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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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A Joint Strategy To Evaluate the Microscopic Origin of the SecondHarmonic-Generation Response in Nonpolar ABCO3F Compounds Qun Jing,*,† Guang Yang,‡ Zhaohui Chen,*,† Xiaoyu Dong,§ and Yunjing Shi§ †

School of Physical Science and Technology, Physical and Chemical Detecting Center, Xinjiang University, 666 Shengli Road, Urumqi 830046, China ‡ Basic Teaching Department, Jiaozuo University, 3066 Renmin Road, Jiaozuo 454000, China § Engineering Department of Chemistry and Environment, Xinjiang Institute of Engineering, 236 Nanchang Road, Urumqi 830091, China S Supporting Information *

ABSTRACT: In this paper, a joint strategy was proposed to investigate the microscopic origin of the second-harmonic-generation (SHG) response in nonpolar ABCO3F compounds. The SHG coefficients of ABCO3F were evaluated using finite-field and sum-over-states methods. The tendency of the obtained SHG tensors is in good agreement with the powder SHG response. The atomic contribution was investigated using variation of the atomic charges and bandwidth of occupied atomic states. The results show that oxygen states play a key role in determining the SHG response, and the neighboring divalent cations exert a indirect influence via covalent interaction. The bidentate bonding pattern is beneficial to obtaining a largely enhanced SHG response.

(1.11KDP), 3 6 CsCaCO 3 F (1.11KDP), 3 6 RbZnCO 3 F (0.83KDP),39 and so on. The ABCO3F compound is made of [BCO3]∞ and [AF]∞ layers, and all of the CO3 anionic groups are aligned parallel in the ab plane, with different rotation angles between adjacent layers. Although these ABCO3F compounds own similar structures, they show different NLO responses. Curiously, what is the microscopic origin of the enhanced SHG response in these carbonate fluorides? To answer this question, lots of effort has been made. On the basis of the anionic group theory,41 Ye et al. pointed out that the CO3 groups give the main contribution to the total SHG response, and the tendency of the NLO efficiency can be explained by the density of the CO3 groups (n/V) and geometrical criterion (g).36,39,40,42 As for CsPbCO3F, the extremely large SHG response may originate from the p−π interaction between the lead atoms and CO3 groups.33 After carefully investigating the geometry and electronic structures, Rondinelli et al. pointed out that the SHG response arises from the unique denticity of the polyhedra and cooperative alignment of the carbonate groups, and they also pointed out that a smaller specific acentric-mode displacement parameter and moderate cation variance could result in a greater SHG efficiency.32,38 It is well-known that macroscopic polarization can be expressed as a Taylor expansion

1. INTRODUCTION During the past decades, plenty of attention has been paid to acentric borates,1−9 carbonates,10,11 phosphates,12−19 and other acentric compounds20−22 to explore ideal ultraviolet (UV)/ deep-ultraviolet (DUV) nonlinear-optical (NLO) materials. Dominant research interest has been focused on acentric borates because of their rich structural chemistry, wide transparent energy region, and high laser damage threshold.23 Among these acentric borates, BBO,24 LBO,25 CBO,26 CLBO,27,28 and KBBF29 have been widely used. Except for borates, the acentric carbonates are also thought to be ideal NLO materials because of their triangular functional basic units CO3 groups. The parallel alignment of CO3 groups is beneficial to generate moderate birefringence to meet the phase-matching conditions, and π orbitals may produce relatively large secondharmonic-generation (SHG) coefficients.30,31 Recently, a family of nonpolar NLO carbonates ABCO3F (A = K, Rb, Cs; B = Mg, Ca, Sr, Zn, Cd, Pb) have been reported. A relatively large powder SHG (PSHG) response was found in lead carbonates, such as RbPbCO3F (6.25KDP)32 and CsPbCO3F (7.5KDP).32 It is interesting to note that Ye et al. pointed out that CsPbCO3F owns ultrahigh SHG efficiency as 13.5KDP,33 which is comparable with the PSHG of Pb2B5O9I.34 A moderate PSHG response was reported in KCdCO3F (4.58KDP),35 KCaCO3F (3.61KDP),36 KSrCO3F (3.33KDP),36 RbSrCO3F (3.33KDP), 3 6 RbMgCO 3 F (4.00KDP), 3 7 KMgCO 3 F (3.00KDP),38 and RbCdCO3F (2.80KDP).39 A relatively smaller PSHG response was reported in KZnCO 3 F (1.76KDP), 3 9 CsSrCO 3 F (1.20KDP), 4 0 RbCaCO 3 F © XXXX American Chemical Society

Received: October 18, 2017

A

DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Obtained polarization (×10−8 au) under different photoelectric fields (×10−4 au). The red solid curves are the fitting curves of polarization along with the photoelectric fields. Noting that 1 au of the electric field is about 514220624373.482 V/m.

Pi(mac) = Pi(0) +

adopted to investigate the NLO properties of binary semiconductors47 and phosphates.57 In this paper, the authors report a joint strategy to investigate the microscopic origin of the SHG response in nonpolar ABCO3F compounds. The SHG coefficients were calculated by the finite electric field along with the widely used sum-overstates (SOS) methods. The obtained results are in good agreement with the experimental values. The atomic contribution to the total optical response was further investigated using the atomic charge analysis based on the finite-electricfield results and the bandwidth of the occupied states of oxygen atoms (BoO) based on the projected densities of states (PDOSs). The results show that the oxygen atoms give the main contribution to the total SHG response, and the cations and carbon atoms give indirect contributions by exerting influence on their neighboring oxygen atoms. The bonding pattern of [BCO3] layers makes an important contribution to determining the SHG efficiency, and bidentate linkage is

∑ χij(1) εj + ∑ χijk(2) εjεk + ... j

jk

(1)

in which P(mac) = P(ion) + P(e) is the macroscopic polarization i i i under electric field, Pi(0) is the zero-field spontaneous (2) polarization, and χ(1) ij and χijk are the linear and second-order NLO susceptibilities, respectively.43 Using the finite-field method, one can easily obtain the atomic charges and macroscopic polarization under different external photoelectric fields. Compared with conventional methods, it can help us to intuitively learn about the optical response under different external photoelectric fields and distinguish atomic contributions (not only anion/anionic groups but also cations) to the total SHG response without special operation. In addition, using the finite-field method, one can also get the third- or higher-order optical susceptibilities without increasing the computational cost.58 Hence, recently this strategy has been B

DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. ΔQ (×10−8 e) per Formula (ABCO3F) When the External Photoelectric Field along [110] Was Applied, Noting That A Represents Alkali-Metal Atoms and B Represents Divalent Cations

beneficial to obtaining a largely enhanced SHG response. The joint strategy used in this paper could be used in other NLO compounds to obtain the SHG coefficients and find out the atomic contributions to the SHG response.

2. NUMERICAL CALCULATION DETAILS Density functional theory (DFT) calculations were performed using the ABINIT code.44−46 The macroscopic polarization and second-order NLO properties were calculated using the finiteelectric-field method.47,48 The total macroscopic polarization is the sum of the polarization of valence electrons and ions: P(mac) i = P(ion) + P(e) i i . Under the UV, visible, and near-infrared photoelectric field, the optical frequency is higher than the frequency of the phonons but lower than the fundamental absorption gap. In this case, the atomic position and unit cell shape are clamped, and only the valence electrons give the contributions to the linear-optical and NLO properties. Hence, in this work, finite-field calculations were performed using the experimental atomic positions and crystal structures. During the calculations, the generalized gradient approximation (GGA) with Perdew−Burke−Ernzerhof functional was used and standard norm-conserving pseudopotentials (NCPs)49 were adopted. The energy cutoff was set as 40.0 hartree along with a dense k-point sample: 11 × 11 × 11 for CsPbCO3F and KSrCO3F; 11 × 11 × 6 for RbCdCO3F, KCdCO3F, and RbSrCO3F; 6 × 6 × 12 for RbCaCO3F. The electronic structure and NLO response were also evaluated using the CASTEP code.50 During the calculation, the GGA with Perdew−Burke−Ernzerhof (PBE) functional51 and NCPs52,53 were adopted. The kinetic energy cutoffs were set as 940 eV for all ABCO3F compounds. The Monkhorst−Pack kpoint meshes spanning less than 0.04 × 2π Å−3 in the Brillouin zone were chosen. On the basis of the obtained electronic structures, the NLO coefficients are calculated using the SOS expressions.54,55 During calculations using the SOS methods, a scissors operator was introduced to shift all of the conduction bands. After the scissors corrections were employed, reliable SHG coefficients can be obtained from the GGA calculations.

CsPbCO3F KCdCO3F RbCdCO3F RbSrCO3F KSrCO3F RbCaCO3F

A

B

C

O

F

30.27 4.71 16.35 16.10 3.87 15.38

7.31 −12.83 −13.35 −9.07 −8.47 −31.43

23.43 0.29 −2.03 −3.17 −2.98 −7.95

367.35 164.01 169.59 142.38 135.27 133.56

35.58 31.66 33.78 31.79 36.84 25.98

Figure 2. Dependence of the PSHG efficiency and BoO.

3. RESULTS AND DISCUSSION 3.1. Induced Polarization and SHG Coefficients. For the hexagonal semiconductors with the D3h point group, there Table 1. Experimental PSHG Intensities and Calculated SHG Tensors Using the Finite-Field and SOS Methodsa

Figure 3. Enhancement of SHG and BoO. The inserts are the bonding patterns of CdCO3, CaCO3, and SrCO3.

SHG

a

compound

PSHG intensity

finite field

SOS

CsPbCO3F KCdCO3F RbCdCO3F KSrCO3F RbSrCO3F RbCaCO3F

13.4KDP33 5.2KDP35 2.84KDP39 3.33KDP36 3.33KDP36 1.11KDP36

9.54 3.40 3.32 2.30 2.36 0.73

6.75 1.77 1.77 1.53 1.56 0.83

(1) the form P(mac) ([100]) = P(0) 1 1 + ε0χ11 E1; hence, one can easily get the second-order term of polarization via ΔP(mac) = 1 (mac) ε0χ(2) = P(mac) ([110]) − P(mac) ([100]). 112E1E2 in which ΔP1 1 1 The obtained second term of the macroscopic polarization is shown in Figure 1. It clearly shows that the macroscopic polarization of each compound is zero when the strength of the external photoelectric field is zero. This is not surprising because these compounds crystallize into nonpolar space groups. However, after the nonzero external photoelectric field was applied on these compounds, the atomic charges are changed, which leads to nonzero macroscopic polarization.56 As shown in Figure 1, the curve of the macroscopic polarization− photoelectric field is parabolic. The values of the independent nonzero SHG tensor d22 are 9.54 (CsPbCO3F), 3.40 (KCdCO3F), 3.32 (RbCdCO3F), 2.30 (KSrCO3F), 2.36

The SHG tensor of KDP is d36(KDP) = 0.39 pm/V.

is only one independent nonzero second-order NLO susceptibility tensor d16 = d21 = −d22. When the photoelectric field along [110] was applied on these compounds, the macroscopic polarization has the form P(mac) ([110]) = P(0) 1 1 + (1) (2) ε0χ11 E1 + ε0χ112E1E2, while after the photoelectric field along [100] was applied, the macroscopic polarization should have C

DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 4. Total electron densities of the ABCO3F and CsPb-sub-AB compounds.

these compounds are also obtained using the SOS method based on the electric structures obtained by the CASTEP code (as shown in Table 1). As shown in Table 1, the tendency of the SHG tensors obtained by the finite-field method is in good

(RbSrCO3F), and 0.73 (RbCaCO3F) pm/V, respectively. The obtained SHG tensors are slightly larger than the experimental values (shown in Table 1) but have similar tendencies like experimental values. For comparison, the SHG tensors d22 of D

DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry agreement with the SHG tensors obtained by the CASTEP code. 3.2. Atomic Contribution to the SHG Tensors. According to the definition of macroscopic polarization, changing the atomic charges would lead to changes of the macroscopic polarization, which determines the SHG response of these nonpolar compounds. To better understanding the atomic contribution to the SHG tensors, the atomic charges and variation of the atomic charge (ΔQ) were roughly evaluated using the finite-field method. ΔQ was defined as the difference of the atomic charges when the finite electronic field was changed as 0.0001 atomic unit (au). The obtained ΔQ values are shown in Table 2. Among all of the atoms, the oxygen atoms have the largest ΔQ values, which indicates that the oxygen atoms give a dominant contribution to the SHG response. Besides the oxygen atoms, the fluorine atoms also play a key role in determining the SHG tensors. Like the alkalimetal cations, they give very little contribution to the total SHG response. It is interesting to note that, except for CsPbCO3F, the divalent cations give negative contribution to the total SHG response (although the contribution from these atoms is also very small). Furthermore, the CsPbCO3F compound has the largest ΔQ from the oxygen atoms, which is about 2.75 times that of RbCaCO3F. The largest ΔQ value from the oxygen atoms would make CsPbCO3F have the largest SHG response. Recently, a new strategy was proposed to investigate the structure−property relationships in NLO materials.57 According to the results obtained from the band model analysis and first-principles calculations, Li et al. pointed out that materials with a strong SHG response should have a wide bandwidth of the valence band and/or a reduced band gap.57 Herein the authors would calculate the bandwidth of the occupied states of oxygen atoms (BoO) to investigate the relationship between the oxygen atoms and SHG response. BoO is defined as BoO =

∑

involves the contribution from the occupied oxygen atoms. Hence, the authors believe that the disagreement of the BoO data and PSHG results of RbCdCO3F may have a relationship with the limitation of BoO and the complicated dependence of the PSHG response. If ignoring the small disagreement of BoO and PSHG for RbCdCO3F, one can find that RbCdCO3F still has a similar dependence of BoO and PSHG like other carbonates, that is, both the BoO and PSHG of RbCdCO3F are smaller than those of CsPbCO3F and larger than those of other alkali/alkaline-earth carbonates. In a word, BoO has a positive correlation with the SHG response, and according to the data from changes of the atomic charges, PDOSs, and BoO, one can find that the oxygen atoms give the main contribution to the total SHG response. 3.3. Microscopic Origin of the Enhanced SHG Response. It is well-known that, under the external photoelectric field, the distribution and changing of the atomic charges are affected by the atomic coordination environment. As for the oxygen atoms, which play a vital role in determining the optical properties, the distribution of the atomic charges is influenced by the carbon atoms and divalent cations that have covalent interactions with the oxygen atoms. For alkali/alkalineearth carbonates, only hybrid C sp−O p states were found at the top of the valence band (shown in Figure S1 in SI), so the distribution of oxygen atomic charges is mainly affected by their neighbor carbon atoms. Hence the density of CO3 groups (n/ V) times the geometrical coefficients (g) is positive correlation with the SHG response. Plentiful comments about the structure-properties relationship in alkali−alkaline earth carbonates have been made by Ye et al.,36,40 so the authors would just pay attention to the carbonates containing transition-metal atoms, or lead atoms. For the ABCO3F compounds containing transition-metal or lead atoms, except for the C−O bonds, the hybridization between the divalent cations and oxygen atoms is also found at the top of the valence band (shown in Figure S1). In other words, the distribution of oxygen atomic charges will be affected by both carbon atoms and divalent cations. Take CsPbCO 3 F and KSrCO 3 F for example. CsPbCO 3 F is isostructural with KSrCO3F. The former has a smaller density of CO3 groups (0.00779 n/V for CsPbCO3F and 0.00889 n/V for KSrCO3F), but it has a stronger SHG response. As shown in Figure S1, the sp states in CsPbCO3F are hybrid in the energy range [−8.6, 0.0] eV, while in KSrCO3F, the hybridization is found in the energy range [−7.6, 0.0] eV. The hybridization causes the former to have a smaller band gap (4.15 eV), and the energy cutoff of the latter is larger than 6.2 eV. A reduced band gap and an enlarged energy region of hybrid occupied states cause the former to have an enhanced SHG response compared with the latter. Compared with CsPbCO3F, KCdCO3F and RbCdCO3F have a relatively weaker hybridization between the transition-metal and oxygen atoms. Take KCdCO3F for example. As shown in Figure S1, the hybridization is found in the energy region [−8.1, 0.0] eV, and the energy cutoff is 5.46 eV. The reduced hybridization and enhanced band gap cause KCdCO3F to have a relatively smaller SHG efficiency than CsPbCO3F. In comparison with other alkali/alkaline-earth carbonates, the hybridization among O p, C sp, and TM d states makes the SHG efficiency of KCdCO3F as large as 5.2KDP. Except for the element type, the bonding patterns of the [B(CO3)]∞ layers also give important contributions to the SHG response. To deeply understand the role played by the

DOS(Op) Eg − E

in which the Eg is the cutoff energy, E is the energy of each state, and DOS(Op) is the DOSs of occupied oxygen atoms. The obtained PDOSs are shown in Figure S1. As shown in Figure S1, at the top of the valence band (in the energy region from −10 eV to the Fermi level), the states are mainly from the O p states, mixed with C sp and F p states. As for the monovalent cations, the Rb p states (in RbSr, RbCa, and RbCd compounds) were found near −9 eV and the Cs p states (in CsPb) were found near −7 eV. The hybrid Zn d (Cd d)−O p states were also found at the top of the valence band. In the CsPbCO3F compound, the hybrid Pb sp−O p states were found at the energy region from −8.5 eV to the Fermi level. The states near the Fermi level indicate that the oxygen atoms could play a key role in determining the optical properties. When the data of the PDOSs were utilized, BoO was obtained. The obtained BoO values along with the experimental PSHG efficiency are shown in Figure 2. As shown in Figure 2, CsPbCO3F has the largest BoO data and RbCaCO3F the smallest BoO data, and moderate BoO data are found in other compounds. The tendency of BoO is similar to the tendency of the PSHG response except for RbCdCO3F. It is well-known that the PSHG response has complex dependencies with the SHG coefficient tensor, the refractive index dispersion, and so on,59 and the SHG coefficient tensor comes from the synergistic action of all atoms, while BoO only E

DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX

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BoO. As described above, BoO has a positive correlation with the SHG response. The largest enhancement of BoO coming from three bidentate bonding patterns causes CsPb-sub-KSr (CsPb-sub-RbSr) to have the largest enhancement of the SHG response. Also, the smallest enhancement of BoO coming from three monodentate bonding patterns causes CsPb-sub-KCd (CsPb-sub-RbCd) to have the smallest enhancement of the SHG response. In a word, the bonding pattern in KSr (three bidentate) is beneficial to obtaining a largely enhanced SHG response. Similar conclusions were also found in our earlier work.6

bonding patterns in determining the SHG response, a series of virtual CsPbCO3F were made. The virtual CsPbCO3F was obtained by substituting mono- and divalent cations in ABCO3F with cesium and lead atoms. For example, the virtual CsPbCO3F can be obtained by substituting potassium and strontium atoms in KSrCO3F with cesium and lead atoms. Hereafter, the virtual CsPbCO3F compound is named CsPbsub-AB, such as CsPb-sub-KSr, and so on. As described earlier, there are four different bonding patterns of [B(CO3)]∞ layers.38,39 The denticity of B-(CO3) is three bidentate (KSrCO3F, RbSrCO3F, CsPbCO3F, marked as group I), three monodentate (KCdCO3F, marked group II), one monodentate and two bidentate (RbCaCO3F, marked as group III), and two monodentate and one bidentate (RbMgCO3F and KMgCO3F, marked as group IV). Herein the authors utilize KCdCO3F, RbCdCO3F, RbCaCO3F, RbSrCO3F, KSrCO3F, and RbMgCO3F to construct the virtual CsPbCO3F compound. The authors checked the ionic radii of the cations, and the crystal volume per chemical formula (ABCO3F) and analyzed the bond valence of the virtual compound (shown in Tables S1−S3). As shown in Tables S1− S3, because of the smallest ionic radius of Mg2+, the RbMgCO3F compound has the smallest volume per chemical formula. After Rb+ and Mg2+ were substituted by Cs+ and Pb2+, respectively, the smallest volume causes the Pb2+ in CsPb-subRbMg to have an incredibly large bond valence. The firstprinciples result shows that, unlike other virtual CsPb-sub-AB compounds, CsPb-sub-RbMg has metallic behavior and a band gap of about zero. Hence, hereafter the authors just pay attention to the virtual compound obtained by groups I−III. The obtained SHG response of the virtual CsPbCO3F is stronger than that of its original compound. The enhancement of the SHG response ( d22(CsPb‐sub‐AB) ) is shown in Figure 3. As

4. CONCLUSIONS In this paper, a joint strategy was proposed to evaluate the microscopic origin of the SHG response in a family of nonpolar ABCO3F compounds. The SHG coefficients were calculated by the finite-electric-field and SOS methods. The obtained results are in good agreement with the experimental values. The atomic contribution was further investigated using atomic charge analysis based on the results coming from the finite-field calculation and BoO based on PDOSs. The results show that the oxygen atomic charges give a direct contribution to the total SHG response, and the neighboring carbon atoms and divalent cations give an indirect contribution via hybridization with their neighboring oxygen atoms. The enlarged hybrid energy region and reduced band gap lead to enlarged SHG coefficients. The bidentate linkage between the divalent cations and oxygen atoms is beneficial to obtaining a largely enhanced SHG response. The joint strategy can be used to analyze the atomic contribution in other NLO compounds.

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ASSOCIATED CONTENT

S Supporting Information *

d 22(ABCO3 F)

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02689. PDOS and ELF of ABCO3F and virtual CsPb-sub-AB compounds, additional tables about ionic radii, volume per formula, and the bond valence analysis of virtual CsPb-sub-AB compounds (PDF)

shown in Figure 3, KSr and RbSr have the largest enhancement of the SHG coefficients and KCd and RbCd have the smallest enhancement of the SHG coefficients. To better understand the microscopic origination of the enhanced SHG response, the total electron density (shown in Figure 4) and electron localization function (ELF; shown in Figure S3) were also obtained. As shown in Figures 4 and S3, for the virtual compounds, the CO3 groups and lead atoms have relatively large total electron density and ELF, indicating that they give the main contribution to the total macroscopic polarization of the virtual CsPb-sub-AB. Similar conclusions are also obtained by the PDOS of the virtual CsPb-sub-AB (shown in Figure S2). Furthermore, after carefully checking the results shown in Figures 4 and S3, one can find that the oxygen atoms have similar distributions of the electron density, but they have different lead−oxygen covalent bonds. The divalent cation of KSrCO3F(RbSrCO3F) is bonded to three bidentate CO3 groups. As for KCdCO3F (RbCdCO3F), the cadmium atom is bonded to three monodentate CO3 groups. Different bonding patterns in these compounds can lead to different hybridizations and different band gaps (shown in Figure S2). To semiquantitatively analyze the role played by the bonding pattern to the total SHG coefficients, BoO was obtained, and the enhancement of BoO ( BoO(CsPb‐sub‐AB) ) obtained is shown

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Q.J.). *E-mail: [email protected] (Z.C.). ORCID

Qun Jing: 0000-0002-1801-2638 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (51462033 and 51562036), the Science Research Projects in University of Xinjiang Education Department (XJEDU2012I07 and XJEDU2014S073), the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (2015211C251), the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China (2014GGJS-283), Colleges and Universities in Henan Province Key Scientific Research Project for 2016

BoO(ABCO3 F)

in Figure 3. It clearly shows that, for different compounds with different bonding patterns of Pb−CO3 layers, the enhancement of BoO is different. KSr and RbSr have the largest enhancement of BoO, but KCd and RbCd have the smallest enhancement of F

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(16B140002), and the Science and Technology Development Program of Henan Province (172102210391).

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DOI: 10.1021/acs.inorgchem.7b02689 Inorg. Chem. XXXX, XXX, XXX−XXX