The covalent channel effect: How covalent metal-oxygen bond reduces bandgap and boosts SHG response in calcium apatites

The covalent channel effect: How covalent metal-oxygen bond reduces bandgap and boosts SHG response in calcium apatites | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 12 March 2025 V1 Latest version Share on The covalent channel effect: How covalent metal-oxygen bond reduces bandgap and boosts SHG response in calcium apatites Authors : Zhi-Hao He , Yun-Jie Wang , Jia-Fu Ding , Xin Su [email protected] , Yu Chu , and Ming-Hsien Lee Authors Info & Affiliations https://doi.org/10.22541/au.174174360.04365933/v1 198 views 104 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Text：Apatite is a versatile and important mineral group with significant roles in geology, biology, and industry. This study employs density functional theory (DFT) to investigate the electronic structures and optical properties of three centrosymmetric (CS) crystals: Ca 10 (PO 4 ) 6 F 2 (FA), Ca 10 (PO 4 ) 6 Cl 2 (ClA), and Ca 10 (PO 4 ) 6 Br 2 (BrA), and two non-centrosymmetric (NCS) crystals: Ca 10 (PO 4 ) 6 (OH) 2 (HA) and Ca 10 (PO 4 ) 6 O(OA). Despite the strong structural resemblance, the optical properties of OA show discrepancy among other apatite analogs. Specifically, the bandgap of OA is reduced from over 6.0 eV to 4.328 eV, and a significant second-harmonic generation (SHG) response ( d 11 = 0.824 pm/V and d 22 = 1.327 pm/V) compared with NCS analog HA ( d 15 = -0.021 pm/V and d 33 = -0.026 pm/V). The main reason for these disparities is that in other compounds the bonds between Ca and X tend to be ionic, whereas in OA, the bonds formed between Ca and O C exhibit covalent character, and almost all of the charge obtained by O C comes from Ca. This not only reduces the bandgap but also enhances the internal charge transfer capability, leading to an increase in the SHG coefficient. Cite this paper: Chin. J. Chem. 2024 , 42 , XXX—XXX. DOI: 10.1002/cjoc.202400XXX The covalent channel effect: How covalent metal-oxygen bond reduces bandgap and boosts SHG response in calcium apatites Zhi-Hao He a,b , Yun-Jie Wang a,b , Jia-Fu Ding a,b , Xin Su a,b* , Yu Chu c* , Ming-Hsien Lee d* a. School of Physical Science and Technology, Yili Normal University, Yining 835000, China; b. Xinjiang Laboratory of Phase Transitions and Microstructures of Condensed Matter Physics, Yili Normal University, Yining 835000, China; c. Xinjiang Key Laboratory of Functional Crystal Materials CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry Xinjiang Key Laboratory of Electronic Information Materials and Devices 40-1 South Beijing Road, Urumqi 830011, China d. Department of Physics, Tamkang University, New Taipei City 25137, China Keywords Calcium apatite | Ab initio calculations | Density functional theory |Fat-band analysis | Covalency | Second-harmonic generation | Electronic structure | Electron transfer Comprehensive Summary Text：Apatite is a versatile and important mineral group with significant roles in geology, biology, and industry. This study employs density functional theory (DFT) to investigate the electronic structures and optical properties of three centrosymmetric (CS) crystals: Ca 10 (PO 4 ) 6 F 2 (FA), Ca 10 (PO 4 ) 6 Cl 2 (ClA), and Ca 10 (PO 4 ) 6 Br 2 (BrA), and two non-centrosymmetric (NCS) crystals: Ca 10 (PO 4 ) 6 (OH) 2 (HA) and Ca 10 (PO 4 ) 6 O(OA). Despite the strong structural resemblance, the optical properties of OA show discrepancy among other apatite analogs. Specifically, the bandgap of OA is reduced from over 6.0 eV to 4.328 eV, and a significant second-harmonic generation (SHG) response ( d 11 = 0.824 pm/V and d 22 = 1.327 pm/V) compared with NCS analog HA ( d 15 = -0.021 pm/V and d 33 = -0.026 pm/V). The main reason for these disparities is that in other compounds the bonds between Ca and X tend to be ionic, whereas in OA, the bonds formed between Ca and O C exhibit covalent character, and almost all of the charge obtained by O C comes from Ca. This not only reduces the bandgap but also enhances the internal charge transfer capability, leading to an increase in the SHG coefficient. Introduction The apatite family, characterized by its unique chemical composition and structural features, occupies a significant position in the fields of materials science, [1-5] biomedical science6-8, and earth science. [9-11] The general chemical formula for apatite is M 10 (PO 4 ) 6 X 2 , [12] where M represents divalent cations such as calcium, strontium, and barium, and X represents monovalent anions such as fluoride, chloride, and hydroxide, referred to as channel ions. Calcium apatite, as a representative of the apatite family, has been extensively studied due to its excellent properties and applications in industry and biology. Currently, attempts have been made by researchers to substitute different anions, which has endowed calcium apatite with a variety of physical and chemical properties, to expand its potential applications. [13-15] Extensive theoretical computational work has been conducted on the calcium apatite system. In the work by Louis-Achille et al.16, the electronic structure of fluorapatite Ca 10 (PO 4 ) 6 F 2 was calculated using density functional theory, including the electronic density of states and Mulliken population analysis. It was discovered that Ca 10 (PO 4 ) 6 F 2 possesses an ionic covalent structure with significant ionic charge. Terra et al. [17] utilized the linear combination of atomic orbitals discrete variational method based on first-principles to calculate the electronic structure of hydroxyapatite Ca 10 (PO 4 ) 6 (OH) 2 with Zn atoms substituting for calcium, indicating a preference for Zn to substitute the hexa-coordinated Ca2 site. Calderin and his team [18] employed first-principles calculations to calculate the total and partial density of states for Ca 10 (PO 4 ) 6 X 2 (X=OH, F, Cl), oxyapatite, and apatite with X vacancies, and studied the influence of c-axis ions on the top of the valence band, which suggests minimal or no effect of c-axis ions at the top of the valence band. Rulis et al. [19] conducted a detailed study of the electronic structure, bonding, and charge transfer of several calcium apatites, revealing that the bandgaps of these materials are within the range of 5.3 eV, classifying them as wide bandgap crystals, with bonding primarily composed of the anionic group PO 4 3- and the cationic group Ca-O. Li and his team [20] , in their study of calcium apatite, found that the state density of the valence band was predominantly influenced by the PO 4 3- group and the state of Ca, with mechanical properties exhibiting a certain degree of anisotropy. The product of dehydrated hydroxyapatite is oxyapatite Ca 10 (PO 4 ) 6 O, which is an important product in the sintering process of apatite that used in orthopedics. [21] This type of apatite is known for its active chemical properties, [22] particularly its high solubility in water, [23] and is considered a promising bioabsorbable material for medical applications. [24] Phosphates are potential candidates for the preparation of ultraviolet optical materials, with numerous high-performance phosphate crystals having been reported. [25-28] Non-π-conjugated phosphate crystals, which have smaller polarity, struggle to form crystals with large birefringence, hindering their development as birefringence materials. [29-31] The PO 4 3- group, being a non-π-conjugated unit, allows for larger bandgaps in crystals, making phosphates excellent candidates for ultraviolet optical materials. Apatite, as an outstanding crystal, has been predominantly studied for its band structure, state density, and mechanical properties, with less focus on its optical properties, particularly birefringence and nonlinear optical properties. Therefore, this paper selects three centro-symmetric apatites containing the PO 4 3- group, Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br), and two non-centro-symmetric Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 O, aiming to provide a comprehensive analysis of their electronic structure, including birefringence, through first-principles calculations. Additionally, the nonlinear optical properties of Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 O are calculated, offering some reference for future research on apatite and apatite-like materials. Results and Discussion Crystal Structure Characteristics The space groups for the selected Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br) are P 6 3 / m . Due to the arrangement of the hydroxyl group along the c-axis, Ca 10 (PO 4 ) 6 (OH) 2 lacks the mirror symmetry along the c-axis compared to the other three systems, resulting in a space group of P 6 3 for this compound. [32-34] Upon dehydration of hydroxyapatite Ca 10 (PO 4 ) 6 (OH) 2 , the Ca atoms at z=1/4 and z=3/4 become non-equivalent, and the original triple helix symmetry transforms into a six-fold rotational symmetry, forming P -6 space group of Ca 10 (PO 4 ) 6 O. All structural factors have their specific effects on the electronic structures of Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O, consequently, on the optical properties. In the crystal structures of Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O, six PO 4 tetrahedra are surrounded by ten Ca atoms distributed around them, with the X ions aligned along the c-axis. In FA, the c-axis ion, fluoride F-, forms an equilateral triangle with three equivalent Ca 2+ ions, centrally located and connected to the Ca atoms. In ClA and BrA, the halogen ions Cl - and Br - , form distorted octahedra sharing upper and lower faces with six equivalent Ca 2+ ions along the c-axis. In HA, the c-axis ion, the oxygen atom of the hydroxyl group, forms a flattened trigonal pyramid with three equivalent Ca 2+ ions, and the hydrogen atom is also aligned along the c-axis. The structure of OA is relatively unique; it is formed by the dehydration of c-axis hydroxyl groups in HA. After dehydration, only one O atom is located at z=1/2 on the c-axis, which, along with three equivalent Ca 2+ ions, forms an equilateral triangle. The O 2- ion is centrally positioned and connected to the Ca atoms. The geometric structures of Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O were optimized using first principles. Table 1 presents the optimized lattice constants for these apatites along with the experimental and theoretical values. It can be observed from the data in Table 1 and Table S1 that the calculated values are in good agreement with the existing experimental values, with errors within 4%. The optimized lattice constants are slightly larger than the experimental values, which is attributed to the inherent characteristics of the selected GGA approximation method. [35-36] Figure 1 Crystal structures of apatite Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O (a) FA (b) ClA / BrA (c) HA (d) OA Table 1 presents the optimized lattice constants for Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O, along with their experimental values. Apatite Space Group a/Å c/Å a/c Reference FA P 6 3 /m Optimized 9.5784 6.9474 1.3787 This work Experimental 9.3783 6.8888 1.3613 [37] ClA Optimized 9.8874 6.6823 1.4796 This work Experimental 9.6280 6.7640 1.4234 [18] BrA Optimized 9.9109 6.7570 1.4668 This work Experimental 9.7610 6.7390 1.4484 [38] HA P 6 3 Optimized 9.5569 6.8764 1.3898 This work Experimental 9.4810 6.8590 1.3823 [39-40] OA P -6 Optimized 9.7374 6.8931 1.4126 This work Experimental 9.4320 6.8810 1.3707 [41] Band Structure and Density of States Figure 2 illustrates the band structures of Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O, calculated along high-symmetry points in the first Brillouin zone. Using the GGA functional, the calculated bandgaps for Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O were determined to be 5.527 eV, 5.431 eV, 4.882 eV, 5.443 eV, and 3.316 eV, respectively. To achieve a more precise description of their band structures, additional calculations were performed using other functionals(in Figure S1), including the HSE06 functional, which yielded values of 7.118 eV, 6.974 eV, 6.096 eV, 6.881 eV, and 4.328 eV. Except for OA, the bandgaps of the other four compounds are close to or within the deep ultraviolet region. Figure 2 illustrates the band structures obtained from GGA calculations. In Figure 2a, which is a direct bandgap compound, the remaining four plot show they are indirect bandgap compounds(Table S2). The results turned out that for the systems FA, ClA, and BrA, the bandgap decreases with the increasing size of the channel ion. The valence band of BrA is not smooth(In Figure 2c), which is attributed to the Br-4p orbitals, while in Figure 2b, the Cl-3p orbitals also exhibit a pronounced peak near the 0 eV, but due to insufficient proximity and weaker intensity, they do not protrude prominently into the bandgap. In HA, the presence of the polar hydroxyl group leads to the formation of hydrogen bonds. The existence of hydrogen bonds locally affects the electronic arrangement of the p orbitals of the hydroxyl group and the O-2p orbitals near the 0 eV, resulting in the valence band maximum of HA not being at a high-symmetry point. In the band structure plot of OA(In Figure 2e), significant level splitting is observed, with two levels splitting out near the 0 eV and -0.2 eV and one level in the 3.3 eV nearby. This is due to the O 2- ions remaining after the dehydration of HA, causing electrons to localize around these ions and resulting in the splitting of energy levels. Consequently, the bandgap value of OA is smaller than that of HA. To elucidate the orbital contributions from different atoms and groups within the band structure, Figure S2 presents the total density of states (DOS) for five types of apatites, along with the projected density of states (PDOS) for the Ca atoms, PO 4 3- groups, and c-axis ions in each apatite. The DOS of FA, ClA, BrA, and HA are generally similar, with only minor differences in detail. For instance, in the valence band at -14 eV, the Figure S2b and Figure S2c, exhibits a pronounced small peak contributed by the s orbitals of their c-axis channel ions. The s orbital of the F atom in FA is more active at deeper energy levels, resulting in higher DOS peak values. At around -20 eV in the valence band, the peaks are mainly contributed by the Ca-4p and the O-2s of the PO 4 3- groups, indicating s-p hybridization between Ca atoms and O atoms at this region, which is observed in the all system. Near the Fermi level, in the Figure 3a b c and d, the PDOS for FA, ClA, BrA, and HA are primarily contributed by the O-2p of the PO 4 3- groups and the p orbitals of the channel ions, indicating p-p hybridization at this region. Figure 2 Band structures of apatites Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O (a) FA (b) ClA (c) BrA (d) HA (e) OA (f) Total Although the p orbitals of Cl and Br atoms exhibit similar trends near the 0 eV, the Br atom is more active and closer to the Fermi level, resulting in a non-smooth appearance of the valence band in the band structure plot, consistent with the conclusions drawn earlier. In Figure S2d, the hydrogen bonding affects the electronic arrangement of the O atoms in the hydroxyl group, causing its DOS peak to be closer to 0 eV. In Figure S2e, the electronic orbitals near the Fermi level exhibit different behavior compared to the other four apatites, being solely contributed by the p orbitals of the O atoms on the c-axis, with the electronic orbitals of the PO 4 3- groups not participating in the contribution. This is because the PO 4 3- group belongs to non-π-conjugated units, with electrons mostly restricted within the P-O bonds, not being able to move freely, and being less oxidative compared to the O atoms. In the context of the band structure analysis, the valence band proximate to the Fermi level is predominantly influenced by the oxygen atoms, exhibiting a characteristic two levels splitting as depicted. Conversely, within the conduction band, there is a notable alignment of electronic orbitals across the five apatites, primarily shaped by the p and d orbitals of Ca atoms, the p orbitals of P atoms and the p orbitals of O atoms. A subtle variation emerges in Figure S2e, In the conduction band minimum of OA, there is a subtle peak(in Figure S3), with the outer electron orbitals of Ca contributing approximately 93%, constituting the vast majority, while the PO 4 3- groups and the c-axis O atoms contribute only about 7%, primarily through their p-orbitals. To further understand the band structures of the five types of apatite, this article also used VASP to calculate their projected band structures. As most of the P atoms occupy deep energy levels in the band structure, the occupation of P atoms near the Fermi level is not shown. In Figure 3, it can be seen that the conduction bands of HA and OA are predominantly filled with Ca atoms, while O atoms contribute only a small portion. In Figures 3(c) and (f), it is evident that the O OH is predominantly distributed in the valence band region, intermingling with O [PO] , with minimal occupation near the Fermi level, and concentrating around -1 and -4 eV. In contrast, the O C in OA ’floats on the valence band surface’ and splits into two energy levels within the valence band, without intermingling with O [PO] . Consequently, it can be deduced that the bandgap of HA is primarily determined by Ca and O [PO] , while the bandgap of OA is determined by Ca and O C . The distribution of Ca and O atoms in the energy bands of FA, ClA, and BrA is roughly similar(in Figure S4), except that as the electronegativity of the c-axis ion decreases, the energy level contributed by the c-axis ion gradually shifts towards the top of the valence band, resulting in a decrease in the band gap with decreasing electronegativity. Figure 3 Projected Band Structure of Ca atoms, O atoms, and c-axis ions in Ca 10 (PO 4 ) 6 (OH) 2 and Ca 10 (PO 4 ) 6 O (a) HA-Ca (b) HA-O [PO] (c) HA-O OH (d) OA-Ca (e) OA-O [PO] (f) OA-O C Electronic Structure Analysis To explore the relationship between microscopic and macroscopic properties, population analysis was conducted on five types of apatites, and differential charge density were created. Initially, the calculated P-O bond lengths for the five apatites were compared with experimental values, and both the average error and the error of the mean were determined (in Figure S5). It was observed that both metrics are relatively low, confirming the validity of the computational approach. Table S3 details the average bond lengths and population for cations interacting with O atoms within the ionic groups and X ions. The internal electron cloud overlap among the five apatites is comparable, with notably higher population values for the P-O bonds within the PO 4 3- group, approximately 0.65, which suggests a significant covalent character. Conversely, the population values for the Ca-O bonds in the cation groups, consisting of Ca and O atoms, are significantly lower than those of the P-O bonds, indicating a predominantly ionic character. Given the substantial distance between Cl and Br atoms and Ca atoms, their impact is considered negligible, leading to the exclusion of Ca-Cl and Ca-Br bonds from the calculations presented in this study. For HA and OA, the bond population values involving Ca and the c-axis ions are 0.21 and 0.4, respectively, HA exhibit ionic properties, whereas OA displays covalent properties. Consequently, OA exhibits a smaller bandgap compared to HA. As shown in Table S4, although the c-axis O atoms in HA and OA receive similar amounts of charge, a portion of the charge associated with the O OH in the hydroxyl group originates from the internal H atoms, leading to a more dispersed charge source and less association with Ca. In contrast, the charge acquired by the O C in OA is almost entirely derived from Ca, further indicating that OA has a stronger charge transfer capability, which results in a smaller bandgap. To further ascertain the bonding types within these apatites, differential charge density maps were plotted(Figure S6), revealing a non-spherical charge distribution around the O atoms, slightly skewed towards the Ca atoms. This non-spherical charge arrangement is indicative of covalent bonding characteristics. [42] However, in OA, it is evident that electrons around Ca atoms inclined towards the c-axis O atoms are being depleted, while the c-axis O atoms have largely accumulated the electrons lost by the Ca atoms, forming a relatively standard circular shape. This indicates a weaker bonding between the c-axis O atoms and Ca atoms, and a higher degree of electron localization around the O atoms. Linear Optical Properties Linear optical properties describe the characteristics where the macroscopic optical properties of a material, when interacting with light, are directly proportional to the intensity of the incident light. These properties generally include the dielectric function, absorption coefficient, reflectivity, and birefringence47-48. The partial linear optical properties of the five crystals are depicted in Figure S7, showing that the overall trends in the dielectric function, absorption coefficient, and reflectivity across the five crystals are quite similar, with no other significant variations. However, slight differences are observed in the birefringence of the five crystals at 1064 nm. Compounds containing PO 4 3- typically exhibit low birefringence, as seen in examples like BPO 4 (0.0001 at 1064 nm), [43] RbMgPO 4 ·6H 2 O (0.005 at 1064 nm) and CsMgPO 4 ·6H 2 O (0.006 at 1064 nm) [44] . The birefringence values of the five apatites at 1064 nm are 0.0092 (FA), 0.009 (ClA), 0.016 (BrA), 0.003 (HA), and 0.0002 (OA). At 532 nm, the birefringence values are 0.0096 (FA), 0.010 (ClA), 0.018 (BrA), 0.001 (HA), and 0.011 (OA), all of which are relatively low. In Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br), the crystal lattice becomes progressively more loosely packed as the electronegativity of the c-axis ions decreases, thereby enhancing anisotropy. Consequently, the birefringence of Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br) increases with the atomic number of the halogen element. Figure S8 shows that HA and OA exhibit interesting characteristics: (i) Unlike the other four apatites, the birefringence of HA gradually increases with wavelength. (ii) In OA, the birefringence is highly sensitive to wavelength. Therefore, the real-space atom-cutting method was employed in this study to quantify the contributions of Ca, PO 4 3- groups, and c-axis ions, and to investigate these two characteristics. The cutting-radii for Ca, P, O, F, Cl, Br, and H were set as 1.22, 0.84, 1.11, 1.33, 1.81, 1.96, and 0.37 Å, respectively. From Table 2, it can be seen that after cutting the hydroxyl group in HA, the same characteristic is still observed; however, this is not the case after cutting the Ca and PO 4 3- groups. It can be concluded that the emergence of this characteristic is unrelated to the hydroxyl group but is associated with the Ca and PO 4 3- groups crystallizing in the special space group P 6 3 , which leads to this characteristic in HA. To further clarify the reasons behind the unusual chromatic dispersion in HA, we also employed the real-space atom-cutting method to quantify the impact of various groups on chromatic dispersion within HA and compared it with OA.(in Figure S9) The findings revealed that the PO 4 3- group constitutes a significant proportion in both HA and OA. Notably, the ratio of hydroxyl groups to PO 4 3- groups is approximately 1:4 in HA and 1:3 in OA. This discrepancy is likely due to the chemical environment of hydroxyl groups within the phosphate system, which may not favor the activity of their O-H bonds, [45] this results in abnormal overall dispersion. In OA, after cutting the c-axis O, the rate of decrease is much slower compared to cutting the Ca and PO 4 3- groups, indicating that the sensitivity of birefringence to wavelength in OA is due to the special position of the c-axis O, its strong electronegativity, and the cooperative interaction with Ca or PO 4 3- groups. In ClA and BrA, after cutting the c-axis ions, the birefringence changes little; however, in FA, the change is significant, mainly because the strong electronegativity of F has a greater impact on the overall structure, reducing the crystal’s anisotropy. Observations from Table 2 also reveal that, compared to Ca and c-axis ions, the combination of PO 4 3- groups with c-axis ions affects the structural arrangement, leading to a greater contribution of the PO 4 3- groups and c-axis ions to their birefringence. SHG Response and Source Analysis The linear optical properties of FA, ClA, and BrA, which belong to the space group P 6 3 / m , can be estimated using density functional theory. However, HA and OA, being non-centrosymmetric crystals, crystallize in higher symmetry space groups P 6 3 and P -6, respectively. In this study, we calculated the SHG coefficients for HA and OA using the real-space atom-cutting method to elucidate the contributions of the c-axis ions and the PO 4 3- groups. The results, as depicted in Figure S10, reveal the SHG coefficients for HA to be d 15 = -0.021 pm/V and d 33 = -0.026 pm/V. Upon removing the hydroxyl group from HA, the coefficients shift to d 33 = 0.093 pm/V and d 15 = -0.064 pm/V. When the PO 4 3- group is removed, the coefficients change to d 33 = -0.147 pm/V and d 15 = 0.068 pm/V. Figure S11 similarly demonstrates that the hydroxyl group and the PO 4 3- group exert opposite effects in the d 33 direction. Collectively, these findings indicate that the small SHG coefficients in HA result from the canceling out of second-harmonic effects between the PO 4 3- group and the hydroxyl group. Consequently, this study focuses primarily on the second-harmonic effect of OA, which possesses two SHG coefficients: d 11 and d 22 . The d 22 coefficient is 1.327 pm/V, while d 11 is slightly lower at 0.824 pm/V. It can be seen that due to the band gap of OA being smaller than that of HA, the electronic transition ability is stronger, so the frequency doubling coefficient of OA is greater than that of HA. Additionally, Figure S10 illustrates that in the d 11 direction, the c-axis oxygen atom and the PO 4 3- group contribute oppositely. To study the contribution of different electronic states to the harmonic generation, band-resolved [46] and SHG density method were employed to analyze the largest tensor d 22 . The partial density of states and band structure analysis for VE and VH are depicted in Figure 4(a). In the valence band, the p orbitals of the c-axis O atoms play a primary role, with contributions also made by the O-2p orbitals of the PO 4 3- groups near the Fermi level. In the conduction band, the active states contributing to the SHG coefficient are widely distributed, notably around 5 eV, these states are composed of the Ca 3d orbitals primarily. Figures 4(b) and (c) also show that the VE occupied states are concentrated around the O atoms within the lattice, with a larger proportion being occupied by the c-axis O atoms. The VH occupied states are mostly concentrated on the c-axis O atoms, with a small portion concentrated near the Ca atoms adjacent to the c-axis O atoms. The unoccupied states of VE and VH are occupied by the Ca atoms. From the above analysis, it can be seen that the significant and strong SHG response of OA is attributed to the p-orbital of the c-axis O atom and the p-orbital of the PO 4 3- group in the valence band and all the electron orbitals involved in the calculation of the Ca atom in the conduction band. Table 2 The birefringence Δn(@532/1064 nm) for Ca 10 (PO 4 ) 6 X 2 (X=F, Cl, Br, OH) and Ca 10 (PO 4 ) 6 O and the corresponding real-space atom-cutting results Apatite Origin Cut Ca Cut XC or OC Cut PO43- nm 532 1064 532 1064 532 1064 532 1064 FA 0.0096 0.0092 0.012 0.011 0.013 0.012 0.009 0.008 ClA 0.010 0.009 0.009 0.008 0.008 0.007 0.009 0.008 BrA 0.018 0.016 0.017 0.014 0.011 0.010 0.0025 0.001 HA 0.001 0.002 0.011 0.009 0.007 0.008 0.007 0.006 OA 0.011 0.0002 0.010 -0.001 0.008 0.005 0.012 -0.003 Figure 4: (a) PDOS and band-resolved for VE and VH processes in OA (b) Contribution of different atoms to VE in OA (c) Contribution of different atoms to VH in OA Conclusions In this paper, the electronic structures and optical properties of three centrosymmetric crystals FA, ClA and BrA and two non-centrosymmetric crystals OA and HA are investigated using density functional theory. The band gaps of the four centrosymmetric crystals are large, while OA exhibits a smaller band gap due to the unique characteristics of its electronic structure, the band gaps of the other four crystals are approximately 5 eV. Research on these five apatite compounds revealed that those containing halogen elements exhibit an increase in birefringence with the increasing atomic number of the halogen. Notably, BrA shows the highest birefringence among them. This suggests that a stronger alkaline nature of the c-axis ions in the five apatites will make a lower level of birefringence. This study employs the real-space atom-cutting method to quantify the contributions of different groups to the system’s birefringence, revealing that the PO 4 3- groups and c-axis ions make significant contributions. We also employed both the real-space atom-cutting method and band-resolved analysis to investigate the sources of second-harmonic generation in HA and OA. It was discovered that on the two effective second-harmonic generation directions of HA and OA, the c-axis ions and PO 4 3- groups exert opposite effects. Supporting Information The supporting information for this article is available on the WWW under https://doi.org/10.1002/cjoc.202400xxx. Conflict of Interest The authors declare no conflict of interest. Acknowledgement This work was completed with the help from the Xinjiang Key Laboratory for Grant No. 2023D04074, the School level Scientific Research Project of Yili Normal University (Grant No. 22XKZZ21), the National Natural Science Foundation of China (52402017), and the Yili Normal University Student Innovation Training Project (s202210764014). Y.C. thanks the support from Tianchi Doctor plan of Xinjiang Uygur Autonomous Region. References 1. J. Gomez-Morales, M. Iafisco, J. M. Delgado-Lopez, S. Sarda and C. 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Mutailipu, X. Su, Z. Yang, J. Li and S. Pan, Zn 2 HgP 2 S 8 : A Wide Bandgap Hg-Based Infrared Nonlinear Optical Material with Large Second-Harmonic Generation Response, Small, 2023 , 19 , 46. Manuscript received: XXXX, 2024 Manuscript revised: XXXX, 2024 Manuscript accepted: XXXX, 2024 Version of record online: XXXX, 2024 The Authors Left to Right: Authors Names You will be invited to submit the most recent photos of all the authors upon acceptance of the manuscript Entry for the Table of Contents The Covalent Channel Effect: How Metal-linking Oxygen Configuration Reduces Bandgap and Boosts Nonlinear Optics in Calcium Apatite Systems Zhi-Hao He a,b , Yun-Jie Wang a,b , Jia-Fu Ding a,b , Xin Su a,b* , Yu Chu c* , Ming-Hsien Lee d* Chin. J. Chem. 2024 , 42 , XXX—XXX. DOI: 10.1002/cjoc.202400XXX As the bond length between channel Ca-O bonds decreases, the covalency increases, thereby enhancing the electron transfer and leading to an exceptional case of a SHG increasement and a bandgap reduction among the nearly isostructural apatite series. Supplementary Material File (image4.tiff) Download 5.84 MB File (image5.tiff) Download 6.65 MB File (image6.tiff) Download 5.18 MB File (image7.tiff) Download 4.36 MB Information & Authors Information Version history V1 Version 1 12 March 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords ab initio calculations calcium apatite covalency density functional theory fat-band analysis second-harmonic generation Authors Affiliations Zhi-Hao He Yili Normal University View all articles by this author Yun-Jie Wang Yili Normal University View all articles by this author Jia-Fu Ding Yili Normal University View all articles by this author Xin Su [email protected] Yili Normal University View all articles by this author Yu Chu Xinjiang Technical Institute of Physics and Chemistry View all articles by this author Ming-Hsien Lee Tamkang University View all articles by this author Metrics & Citations Metrics Article Usage 198 views 104 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Zhi-Hao He, Yun-Jie Wang, Jia-Fu Ding, et al. The covalent channel effect: How covalent metal-oxygen bond reduces bandgap and boosts SHG response in calcium apatites. Authorea . 12 March 2025. 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