Discovery of excellent ultraviolet nonlinear optical materials in chlorates and bromates with highly stereochemically active lone pairs

Abstract

The discovery of short-wave ultraviolet (SWUV, λ_PM < 266 nm, PM = phase-matching) and deep ultraviolet (DUV, λ_PM < 200 nm) nonlinear optical (NLO) crystals is urgently required and full of challenges. Unlike the conventional strategy of using π-conjugated groups (such as BO₃) as core motifs for constructing UV NLO crystals, herein the long-neglected stereochemically active lone pair (SCALP) groups ClO₃ and BrO₃ are innovatively proposed to be good UV NLO functional motifs based on the group property prediction, and the NLO performance of chlorates and bromates has been investigated systematically for the first time by first-principles methods. Benefiting from the high polarizability of ClO₃ and BrO₃ and their favorable alignments, the halate crystals AClO₃ and ABrO₃ (A = NH₄, K, Rb and Cs) exhibit high SHG coefficients comparable to that of classical β-BaB₂O₄ (4.2–4.8 × KDP for AClO₃ and 6.1–7.1 × KDP for ABrO₃). Meanwhile, their wide band gaps and large optical anisotropy lead to very short λ_PM deep into DUV and SWUV (185–195 nm for AClO₃ and 210–220 nm for ABrO₃). Remarkably, ABrO₃ shows a rare full-wavelength phase-matching capability. Hence AClO₃ and ABrO₃ could be promising DUV and SWUV NLO candidates, respectively, and the UV NLO potential of ClO₃ and BrO₃ is further demonstrated by profound mechanism analysis. This work opens up a new avenue for the development of SWUV and even DUV NLO materials.

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Introduction

As vital optoelectronic functional materials, nonlinear optical (NLO) crystals can extend limited and fixed laser wavelengths to the ultraviolet and infrared spectral ranges through various kinds of frequency conversion techniques, such as second harmonic generation (SHG), etc. Due to their wide applications in many important fields, such as ultrahigh-resolution laser lithography, biomedicine and high-precision scientific instruments, short-wave ultraviolet (SWUV, λ_PM < 266 nm, PM = phase-matching) and deep ultraviolet (DUV, λ_PM < 200 nm) NLO crystals have attracted ever-growing attention from chemists and materials scientists.^1–5

The indispensable prerequisite for being an NLO crystal is the noncentrosymmetric structure constructed by NLO functional motifs.^6,7 Over the past decades, several important NLO-active motifs with wide UV transmittance windows, including the π-conjugated BO₃, CO₃ and C(NH₂)₃ planar triangles and the σ-bonded BO_nF_4−n and PO_nF_4−n tetrahedra, have been frequently involved in the exploration of UV NLO materials and some potential SWUV and DUV NLO borates, carbonates, guanidinium salts and phosphates have been developed, including the notable β-BaB₂O₄ (β-BBO) and KBe₂BO₃F₂ (KBBF), as well as the newly discovered CsB₄O₆F, C(NH₂)₃BF₄, ABCO₃F, NaNH₄PO₃F·H₂O, etc.^8–12

The stereochemically active lone pair (SCALP) groups, represented by IO₃, SeO₃ and TeO₃, exhibit their natural advantages in the nonlinear optical field because the SCALP electrons can induce cations (I⁵⁺, Se⁴⁺ and Te⁴⁺) to undergo second-order Jahn–Teller (SOJT) distortion and endow the groups with large hyperpolarizability and polarizability anisotropy.^13,14 In recent years, numerous excellent NLO crystals with such groups have been discovered, such as AIO₃ (A = Li, Rb, Cs), Li₂M(IO₃)₆ (M = Ge, Sn, Ti), BiFSeO₃, Pb₂Bi(SeO₃)₂Cl₃, TlSb₃Te₂O₁₂, etc.^15–23 They are mostly only used in the IR NLO field due to their relatively small band gaps. Therefore, the SCALP groups are generally considered to be the IR NLO-active motifs rather than the UV ones. However, our calculations have revealed that other less-common SCALP groups have the potential to be excellent UV NLO-active motifs.

The elements chlorine and bromine are located in the same main group as iodine in the periodic table and have the pentavalent ionic forms with Cl⁵⁺-3s² and Br⁵⁺-4s² SCALP electrons. Like I⁵⁺ in iodates, Cl⁵⁺ and Br⁵⁺ are commonly found in the forms of ClO₃ and BrO₃, and the coordinated oxygen atoms also adopt a lopsided mode in the known chlorates and bromates.^24,25 We have performed the quantum chemical calculations on the microscopic NLO properties of ClO₃ and BrO₃ using Gaussion09,²⁶ and the results are shown in Fig. 1. First, the HOMO–LUMO gaps of ClO₃ and BrO₃ are calculated to be 8.23 and 7.17 eV, respectively, which fall within the UV (even deep-UV) region and are comparable to those of BO₃ and CO₃ (especially for ClO₃); moreover, due to the SCALP effect, ClO₃ and BrO₃ possess relatively large hyperpolarizabilities of 36.08 and 39.53 a.u., respectively, which are superior to BO₃ and CO₃ though inferior to IO₃. Meanwhile, their polarizability anisotropy is sufficiently large and comparable to that of IO₃, enabling them to achieve shorter-wavelength phase-matching SHG output. Therefore, given the favorable properties of the microscopic groups, chlorates and bromates have the potential to be UV (even short-wave UV and deep-UV) NLO candidates. However, few exploratory studies on the NLO properties of chlorates and bromates have been reported to date.²⁷

Fig. 1 Calculated HUMO–LUMO band gaps, hyperpolarizabilities and the polarizability anisotropy of ClO₃ and BrO₃ groups. The corresponding data of BO₃, CO₃ and IO₃ are also calculated for comparison.

In this work, the potential of chlorates and bromates as UV NLO materials is systematically explored for the first time. We search the Inorganic Crystal Structure Database (ICSD) for noncentrosymmetric ternary chlorates and bromates, excluding fluorides, transition metal and rare earth halates and nonstoichiometric compounds. Cubic symmetric compounds, such as NaClO₃ and NaBrO₃ (P2₁3, No. 198), are also excluded because they cannot achieve phase-matching.^28,29 In this way, 15 cases of ternary main group chlorates and bromates are finally screened out and their NLO-related properties are carefully studied by first-principles methods. The results indicate that the halate crystals AClO₃ and ABrO₃ (A = NH₄, K, Rb and Cs) with well-aligned motifs exhibit excellent UV NLO performance, including very short λ_PM deep into SWUV and DUV together with high SHG coefficients comparable to β-BaB₂O₄, being highlighted as important candidates for solar blind and even DUV NLO materials.

Methods

The crystal structures of the halates are fully relaxed by employing the pseudopotential plane-wave method based on density functional theory within the total energy code of CASTEP.^30–32 Based on the optimized structures, the electronic structures and optical properties are also calculated. We choose the GGA-PBE functional and norm-conserving pseudopotential, in which Cl-3s²3p⁵, O-2s²2p⁴, K-3s²3p⁶4s¹, Rb-4s²4p⁶5s¹, Cs-5s²5p⁶6s¹, Sr-4s²4p⁶5s², Ba-5s²5p⁶6s², Tl-5d¹⁰6s²6p¹, Pb-5s²5p⁶5d¹⁰6s²6p², Bi-5d¹⁰6s²6p³, N-2s²2p³ and H-1s¹ are considered as valence electrons.^33,34 The number of plane waves is determined by the cutoff energies of 820 and 750 eV for Pb(ClO₃)₂ and other compounds, respectively, while the Monkhorst–Pack k-point separation is set to 0.04 Å⁻¹ to perform numerical integration of the Brillouin zone. During the optical property calculations, the number of empty bands is set to twice the number of valence bands to ensure convergence of refractive indices and SHG coefficients.

It is well known that DFT-GGA cannot accurately describe the eigenvalues of the electronic states, leading to a quantitative underestimation of the band gaps. Thus, the hybrid exchange and correlation functional of HSE06 is used to obtain more accurate band gaps.³⁵ When assessing the optical properties, the scissor operators (the gap differences between hybrid HSE06 and conventional GGA-PBE) are applied. This strategy has been demonstrated to be effective and reliable for the evaluation of optical properties of compounds without experimental band gaps.³⁶

The NLO properties of the halates are calculated according to the full sum-over-states (SOS) formalism in the independent particle approximation,^37,38 and the static second-order NLO susceptibility can be expressed as^39,40

χ^αβγ = χ^αβγ (VE) + χ^αβγ (VH)

where χ^αβγ (VE) and χ^αβγ (VH) are the contributions to χ^αβγ from virtual-electron and virtual-hole processes, respectively, and can be given by

Based on the SOS formalism, the “band-resolved” χ⁽²⁾ can be readily given, and the relationship between each band/orbital and a specific SHG coefficient (d_ij = 1/2χ⁽²⁾) can be conveniently established. Using the normalized SHG value of each band/orbital as the weighting coefficient, and summing all the SHG-weighted bands/orbitals in VB or CB over different k-points in space, the SHG-weighted electron density (SHG-density) can be obtained.⁴¹ Through the “SHG-density” plots, the crystal orbitals that make significant contributions to the optical nonlinearity can be intuitively visualized.

In addition, to reveal the structural origin of birefringence, the polarizability anisotropy-weighted electron density [PAWED, ρ_Δχ(r)] has been defined.⁴² It contains two parts of contributions (VB and CB) and can be formulated as

where |ψ_i(r)|² is the electron density of the ith band/orbital; and ω_i is the weighting factor describing the contribution ratio of the ith band/orbital to the total polarizability anisotropy (Δχ⁽¹⁾) of a crystal. In the low-frequency region, ω_i can finally be quantified by the dielectric function ε,

By utilizing the PAWED technique, the group/ion contributions to the birefringence (optical anisotropy) of compounds can be identified.^43,44

Results and discussion

Crystal structures

Rigorous screening yields 15 cases of simple noncentrosymmetric chlorates and bromates, including AClO₃ (A = NH₄, K, Rb, Cs, Tl), M(ClO₃)₂ (M = Sr, Ba, Pb), ABrO₃ (A = K, Rb, Cs, Tl), M(BrO₃)₂ (M = Sr, Ba) and BiO(BrO₃).^{24,25,45–50} We have performed the structural optimization on them, and the structural rationality is proved by the suitable bond valence sum of 4.8–5.2 for Cl⁵⁺/Br⁵⁺ in ClO₃/BrO₃ groups. They are all in the polar crystal symmetries and most of them with similar chemical formula are isostructural and the crystal structures resemble one another.

For the alkali metal/alkaline earth metal and NH₄ halates, the anionic groups ClO₃/BrO₃ are all isolated, so the geometric structures can be regarded as zero-dimensional. AClO₃ and ABrO₃ (A = NH₄, K, Rb, Cs, Tl) are crystallized in the trigonal R3m space group (No. 160) and the ClO₃/BrO₃ themselves have C3v symmetry with three identical Cl–O/Br–O bonds and all the isolated groups show perfect alignment with the dipoles pointing towards the crystallographic axis c (Fig. 2a).^{24,25,45–47} M(ClO₃)₂ and M(BrO₃)₂ (M = Sr, Ba) belong to the lower-symmetry monoclinic or orthorhombic crystal systems: Sr(BrO₃)₂ crystallizes in the Cc space group (No. 9), while Sr(ClO₃)₂, Ba(ClO₃)₂ and Ba(BrO₃)₂ are in the Fdd2 space group (No. 43).^48,49 They are all characterized by distorted triangular pyramidal ClO₃/BrO₃ and ionically bonded dodecahedral MO₈.

Fig. 2 Crystal structures of KClO₃ (a), TlClO₃ (b), Pb(ClO₃)₂ (c) and BiO(BrO₃) (d).

It is interesting that Tl⁺ also adopts a lopsided coordination style with three equivalent oxygen atoms in TlClO₃ and TlBrO₃ (Fig. 2b), but the stereochemical activity of the Tl⁺-6s² lone pair is to be investigated. Pb(ClO₃)₂ is isostructural to Sr and Ba chlorates, and the Pb²⁺ cations are bisphenoidally coordinated with eight oxygen atoms from eight different ClO₃, forming dodecahedral geometries (Fig. 2c).⁴⁹ The stereochemical activity of the Pb²⁺-6s² lone pairs is not obvious because the eight Pb–O bond lengths are relatively close, but this remains to be verified by electron localization function analysis. BiO(BrO₃) crystallizes in the polar space group Pca2₁ (No. 29) and exhibits a layered structural topology with the BrO₃ neatly hanging up and down from the infinite [Bi₂O₂]_∞ layers (Fig. 2d).⁵⁰

Nonlinear optics-related properties

For the noncentrosymmetric halates, we focus on their band gaps (UV transmittance), second-order nonlinear optical coefficients, birefringence (optical anisotropy) and phase-matching properties, all of which are closely correlated to the practical applications of NLO materials. The calculated NLO-related property data of the halates are listed in Table 1, and RbIO₃ and CsIO₃ with available experimental/theoretical data are taken as references to check our computations. It is found that our calculated optical properties of RbIO₃ and CsIO₃ are in good agreement with the reported results, fully demonstrating the rationality and reliability of the calculation methods.

Table 1 Space groups, calculated band gaps (E_g) by hybrid HSE06, largest SHG coefficients (d_ij), birefringence at 1064 nm (Δn), UV cutoff wavelengths (λ_cutoff), shortest phase-matching wavelengths (λ_PM) and potential SHG applications for the halates

Material	Space group	E g (eV)	d ij (pm V^−1)	Δn	λ cutoff (nm)	λ PM (nm)	Potential SHG application
a Experimentally measured data in references. b Theoretically calculated data in references.
(NH4)(ClO3)	R3m	6.79	d 11 = 1.80	0.168	182.6	194.9	DUV
KClO3	R3m	6.86	d 11 = 1.85	0.186	180.8	185.3	DUV
RbClO3	R3m	6.81	d 11 = 1.88	0.176	182.1	189.9	DUV
CsClO3	R3m	6.99	d 11 = 1.63	0.159	177.4	188.7	DUV
TlClO3	R3m	5.23	d 11 = 2.37	0.173	237.1	273.9	1064 → 532 nm
Sr(ClO3)2	Fdd2	7.03	d 24 = 1.23	0.084	176.4	260.5	532 → 266 nm
Ba(ClO3)2	Fdd2	6.97	d 24 = 1.19	0.089	177.9	255.7	532 → 266 nm
Pb(ClO3)2	Fdd2	5.62	d 24 = 2.37	0.102	220.6	336.5	1064 → 532 nm
KBrO3	R3m	5.65	d 11 = 2.76	0.227	219.5	219.5	532 → 266 nm
RbBrO3	R3m	5.77	d 11 = 2.61	0.218	214.9	214.9	532 → 266 nm
CsBrO3	R3m	5.90	d 11 = 2.39	0.203	210.2	210.2	532 → 266 nm
TlBrO3	R3m	5.00	d 11 = 3.19	0.213	248.0	278.8	1064 → 532 nm
Sr(BrO3)2	Cc	6.14	d 26 = 1.64	0.062	202.0	352.4	1064 → 532 nm
Ba(BrO3)2	Fdd2	6.18	d 24 = 1.80	0.091	200.6	299.6	1064 → 532 nm
BiO(BrO3)^50	Pca21	3.89	d 15 = 2.35	0.040	318.8	815.5	NPM in UV-Vis SHG output
		3.52^a, 3.77^b
RbIO3^16	R3m	4.06	d 31 = 3.08 20 × KDP^a	0.065	305.4	433.0	1064 → 532 nm
		4.0^a		0.063^b
CsIO3^17	R3m	4.38	d 31 = 1.99	0.152	283.1	331.1	1064 → 532 nm
		4.2^a	15 × KDP^a	0.19^b

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From the band structure data obtained by HSE06, we can see that there is an absolutely clear tendency for the band gaps of the halates being E_g(chlorate) > E_g(bromate) > E_g(iodate) (Fig. S1,†Fig. 3a and Table 1), which is in agreement with the results of the microscopic groups. The band gaps of alkali metal/alkaline earth metal chlorates are as wide as 6.8–7.0 eV, being comparable to or larger than those of some classical borates, such as K₂Al₂B₂O₇ (6.89 eV), CsLiB₆O₁₀ (6.89 eV), Cs₂Al₂(B₃O₆)₂O (7.05 eV), Rb₃Ba₃Li₂Al₄B₆O₂₀F (6.26 eV), K₃Sr₃Li₂Al₄B₆O₂₀F (6.53 eV), LaBGeO₅ (6.40 eV), the well-known UV NLO crystal β-BaB₂O₄ (6.43 eV), etc.^51–56 Hence, they are all deep-UV transparent, which is the most important requirement for DUV NLO materials. For alkali metal/alkaline earth metal bromates, the band gaps range from 5.65 to 6.18 eV, comparable to or larger than many carbonates, such as ABCO₃F (A = alkali metal, B = alkaline earth metal, ∼6.20 eV), Cs₃Ba₄(CO₃)₃F₅ (5.90 eV), [C(NH₂)₃]₂Zn(CO₃)₂ (5.90 eV), Zn(NH₃)CO₃ (6.08 eV), NaZnCO₃F (4.61 eV), Na₄Zn(CO₃)₃ (4.06 eV), etc.^9,57–59 Although the band gaps of the bromates are narrower than those of the corresponding chlorates by up to 0.79–1.21 eV, they still can be used as UV optical materials considering the good transparency in the short-wave UV region. It is worth noting that the Tl, Pb and Bi halates have much narrower band gaps than the alkali metal/alkaline earth metal halates, which is caused by the intrinsic intra-shell s–p transitions in the Tl⁺, Pb²⁺ and Bi³⁺ cations.

Fig. 3 (a) Distribution of band gaps of the halates and (b) summarization of the birefringence, UV cutoff wavelengths (λ_cutoff) and the shortest phase-matching wavelengths (λ_PM) for the halates.

From Table 1, we can see that for the alkali metal and ammonium chlorates with R3m symmetry, the largest SHG tensor d₁₁ values are 1.63–1.88 pm V⁻¹, being up to 4.2–4.8 times that of KDP and 0.7–0.8 times that of β-BaB₂O₄, which have similar DUV transmittance to these chlorates. In comparison, the alkaline earth metal chlorates with Fdd2 symmetry have relatively smaller SHG coefficients, where d₂₄ = 1.23 pm V⁻¹ for Sr(ClO₃)₂ and 1.19 pm V⁻¹ for Ba(ClO₃)₂, but they are still 3 times larger than that of KDP and 0.5 times that of β-BaB₂O₄. Furthermore, the largest SHG tensors of TlClO₃ (d₁₁) and Pb(ClO₃)₂ (d₂₄) share the same value of 2.37 pm V⁻¹ and are 6.1 times larger than that of KDP.

Not surprisingly, the SHG responses of the bromates are stronger than those of the corresponding chlorates, and there is a 35%−49% increase in SHG coefficients, resulting from the greater hyperpolarizability of BrO₃ compared to ClO₃. Remarkably, the SHG effects of ABrO₃ (A = K, Rb, Cs; d₁₁ = 2.39–2.76 pm V⁻¹ ≈ 6.1–7.1 × KDP) are greater than those of many NLO carbonates and cyanurates with similar band gaps, such as KCdCO₃F (5.46 eV & 5.2 × KDP), KLi(HC₃N₃O₃)·2H₂O (5.23 eV & 5.3 × KDP), Ln₅(C₃N₃O₃)(OH)₁₂ (Ln = Y, Lu; 5.28–5.51 eV & 2.5–4.2 × KDP), etc.^60–62 Meanwhile, Sr(BrO₃)₂ in Cc and Ba(BrO₃)₂ in Fdd2 show moderate SHG effects with the largest tensors being 1.64 and 1.80 pm V⁻¹, respectively. In addition, TlBrO₃ exhibits the highest SHG effect among the bromates (d₁₁ = 3.19 pm V⁻¹), which originates from its well-aligned motifs and smaller band gap. However, the SHG effect of BiO(BrO₃) with its very narrow band gap (3.89 eV & d₁₅ = 2.35 pm V⁻¹) is weaker than those of the alkali metal bromates, which may be because the polarity of BrO₃ is partially cancelled out in the compound.

The calculated refractive index results (Fig. S2† and Table 1) indicate that AClO₃ and ABrO₃ (A = NH₄, K, Rb, Cs) in R3m possess very strong optical anisotropy and large birefringence (0.159–0.186 for AClO₃ and 0.203–0.227 for ABrO₃), enabling them to achieve phase-matching (PM) near their UV cutoff edges (λ_cutoff; the deep-UV region for AClO₃ and the short-wave UV region for ABrO₃). In particular, ABrO₃ crystals (A = K, Rb and Cs) are even full-wavelength phase-matchable (FWPM) owing to their sufficiently large birefringence and small dispersion extent of their refractive index curves. In comparison, the alkaline earth metal halates in Fdd2 and Cc show relatively small birefringence (0.062–0.091@1064 nm) and thus cannot achieve PM SHG output near their λ_cutoff. For example, although the λ_cutoff values of Sr(ClO₃)₂ and Ba(ClO₃)₂ are as short as 176.4 and 177.9 nm in the deep-UV region, their shortest PM wavelengths (λ_PM) are as long as 260.5 and 255.7 nm, implying that they can only output PM SHG light from 532 to 266 nm; so do Sr(BrO₃)₂ and Ba(BrO₃)₂, which can only output PM SHG light from 1064 to 532 nm, despite their much shorter λ_cutoff values of 202.0 and 200.6 nm. It is worth noting that BiO(BrO₃) cannot realize phase-matching in the 1064 → 532 nm process due to its very small birefringence of 0.040@1064 nm. Interestingly, the birefringence Δn, the UV cutoff edges λ_cutoff and the shortest phase-matching wavelengths λ_PM of the halates are summarized in Fig. 3b, from which we can find the intrinsic relationship among the three optical indicators, i.e., the larger the Δn, the closer the λ_PM is to λ_cutoff, even equalling λ_cutoff, namely the full-wavelength phase-matching (FWPM).¹¹

Summarizing the above results, it is found that AClO₃ (A = NH₄, K, Rb, Cs) can be promising DUV NLO crystals with strong SHG responses; meanwhile, M(ClO₃)₂ (M = Sr, Ba) and ABrO₃ (A = K, Rb, Cs), particularly the latter with higher SHG effects and FWPM capability, can be important short-wave UV NLO materials capable of producing a 266 nm laser by SHG or quadruple frequency generation techniques. In addition, TlClO₃, Pb(ClO₃)₂, TlBrO₃, Sr(BrO₃)₂ and Ba(BrO₃)₂ can also be potential SHG materials for application in the 1064 → 532 nm range of green light output.

Structure–property relationship

For the screened NLO halates, the typical KClO₃, TlClO₃ and Pb(ClO₃)₂ are taken as representatives to study their electronic structures and analyze the origin of their strong SHG effects and large birefringence. The effects of Tl⁺ and Pb²⁺ on the optical properties are also to be discussed.

From the partial density of states shown in Fig. 4a–c, it can be seen that there are fully overlapping electronic states between Cl and O in the VB range of −12–−5 eV and in the CB range of 5–10 eV, indicating the strong covalent interactions of Cl–O bonds in the halates. K-3p, Tl-5d and Pb-5d are highly localized in the deep energy levels (<−8 eV), so they would have little effect on the optical properties. For KClO₃, the upper part of VB is dominated by the O-2p nonbonding states, mixed with a few Cl-3s3p nonbonding states, and the lower part of CB consists of the unoccupied O-2p and Cl-3p orbitals, so the wide band gap of KClO₃ is determined by the ClO₃ groups. The electronic structures of TlClO₃ and Pb(ClO₃)₂ are more complicated: except for the usual O-2p and Cl-3s3p, Tl-6s6p and Pb-6s6p are also involved in the VB top and CB bottom, so their band gaps are determined by ClO₃ together with the Tl⁺/Pb²⁺ cations. Considering the much narrower band gaps of TlClO₃ and Pb(ClO₃)₂ compared to that of KClO₃, it can be confirmed that Tl⁺/Pb²⁺ has a weakening effect on the band gaps of the compounds. To further investigate the stereoactivity of the lone pair electrons (6s²) on the Tl⁺ and Pb²⁺ cations, the electron localization functions (ELFs) of TlClO₃ and Pb(ClO₃)₂ are calculated and plotted with η = 0.9 (Fig. S3†). It clearly shows that there are lobe-like isosurfaces on the Cl⁵⁺ ions in both compounds, confirming the highly stereoactive Cl⁵⁺-3s² lone pair, whereas the isosurfaces around Tl⁺ and Pb²⁺ (especially Pb²⁺) are nearly spherical, indicating that the Tl⁺-6s² and Pb²⁺-6s² lone pair electrons are much less stereoactive and almost inert.

Fig. 4 Partial density of states and band-resolved NLO susceptibility χ⁽²⁾ (a–c) and SHG-density plots (d–f) for KClO₃, TlClO₃ and Pb(ClO₃)₂, respectively.

Band-resolved χ⁽²⁾ and SHG-density techniques are used to explore the origin of the strong SHG effects for these simple halates. The former can help us to know which energy levels give large contributions to SHG, and the latter can intuitively show the specific SHG-contributing orbitals and atoms in real space. From the band-resolved χ⁽²⁾ in the bottom panels of the DOS graphs (Fig. 4a–c), we can see that the states distributed on both sides of their forbidden bands (−4–0 eV and 5–10 eV) give the majority of the SHG contributions, corresponding to O-2p nonbonding states and a small amount of Cl-3s3p, Tl-6s and Pb-6s6p states in VB and the empty orbitals of Cl-3p, O-2p, K-4s4p, Tl-6p and Pb-6p in CB. The SHG-density graphs (Fig. 4d–f) for the three compounds indicate that not all of the above electronic states are involved in contributing to the SHG process. In fact, only the nonbonding states of O-2p in VB and the unoccupied Cl-3p, O-2p and a few Pb-6p orbitals in CB make real contributions to the strong NLO responses of KClO₃, TlClO₃ and Pb(ClO₃)₂. Furthermore, based on the SHG-density data, the contribution percentages of all groups and ions can be obtained (Table 2); apart from the core ClO₃ groups, which play an overwhelming role in the SHG effects, TlO₃ and PbO₈ groups also make some contributions, 29.37% and 26.17% respectively, while the contributions from K⁺ are negligible.

Table 2 Calculated contribution percentages of different groups to SHG coefficients and the birefringence for KClO₃, TlClO₃ and Pb(ClO₃)₂

Material	Group	d ij (pm V^−1)	Δn
KClO3		d 11 = 1.85	0.186
	ClO3	98.46%	96.78%
	K^+	1.53%	3.18%
TlClO3		d 11 = 2.37	0.173
	ClO3	70.63%	74.00%
	TlO3	29.37%	25.96%
Pb(ClO3)2		d 24 = 2.37	0.102
	ClO3	72.31%	73.22%
	PbO8	26.17%	25.40%

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In addition, we use the polarizability anisotropy-weighted electron density (PAWED) method to investigate the structural source of the large birefringence of these compounds (Fig. S4†). In VB, the birefringence originates from the O-2p nonbonding states, and in CB, it is mainly from the Cl-3p and O-2p, mixed with some Pb-6p empty orbitals. The calculated contribution values (Table 2) are similar to those obtained for SHG effects: ClO₃ groups also play a predominant role in generating large birefringence, while the contributions from TlO₃ and PbO₈ groups are not very large, which can be attributed to the almost inert stereoactivity of the 6s² lone pairs on the Tl⁺ and Pb²⁺ cations.

Conclusions

In summary, the long-neglected stereochemically active lone pair (SCALP) groups ClO₃ and BrO₃ are innovatively proposed to be good UV NLO functional motifs based on the group property prediction, and the NLO performance of chlorates and bromates is firstly investigated systematically by employing the density functional theory method within the CASTEP code. Through careful compound screening, structural optimization, property simulation and mechanism analysis, the halate crystals AClO₃ and ABrO₃ (A = NH₄, K, Rb and Cs) with well-arranged SCALP motifs are highlighted as promising UV NLO materials in view of their excellent properties, including wide UV transparent ranges deep into DUV for chlorates and SWUV for bromates, high SHG effects comparable to β-BaB₂O₄, large birefringence and strong phase-matching ability. Concretely, AClO₃ crystals can be potential DUV NLO candidates (4.2–4.8 × KDP & λ_PM = 185–195 nm), and ABrO₃ crystals, showing very strong SHG responses (6.1–7.1 × KDP) and rare full-wavelength phase-matching capability (λ_PM = λ_cutoff = 210–220 nm), can be important short-wave UV NLO materials. Hence the UV NLO potential of ClO₃ and BrO₃ is fully demonstrated, and this work provides novel functional motifs and opens up a new avenue for the development of SWUV and even DUV NLO materials.

Author contributions

Chun-Li Hu performed the theoretical calculations, data analyses, and paper writing. Qian-Qian Chen and Fang Kong performed crystal structure screening. Jiang-Gao Mao provided data analyses and major revisions of the manuscript. All the authors discussed the results and commented on the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 22375201, 22031009 and 21921001) and Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR121).

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Footnote

† Electronic supplementary information (ESI) available: Calculated band structures, refractive index curves and the electron localization function. See DOI: https://doi.org/10.1039/d4qi00462k

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