Designing Two-Dimensional KBBF Family Second Harmonic

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C: Physical Processes in Nanomaterials and Nanostructures

Designing Two-Dimensional KBBF Family Second Harmonic Generation Monolayer Guoyu Yang, and Kechen Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00323 • Publication Date (Web): 22 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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The Journal of Physical Chemistry

Designing Two-Dimensional KBBF Family Second Harmonic Generation Monolayer Guoyu Yang†,‡ and Kechen Wu∗,† State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, People’s Republic of China , and University of Chinese Academy of Sciences, Beijing 100049,People’s Republic of China E-mail: [email protected]

∗ To

whom correspondence should be addressed Institute of Research on the Structure of Matter ‡ University of Chinese Academy of Sciences † Fujian

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Abstract Two-dimensional nonlinear optics materials are key to miniaturization of laser devices. Layered structure of KBe2 BO3 F2 (KBBF) is regarded as a point cutting into low dimension. Two-dimension AlBeBO3 F2 (2D-ABBF), the layered structure without potassium in KBBF and half beryllium substitute by aluminum, was predicted to work as second-harmonic generation(SHG) material in >200 nm range in UV and visible. The similarity with bulk is that BO3 and F groups are making main contribution to SHG effect. While the dimensionality compensates the negativity in bulk on SHG enhancement. Other modification strategies in KBBF family are also expected in 2D system.

Introduction With the rise of micro- and nanoelectronics, nonlinear optical (NLO) materials and all-solid-state lasers 1–3 are developing into nano-scale, for example, laser welding, 4 laser lithography, 5 laser marking 6 and laser cleaning. 7 Two-dimensional(2D) monolayer is probably the most promising nano structure for the versatile and manageable preparation methods including exfoliation 8,9 and deposition, 10 diverse absorption spectrum and exotic exciton, polariton, and phonon properties 11–13 . Though the specific mechanism is still mysterious and controversial 14,15 , experiments do have shown that mono layer exhibits much larger second-harmonic generation (SHG) coefficient than the bulk for several years. 16 Though the phase match behavior differs by scales, 17 our previous work shows that the designing strategy also works on 2D material: 18 first, the material should be reasonably available, physically and chemically stable, transparent at working wavelength; 19,20 second, the large SHG material is usually attributed to the anion, while the cation is responsible for stability 21 . In sum, 2D material prevails over 3D in the following aspects: first, it is easier to prepare in nanoscale, 8,9 and there is no worry about walk-off effect or phase mismatch, since the thickness is smaller than the accuracy of most laser source. 22 Second, in general, low dimension enhances 2


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the nonlinear optical effect. 16 Thirdly, monolayer usually has larger bandgap, 23,24 so the material remains stable, also the absorption is blue shifted into deeper UV, thus the monolayer would better survive in high-energy UV laser. 23,24 Among those commercial available phosphates, niobates and borates working in UV and visible, KBBF is the only one having realized SHG in deep UV (200 nm region in ultraviolet and the visible region transparent. This means that 2D-ABBF could work at the short wave UV (λ < 300 nm), which is a crucial but challenging range for a lot of laser technologies. 45–47 Both DFT and GW0 calculation result were presented, and they are consistent with previous research 48 that the in-plane absorption of this two methods are basically the same, and perpendicular GW0 absorption happens at higher energy (smaller wavelength) than DFT due to exciton effect. Also the relative intensity differs. This means the absorption in parallel and perpendicular direction is relatively independent. 18,44 This blue shift of electron absorption, together with the larger bandgap, compared to KBBF bulk 38 is consistent with previous computational and experimental result on black phosphorus layers 23 and h-BN. 24 Interactions between layers reduces the band gap.

A(ω) =

ω L × Imε(ω) C

(1)

For vibrational absorption, the largest absorption energy happens at 1254 cm−1 (8000 nm), which is in IR region (SI, IR Absorption). So the ultraviolet and visible region is not affected by that.

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Nonlinear Optical Properties Due to the symmetry of 3D KBBF (R32, group 155), the only SHG coefficient concerned is d11 (dXXX ). 26 But the 2D-ABBF belongs to symmetry group P3 (group 143) , so there are three couples of SHG coefficients di jk (i, j, k = X,Y, Z) need to take into consideration (eq 2, 3, 4 ). 49,50

group1 : −dXXX = dXYY

(2)

group2 : −dXXY = dYYY

(3)

group3 : dXXZ = dYY Z

(4)

X,Y, Z in Figure 1 also denoting the direction of dielectric constant coordinate system. 50 Nonlinear Optical Result. As in our previous work, 18 the definition of SHG coefficient of 2D materials could by per unit area (d(2D) , eq 5, Figure 3, left Y axis) and per volume (d(3D) , eq 6, Figure 3, right Y axis). Here the layer thickness is defined by Bohr radius (SI, Geometry). 51

d(2D) = d(vac) · h

(5)

d(3D) = d(vac) · h/l

(6)

d(2D) and d(3D) are 2D SHG coefficients presented in 2D (per area) and 3D (per volume, thickness defined by l); d(vac) is the result calculated with vacuum estimated by Bohr radius; h is the hight of vacuum layer ( h = 25 Å); l is the layer thickness estimated by Bohr radius 51 (See also SI Geometry). The SHG coefficients give us several information points: (1) the dXY Z , dXZZ , dY ZZ is all zero, 7



Figure 3: SHG Coefficient of 2D-ABBF and Some 3D KBBF Family Members Here, the solid square is for d(2D), and the circle is for d(3D). The different region is defined for three couples of directions (eq. 2, 3, 4). The colorful lines are for some KBBF family bulk materials SHG coefficients.

which is consistent with the symmetry analyzation, and could act as nice zero point (see SI SHG Coefficient Value); (2) the d(3D) value is similar or a little larger than 3D KBBF crystal (figure 3). And the explanation, based on previous theoretical and experimental studies , could be explained as the balance between charge negativity 21 and low dimension effect 9,16,18 . Specifically, the monolayer in 3D KBBF without potassium cation is negatively charged, and the negativity creates large hyperpolarizability, while the neutral 2D-ABBF monolayer benefits from the low dimension, probably specifically exotic exciton, polariton and phonon corelation. 11–13 The SHG coefficient calculated by our method is considered under-estimated by previous work. 18,52 And for low energy region, like IR, the deviation is small, for visible and UV region, the actual value should be larger 53 .

Analysis on Elements. Previous study on bulk KBBF has revealed that BO3 and F anions contribute most to the SHG effect 38 , while the beryllium and potassium cations is negligible. Here using the methods we developed before, 18 the band and partial charge analysis of 2D-ABBF also get the same result (Figure 4 , S3, S4, S5. ). It is noted here since the 3D KBBF and 2D-ABBF has different

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symmetry, dXXX and dXYY (also noted as d11 ) is the only coefficient needed for 3D KBBF, but 2D-ABBF needs three couples of double frequency coefficients: −dXXX = dXYY ; −dXXY = dYYY ; and dXXZ = dYY Z .

dXXX=dXYY

dXXY=dYYY dXXZ=dYYZ

DOS( ar bi . uni t )

Figure 4: Electronic Properties of 2D-ABBF The left part is for band, only some most contributing bands are highlighted, the dark color means the contribution is larger, and the light color means the contribution is smaller: Orange: important to −dXXX = dXYY ; Green: important to −dXXY = dYYY ; Blue: important to dXXZ = dYY Z ; It can be seen from the band part that the band is in general close to fermi level, but not just energy dependent. And the bands has overlaps, the SI Band and DOS has pictures separately for three directions. The bands are sorted by their energy at Gamma point, the top valence band is No. 180 (see SI BAND and DOS). The right part is the DOS. Most density of states near fermi level is from BO3 and F.

Other Issues. The real double frequency coefficient should be larger than our calculated value, especially in UV region. Since previous research suggests that many-body effect enhances exciton, 52 and the enhancement of SHG coefficient in higher frequency region is larger. 53 So we expect that our conclusion would survive future GW+BSE calculation. 54–56 Similar with the requirements 19,20 for bulk crystal, we propose there should also be five requirements for 2D SHG materials: none/low absorption in working wavelength, large SHG coefficient, reasonably available preparation, high laser induced damage thresholds(LIDTs), chemical and mechanical stability. For LIDTs, larger bandgap means higher LIDTs, so the larger band gap in monolayer suggests higher physical stability. 57 And details 19 related to first principle calculation is closely related to phase transition temperature by dynamic simulation, 58 thermo-conductivity 37,59 9



and heat capacity. 37 Other strategies applied in 3D materials, including substitution of beryllium by aluminum, boron and lithium, recombination of BO3 to other Bx Oy group, changing potassium to be Na, Cs, Sr and so on could also be applied in 2D system (See SI, KBBF Family).

Conclusion In this article, a KBBF based stable 2D SHG material 2D-ABBF was predicted with the method we developed before. 2D-ABBF should be stably working in λ >200 nm UV and visible region. Other KBBF family material developing strategies are also expected in future works.

Author contributions The manuscript was written with contributions from all authors. All authors have given approval to the final version of the manuscript.

Supporting Information Important Parameters: Figure S1: The GW0 Calculated Band Structure Phonon Spectrom: Figure S2: The Phonon Spectrum of AlBeBOF Monolayer SHG Value: Table S1: The d(vac) SHG Coefficient BAND and DOS: Figure S3.1-3.3: Band Analysis of Three groups; Figure S4: DOS Analysis Partial Charge Analysis: Table S2-S7: The Contribution to SHG of Some Important Bands Figure S5: The Partial Charge Analysis of AlBeBOF Vibration Absorption: Table S8: The Vibration Frequency of AlBeBOF Bond Valence Calculation Example; KBBF Family ; Cohesive Energy; SHG Coefficient Compared with Experimental Results.

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ACKNOWLEDGMENTS This study was supported by the National Natural Science Foundation of China (No. 21673240), Foreign Cooperation Project of Fujian Province (No. 2017I0019), and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).

Notes The authors declare no competing financial interest.

References (1) Eaton, D. F. Nonlinear Optical Materials. Science 1991, (2) Nikogosyan, D. N. Nonlinear Optical Crystals: A Complete Survey; Springer Science: New York, 2005. (3) Chen, C. T.; Sasaki, T.; Li, R. K.; Wu, Y. C.; Lin, Z. S.; Mori, Y.; Hu, Z. G.; Wang, J. Y.; Gerard, A.; Masashi, Y.; Yushi, K. Nonlinear Optical Borate Crystals: Principals and Applications; Wiley-VCH: Weinheim, 2012. (4) Gobin, A. M.; Oneal, D. P.; Watkins, D. M.; et al., Near Infrared Laser Tissue Welding Using Nanoshells as an Exogenous Absorber. Lasers in Surgery and Medicine 2005, 37. (5) Wachulak, P. W.; Capeluto, M. G.; Marconi, M. C.; et al., Patterning of Nano-Scale Arrays by Table-Top Extreme Ultraviolet Laser Interferometric Lithography. Optics Express 2007, 15. (6) Sohn, I.-B.; Choi, H.-K.; Yoo, D.; Noh, Y.-C.; Sung, J.-H.; Lee, S.-K.; Ahsan, M. S.; Lee, H. Synchronized Femtosecond Laser Pulse Switching System Based Nano-Patterning Technology. Optical Materials 2017, 69, 295 – 302.

11



(7) Jia, Y.; Gong, X.; Peng, P.; Wang, Z.; Tian, Z.; Ren, L.; Fu, Y.; Zhang, H. Toward High Carrier Mobility and Low Contact Resistance: Laser Cleaning of PMMA Residues on Graphene Surfaces. Nano-Micro Letters 2016, 8, 336–346. (8) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666–669. (9) Li, Y.; Rao, Y.; Mak, K. F.; You, Y.; Wang, S.; Dean, C. R.; Heinz, T. F. Probing Symmetry Properties of Few-Layer MoS2 and h-BN by Optical Second-Harmonic Generation. Nano Lett 2013, 13, 3329–33. (10) Davila, M. E.; Xian, L.; Cahangirov, S.; Rubio, A.; Le Lay, G. Germanene: a Novel TwoDimensional Germanium Allotrope Akin to Graphene and Silicene. New Journal of Physics 2014, 16. (11) Chow, C. M.; Yu, H.; Jones, A. M.; Schaibley, J. R.; Koehler, M.; Mandrus, D. G.; Merlin, R.; Yao, W.; Xu, X. Phonon-assisted oscillatory exciton dynamics in monolayer MoSe 2. 2017, (12) Woessner, A.; Parret, R.; Davydovskaya, D.; Gao, Y.; Wu, J. S.; Lundeberg, M. B.; Nanot, S.; Alonsogonz´l´clez, P.; Watanabe, K.; Taniguchi, T. Electrical detection of hyperbolic phononpolaritons in heterostructures of graphene and boron nitride. 2017, 1. (13) Lerario, G.; Fieramosca, A.; Barachati, F.; Ballarini, D.; Daskalakis, K. S.; Dominici, L.; Giorgi, M. D.; Maier, S. A.; Gigli, G.; K´l˛enacohen, S. Room-temperature superfluidity in a polariton condensate. Nature Physics 2017, (14) Cao, H.; Wu, J. Y.; Ong, H. C.; Dai, J. Y.; Chang, R. P. H. Second harmonic generation in laser ablated zinc oxide thin films. Applied Physics Letters 1998, 73, 572–574. (15) Cudazzo, P.; Tokatly, I. V.; Rubio, A. Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane. Phys. Rev. B 2011, 84, 085406. 12


Page 12 of 18

Page 13 of 18 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


(16) Varma, S. J.; Kumar, J.; Liu, Y.; Layne, K.; Wu, J.; Liang, C.; Nakanishi, Y.; Aliyan, A.; Yang, W.; Ajayan, P. M.; Thomas, J. 2D TiS2 Layers: A Superior Nonlinear Optical Limiting Material. Advanced Optical Materials 1700713–n/a, 1700713. (17) Liu, T.; Qin, J.; Zhang, G.; Zhu, T.; Niu, F.; Wu, Y.; Chen, C. Mercury Bromide (HgBr2): A Promising Nonlinear Optical Material In Ir Region With A High Laser Damage Threshold. Applied Physics Letters 2008, 93, 091102. (18) Yang, G.; Wu, K. Absorption and Mid-IR SHG in Two-Dimensional Halogen and Hydrogen Saturated Silicene Series. The Journal of Physical Chemistry C 2017, 121, 27139–27146. (19) Lin, Z.; Jiang, X.; Kang, L.; Gong, P.; Luo, S.; Lee, M.-H. First-principles Materials Applications and Design of Nonlinear Optical Crystals. Journal of Physics D: Applied Physics 2014, 47, 253001. (20) Liu, B.-W.; Zeng, H.-Y.; Jiang, X.-M.; Wang, G.-E.; Li, S.-F.; Xu, L.; Guo, G.-C. [A3X][Ga3PS8] (A = K, Rb; X = Cl, Br): Promising IR Non-linear Optical Materials Exhibiting Concurrently Strong Second-harmonic Generation and High Laser Induced Damage Thresholds. Chem. Sci. 2016, 7, 6273–6277. (21) Chen, C.; Wu, Y.; Li, R. The anionic group theory of the non-linear optical effect and its applications in the development of new high-quality NLO crystals in the borate series. International Reviews in Physical Chemistry 1989, 8, 65–91. (22) Zhou, X.; Cheng, J.; Zhou, Y.; Cao, T.; Hong, H.; Liao, Z.; Wu, S.; Peng, H.; Liu, K.; Yu, D. Strong Second-Harmonic Generation in Atomic Layered GaSe. J Am Chem Soc 2015, 137, 7994–7. (23) Woomer, A. H.; Farnsworth, T. W.; Hu, J.; Wells, R. A.; Donley, C. L.; Warren, S. C. Phosphorene: Synthesis, Scale-Up, and Quantitative Optical Spectroscopy. ACS Nano 2015, 9, 8869–8884, PMID: 26256770.

13



(24) Gorbachev, R. V.; Riaz, I.; Nair, R. R.; Jalil, R.; Britnell, L.; Belle, B. D.; Hill, E. W.; Novoselov, K. S.; Watanabe, K.; Taniguchi, T.; Geim, A. K.; Blake, P. Hunting for Monolayer Boron Nitride: Optical and Raman Signatures. Small 2011, 7, 465–468. (25) Wu, B.; Tang, D.; Ye, N.; Chen, C. Linear and nonlinear optical properties of the KBe 2 BO 3 F 2 (KBBF) crystal. Optical Materials 1996, 5, 105–109. (26) Midwinter, J. E.; Warner, J. The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization. British Journal of Applied Physics 1965, 16. (27) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Open-Shell Transition Metals. Physical Review B 1993, 48, 13115–13118. (28) Bl?chl, P. E. Projector Augmented-Wave Method. Physical Review B 1994, 50, 17953–17979. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, 3865–3868. (30) Rödl, C.; Bechstedt, F. Optical and Energy-Loss Spectra of the Antiferromagnetic Transition Metal Oxides MnO, FeO, CoO, and NiO Including Quasiparticle and Excitonic Effects. Phys. Rev. B 2012, 86, 235122. (31) Rinke, P.; Schleife, A.; Kioupakis, E.; Janotti, A.; Rödl, C.; Bechstedt, F.; Scheffler, M.; Van de Walle, C. G. First-Principles Optical Spectra for F Centers in MgO. Phys. Rev. Lett. 2012, 108, 126404. (32) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Physical Review B 1976, 13, 5188–5192. (33) Aversa, C.; Sipe, J. E. Nonlinear Optical Susceptibilities of Semiconductors: Results with a Length-Gauge Analysis. Physical Review B 1995, 52, 14636–14645.

14


Page 14 of 18

Page 15 of 18 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


(34) Rashkeev, S. N.; Lambrecht, W. R. L.; Segall, B. Efficient Ab Initio Method for the Calculation of Frequency-Dependent Second-Order Optical Response in Semiconductors. Phys. Rev. B 1998, 57, 3905–3919. (35) Fang, Z.; Lin, J.; Liu, R.; Liu, P.; Li, Y.; Huang, X.; Ding, K.; Ning, L.; Zhang, Y. Computational Design of Inorganic Nonlinear Optical Crystals Based on a Genetic Algorithm. CrystEngComm 2014, 16, 10569–10580. (36) Levine, Z. H.; Allan, D. C. Calculation of the Nonlinear Susceptibility for Optical SecondHarmonic Generation In III-V Semiconductors. Phys Rev Lett 1991, 66, 41–44. (37) Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science. Scripta Materialia 2015, 108, 1–5. (38) Chen, C. T.; Wang, G. L.; Wang, X. Y.; Xu, Z. Y. Deep-UV nonlinear optical crystal KBe2BO3F2ałdiscovery, ˛ growth, optical properties and applications. Applied Physics B 2009, 97, 9–25. (39) Fan, X.; Chang, D.; Chen, X.; Baek, J. B.; Dai., L. Functionalized Graphene Nanoplatelets From Ball Milling For Energy Applications. Current opinion in Chemical Engineering, 2016, (40) Sun, Y.; Zhuo, Z.; Wu, X.; Yang, J. Room-Temperature Ferromagnetism in Two-Dimensional Fe2Si Nanosheet with Enhanced Spin-Polarization Ratio. Nano Letters 2017, 17. (41) Chen, X.; Liu, J.; Zhang, W.; Xiao, B.; Zhang, P.; Li, L. First-Principles Study on the Mechanism of Hydrogen Decomposition and Spillover on Borophene. The Journal of Physical Chemistry C 2017, 121, 17314–17320. (42) Akt´l´zrk, E.; Akt´l´zrk, O. z.; Ciraci, S. Single and bilayer bismuthene: Stability at high temperature and mechanical and electronic properties. Physical Review B 2016, 94. (43) Brown, I. D., Poeppelmeier, K. R., Eds. Bond Valences; Proceedings of SPIE; Springer„ 2014; Vol. 158. 15



(44) Matthes, L.; Gori, P.; Pulci, O.; Bechstedt, F. Universal Infrared Absorbance of TwoDimensional Honeycomb Group-IV Crystals. Physical Review B 2013, 87. (45) Xia, Y. N.; Chen, C. T.; Tang, D. Y.; Wu, B. C. New Nonlinearoptical Crystals For UV And VUV Harmonicgeneration. Adv. Mater. 1995, 7. (46) Xu, Y. M.; Huang, Y. B.; Cui, X. Y.; Razzoli, E.; Radovic, M.; Shi, M.; Chen, G. F.; Zheng, P.; Wang, N. L.; Zhang, C. L.; Dai, P. C.; Hu, J. P.; Wang, Z.; Ding, H. Observation of a Ubiquitous Threedimensional Superconducting Gap Function in Optimally Doped Ba0.6K0.4Fe2As2. Nat. Phys. 2011, 7. (47) Sasaki, T.; Mori, Y.; Yoshimura, M.; Yap, Y. K.; Kamimura, T. Recent Development of Nonlinear Optical Borate Crystals: Key Materials for Generation of Visible and UV Light. 2000, 30. (48) Wei, W.; Dai, Y.; Huang, B.; Jacob, T. Many-Body Effects in Silicene, Silicane, Germanene and Germanane. Phys. Chem. Chem. Phys. 2013, 15, 8789–8794. (49) Valentin, G.; Dmitriev,; Gurzadyan, G. G.; Lotsch,; V., H. K. Handbook of Nonlinear Optical Crystals; Springer„ 1997; pp 3225–3231. (50) Kleinman, D. A. Nonlinear Dielectric Polarization in Optical Media. Physical Review 1962, 126, 1977–1979. (51) Lherbier, A.; Botello-M´l˛endez, A. R.; Charlier, J. C. ELectronic And Optical Properties Of Pristine And Oxidized Borophene. 2D Materials 2016, 3. (52) Baer, R.; Rabani, E. Expeditious Stochastic Calculation of Multiexciton Generation Rates in Semiconductor Nanocrystals. Nano Lett 2012, 12, 2123–8. (53) Stamova, M.; Rebentrost, F. Excitonic effects in the nonlinear optical response of a Si(111) surface. Phys. Status Solidi B 2010, 247.

16


Page 16 of 18

Page 17 of 18 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


(54) Hybertsen, M. S.; Louie, S. G. Electron Correlation in Semiconductors and Insulators: Band Gaps and Quasiparticle Energies. Phys. Rev. B 1986, 34, 5390–5413. (55) Rohlfing, M.; Louie, S. G. ElectRon-Hole Excitations and Optical Spectra from First Principles. Phys. Rev. B 2000, 62, 4927–4944. (56) Deslippe, J.; Samsonidze, G.; Strubbe, D. A.; Jain, M.; Cohen, M. L.; Louie, S. G. BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures. Computer Physics Communications 2012, 183, 1269–1289. (57) Yang, G.; Gong, P.; Lin, Z.; Ye, N. AZn2BO3X2(A = K, Rb, NH4; X = Cl, Br): New Members of KBBF Family Exhibiting Large SHG Response and the Enhancement of Layer Interaction by Modified Structures. Chemistry of Materials 2016, 28, 9122–9131. (58) Bucher, D.; Pierce, L. C. T.; McCammon, J. A.; Markwick, P. R. L. On the Use of Accelerated Molecular Dynamics to Enhance Configurational Sampling in Ab Initio Simulations. Journal of Chemical Theory and Computation 2011, 7, 890–897, PMID: 21494425. (59) Feng, J.; Wan, C.; Xiao, B.; Zhou, R.; Pan, W.; Clarke, D. R. Calculation of the Thermal Conductivity of L2 SrAl2 O7 (L = La, Nd, Sm, Eu, Gd, Dy). Phys. Rev. B 2011, 84, 024302.

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Graphical TOC Entry 2D:ABBF

3D:KBBF Be+Be Be+Al

SHG

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Designing Two-Dimensional KBBF Family Second Harmonic

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