A Cation-Driven Approach toward Deep-Ultraviolet Nonlinear Optical Materials

The design of new materials with special performances is still a great challenge, especially for the deep-ultraviolet nonlinear optical materials in which it is difficult to balance large bandgaps and strong second harmonic generation responses due to their inverse relationship. Cation variation not only influences the whole structure frameworks but also directly participates in the formation of electronic structures, both of which could lead to the uncontrollability of the properties of the designed materials. Here, a novel approach, aiming at purposeful and foreseeable material designs, is proposed to characterize the role of cations. By the verification of several series of borates, the influences of cation variation on property changes are explored systematically. Accordingly, a feasible strategy of designing deep-ultraviolet nonlinear optical materials by substituting barium for lead has been concluded, which could obviously blue-shift the ultraviolet cutoff edge and maintain the relatively strong second harmonic generation response (more than 2 times of KH2PO4), achieving the property optimization, and especially works efficiently in fluorooxoborates. The property optimization design strategy and the cation characterization method are not only helpful in exploring nonlinear optical materials but also enlightening in material design and selection.


Introduction
Aiming at desirable performances, the material exploration assisted by quantum chemical calculation on computers has led to many new approaches, such as high-throughput screening and machine learning in data mining, or structure prediction by exploratory algorithms [1,2]. With the great demand in laser photolithography, micro-nano processing, optical communication, and medical treatment [3][4][5][6][7][8][9][10], a series of nonlinear optical (NLO) crystals have been discovered and commercialized successfully [11][12][13][14][15][16][17]. At present, deep-ultraviolet (DUV) NLO materials particularly attract many academic and commercial interests as the frequency conversion core to achieve coherent light with large photon flow and ultrahigh resolution and are expected to break the "200 nm wall" [18]. However, a large bandgap (E g > 6.2 eV) is indispensable for DUV transparency, while E g is inversely proportional to the second harmonic generation (SHG) response (d ij ) [19]. Therefore, how to satisfy the balance between the two critical performances (E g and d ij ) is a key factor in the design of outstanding DUV NLO materials. KBe 2 BO 3 F 2 (KBBF) exhibits excellent properties as a promising DUV NLO crystal [20,21], but the toxicity and layer-growing habit seriously impede its application. Finding KBBF replacements and balancing E g and d ij in the DUV region are still urgent.
To guarantee appropriate E g and d ij of designed NLO materials, several advantageous NLO-active (the sources of NLO effects) anion units are introduced, such as conjugated π configurations [BO 3 ] 3− , [B 3 O 6 ] 3− , distorted d 0 or d 10 transition-metal-centered (V 5+ , Cd 2+ ) polyhedra, fluorooxoborate anionic units [BO n F 4-n ] (n+1)− (n = 1, 2, 3), and so on [22][23][24][25]. Actually, as parts of the whole electron structures, A-site metal cations could also directly influence the optical properties besides the size effects in crystal structures, but a special study of the role of cation variation is rare. Here, a convenient cation characterization approach, "Cation differentiation by electron spatial distribution" (CRESD), is proposed to distinguish the role of cations in optical properties, and an accompanying design strategy is concluded from cation variation to achieve property optimization, for example, balancing large E g and large d ij in the DUV region. We note that the property optimization strategy and cation characterization approach can be applied in the design of high-performance materials not only for the NLO functions but also for other objects, such as perovskite solar cells.
To  Fig. 2D to F). The structural information of predicted Ba 2 BO 3 Br, BaB 5 O 7 F 3, and BaB 2 O 3 F 2 are shown in Tables S2-S4, and their crystallographic details (atomic coordinates, bond distances, angles, etc.) have been listed in Tables S5-S12.

CRESD method
To clarify the role of cations in property changes, the CRESD method is proposed to characterize the volumetric effects of various metal cations by the occupied volume of electrons, namely, electron spatial distribution (ESD). Taking the above isostructural substitutions of lead/barium borates as examples, the magnitudes of ESD between lead and barium atoms are compared on the basis of atom radius R(M), cation radius R(M 2+ ), and cation volume V(M 2+ ), where V(M 2+ ) = (2 × R(M 2+ )) 3 (Table 1). Here, deviation γ is defined as (P 1 − P 2 )/ ((P 1 +P 2 )/2) to evaluate the differentiation of P 1 and P 2 , where parameter P could be the magnitudes of ESD based on atom/ cation radius and cation volume, or any other parameters, such as crystal volume, in the following contents. The deviations γ of Pb 2+ /Ba 2+ ESD based on R(M), R(M 2+ ), and V(M 2+ ) are 21.4%, 13.3%, and 39.5%, respectively. Considering the isostructural substitutions, the deviation γ of ESD between Pb 2+ and Ba 2+ should change slightly. ESD [R(M 2+ )] is better to characterize the cations but hard to sum arithmetically for composite cations. ESD [V(M 2+ )] can also be summed arithmetically, but its deviation γ is too large. More importantly, all of the above ESD values are incapable of ion groups, such as [NH 4 ] + , [CH 3 NH 3 ] + , and so on. Consequently, ESD based on Bader volumes could overcome the above restrictions, where the electron density in the whole space is partitioned by DFT calculation [65,66], and hereinafter the ESD refers to the results on Bader volumes. Pb 2+ and Ba 2+  ESD can be not only applied in the comparison of experimental structures but also introduced to analyze the change regulations on structures and performances of theoretical structures, such as Ba 2 BO 3 Br and BaB 2 O 3 F 2 mentioned above. As the lattice parameters are relaxed in geometric structure optimization, the values of ESD have been calculated from both optimized and experimental (no-optimization) structures. The ESD and crystal volume in Pb 2 BO 3 Br are 27.7/28.3 and 143.6/149.0 Å 3 without/with optimization, and their deviation γ is 2.2% and 3.7% (Table S2), indicating the feasibility of structure optimization. Interestingly, the ESD of Pb/Ba in  Pb 2 BO 3 Br/Ba 2 BO 3 Br is 28.3/32.5 Å 3 , distinctly larger than those of the other 4 couples of lead/barium borates, ~22.0/24.0 Å 3 , and the deviation γ of cation ESD is 13.9%, the largest one among the 6 couples of lead/barium borates. The reason mainly comes from incompact structures. Pb 2 BO 3 Br/Ba 2 BO 3 Br belongs to rich metal borates with metal:boron = 2:1, resulting in the delocalization of electrons around metals, where the evidence is the larger deviation γ of crystal volumes between Pb 2 BO 3 Br and Ba 2 BO 3 Br, 18.6%. On the contrary, PbB 2 O 3 F 2 / BaB 2 O 3 F 2 contains fewer metal atoms, metal:boron = 1:2, and the cation ESD is also relatively small, 22.0/22.3 Å 3 . The deviation γ of ESD is the smallest, 5.7%, and the deviation γ of crystal volumes is only 3.0% (Table S3).

Property optimization for balancing bandgaps and SHG responses
To assess the influence of cation variation on property change, the optical properties of the selected lead/barium borates are evaluated and analyzed in detail by DFT calculation. Based on generalized gradient approximation (GGA)-Perdew-Burke-Ernzerhof (PBE) functionals, the calculated bandgaps of these lead borates, Pb 2 Ba 3 (BO 3 ) 3 Cl, Pb 3 B 6 O 11 F 2, and Pb 2 B 5 O 9 Cl, are 3.54, 3.81, and 3.36 eV, which are lower than their experimental or HSE06 values, 3.97 eV (312 nm), 5.17 eV (240 nm), and 4.41 eV (281 nm, HSE06), respectively. Here, the underestimation of bandgaps under GGA-PBE functional is derived from the inherent discontinuous exchange-correlation energy [67], and a scissors operator is adopted as the difference between the GGA bandgap and the experimental bandgap to eliminate this underestimation in the calculation of optical properties. In addition, a more expensive calculation, hybrid functional HSE06 [68], is used to achieve the value of bandgap more accurately for the lack of experimental bandgaps.
To verify the theoretic simulations, a couple of borates, M 2 B 5 O 9 Cl (M = Pb, Ba), were synthesized in experiments, and the UV cutoff edge and SHG intensity were also measured  (powder X-ray diffraction [XRD] patterns are shown in Fig. S2). As shown in Fig. 4 to analyze the source of the variation in bandgaps among the above metal borates, the total and partial density of states are shown in Figs. S3 to S8. Compared to the partial density of states among these metal borates, it is found that the conduction band minima are mainly composed of Pb-p or Ba-d and a little of B-p orbitals, while the valence band maxima mainly contain O-p, a little of halogen p orbitals, along with slight Pb/Sn-s orbitals for the stereochemically active lone pairs. According to the revised lone pair model [69], the interaction between Pb and O drives from the mixture of empty Pb p and a filled antibonding state between Pb-s and O-p states in PbO, and the lone pair stereochemical activity of Pb cations greatly influences the reduction of bandgaps in series of metal borates [70]. Therefore, the cation substitution from Pb to Ba could avoid the stereochemical activity of the lone pairs to achieve a relatively large bandgap, a similar effect that introducing the F atom could eliminate the dangling bonds of BO 3 groups in a series of fluorooxoborates [25,47,50,59]. As far as the purpose of property optimization, doubtless, the cation substitution in the fluorooxoborates BaB 5 O 7 F 3 and BaB 2 O 3 F 2 is more successful. Figure 5 shows the changes for bandgap (E g ) and SHG response in the cation substitution from lead to barium. The whole region is divided into 4 sections: I, E g < 6.2 eV, SHG < 2 KDP; II, E g ≥ 6.2 eV, SHG < 2 KDP; III, E g < 6.2 eV, SHG ≥ 2 KDP; IV, E g ≥ 6.2 eV, SHG ≥ 2 KDP, where 6.2 eV and 2 KDP are DUV and relatively strong SHG response bounds, respectively. Here, before the cation substitution, 5 lead borates in 6 are all located at Section III, indicating strong SHG responses but not DUV cutoff edges. After the cation substitution, these 5 barium borates scatter into 3 sections, 1 (Ba 2 BO 3 Br) still in Section III, 1 (Ba 5 (BO 3 ) 3 Cl) in Section I, and 3 in Section IV (Ba 3 B 6 O 11 F 2 , BaB 5 O 7 F 3 , and BaB 2 O 3 F 2 ). Although Ba 2 B 5 O 9 Cl shows a DUV bandgap, its SHG response is relatively small for the reason that the SHG intensity of its prototype is not strong. It is found that these lead borates could keep strong SHG responses (≥2 KDP) after cation substitution except Pb 2 Ba 3 (BO 3 ) 3 Cl and Pb 2 B 5 O 9 Cl, whose SHG response is the smallest among the 6 lead borates. What is more important, the bandgaps of all the lead borates have visibly widened, and especially four of them have exceeded the DUV limit (6.2 eV, 200 nm) after cation substitution. Therefore, the cation substitution from lead to barium could optimize the combination properties.
Considering the importance of SHG response for NLO materials, exploring the role of cation variation on SHG response is vital to deepen the understanding of the structure-property relationship. The real-space atom-cutting technique is an efficient postprocessing tool to evaluate the contribution of microscopic structural groups to optical properties, such as the SHG coefficient. Table 3 shows the results of the calculated SHG coefficients before (original) and after (e.g., cut Pb) cutting the metal cations, and the "SHG reducing" is expressed as "SHG  Furthermore, in M 2 BO 3 Br 2 and MB 2 O 3 F 2 (M = Pb, Ba), the cations exert a remarkable contribution to the SHG responses. In addition, in the SHG density map (Fig. S9), there are plenty of unoccupied states contributing to the VE and virtual-hole (VH) process and occupied states contributing to the VH process around Pb and Ba. In MB 2 O 3 F 2 (M = Pb, Sn, Ba), Sn shows a vitally negative contribution for d 33 (−130%), which is the reason that the SHG response of SnB 2 O 3 F 2 is much lower than that of isostructural PbB 2 O 3 F 2 , in accordance with the results from another group [54], while Sn and Pb play similar contributions to d 22 Fig. 6A, along with the bandgap increasing, the |d 33 | and |d 22 | decrease, as the negative relationship between bandgap and SHG response. Here, we add a trend line with the formula d = a / E g 5 , where d and E g are SHG coefficient and HSE06 bandgap values, and the constant a is calculated by the value of d and E g . Of course, this formula only considers the bandgap effect and ignore the momentum matrix elements [71], so it is a very rough approximation to estimate the trends of SHG coefficients along with bandgaps semiquantitatively. Furthermore, as shown in Table S13, a single Pb atom makes much more contributions to d 22  From Fig. S10, the location of Pb-6p in conduction band minimum is nearer to the Fermi surface than that of Ba-5d for the stereochemical activity of the lone pairs. Meanwhile, the SnB 2 O 3 F 2 obtains a smaller bandgap than PbB 2 O 3 F 2 for stronger stereochemical activity. Then, Fig. 6B shows SHG response decreasing along with the increase of ESD in MB 2 O 3 F 2 (M = Pb, Ba). It is important to note that the above conclusion has only been obtained in the case of cation substitution between Pb and Ba in MB 2 O 3 F 2 structures.

Conclusion
Through the investigation of a series of barium borates, Ba 5 (BO 3 ) 3 Cl, Ba 3 B 6 O 11 F 2 , Ba 2 B 5 O 9 Cl, Ba 2 BO 3 Br, BaB 5 O 7 F 3 , and BaB 2 O 3 F 2 , along with their prototypes of cation substitutions lead borates, we found that ESD is very useful to describe the electron occupied space, and the magnitudes of ESD are similar in the isostructural substitutions. As the aim of chemical substitutions is to develop performances, three cases, one borate fluoride, and two fluorooxoborates, in 6 cation substitutions from lead to barium have achieved the property optimization, enlarging bandgaps to enter the DUV region (6.2 eV, 200 nm) from outside DUV as the absence of lone pair in metal cations, and maintaining relatively strong SHG responses (> 2 KDP) for the reason that metal cations show less contribution to SHG responses than the anion frames. The cation substitution between Pb and Ba in MB 2 O 3 F 2 structures shows the negative relation between ESDs and SHG responses, which indicates the direction of searching for the NLO material with larger SHG responses. In conclusion, by analyzing the cation variations, a cation substitution approach toward DUV NLO materials has been proposed, and two predicted fluorooxoborates BaB 5 O 7 F 3 and BaB 2 O 3 F 2 have achieved the balance between large bandgaps and strong responses.

Solid-state synthesis
Polycrystalline samples of Ba 2 B 5 O 9 Cl and Pb 2 B 5 O 9 Cl were prepared by using standard high-temperature solid-state techniques. For Pb 2 B 5 O 9 Cl, a stoichiometric mixture of PbCl 2 and   Powder X-ray diffraction XRD patterns of Ba 2 B 5 O 9 Cl and Pb 2 B 5 O 9 Cl were obtained on an automated Bruker D2 X-ray diffractometer equipped with a diffracted beam monochromator set for Cu-Kα radiation (λ = 1.5418 Å) at room temperature in the angular range of 2θ = 10° to 70° with a scan step of 0.01° and a fixed counting time of 0.1 s/step.

UV-visible-near-infrared diffuse reflectance spectrum
The diffuse reflectance spectrum was measured by a Shimadzu SolidSpec-3700DUV spectrophotometer at room temperature from 175 to 2600 nm.

Second-order NLO measurements
Powder SHG effects were measured by using the Kurtz-Perry method with a Q-switched Nd: YVO 4 solid-state laser at 1064 nm [72]. Polycrystalline samples of Ba 2 B 5 O 9 Cl and Pb 2 B 5 O 9 Cl were ground and sieved into the following particle size ranges: 38 to 55, 55 to To make relevant comparisons with known SHG materials, the crystalline KDP sample was also ground and sieved into the same particle size ranges.

SHG coefficient calculation
When the phase-matching condition is met, the SHG conversion efficiency of an NLO material is significantly determined by the SHG coefficients [76]. Also, the SHG coefficient components are relevant to second-order nonlinear susceptibilities, d = χ/2. Through the result of the band structure from the CASTEP package, the second-order nonlinear susceptibilities at the limit of zero frequency, χ ijk (2) (0), can be expressed as the sum of the contribution of the virtual-electron processes and the VH processes [19,71].
Here, i, j, and k are Cartesian components, v (v') and c (c') are valence and conduction bands, and P(ijk) represents full permutation.

Supplementary Materials
Phonon spectra, powder XRD patterns, total and partial density of states, SHG density, comparison of typical NLO materials in bandgap and SHG response, structure information of predicted structures, and real-space atom-cutting results of SHG coefficients are shown in the Supplementary Materials.

Data Availability
Data will be made available from the corresponding author upon reasonable request.