BDC linker of MIL-125, three derivatives built by introducing a series of functional groups including -NH2, -OH and -NO2 into BDC units are explored. As an example, the structure of NH2-MIL-125 is given in Figure 1b. For the amine-functionalization, the diaminated derivatives are also involved to study how the amount of NH2 group affects the optical property of MIL-125, in which the para (Figure 1c) and meta (Figure 1d) arrangements of two NH2 groups are investigated. By comparing the total energies of two structures, the meta arrangement is more stable than the para configuration by about 0.75 eV. Thus, in the following sections, the results of meta arrangement of two amino groups are discussed. It is noted that except the case of -NO2 group, other MIL-125 derivatives have been synthesized in experiments.10 Furthermore, to examine the influences of the extending of aromatic linking units, two additional derivatives that the BDC units are replaced by the similar linkers contained two and 7



Page 8 of 31

three benzene rings, namely BPDC and TPDC ligands are also considered. Experimentally, BPDC and TPDC linkers have been successfully incorporated in the framework of Zr-MOFs,29 and following the same definition, we denote the Ti-MOFs with BPDC and TPDC linkers as MIL-126 (Figure 1e) and MIL-127(Figure 1f), respectively. The stoichiometries of the primitive cells of these MOFs are Ti8O36C84H52 and Ti8O36C120H76, respectively.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1 Structures of the unit cell of (a) MIL-125, (b) NH2-MIL-125, (c) para-(NH2)2-MIL-125, (d) meta-(NH2)2-MIL-125, (e) MIL-126 and (f) MIL-127. The Ti, C, O, N, and H atoms are denoted by yellow, gray, red, blue, and white spheres, respectively. The hydrogen atoms connected to benzene rings are not shown.

Table 1 lists the optimized cell parameters of MIL-125 and its six derivatives. For the pristine MIL-125, it crystallizes in the noncentrosymmetric I4mm space group (No. 107) with a quasi-cubic tetragonal unit cell, and the calculated lattice parameters are a = b = 18.970 Å, c = 18.066 Å, which agree well with the experimental measurements (a = b = 18.654 Å, c = 18.144 Å).8 We also have

8


Page 9 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


found another tetragonal phase of MIL-125 that it belongs to the centrosymmetric I4/mmm space group (No. 139). The configurations of two tetragonal phases are quite similar except that in I4/mmm the bridging hydroxo groups are coplanar with two neighboring Ti atoms. However, due to this structure is higher in energy (about 0.23 eV with respect to the I4mm phase), it is not taken into account in the present work. As displayed in Figure 1a, for MIL-125, the Ti atom is coordinated with six oxygen atoms, including three O atoms (Oc) of surrounding BDC linkers, one oxygen (Oh) of bridging hydroxo group, and two bridging oxygens (Ob) between two neighboring Ti atoms. The average lengths of three kinds of Ti-O bonds are also given in Table 1, and the bond distances show a sequence of Ti-Ob < Ti-Oh ~ Ti-Oc, indicating that Ti-Ob bond is relatively difficult to be broken. As expected, the volume of MIL-125 will increase when the BDC linker is functionalized by -NH2, -OH or -NO2 group. However, the volume expansion is very small, even in the case of incorporation two -NH2 groups into BDC linker, the volume only expands by about 0.8%. Moreover, the functionalization of BDC has a small influence on the configuration of TiO5(OH) octahedra, and correspondingly, the average lengths of three types of Ti-O bonds vary slightly (< 0.02 Å, see Table 1). Although after introducing a single substitution the symmetry of MIL-125 is reduced to P1 space group, the cell shape also changes slightly. This is reflected in the facts that the values of a and b lattice parameters are approximately equal and the angles of , , and  are close to 90, suggesting that the original tetragonal lattice shape is nearly preserved. For the diaminated MIL-125 derivative (Figure 1d), a Cm symmetry is identified. The radii of the largest pores of MIL-125 and its derivatives are also estimated, and according to the results shown in Table 1, the decreasing of the pore size can be observed after introducing functional groups on the BDC linker.

9



Page 10 of 31

Table 1 Optimized cell parameters, the average lengths of three kinds of Ti-O bonds, and the radius (r) of the largest pore for MIL-125 and its different derivatives Cell parameters

Ti-Oc

MOFs

Ti-Oh

Ti-Ob

r

a (Å)

b (Å)

c (Å)

α ()

β ()

 ()

(Å)

(Å)

(Å)

(Å)

MIL-125

18.970

18.970

18.066

90.00

90.00

90.00

2.055

2.038

1.867

7.56

NH2-MIL-125

18.972

18.981

18.096

89.89

89.95

90.00

2.064

2.040

1.852

6.80

OH-MIL-125

19.006

18.989

18.098

89.90

89.76

90.11

2.072

2.040

1.851

6.92

NO2-MIL-125

18.964

19.023

18.053

91.20

91.02

90.04

2.054

2.044

1.849

6.72

(NH2)2-MIL-125

19.032

19.032

18.088

90.00

90.00

89.99

2.055

2.035

1.852

6.66

MIL-126

23.324

23.324

24.509

90.00

90.00

90.00

2.057

2.039

1.853

9.67

MIL-127

27.724

27.724

30.628

90.00

90.00

90.00

2.058

2.040

1.852

11.93

Comparing to MIL-125, the replacing of BDC units with BPDC and TPDC ligands leads to a significant expansion of the volume, and it seems that the c parameter is increased more obviously than a and b parameters. Meanwhile, the radius of the largest pore in the framework enlarges from 7.56 Å to 9.67 Å, and to 11.93 Å, respectively. However, the lengths of three kinds of Ti-O bonds (Table 1) of both MIL-126 and MIL-127 are close to those of MIL-125, indicating that the configurations of TiO5(OH) octahedra of these MOFs are quite similar. 3.2 Electronic Structures of MIL-125 and its Derivatives By using the hybrid HSE06 functional, the band gaps of MIL-125 and its derivatives are determined (see Table 2), and to analyze the electronic structure, the partial density of states (PDOSs) of monosubstituted MIL-125 are displayed in Figure 2.

10


Page 11 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2 Calculated band gaps (Eg), static dielectric constants [(0)], refractive indices [n(0)], birefringences [n(0)], and the SHG coefficients with the largest magnitude of MIL-125 and its different derivatives SHG coefficients

MOFs

Eg (eV)

xx(0)

yy(0)

zz(0)

nxx(0)

nyy(0)

nzz(0)

n(0)a

MIL-125

3.80

1.967

1.967

1.851

1.403

1.403

1.361

0.042

0.76 (d33)

NH2-MIL-125

2.57

2.129

2.090

1.960

1.459

1.446

1.400

0.059

1.54 (d33)

OH-MIL-125

2.99

2.055

2.024

1.910

1.434

1.423

1.382

0.051

0.54 (d33)

NO2-MIL-125

3.84

2.070

2.041

1.949

1.439

1.429

1.396

0.043

0.24 (d11)

(NH2)2-MIL-125

2.00

2.003

2.229

2.229

1.415

1.493

1.493

0.078

1.76 (d11)

MIL-126

3.31

1.748

1.748

1.680

1.322

1.322

1.296

0.026

0.88 (d33)

MIL-127

2.95

1.590

1.590

1.538

1.261

1.261

1.240

0.021

1.07 (d33)

(pm/V)

a. In here, the birefringence is quantified as the maximum difference between three refractive indices, namely n = nmax -nmin.

(a)

(b)

(c)

(d)

Figure 2 The atomic partial density of states (PDOSs) of (a) MIL-125, (b) NH2-MIL-125, (c) OH-MIL-125, and (d) NO2-MIL-125. The Fermi level (EF) is set to zero. The partial charge density maps of VBM or CBM are shown in the insets. 11



Page 12 of 31

For the pristine MIL-125, its band gap is predicted to be 3.80 eV, which is consistent with the experimental results of 3.6 ~ 4.0 eV.8,10,30 According to the PDOSs of Ti, O, and C atoms shown in Figure 2a, the carbon atoms belonged to benzene rings have significant contributions to the valence band maximum (VBM) at the Fermi level, while the conduction band minimum (CBM) is mainly derived from Ti-3d orbitals. For clarity, the partial charge density maps of VBM and CBM are provided in the insets of Figure 2a. It is clear that the VBM of MIL-125 is dominated by the π-bonding interactions of benzene rings with a mixture of small components of Oc-2p orbitals, and for the CMB the obvious contributions of Ti-3d orbitals can be observed. When the strong electron-donating substituent, amine is introduced into BDC linker, the band gap of MIL-125 decreases obviously from 3.80 eV to 2.57 eV. This result is in good agreement with the experimental measurement (about 2.6 eV)10 as well as the values obtained in other theoretical works.25,31 Such narrowing of the band gap suggests that the transparency range of MIL-125 will be reduced, in which the absorption edge is increased from 0.33 m to 0.48 m. As shown in Figure 2b, besides those carbon atoms of benzene rings, now the nitrogen atoms of -NH2 groups have great contributions to VBM, which also can be confirmed by the partial charge density map. On the other hand, such substituent has a neglectable influence on the composition of CBM, and it is still dominated by Ti-3d orbitals. If more -NH2 groups are simultaneously incorporated, namely in the case of (NH2)2-MIL-125, the band gap can be further decreased to 2.00 eV. The band gap of MIL-125 also becomes narrow (2.99 eV) through modifying BDC linker by hydroxyl group. However, compared to NH2-MIL-125, the incorporation of -OH group reduces the band gap to a lesser extent because the electron-donating ability of -OH is relatively weak.10 According to PDOSs and the partial charge density map displayed in Figure 2c, the VBM is mainly composed of 2p

12


Page 13 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


orbitals of O atom of hydroxyl group and the π-bonding orbitals of benzene ring. It is interesting that the presence of -NO2 group has little impact on the band gap of MIL-125 (Table 2), although obvious contributions of 2p orbitals of two oxygen atoms of -NO2 can be found in the VBM (see Figure 2d). For MIL-126 and MIL-127, the band gaps calculated by HSE06 functional are 3.31 and 2.95 eV (Table 2), respectively, indicating that increasing the length of aromatic chain provides another route to decrease the band gap of MIL-125. However, like MIL-125, the VBM and CBM of both MIL-126 and MIL-127 are still mainly originated from the π-bonding orbitals of organic linkers and Ti-3d orbitals, respectively (see Figure S1). As discussed above, the band gaps of different MOFs based on MIL-125 are sensitive to the compositions of the organic linkers, which will affect the optical properties (such as transparency range and SHG strength) of the material. Meanwhile, the organic functionalization also has an impact on the band edge positions. Considering extensive attentions have been attracted on tailoring the photocatalytic properties of MIL-125,7 the band edge alignments of the VBM and CBM are further determined by calculating the electrostatic potential at the center of the internal hollow of MOF.32 As presented in Figure 3, the band edges of pristine MIL-125 are -7.58 and -3.78 eV, respectively, quite consistent with the previous results (-7.64 and -3.84 eV) obtained by Butler et. al.32 Since the CBM of MIL-125 is primarily composed of the Ti-3d states of TiO5(OH) octahedra, the functionalization of BDC organic ligand has a small influence on the components of CBM, correspondingly the variations of the positions of CBM edges are not obvious and they are all above the standard reduction potential for H+/H2. In contrast, the position of VBM edge is closely related to the type of chemical group introduced into BDC linker. When the substituent group changes from -NO2 to -OH to -NH2, the position of VBM moves up gradually from -7.92 to -6.57 and then to 13



Page 14 of 31

-6.02 eV, respectively. A further rising of the VBM edge to -5.46 eV can be observed for the diaminated MIL-125 derivative. In addition, a comparison of the results of MIL-125, MIL-126 and MIL-127 shows that the inclusion of more benzene rings results in the upward shifts of both edges of VBM and CBM. As illustrated in Figure 3, except (NH2)2-MIL-125, the band edges of all Ti-based MOFs studied in here locate at energetically favorable positions for the photocatalytic water splitting. However, it seems that only NH2-MIL-125 may possess good photocatalytic activity under visible-light irradiation due to its relatively small band gap.

Figure 3 Calculated edge positions of the VBM and CBM with respect to the vacuum level of MIL-125 and its different derivatives. The redox potentials of water are drawn as horizontal lines.

3.3 Linear Optical Susceptibilities of MIL-125 and its Derivatives Due to their low density, recent investigations have demonstrated that MOFs show small value of the dielectric constant (), which can be utilized as promising candidates for next generation of low- dielectrics in microelectronics.33,34 Only a few experiments have been carried out to date on the dielectric behavior of MOF materials, including MIL-53(Al),35 zinc MOFs,36–39 and Sr-based MOF.40 To the best of our knowledge, the dielectric properties of Ti-based MOFs have not been reported.

14


Page 15 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


We first focus on the linear optical properties of the pristine MIL-125. As a compound with tetragonal lattice, MIL-125 belongs to uniaxial crystal, and there are two dielectric tensor components, namely xx() and zz(), corresponding to electric field perpendicular and parallel to the c-axis, respectively. The calculated complex dielectric functions are displayed in Figure 4a. From the dielectric function, the refractive indices, nxx() and nzz() can be obtained (Figure 4b), and then the birefringence n() can be calculated as the maximum difference between three refractive indices, i.e., n = nmax - nmin (Figure 4c). Additionally, the corresponding static (i.e.,  = 0) dielectric constants [(0)], refractive indices [n(0)], and birefringence [n(0)] are listed in Table 2. The values of nxx(0) and nzz(0) of MIL-125 are predicted to be 1.967 and 1.851, respectively. It seems that with respect to other MOF materials, MIL-125 has relatively smaller dielectric constants at low energy region. For example, the dielectric constants of ZIF-8 and Sr-based MOF are about 2.33 and 2.40 at 100 kHz, respectively.37,40 Therefore, MIL-125 is also a good candidate of low- material. According to the frequency-dependent dielectric functions shown in Figure 4a, there are strong transitions just at the band gap energy, and based on the analyses of PDOSs mentioned above, these transitions are dominated by the electron transitions from  bonding of BDC linkers to Ti-3d orbitals. It is well known that the birefringence is an important parameter to determine the phase matching ability of a NLO material. Our result shows that the static birefringence of MIL-125 (about 0.042) is slightly small in comparison with the reasonable range of 0.06 – 0.1 required in the practical applications,41 but it is close to the value (0.047) of silver thiogallate crystal (AgGaS2),42 the most common and representative NLO crystal in the infrared region. Considering that the relationship between refractive index and wavelength is one of important optical properties of a material, the calculated data of refractive indices are used to fit the coefficients of the Sellmeier

15



Page 16 of 31

equation that is defined as following, n 2 ( )  A 

B  D 2  E 4  F  6  C

(6)

2

where  is the wavelength of light (in the unit of m). The Sellmeier equation is usually used to determine the dispersion of light in a material at the transparent range. The fitting results of six Sellmeier coefficients of MIL-125 at the wavelength range of 0.33 – 4.0 m are provided in SI (Table S2), which may be useful for the future experimental studies on the linear optical response of MIL-125.

(a)

(b)

(c)

Figure 4 (a) The calculated complex dielectric functions (), (b) the refractive indices (n), and (c) the birefringence (n) of pristine MIL-125.

When the BDC linker of MIL-125 is functionalized by introducing a single -NH2 group, the original I4mm symmetry is broken, and now it corresponds to a biaxial crystal that has three independent dielectric tensors. Three dielectric tensors, xx, yy, and zz of NH2-MIL-125 crystal are determined along the directions of principal optical axes, and the results are presented in Figure 5a. Since for the monosubstituted case the distortion of the tetragonal cell is very small with respect to the pristine MIL-125 (see Table 1), the real and imaginary parts of xx are close to those of yy tensor. Correspondingly, the variations of nxx and nyy are also similar, especially as the energy goes up two curves nearly coincide with each other (Figure 5b). At the static limit, the calculated dielectric constants are xx(0) = 2.129, yy(0) = 2.090, zz(0) = 1.960, respectively, which are larger than those

16


Page 17 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of MIL-125. In order to see more clearly how the organic functionalization affects the dielectric constants of MIL-125, the average values of the real parts of three dielectric tensors of MIL-125 and its different derivatives are calculated, and the results are presented in Figure 6a. It is clear that when the energy is smaller than the band gap (about 2.6 eV) of NH2-MIL-125, the incorporation of one amino group into BDC linker tends to increase the dielectric constants of MIL-125. Therefore, the organic functionalization has a negative influence on employing MIL-125 as a low- material. However, such functionalization will enhance the optical anisotropy of the system due to the deformation of the crystal cell, and consequently the magnitude of birefringence of MIL-125 is increased. The birefringence curve of NH2-MIL-125 is shown in Figure 6b. At the transparent region, the birefringence of NH2-MIL-125 is in the range of 0.06 – 0.10, and it is larger than that of original MIL-125. Therefore, the phase matchability of MIL-125 is improved upon amination of the BDC ligand. The linear optical properties of the -OH and -NO2 substituents are also computed (see Figures S2 and S3), and as displayed in Figure 6, the increasing of the dielectric constant and the enlarging of the birefringence are also observed at low energy region, but the influences on the linear optical performances of parent MIL-125 are less pronounced with respect to the case of NH2-MIL-125. Therefore, our results indicate that amines are an activating substituent to modify the optical properties of MIL-125. This conclusion can be confirmed by incorporating more -NH2 groups into the BDC linkers. After introducing two amino groups (Figure S4), the real part of dielectric tensor of MIL-125 is increased more dramatically. The average dielectric constant of (NH2)2-MIL-125 at the static limit is about 2.154 (Figure 6a), which is larger than that of monoaminated derivative (2.060) and the pristine MIL-125(1.928). Meanwhile, the increasing of birefringence becomes more obviously (Figure 6b). Thus, the linear optical properties of MIL-125 are also dependent on the degree of amination. Furthermore, the fitting results of the coefficients of Sellmeier equation for above derivatives are gathered in Table S2 in SI. 17



(a)

Page 18 of 31

(b)

Figure 5 (a) The calculated complex dielectric functions (), and (b) the refractive indices (n) of NH2-MIL-125

(a)

(b)

Figure 6 (a) Average real parts of three dielectric tensors and (b) the magnitude of birefringence (n) of MIL-125 and its different derivatives. In Figure (b), the birefringence is defined as the maximum difference between three refractive indices, so the corresponding values are nonnegative.

As for MIL-126 and MIL-127, they are also uniaxial crystals and have two independent dielectric tensors. Some linear optical properties of these two analogues at zero frequency limit are shown in Table 2, and the frequency-dependent complex dielectric functions, the refractive indices and birefringences are given in Figures S5 and S6. Compared with MIL-125, the most distinct feature of these two compounds is that they have smaller dielectric constants at the low energy region (Figure 6a). The average static dielectric constants of MIL-126 and MIL-127 are 1.725 and 18


Page 19 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.573, respectively, which are about 10.5% and 18.4% smaller than that of MIL-125. According to Eq. (1), such decreasing of the dielectric constants mainly relates to a significant expansion of cell volume caused by the inclusion of more benzene rings into BDC linkers, although at the same time the energies for the electron transitions are reduced because of the narrowing of the band gap. So it seems that the larger pore size of a MOF material leads to a lower of the dielectric constant. On the other hand, as the organic linkers change from BDC to BPDC then to TPDC, the static birefringence is reduced gradually from 0.042 to 0.026 then to 0.021 (Table 2). This tendency implies that the optical anisotropy of MIL-125 becomes weaker as the length of aromatic chain is increased. Due to the small magnitude of birefringence (< 0.03) at the transparent region (Figure 6b), the poor phase matching performance can be expected for MIL-126 and MIL-127, which will cause the limitation in the NLO applications. However, the small dielectric constant makes these two compounds have potential applications as low- materials. 3.4 SHG susceptibilities of MIL-125 and its Derivatives Now let us discuss the second-order nonlinear optical properties of MIL-125 and its six derivatives. The calculated SHG coefficients of these Ti-based MOFs at the zero-frequency limit are given in Table S3, and for clarity, the static SHG coefficient with the largest magnitude of each compound is also listed in Table 2. For the pristine MIL-125 crystallized in the tetragonal phase, there are five nonvanishing components of the SHG tensors, including d15, d24, d31, d32, and d33, and based on the Kleinman symmetry, the values of d15, d24, d31 and d32 are equal at static limit. So there are only two independent SHG tensors, namely, d15 and d33, respectively (Table S3). Since the magnitude of d33 (0.76 pm/V) is obviously larger than d15 (0.05 pm/V), the d33 tensor has a significant contribution to

19



Page 20 of 31

the SHG response of MIL-125. It is worth pointing out that the SHG activity of MIL-125 is slightly stronger than KDP, which is a commercial inorganic NLO crystal with a SHG coefficient about 0.40 pm/V.43 The frequency-dependent variation of the d33 tensor of MIL-125 is plotted in Figure 7. At the beginning region when the energy is less than 1.6 eV, the d33 coefficient increases slowly, and with further increasing of the energy, the SHG intensity rapidly increases. The first peak with a SHG magnitude of 54.42 pm/V is at about 1.9 eV, which is close to half of the band gap of MIL-125. To deeply understand the relationship between the band structure and the SHG activity of MIL-125, the variations of the magnitude of d33 coefficient as a function of the numbers of occupied and unoccupied bands are given in Figure 8. In here, the 258th and 259th bands are corresponding to the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO), respectively. From Figure 8a, a notable change of the SHG coefficient can be observed for the occupied bands in the regions from the 200th to the 252nd. According to the partial charge density shown in the inset of Figure 8a, it is apparent that these bands are dominated by the components of three kinds of oxygen atoms coordinated with Ti atoms. Actually, if only these bands are involved in the SHG calculation, a value of 0.44 pm/V is obtained for the magnitude of d33 coefficient, also confirming the prominent contribution of above energy bands to the SHG response of MIL-125. On the other hand, as shown in Figure 8b, the unoccupied bands in the range from the 259th to the 310th obviously influence the d33 coefficient, and we can see that titanium atoms contribute greatly to these bands. Therefore, the SHG response of MIL-125 can be mainly attributed to the transitions from the occupied bands dominated by oxygen atoms to the unoccupied bands provided by Ti atoms. This means that TiO5(OH) octahedra show primary responsibility for the SHG susceptibility of MIL-125, and in contrast the contribution of organic part is small. The

20


Page 21 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


main reason for such difference is that, if we ignore the TiO5(OH) octahedra, as displayed in Figure S7 the rest part of MIL-125 will have no SHG activity due to it nearly adopts an arrangement in I4/mmm space group with an inversion center.

Figure 7 Calculated frequency-dependent SHG coefficients of MIL-125 and its derivatives

(a)

(b)

Figure 8 Variations of the magnitudes of d33 coefficient as a function of the numbers of (a) occupied and (b) unoccupied energy bands of MIL-125. The 258th band is corresponding to the highest occupied crystal orbital (HOCO), and the 259th band is corresponding to the lowest unoccupied crystal orbital (LUCO). The partial charge density maps shown in the insets of are calculated by considering those energy bands in the regions from the 200th to the 252nd, and from the 259th to the 310th, respectively. The cyan horizontal line indicates the direction of increasing occupied/empty energy bands involved in the SHG calculation. 21



Page 22 of 31

When the BDC linker is functionalized by a single -NH2 group, there are 10 nonvanishing independent SHG tensors at static limit. As listed in Table S3, the static SHG coefficient with the largest magnitude of NH2-MIL-125 is still d33, and the corresponding value (1.54 pm/V) is larger than that of original MIL-125. The frequency-dependent SHG coefficient of d33 tensor is shown in Figure 7, and the first peak is red-shifted to 1.30 eV with a magnitude of 60.48 pm/V. Compared with the pristine MIL-125, the introducing -NH2 group can obviously enhance the SHG response of the system. To see how the incorporation of amino group impacts the SHG susceptibility of MIL-125, Figure 9 presents the variations of the d33 magnitude as a function of the numbers of occupied and unoccupied bands. It is interesting that, unlike parent MIL-125, now the occupied bands appeared near the VBM in the region from the 267th to the 276th have significant influences on the SHG response, and they have positive contributions to the SHG strength. From the inset of Figure 9a, these bands are mainly composed of the N-2p orbitals and the  bonding orbitals of benzene rings. At the same time, the remarkable variation of d33 coefficient is observed in the region from the 220th to the 255th. These energy bands are mainly derived from the contributions of oxygen atoms, and the SHG response becomes weak when these bands are taken into account. Furthermore, the bands distributed from the 155th to the 219th also have an impact on the SHG strength. The major components of these bands are the O-2p states and the  bonding between carbon atoms of benzene rings. For the unoccupied states, as shown in Figure 9b, besides the energy bands (from the 277th to the 367th) dominated by Ti-3d orbitals, those bands in the region from the 368th to the 667th also have a notable influence on the d33 magnitude, in which the compositions of BDC linkers can be found. The above results imply that for NH2-MIL-125 the inorganic metal nodes and organic linkers both contribute to the SHG susceptibility, which is different from the case

22


Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of the pristine MIL-125. From a structural point of view, the introducing a single -NH2 group changes the original nearly centrosymmetric arrangement of BDC linkers to a configuration without an inversion center, and as a result the organic parts have an obvious effect on the SHG response of NH2-MIL-125. Moreover, the NLO property of diaminated MIL-125 derivative is also explored. The static SHG coefficient with the largest magnitude is d11, and the corresponding value is 1.76 pm/V (Table 2), indicating that the further enhancement of SHG intensity may be achieved after incorporation more NH2 groups into the framework of MIL-125.

(a)

(b)

Figure 9 Variations of the magnitude of d33 coefficient as a function of the numbers of (a) occupied and (b) unoccupied energy bands of NH2-MIL-125. The 276th and 277th bands are corresponding to HOCO and LUCO, respectively. The partial charge density maps shown in the inset of are calculated by considering the energy bands in the specific regions.

The SHG susceptibilities of the other two monosubstituted systems, OH-MIL-125 and NO2-MIL-125 are also investigated. The static SHG tensors (Table S3) with the largest magnitude of two compounds are d33 (0.54 pm/V) and d11 (0.24 pm/V), respectively, and the corresponding frequency-dependent variations are given in Figure 7. Our results reveal that the inclusions of -OH and -NO2 groups lead to the weakening of the SHG strength of MIL-125. So the SHG activity of MIL-125 is dependent on the property of functional group. For OH-MIL-125, the variation of d33 23



Page 24 of 31

magnitude as a function of the numbers of occupied energy bands is shown in Figure S8, and like NH2-MIL-125 those occupied bands near the VBM that mainly come from O-2p of hydroxy groups and  bonding orbitals of benzene rings have obvious influences on the SHG response. By comparing the d33 magnitudes when these energy bands are considered (1.00 pm/V for -OH vs. 2.68 pm/V for -NH2), the enhancement of the SHG susceptibility through introducing of -OH group values is significantly reduced with respect to the case of NH2-MIL-125. When the substituent group is changed to -NO2, the occupied bands near the VBM still have contributions to the SHG activity (Figure S8), but the SHG strength is very weak (about 0.15 pm/V). Therefore, above results suggest that the SHG response of MIL-125 is sensitive to the type of functional group incorporated into BDC ligand. As a strong electron-donating substituent, -NH2 can act as the most favorable substitution to increase the SHG activity of MIL-125. On the contrary, the addition of -NO2 group that is strongly electron-withdrawing results in a decrease in SHG activity. Furthermore, we also study the SHG response of the structure that one amino group of diaminated derivative is replaced by -NO2 group. According to the results listed in Table S4, the largest magnitude of the static SHG coefficient is reduced from 1.76 pm/V to 0.80 pm/V, which also indicates the weakening of the SHG activity after introducing -NO2. The main reason is that the band gap of this mixed-substituted derivative (2.53 eV) is larger than that of diaminated derivative (2.00 eV). According to the Eq. (3), the increasing of the band gap will lead to enlarge the energy difference between the energy bands m and n, namely, the mn term in the denominators, and consequently, the magnitude of the SHG coefficient is decreased. Finally, we also investigate the SHG responses of two other analogues, MIL-126 and MIL-127. The magnitudes of d33 coefficient of two compounds are predicted to be 0.88 and 1.07 pm/V (Table

24


Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2), respectively. It seems that the inclusion of more benzene rings into BDC linkers is beneficial for improving the SHG strength of MIL-125. Such variation of the SHG response may be caused by the narrowing of the band gap as mentioned in the section 3.2. Thus, the SHG intensity is enhanced as the length of aromatic chain is increased. However, as mentioned above one drawback is that the phase matching performance becomes poor when the aromatic chain is extended.

4. CONCLUSIONS In summary, in the present work, the linear and second-order NLO properties of pristine and some functionalized MIL-125 MOFs have been explored by using periodic DFT calculations. Our results indicate that among three types of functional groups, the inclusion of amino group can dramatically reduce the band gap of MIL-125, suggesting the narrowing of the transparency range of MIL-125. The decreasing of band gap is also predicted for MIL-126 and MIL-127. The organic functionalization of BDC ligand remarkably affects the band structure of MIL-125, especially the obvious compositions derived from the substituent group can be found in those energy bands near the VBM, while the main components of CBM remain essentially unchanged. This result means that when the functionalized MIL-125 is exposed to light, the electron transitions between the substituent group and the titanium oxide unit have significant contributions to the optical responses, which is responsible for the differences in optical preferences with respect to the pristine MIL-125. With regard to the linear optical susceptibilities, three kinds of chemical modifications of BDC linkers tend to increase the dielectric constants and the magnitude of birefringence of MIL-125 at the low energy region, especially for two aminated derivatives, NH2-MIL-125 and (NH2)2-MIL-125. Thus the incorporation of substituent group will improve the phase matching ability of MIL-125. On the contrary, with the increasing of the length of aromatic linking unit, the dielectric constants

25



Page 26 of 31

and the magnitude of birefringence are reduced gradually as MOF varies from MIL-125 to MIL-126 and then to MIL-127. As for the NLO response, the SHG intensity of the pristine MIL-125 is comparable to KDP. The NLO activity of MIL-125 is mainly originated from TiO5(OH) octahedra, while the contribution of organic part is small due to a nearly centrosymmetric organization of the organic linkers. After introducing -NH2, -OH or -NO2 group into BDC linker, the organic part has a notable effect on the SHG intensity. However, the specific influences on the SHG response of MIL-125 depend on the type of functional group incorporated into BDC ligand. As a strong electron-donating substituent, the inclusion of single -NH2 group can enhance the SHG activity of MIL-125, and the further improvement of SHG intensity is predicted for the diaminated derivative. In contrast, the presence of strongly electron-withdrawing -NO2 group causes an obviously weakening of the SHG activity. Moreover, although MIL-126 and MIL-127 with longer aromatic linking unit tend to show larger intrinsic second-order NLO response than MIL-125, they have a serious drawback in the phase matching performance, which causes difficulties in applications as NLO materials. However, MIL-126 and MIL-127 are the promising candidates for the low dielectric constant materials required for future electronics.

26


Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Supporting Information The partial charge density maps of VBM and CBM of MIL-126 and MIL-127; the calculated complex dielectric functions and the refractive indices of OH-MIL-125, NO2-MIL-125, (NH2)2-MIL-125, MIL-126 and MIL-127; fitting results of the Sellmeier coefficients; and the calculated magnitudes of all SHG coefficients. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGEMENTS This work was supported by National Natural Science Foundation of China (grant nos. 21773030, 21373048, 21203027, and 51574090), the Independent Research Project of State Key Laboratory of Photocatalysis on Energy and Environment (2014A02), and Natural Science Foundation of Fujian Province (2017J01409). The calculations were performed on the supercomputing center of Fujian Province installed at the Fuzhou University.

27



Page 28 of 31

REFERENCES (1) Cook, T. R.; Zheng, Y. R.; Stang, P. J. Metal-Organic Frameworks and Self-Assembled Supramolecular Coordination Complexes: Comparing and Contrasting the Design, Synthesis, and Functionality of Metal-Organic Materials. Chem. Rev. 2013, 113, 734-777. (2) Medishetty, R.; Zareba, J. K.; Mayer, D.; Samoc, M.; Fischer, R. A. Nonlinear Optical Properties, Upconversion and Lasing in Metal-Organic Frameworks. Chem. Soc. Rev. 2017, 46, 4976-5004. (3) Zhang, W.; Xiong, R. G. Ferroelectric Metal-Organic Frameworks, Chem. Rev. 2012, 112, 1163-1195. (4) Wang, C.; Zhang, T.; Lin, W. B. Rational Synthesis of Noncentrosymmetric Metal-Organic Frameworks for Second-Order Nonlinear Optics. Chem. Rev. 2012, 112, 1084-1104. (5) Yang, X.; Lin, X.; Zhao, Y. S.; Yan, D. Recent Advances in Micro-/Nanostructed Metal-Organic Frameworks towards Photonic and Electronic Applications. Chem. Eur. J. 2018, 24, 6484-6493. (6) Cleuvenbergen, S. V.; Stassen, I.; Gobechiya, E.; Zhang, Y.; Markey, K.; De Vos, D. E.; Kirschhock, C.; Champagne, B.; Verbiest, T. ZIF-8 as Nonlinear Optical Material: Influence of Structure and Synthesis. Chem. Mater. 2016, 28, 3203-3209. (7) Assi, H.; Mouchaham, G.; Steunou, N.; Devic, T.; Serre, C. Titanium Coordination Compounds: from Discrete Metal Complexes to Metal-Organic Frameworks. Chem. Soc. Rev. 2017, 46, 3431-3452. (8) Dan-Hardi, M.; Serre, C.; Frot, T.; Rozes, L.; Maurin, G.; Sanchez, C.; Ferey, G. A New Photoactive Crystalline Highly Porous Titanium(IV) Dicarboxylate. J. Am. Chem. Soc. 2009, 131, 10857-10859. (9) Fu, Y.; Sun, D.; Chen, Y.; Huang, R.; Ding, Z.; Fu, X.; Li, Z. An Amine-Functionalized Titanium Metal-Organic Framework Photocatalyst with Visible-Light-Induced Activity for CO2 Reduction. Angew. Chem. Int. Ed. 2012, 51, 3364-3367. (10) Hendon, C. H.; Tiana, D.; Fonecave, M.; Sanchez, C.; D’arras, L.; Sassoye, C.; Rozes, L.; Mellot-Draznieks C.; Walsh, A. Engineering the Optical Response of the Titanium-MIL-125 Metal-Organic Framework through Ligand Functionalization. J. Am. Chem. Soc. 2013, 135, 10942-10945. (11) Chambers, M. B.; Wang, X.; Ellezam, L.; Ersen, O.; Fontecave, M.; Sanchez, C.; Rozes L.; Mellot-Draznieks, C. Maximizing the Photocatalytic Activity of Metal-Organic Frameworks with Aminated-Functionalized Linkers: Sub-stoichiometric effects in MIL-125-NH2. J. Am. Chem. Soc. 2017, 139, 8222-8228. (12) Kong, X. Q.; Deng, H. X.; Yan, F. Y.; Kim, J.; Swisher, J. A.; Smit, B.; Yaghi, O. M.; Reimer, J. A. Mapping of Functional Groups in Metal-Organic Frameworks. Science 2013, 341, 882-885. (13) Zou, L. F.; Feng, D. W.; Liu, T. F.; Chen, Y. P.; Yuan, S.; Wang, K. C.; Wang, X.; Fordham, S.; Zhou, H. C. A Versatile Synthetic Route for the Preparation of Titanium Metal-Organic Frameworks. Chem. Sci. 2016, 7, 1063-1069. (14) Butler, K. T.; Hendon C. H., Walsh, A. Electronic Chemical Potentials of Porous Metal-Organic Frameworks. J. Am. Chem. Soc. 2014, 136, 2703-2706. (15) Li, Y.; Fu, Y.; Ni, B; Ding, K.; Chen, W.; Wu, K; Huang, X.; Zhang, Y. Effects of Ligand Functionalization on the Photocatalytic Properties of Titanium-Based MOF: A Density Functional Theory Study. AIP Adv. 2018, 8, 035012. (16) Zhang, Y.; Champagne, B. Theoretical Insight into the Second-Order NLO Response of the Bis{4-[2-(4pyridyl)ethenyl]benzoato}-zinc(II) Metal–Organic Framework. J. Phys. Chem. C 2012, 116, 21973-21981. (17) Seidler, T.; Chamgagne, B. Second-Order Nonlinear Optical Susceptibilities of Metal–Organic Frameworks Using a Combined Local Field Theory/Charge Embedding Electrostatic Scheme. J. Phys. Chem. C 2016, 120, 6741-6749. (18) Markey, K.; Kruger, M.; Seidler, T.; Reinsch, H.; Verbiest, T.; E. De Vos, D. E.; Champagne, B.; Stock, N.; 28


Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


van der Veen M. A. Emergence of Nonlinear Optical Activity by Incorporation of a Linker Carrying the p-Nitroaniline Motif in MIL-53 Frameworks. J. Phys. Chem. C 2017, 121, 25509-25518. (19) Kresse, G.; Hafner, J. Ab initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558. (20) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. (21) Kresse, G.; Furthmuller, J. Efficiency of ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15-50. (22) Grimme, S. Semiempirical GGA-type Density Functional Constructed with a Long-Range Dispersion Correction. J Comput. Chem. 2006, 27, 1787-1799. (23) Hughes, J. L.; Sipe, J. Calculation of Second-Order Optical Response in Semiconductors. Phys. Rev. B 1996, 53, 10751-10763. (24) Aversa, C.; Sipe, J. E. Nonlinear Optical Susceptibilities of Semiconductors: Results with a Length-Gauge Analysis. Phys. Rev. B 1995, 52, 14636. (25) Nasalevich, M. A.; Hendon, C. H.; Santaclara, J. G.; Svane, K.; van der Linden, B.; Veber, S. L.; Fedin, M. V.; Houtepen, A. J.; van der Veen, M. A.; Walsh A.; Gascon, J. Electronic Origins of Photocatalytic Activity in d0 Metal Organic Frameworks. Sci. Rep. 2016, 6, 23676. (26) Fang, Z. X.; Lin, J.; Liu, R.; Liu, P.; Li, Y.; Huang, X.; Ding, K. N.; Ning, L.; Zhang, Y. F. Computational Design of Inorganic Nonlinear Optical Crystals Based on a Genetic Algorithm. CrystEngComm 2014, 16, 10569-10580. (27) Li, Y.; Lin, J.; Fang, Z. X.; Qiu, M.; Huang, X.; Ding, K. N.; Chen, W. K.; Zhang, Y. F. Pressure-Tuning the Nonlinear-Optical Properties of AgGaS2 Crystal: A First-Principle Study. Opt. Mater. Express 2015, 5, 1738-1751. (28) Wu, R. Z.; Fang, Z. X.; Liu, P.; Cao, Q. Z.; Qiu, M.; Li, Y.; Chen, W. K.; Huang, X.; Zhang, Y. F. Electronic Structures and Optical Properties of the Organic DAST and DSTMS Crystal Materials. Acta Phys.-Chim. Sin. 2013, 29, 2534-2542. (29) Cavka, J. H.; Jakobsen, S.; Olsbye, U.; Guillou, N.; Lamberti, C.; Bordiga, S.; Lillerud K. P. A New Zirconium Inorganic Building Brick Forming Metal Organic Frameworks with Exceptional Stability. J. Am. Chem. Soc. 2008, 130, 13850-13851. (30) Walsh A., Catlow C. R. A. Photostimulated Reduction Processes in a Titania Hybrid Metal-Organic Framework. ChemPhysChem 2010, 11, 2341-2344. (31) Nasalevich, M. A.; Goesten, M. G.; Savenije, T. J.; Kapteijn F.; Gascon, J. Enhancing Optical Absorption of Metal-Organic Frameworks for Improved Visible Light Photocatalysis. Chem. Commun. 2013, 49, 10575-10577. (32) Butler, K. T.; Hendon, C. H.; Walsh, A. Electronic Chemical Potentials of Porous Metal Organic Frameworks. J Am. Chem. Soc. 2014, 136, 2703-2706. (33) Stassen, I.; Burtch, N.; Talin, A.; Falcaro, P.; Allendorf, M.; Ameloot, R. An Updated Roadmap for the Integration of Metal-Organic Frameworks with Electronic Devices and Chemical Sensors. Chem. Soc. Rev. 2017, 46, 3185−3241. (34) Zagorodniy, K.; Seifert, G.; Hermann, H. Metal-Organic Frameworks as Promising Candidates for Future Ultralow- Dielectrics. Appl. Phys. Lett. 2010, 97, 251905. (35) Titov, K.; Zeng, Z. X.; Ryder, M. R.; Chaudhari, A. K.; Civalleri, B.; Kelley, C. S.; Frogley, M. D.; Cinque, G.; Tan, J. C. Probing Dielectric Properties of Metal-Organic Frameworks: MIL-53(Al) as a Model System for Theoretical Predictions and Experimental Measurements via Synchrotron Far- and Mid-Infrared Spectroscopy. J. Phys. Chem. Lett. 2017, 8, 5035-5040. 29



Page 30 of 31

(36) Mendiratta, S.; Usman, M.; Chang, C. C.; Lee, Y. C.; Chen, J. W.; Wu, M. K.; Lin, Y. C.; Hsu, C. P.; Lu, K. L. Zn(II)-based Metal-Organic Framework: an Exceptionally Thermally Stable, Guest-Free Low Dielectric Material. J. Mater. Chem. C 2017, 5, 1508-1513. (37) Eslava, S.; Zhang, L. P.; Esconjauregui, S.; Yang, J. W.; Vanstreels, K.; Baklanov, M. R.; Saiz, E. Metal-Organic Framework ZIF-8 Films As Low-k Dielectrics in Microelectronics. Chem. Mater. 2013, 25, 27-33. (38) Li, W. J.; Liu, J.; Sun, Z. H.; Liu, T. F.; Lu, J.; Gao, S. Y.; He, C.; Cao, R.; Luo, J. H. Integration of Metal-Organic Frameworks into an Electrochemical Dielectric Thin Film for Electronic Applications. Nature Comm. 2016, 7, 11830. (39) Ryder, M. R.; Zeng, Z. X.; Titov, K.; Sun, Y. T.; Mandi, E. M.; Flyagina, I.; Bennett, T. D.; Civalleri, B.; Kelley, C. S.; Frogley, M. D.; Cinque, G.; Tan, J. C. Dielectric Properties of Zeolitic Imidazolate Frameworks in the Broad-Band Infrared Regime. J. Phys. Chem. Lett. 2018, 9, 2678-2684. (40) Usman, M.; Lee, C. H.; Hung, D. S.; Lee, S. F.; Wang, C. C.; Luo, T. T.; Zhao, L.; Wu, M. K.; Lu, K. L. Intrinsic Low Dielectric Behaviour of a Highly Thermally Stable Sr-Based Metal-Organic Framework for Interlayer Dielectric Materials. J. Mater. Chem. C 2014, 2, 3762-3768. (41) Zhang, K.; Wang X. Nonlinear optics crystal material science; Science Press, Beijing, 1996. (42) Weber, M. J. Handbook of Optical Materials; CRC Press: Boca Raton, FL, 2002. (43) Alford, W. J.; Smith, A. V. Wavelength Variation of the Second-Order Nonlinear Coefficients of KNbO3, KTiOPO4, KTiOAsO4, LiNbO3, LiIO3, β-BaB2O4, KH2PO4, and LiB3O5 Crystals: A Test of Miller Wavelength Scaling. J. Opt. Soc. Am. B 2001, 18, 524-533.

30


Page 31 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic

31


Tailoring the Linear and Second-Order Nonlinear Optical Responses

Recommend Documents