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Application of Voronoi Polyhedra for Analysis of Electronic Dimensionality in Emissive Halide Materials
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Application of Voronoi Polyhedra for Analysis of Electronic Dimensionality in Emissive Halide Materials
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Journal of the American Chemical Society

Cite this: J. Am. Chem. Soc. 2024, 146, 51, 35449–35461
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https://doi.org/10.1021/jacs.4c14554
Published December 10, 2024

Copyright © 2024 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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The synthesis of new hybrid halide materials is attracting increasing research interest due to their potential optoelectronic applications. However, general design principles that explain and predict their properties are still limited. In this work, we attempted to reveal the role of intermolecular interactions on the optical properties in a series of hybrid halides with an (EtnNH4–n)2Sn1–xTexCl6 (n = 1–4) composition. DFT calculations showed that the dispersions of the bands involving the Te 5s orbital character gradually decrease as the size of the organic cation increases, indicating a reducing orbital overlap between neighboring TeCl62– complexes. We characterized the photoluminescence (PL) of the Sn/Te solid solutions in (EtnNH4–n)2Sn1–xTexCl6 (n = 1–4) phases to correlate the electronic and optical properties. The PL response shows no concentration quenching effects in the (Et4N)2Sn1–xTexCl6 series, which demonstrated electronically isolated TeCl62– complexes. However, the series with smaller organic cations (n = 1–3) and higher electronic dimensionality show concentration quenching effects, which decrease as a function of the Te 5s band dispersions in these compounds. Similar trends can be revealed using a simple semiquantitative electronic dimensionality analysis method by means of Voronoi polyhedra. Since this approach relies only on structural data, it enables rapid characterization of orbital overlap between metal halide complexes in hybrid materials without DFT calculations. The present results allow us to conclude that electronic dimensionality plays an essential role in the photophysical properties of hybrid halide compounds and can be used to fine-tune their properties.

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Introduction

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Compositional tunability and almost limitless structural variations in hybrid organic–inorganic metal halides (OIMHs) have made them one of the most widely studied classes of contemporary materials. Apart from fundamental interest in OIMHs, their remarkable optoelectronic properties, tunable band gaps, broadband photoluminescence, and high photoluminescence quantum yields make them excellent candidates for solar cell, (1−8) light-emitting diode, (9−12) radiation detector, and photodetector applications. (13−21) While hybrid lead halide semiconductors with perovskite and perovskite-related structures remain the benchmark for photovoltaics, other classes of hybrid materials have been studied to circumvent the use of toxic lead and expand the new materials library. (22−28) Particular interest has been paid to cations with an ns2 electron configuration and transition metal ions for the synthesis of air-stable lead-free OIMHs. (29−37)
The tremendous structural diversity of halides with ns2 ions is contributed by various coordination modes of metal cations, different dimensionalities of the structures, and a vast choice of organic cations. Besides the most common MX6 octahedral coordination (M = main group elements, X = halides), cations with stereoactive ns2 lone pairs can form MX3 pyramids, MX4 disphenoids, or MX5 square pyramids. (38) MXn units’ connection defines the structure’s dimensionality: corner-, edge-, and rarely face-sharing MXn polyhedra form 3D frameworks, 2D layers, 1D chains, or 0D mono- and polynuclear anionic units. To balance the negative charge of metal halide units, various organic amines, which can act as structure-directing agents, (39,40) are employed. The dimensionality of the OIMHs defines their properties and practical applications. Extended structure semiconductors favor properties, such as high charge carrier mobility, that are required for photovoltaics and photodetection. (41−43) On the other hand, the extended structures demonstrate lower luminescence quantum yields and are more prone to photon reabsorption due to lower Stokes shifts of their luminescence compared to 1D and 0D materials. (32,34,44) On the contrary, typically broad emission of 1D and 0D materials makes them perfect for luminescence applications.
One general assumption commonly made when studying 0D hybrid compounds is the isolated nature of the metal centers in these materials. Since 0D hybrid halides show no direct M–X–M bonds, this assumption is partially justified. However, the importance of anion interactions in some purely inorganic 0D halide compounds has been realized to contribute to band dispersions, increasing the charge carrier mobilities and enabling the resonant transfer of excitons in these compounds. (45) In some cases, their conductivity is on par with materials that have generally recognized semiconducting properties due to their framework metal halide structures. (46) For example, halide interactions are essential in Cs2SnI6 and Cs2TeI6, which have vacancy-ordered double perovskite structures. (47) From a structural chemistry point of view, both of these compounds are built from isolated [SnI6]2–/[TeI6]2– octahedra and Cs+ cations, representing a typical example of 0D structure. However, their electronic structures consist of highly dispersive bands due to interactions between the halogen atoms, rendering them with high charge carrier mobilities. While the importance of halogen orbital interactions has been realized, their influence on the properties of hybrid materials remains underexplored. (48−52) Moreover, the elucidation of the electronic structures of these compounds requires somewhat costly DFT calculations, especially when it comes to hybrid functionals, which generally are not readily available to chemists. Because the electronic coupling in compounds depends on their crystal structures, information about interactions between the metal halide complexes should be available, at least in some approximation, from crystallographic data. However, no robust and universal tool for such an assessment has been developed so far.
In this report, we aim to develop tools that enable a simple assessment of halogen orbital overlap in hybrid halide materials. As a platform system, a series of tin and tellurium chloride compounds with an A2MCl6 general composition (A = (C2H5)nNH4–n+, n = 1–4, M = Sn or Te) has been selected. This system allows for convenient variation of the interactions between the MCl6 octahedra as a function of the organic cation volume (Figure 1). DFT calculations showed a changing degree of band dispersions in the series, from disperse to flat bands when n changes from 1 to 4. The photoluminescence properties of solid solutions with isomorphous Sn substitution for Te show agreement with the DFT data: PL concertation quenching effects are reduced as n increases. Importantly, we showed that the orbital overlap between the metal halide complexes could not be considered as a function of the metal–metal distance in the structure, and the mutual orientation of the complexes must be taken into account. Finally, the implementation of the Voronoi tessellation method for the analysis of intermolecular interactions between MCl6 complexes showed very promising results by providing semiquantitative data without time-consuming DFT calculations. We expect that further utilization of this method will enable a rational structural description to design highly efficient optoelectronic hybrid materials.

Figure 1

Figure 1. Schematic representation of two major components of energy transfer and photoluminescence quenching in 0D organic–inorganic metal halides.

Results and Discussion

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Crystal Structures

We used single-crystal X-ray diffraction to characterize four new compounds with the A2TeCl6 general composition (A = EtnNH4–n+, Et = −C2H5, n = 1–4, Tables S1–S22). (EtNH3)2TeCl6 crystallizes with the trigonal space group Pm1 with single crystallographically unique Te and Cl atoms occupying 1b and 6i Wyckoff positions. The ethylammonium cations are disordered over a 3-fold rotation axis. Both (Et2NH2)2TeCl6 and the monoclinic polymorph of (Et3NH)2TeCl6 (m-(Et3NH)2TeCl6) crystallize with the same P21/n space group and have similar unit cell parameters and structural unit arrangements (Table S1). A single Te atom occupies the 2a Wyckoff position in both structures, while three independent Cl atoms are in general 4e positions (Table S2). The orthorhombic polymorph of (Et3NH)2TeCl6 (o-(Et3NH)2TeCl6) crystallizes with the Pbca space group. Unlike the other three hybrid halide structures discussed here, this phase has two independent Te atoms in the general 8c Wyckoff position.
In all new structures with an A2TeCl6 composition, each Te4+ cation is coordinated by six Cl anions in an octahedral manner. The octahedral TeCl62– units are isolated from each other, and their negative charges are balanced by the organic cations (Figure 2). As expected, a hydrogen bonding system is present in the new compounds (Table S23). In the (Et2NH2)2TeCl6 structure, each chlorine in a TeCl62– octahedron participates in hydrogen bonding with diethylammonium cations. As a result, this structure has infinite layers formed by N–H···Cl bonds running parallel to the (101̅) plane (Figure S1). In m- and o-(Et3NH)2TeCl6, hydrogen bonding forms 0D units. In the m phase, the sole TeCl62– octahedron is connected to two Et3NH+ cations, while the o phase shows a distinct hydrogen bonding pattern: only one of two independent TeCl62– anions forms hydrogen bonds with four Et3NH+ cations (Figure S1).

Figure 2

Figure 2. Views on the structures of hybrid tellurium halides of interest: (a) (EtNH3)2TeCl6, (b) (Et2NH2)2TeCl6, (c) m-(Et3NH)2TeCl6, and (d) (Et4N)2TeCl6. (53) The yellow octahedra are TeCl62–, Cl atoms are green, C atoms are gray, N atoms are blue, and H atoms (if located) are light blue.

Electronic Structures

Recent detailed studies on Cs4PbBr6 and Cs2SnI6 showed that band structure dispersion is a convenient tool to assess noncovalent interactions between neighboring halide complexes. (45−47) Although this approach is somewhat universal, (54) it is rarely discussed in the context of hybrid halide materials, which usually show a greatly reduced degree of orbital overlap compared to 3D halide perovskites. While it is commonly accepted that the dimensionality of hybrid halides with structurally isolated AX6 octahedra is 0D, their electronic dimensionality is strongly affected by the mutual arrangement and interactions between the octahedra. This section begins with a discussion of the molecular orbital (MO) diagrams of the SnCl6 and TeCl6 octahedral complexes. After introducing the MOs, we consider their interactions in a structure by paying close attention to the dispersion of bands formed by the Sn 5s, Te 5s, and Te 5p orbitals.
Schematic molecular orbital diagrams of SnCl6 and TeCl6 complexes are given in Figure 3. (46) In the SnCl6 MO diagram, the Sn 5s and Cl 3p orbitals with A1g symmetry form a pair of bonding and antibonding orbitals. The interaction of the T1u Sn 5p and Cl 3p orbitals results in another pair of bonding and antibonding orbitals at different energy levels. The remaining Cl 3p orbitals form numerous nonbonding states. For Sn4+, both the antibonding A1g and T1u orbitals hold no electrons. Thus, lower-energy A1g orbitals form the conduction band in the Sn4+X6-containing periodic compounds. In contrast, the valence bands are contributed by nonbonding Cl 3p orbitals, making a transition from the HOMO to LUMO (from the valence band to the conduction band in a periodic compound) a nominal ligand-to-metal charge transfer transition. Unlike Sn4+, more electronegative Te4+ retains its 5s2 electrons in the TeCl62– complexes. Due to a large energy difference between Te 5s and Cl 3p orbitals, their overlap causes only a small energy splitting, resulting in antibonding A1g orbitals being slightly higher in energy than nonbonding Cl 3p orbitals. Larger overlap between Te 5p and Cl 3p orbitals leads to greater energy splitting of the resulting bonding and antibonding MOs. Due to this, the LUMO orbitals are contributed by Te 5p and Cl 3p T1u orbitals. Since both the HOMO and LUMO of the Te4+Cl6 complexes are contributed by Te orbitals, 5s for the HOMO and 5p for the LUMO, one can consider an electron excitation as a well-known 5s25p0 → 5s15p1 transition, assuming that there are no orbital interactions between neighboring TeCl6 complexes. In periodic compounds with isolated TeCl62– complexes, MOs mostly retain their individuality, often resulting in flat or nearly flat bands.

Figure 3

Figure 3. (a,f) Schematic molecular orbital diagrams of octahedral SnCl6 and TeCl6 complexes. (b–e) Band structure diagrams of ((C2H5)nNH4–n)2SnCl6 and (g–j) ((C2H5)nNH4–n)2TeCl6 (n = 1–4). A1g MO orbitals (σ bonds formed by Sn/Te 5s and Cl 3p orbitals) are highlighted with blue, and T1u orbitals (σ and π bonds formed by Te 5p and Cl 3p orbitals) are highlighted with orange.

Although 0D hybrid structures contain structurally distinct octahedral units with no apparent covalent bonds between them, noncovalent interactions can contribute to the corresponding band dispersion. (45) To study this effect in greater detail, we calculated the band structures of all eight compounds in the A2MCl6 (A = EtnNH4–n+, Et = −C2H5, n = 1–4, M = Sn or Te) family (Figure 3). In the case of the bulky cation Et4N+, the band structures consist of almost perfectly flat bands corresponding to the isolated MOs of the SnCl6 or TeCl6 complexes. The lack of band dispersions indicates nearly no orbital interactions between the complexes, which are structurally and electronically isolated by organic cations, thus making (Et4N)2SnCl6 and (Et4N)2TeCl6 truly 0D compounds. As the size of the organic cation decreases, the band dispersion increases. Since the A1g MO in MCl6 complexes consists of Cl 3p orbitals that form σ bonds and extend further away from the complex (Figure 3a), we chose Sn 5s and Te 5s band dispersions to assess the interactions between the complexes (Figure S2). As expected, the most dispersed bands are observed in the (EtNH3)2MCl6 (M = Sn or Te) electronic structures, where the bands with Sn 5s and Te 5s characters have dispersions of 0.486 and 0.368 eV, respectively. These values indicate that the ethylammonium cations’ sizes are insufficient to shield the MCl6 octahedra completely. Increasing the cation size by one ethyl group results in lower band dispersions of 0.401 and 0.314 eV for (Et2NH2)2MCl6, where M = Sn and Te, respectively. Interestingly, in a very similar structure of (Et3NH)2MCl6, the band dispersions are twice as small as those in the diethyl counterpart, 0.202 and 0.127 for Sn and Te, respectively. Although the change in the band dispersion shows a gradual decrease in the orbital overlap between neighboring octahedra, it is not directly proportional to the M···M distance in these structures. This somewhat unexpected trend can be illustrated in the Sn series, where the shortest experimental Sn···Sn distances of 7.27, 8.40, 8.51, and 9.59 Å correspond to the dispersions of 0.486, 0.401, 0.202, and <0.001 eV. Although these values of dispersion are significantly less than the ranges that are typically observed for 3D perovskites (>2 eV) (55,56) or vacancy-ordered double perovskite (∼1 eV), (47) they can be sufficient to promote electronic coupling between the complexes. These energy interactions can be characterized by measuring the optical properties of the A2Sn1–xTexCl6 solid solutions.

Photoluminescence Properties of ((C2H5)nNH4–n)2Sn1–xTexCl6 (n = 1–4) Solid Solutions

Since (EtnNH4–n)2TeCl6 phases are isostructural with (EtnNH4–n)2SnCl6 compounds with the same organic cations (Table S1), (53,57−61) the isomorphous substitution of Sn4+ for Te4+ in all ranges of concentrations is highly favorable. The varying degree of band dispersions makes these solid solutions highly suitable for characterizing energy exchange as a function of Te dopant concentration. Due to this, we synthesized four series of solid solutions and characterized their photoluminescence properties.
In all four series of the hydrothermally prepared (EtnNH4–n)2Sn1–xTexCl6 solid solutions (x = 0.0–1.0), along with selected compounds from the (Et2NH2)2Sn1–xTexCl6 series prepared by solid-state reactions, gradual diffraction peak shifts were observed (Figure 4). Bragg peak splitting is another clear sign of successful solid solution formation. For example, in the pristine (EtNH3)2TeCl6 phase, two peaks corresponding to the (103) and (022) families of crystallographic planes are separated by ≈0.06° 2θ, while in (EtNH3)2SnCl6, this separation is ≈0.6°, which can be easily detected experimentally (Figure 4). Similarly, peak splitting is observed for the (Et2NH2)2MCl6 phases at around 27° (Figure 4). Additionally, we collected EDS data (Figure S3 and Table S24) to confirm Te incorporation in the desired ratios. Raman spectroscopy can also serve as evidence of the solid solution formation. Pristine phases feature two peaks associated with ν1 and ν2 bands of the MCl62– anions in the low-frequency region. (62−65) In comparison, the Raman spectrum of an (Et2NH2)2Te0.5Sn0.5Cl6 sample with three peaks appears as an overlap of the pristine phase spectra (Figure S6).

Figure 4

Figure 4. PXRD patterns of the (EtnNH4–n)2Sn1–xTexCl6 series: (a) (EtNH3)2Sn1–xTexCl6, (b) (Et2NH2)2Sn1–xTexCl6, (c) (Et3NH)2Sn1–xTexCl6, and (d) (Et4N)2Sn1–xTexCl6. Ref. stands for the reference line; (Et4N)2Sn1–xTexCl6 samples were collected with the Ge powder as an internal standard.

(EtnNH4–n)2Sn1–xTexCl6 samples emit visible light in the orange-red region under UV-light excitation. The corresponding photoluminescence excitation (PLE) and emission (PL) data are listed in Figure 5. Independent of the organic cation, the photoluminescence of all (EtnNH4–n)2Sn1–xTexCl6 samples features a broad asymmetric excitation band and broad emission with one near-Gaussian shape peak. At lower concentrations of Te4+, the PLE spectra have two distinguished regions with maxima at ≈330 and ≈400 nm, while at high Te4+ concentrations, the regions overlap (Figure 5). These two regions are referred to as the A and B bands of ns2 ion in octahedral surroundings. (66,67) The lower-energy A band originates in the spin-forbidden 1S03P1 transition. The A band is a doublet since the 3P1 level is split in the octahedral field by the dynamic Jahn–Teller effect, so the experimentally observed peak is asymmetric. (66) The singlet B band originates in the forbidden electric dipole 1S03P2 transition, while the high-intensity and highest-energy C band arises from the spin-allowed 1S01P1 transition and usually lies in the UV-B region. (67) PL spectra of (EtnNH4–n)2Sn1–xTexCl6 samples feature single broad (fwhm ≈ 110–130 nm, Figure S4) symmetric peaks.

Figure 5

Figure 5. PLE and PL spectra of (EtnNH4–n)2Sn1–xTexCl6 series: (a) (EtNH3)2Sn1–xTexCl6 (x = 0.05–0.80, λex. = 388 nm, and λem. = 620 nm), (b) (Et2NH2)2Sn1–xTexCl6 (x = 0.05–1.00, λex. = 375 nm, and λem. = 600 nm), (c) (Et3NH)2Sn1–xTexCl6 (x = 0.05–0.80, λex. = 405 nm, and λem. = 650 nm), and (d) (Et4N)2Sn1–xTexCl6 (x = 0.1–1.0, λex. = 395 nm, and λem. = 600 nm).

The peak positions do not change significantly with x in (EtnNH4–n)2Sn1–xTexCl6 but depend on the organic cation. The lowest emission wavelengths (600 nm) are observed in the (Et2NH2)2Sn1–xTexCl6 and (Et4N)2Sn1–xTexCl6 series. (EtNH3)2Sn1–xTexCl6 samples have an emission peak at 620 nm. Finally, the emission of (Et3NH)2Sn1–xTexCl6 samples is redshifted to 650 nm. PL peaks correspond to the 3P11S0 relaxation of the Te4+ species. (68) All four compounds have similar Stokes shifts of 1.20, 1.24, 1.15, and 1.07 eV for n = 1–4, respectively, indicating a similar spectral overlap among them.
The compounds with smaller organic cations, n = 1–3, show different PL dependence on the Te concentration from the n = 4 series. In the (Et4N)2Sn1–xTexCl6 series, the Te concentration has little effect on the PL intensity, indicating low energy exchange between the Te centers. This observation agrees well with the 0D electronic band structure of the (Et4N)2SnCl6 and (Et4N)2TeCl6 compounds, as evidenced by their nearly flat bands. Reducing the organic cation size in the compounds with n = 1–3 “switches on” the orbital overlap and energy exchange between the complexes. In all three series, the PL intensity increases as the concentration of Te decreases, showing prominent concentration quenching effects. The effect is especially remarkable in the (EtNH3)2Sn1–xTexCl6 series where samples with x ≥ 0.8 appear nonluminous, and Te dilution causes a multifold emission intensity increase. This observation is in excellent agreement with the theoretically calculated highest band dispersion in both (EtNH3)2MCl6 (M = Sn or Te) compounds.
The concentration effects on the PL lifetimes in the series from n = 1 to 4 provide additional experimental evidence for energy exchange reduction (Figure 6 and Table S25). Nearly absent orbital overlap between the octahedral complexes in the (Et4N)2Sn1–xTexCl6 series makes the PL lifetime independent of the Te concentration changes. The small EtNH3+ cation promotes the energy exchange that leads to a strong concentration quenching effect and shorter PL lifetimes at higher Te concentrations. Despite very similar structures and similar shortest Te···Te distances, the two intermediate series (Et2NH2)2Sn1–xTexCl6 and (Et3NH)2Sn1–xTexCl6 behave differently. In (Et2NH2)2Sn1–xTexCl6, which has a relatively strong orbital overlap between the complexes, the PL lifetime rapidly decreases from 36(1) ns for x = 0.05 to 4.0(1) ns for x = 0.8. The (Et3NH)2Sn1–xTexCl6 series that has half of the band dispersion compared to the Et2NH2 analog demonstrates significantly longer PL lifetimes varying from 959(6) to 278(6) ns for x = 0.05 and 0.8, respectively.

Figure 6

Figure 6. Time-resolved PL spectra of (EtnNH4–n)2Sn1–xTexCl6 series, λex. = 372 nm: (a) (EtNH3)2Sn1–xTexCl6 (x = 0.05–0.80), (b) (Et2NH2)2Sn1–xTexCl6 (x = 0.05–1.00), (c) (Et3NH)2Sn1–xTexCl6 (x = 0.05–0.80), and (d) (Et4N)2Sn1–xTexCl6 (x = 0.1–1.0).

Results of PLQY measurements for the (EtnNH4–n)2Sn1–xTexCl6 series also agree with the calculated energy exchange interactions (Figure 7). Samples with ethyl- and diethylammonium demonstrate low quantum yields (Table S26) below the measurement limit. For the (Et3NH)2Sn1–xTexCl6 series, PLQY values demonstrate significant growth with lowering Te4+ concentration, and the highest η = 20.5% was achieved in the (Et3NH)2Sn0.95Te0.05Cl6 sample. For the (Et4N)2Sn1–xTexCl6 series, no significant changes of PLQY were observed with the change of the Te4+ content: the experimental η values of all samples are close to those of the pristine (Et4N)2TeCl6 phase. Notably, the distortion levels of TeCl62– units cannot be considered as a factor predetermining higher lifetimes or quantum yields of the (EtnNH4–n)2Sn1–xTexCl6 phases. For example (Table S27), (EtNH3)2MCl6 (M = Sn or Te) has the lowest Δd, (69) while (Et2NH2)2SnTeCl6 the lowest Σ, (70) yet both phases have PLQY near the background of the measurement.

Figure 7

Figure 7. Photoluminescence quantum yield (PLQY) as a function of the organic cation and Te concentration.

Assessment of Orbital Overlap between Halide Complexes in Hybrid Phases

Photoluminescence measurements show that the orbital overlap between the halide complexes plays a central role in the optical properties of these materials. While the lack of orbital overlap in (Et4N)2Sn1–xTexCl6 solid solutions results in independent TeCl6 centers that show no concentration quenching effects, their PLQY is also relatively low, likely because of the absence of energy exchange between the complexes. On the other hand, the presence of the strong orbital overlap in (EtNH3)2Sn1–xTexCl6 and (Et2NH2)2Sn1–xTexCl6 results in the dominant concentration quenching effects and, therefore, low PLQY of the solid solutions even at low Te concentrations. The optimal balance in orbital overlap and Stokes shift is achieved when Et3NH+ serves as an organic cation, which enables the highest among these series PLQY values in diluted (Et3NH)2Sn1–xTexCl6 solid solutions.
Despite the apparent importance of orbital overlap between the isolated octahedral complexes, its influence on the optical properties of hybrid materials remains largely underexplored, although some attempts have been made in recent years. For example, Mao et al. established the influence of interatomic Mn···Mn distances on PLQY of a series of hybrid manganese bromides. (71) Similarly, Sb···Sb distances in hybrid antimony halides play an important role in defining PLQY of these compounds. (72) These examples can be considered as one of the attempts to quantify interactions between halide complexes in optical hybrid materials, which in the case of the Mn hybrids showed that concentration quenching effects become predominant in compounds where Mn···Mn distances are below 9 Å. Although M···M distances seem to be an intuitive measure of interactions between the metal halide complexes, our attempt to implement it to the (EtnNH4–n)2Sn1–xTexCl6 (n = 1–4) series did not provide satisfactory results. For example, the shortest Sn···Sn distances in (Et2NH2)2SnCl6 and (Et3NH)2SnCl6, 8.40 and 8.51 Å, cannot explain a dramatic change in the optical properties of their solid solutions with Te. Moreover, these compounds have the same packing of cations and octahedral complexes in their structures, highlighting the importance of subtle changes in their structures for their optical properties.
To study the effect of mutual orientation of the MCl6 octahedra on exchange interactions, we performed a series of DFT calculations on chains of TeCl6 octahedra with two distinct orientations: in one case, the Cl–Te–Cl···Cl–Te–Cl fragments are linear (vertex to vertex); in the other one, they are rotated by 45° (edge to edge) as shown in Figure 8. The A1g band dispersion plotted as a function of the interatomic Te distance indicates a strong dependence of the orbital overlap on the mutual orientation of the octahedra. As expected, the linear orientation results in much higher band dispersion even at significantly longer Te···Te distances. One apparent reason for this is shorter Cl···Cl distances for the linear configuration (Figure 8b). However, when the band dispersions are plotted as a function of Cl···Cl distances, the interactions become very similar when d(Cl···Cl) > 3.5 Å. The increasing difference in dispersions below 3.5 Å arises due to better orbital overlap in σ vs non-σ bonds and has little effect on noncovalent bonding. For example, the shortest Cl···Cl contact within a TeCl6 complex in (EtNH3)2TeCl6 is 3.50 Å, which can arbitrarily be set as the shortest noncovalent interaction between Cl atoms in real structures. Assuming this shortest bond limit, there is virtually no difference in band dispersions for these two mutual orientations. This allows one to come to a somewhat intuitive conclusion that the main deciding factor in orbital overlap between halide complexes is the shortest distance between halide atoms.

Figure 8

Figure 8. A1g band dispersion energy as a function of (a) Te···Te or (b) Cl···Cl distances in chains of TeCl6 complexes. Two octahedral complex orientations are shown: linear (red plots) and rotated by 45° around the z-axis (blue plots).

While using simple geometric parameters such as Cl···Cl distances seems to be a straightforward way of assessing interactions between the complexes, this characterization can become tedious for all possible contacts in a structure. Voronoi polyhedra provide a more convenient visual and quantitative characterization of Cl···Cl interatomic contacts that also consider other structural fragments. A Voronoi polyhedron (VP) can be viewed as an atom’s electron density in a crystal structure, where each point of a Voronoi polyhedron is closer to its central atom than to any other atom in the structure (Figure 9a). (73) One can, therefore, conclude the dimensionality and the strength of Cl orbital overlap by assessing the Cl atoms’ Voronoi polyhedra contacts. For example, a fragment of the (EtNH3)2TeCl6 structure is shown in Figure 9b. In this fragment, there are strong interactions between neighboring TeCl6 complexes, which correspond to short 3.77 Å contacts between the Cl atoms. These contacts correspond to relatively large solid angles, 4–5% of the total 2π steradian solid angle, of the Voronoi polyhedron (for comparison, valence bonds correspond to 5–21% solid angles). (73,74) Strong Cl···Cl contacts form dense 2D slabs of overlapping Cl orbitals (Figure 9c). In each TeCl6 complex of the slabs, six Cl atoms form Cl···Cl contacts, corresponding to a total of 51.3% solid angle. These slabs have virtually no overlap since the shortest Cl···Cl contact between them is 5.9 Å long with a negligible total solid angle of 0.02%. This geometric analysis allows one to conclude that (EtNH3)2TeCl6 has a 2D electronic structure with strong orbital overlap between the TeCl6 complexes, which agrees with the DFT calculations (note the flat band in the Γ–Z direction vs disperse bands in the Γ–X and Y–Γ directions in Figure 3g).

Figure 9

Figure 9. Voronoi polyhedra (VP) analysis of intermolecular interactions in (EtnNH4–n)2TeCl6 structures. (a) View on the Te atom VP in a [TeCl6]2– complex. (b,c) Cl atom VPs show a strong interaction between two complexes. (d,e) Decreasing interaction between the octahedral TeCl6 complexes as d(Cl···Cl) and the corresponding solid angle decrease. (f) Electronically isolated TeCl6 complexes in (Et4N)2TeCl6.

Simple geometric structure analysis with Voronoi polyhedra also enables an understanding of decreasing orbital overlap interactions in the remaining series. The other end member of the series, (Et4N)2TeCl6, has no short Cl···Cl contacts in its structure. Therefore, the Cl Voronoi polyhedra of the neighboring TeCl6 octahedra share no common faces (Figure 9f). This TeCl6 octahedra isolation results in a 0D electronic structure, which agrees well with the results of DFT calculations and optical properties measurements. The two intermediate cases, (Et2NH2)2TeCl6 and (Et3NH)2TeCl6, offer a convenient way of probing the effect of slight changes in the outer sphere cation on the nonvalent interactions between the TeCl6 complexes. Both compounds have a 2D net of Cl···Cl contacts between TeCl6 octahedra (Figure 9d,e), which arrange them in a square net motif. In the case of the smaller Et2NH2+ cation, each TeCl6 complex forms four Cl···Cl contacts, which are 3.76 Å apart, with the corresponding Voronoi polyhedron solid angle of 3.59%. The total solid angle of the interacting Cl atoms is 14.36%. The addition of one more ethyl group to the organic cation does not alter the packing of structural units, and similar square layers of interacting TeCl6 octahedra form in the structure of (Et3NH)2TeCl6. Moreover, the Te···Te distance demonstrates only a marginal increase from 8.52 to 8.58 Å. Despite this seemingly subtle difference, TeCl6 undergoes a slight reorientation that results in Cl···Cl distance elongation from 3.76 to 4.19 Å. This more apparent change leads to a double reduction in the solid angles, from 3.59 to 1.79% (or from a total of 14.36 to 7.16%), which is also associated with reducing the band dispersion of the A1g bands from 0.314 to 0.127 eV for A = Et2NH2+ and Et3NH+, respectively. This example shows that two nominally electronically 2D structures can have a significantly different degree of orbital overlap, which requires quantification for assessing the properties of the compounds.
Notably, the orbital overlap (i.e., electron coupling) is one of the two components necessary for enabling energy transfer between complexes in hybrid halide compounds, which leads to luminescence quenching. The other requirement is the presence of sufficient spectral overlap according to the Dexter equation. (75,76) Since spectral overlap is roughly similar in the (EtnNH4–n)2Sn1–xTexCl6 series due to close Stokes shifts, most of the changes in concentration quenching are due to electron coupling between the metal halide complexes. However, it is important to take into account spectral overlap effects when comparing series with sufficiently different Stokes shifts due to its competing role in luminescence quenching. This interdependence can be illustrated by temperature-dependent PL effects in compounds with high electron coupling. For example, Cs2TeCl6 exhibits thermal quenching at 200–300 K that occurs as spectral overlap increases with temperature due to exciton–phonon coupling. (77) At low temperatures, however, there is no significant spectral overlap, thus leading to a “turning off” of PL quenching. On the other hand, PL quenching can be suppressed by strongly diluting Te in a Cs2HfCl6 matrix, which results in an efficient emission in Cs2Hf0.99Te0.01Cl6 at room temperature. (68)

Conclusions

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This report illustrates the difference between electronic and structural dimensionalities and their influence on the optical properties of hybrid halide compounds. Using the (EtnNH4–n)2Sn1–xTexCl6 series as an example, we showed that interactions between the TeCl62– complexes are strongly dependent on the organic cations. The bulkiest cation, Et4N+, almost completely shields the complexes from each other, resulting in the lack of an orbital overlap between them as shown by nearly flat bands corresponding to TeCl6 A1g orbitals. The near absence of exchange interactions between the complexes results in no concentration quenching effects in the (Et4N)2Sn1–xTexCl6 solid solutions. On the other hand, the small cation EtNH3+ offers little shielding and promotes strong interactions between closely arranged TeCl6 complexes, leading to a rapid PL concentration quenching in the corresponding Sn/Te solid solutions. The intermediate examples, Et2NH2+ and Et3NH+, show a decreasing degree of orbital overlap as the cation size increases. Interestingly, the highest PL quantum yields of ∼20% were observed for highly Te-diluted compounds in the (Et3NH)2Sn1–xTexCl6 series. Since this PLQY value is significantly higher than that in the (Et4N)2Sn1–xTexCl6 solid solutions, ∼ 4%, the orbital overlap may play a positive role in quantum yields, although further analysis is required to establish this trend unambiguously.
We also demonstrated the application of a simple geometric approach for crystal structure analysis, Voronoi tessellation, for semiquantitative characterization of orbital overlap (and, therefore, band dispersions) in structurally 0D hybrid halide compounds. This automated method allows one to visualize interactions among the isolated complexes and determine their dimensionality and strength. As an example, we demonstrated the correlation between the Cl atoms’ Voronoi polyhedra parameters and optical properties. This method is universal and can be readily extended to other hybrid structures for quick characterization of energy transfer between structurally isolated metal halide complexes. Since many properties of hybrid solid-state materials depend on the degree of the orbital overlap between the isolated complexes, this method offers a fast and simple insight into the properties of the previously synthesized or new materials.

Experimental Methods

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Synthesis of (EtnNH4–n)2TeCl 6(n = 1–3) and (Et3NH)2Te2Cl10 Single Crystals for X-ray Diffraction (XRD)

For the synthesis of all compounds, TeO2 (99.995%) was completely dissolved in excess of concentrated HCl (≥36.5 wt %) on stirring and moderate heating on a hot plate. After dissolution, EtnNH3–n (99%) was slowly added to the solution. In all cases, a stoichiometric ratio TeO2:EtnNH3–n of 1:2 was used. Yellow crystals of (EtNH3)2TeCl6 and (Et3NH)2TeCl6 formed upon slow evaporation of solutions at room temperature within several days, while (Et2NH2)2TeCl6 crystals formed almost immediately. Two polymorphic modifications of the (Et3NH)2TeCl6 phase, monoclinic and orthorhombic, were found to crystallize simultaneously. Variations in starting molar ratios yielded identical products when ethylamine and diethylamine were used. However, using a 1:1 TeO2:Et3NH ratio yields a different composition, (Et3NH)2Te2Cl10 (Table S28).

Synthesis of (EtnNH4–n)2Sn1–xTexCl6 Solid Solutions for Optical Characterization

Four series of (EtnNH4–n)2Sn1–xTexCl6 (n = 1–4) solid solutions with isomorphous substitutions of Sn4+ for Te4+ were prepared to study the effect of the substitution on the photoluminescent properties. To ensure the starting reagents' complete dissolution (especially sparsely soluble at room temperature SnO2) and homogenization, we employed a hydrothermal reaction: (1 – x)SnO2 + xTeO2 + 2(Et)3NH3–n/Et4NCl → (EtnNH4–n)2Sn1–xTexCl6 at 190 °C for 3 h in excess of concentrated HCl (Table S28). The reactions yielded crystalline target phases. For Et3NH+, the hydrothermal reactions yielded transparent solutions, and the target products crystallized after partial solution evaporation. Since the solid-state synthesis route provides more control over the composition, we synthesized several (Et2NH2)2Sn1–xTexCl6 phases via solid-state reactions for comparison with the hydrothermal products. Three (Et2NH2)2Te1–xSnxCl6 phases with x = 0.5, 0.1, and 0.05 were prepared by mixing and grounding of (Et2NH2)2SnCl6 and (Et2NH2)TeCl6 powders in the corresponding molar ratios. Mixed powders were pressed into pellets using steel dies and annealed for 12 h at 120 °C in a sealed silica tube. After slow cooling (10°/h) to room temperature, pellets were reground and annealed for another 12 h.

Single-Crystal XRD

Single-crystal X-ray diffraction experiments (Mo Kα radiation) were performed on a Bruker D8 QUEST diffractometer equipped with a PHOTON 100 CMOS area detector at room temperature. Data integration was performed via SAINT-Plus software; (78) absorption correction was done with the SADABS program. (79) Structures of new tellurium hybrid chlorides were solved by the intrinsic phasing method (SHELXT (80) and Olex2 (81)) and refined by the full-matrix least-squares method against F2 in an anisotropic approximation (SHELXL (82)). Hydrogen atoms were placed in geometrically calculated positions if no disorder was presented. Tables S1 and S2 contain crystallographic data on the new hybrid tellurium chlorides with no matches on CCDC. (83) Note that the structure of (Et4N)2TeCl6 phase was reported earlier. (53)

Powder XRD

Powder X-ray diffraction patterns for (EtnNH4–n)2Sn1–xTexCl6 (n = 1–4, x = 0–1) polycrystalline samples were collected on a Bruker D2 PHASER diffractometer featuring a LYNXEYE XE-T energy-discriminating detector (Cu Kα radiation) over a 5–65° 2θ range.

Photoluminescence Measurements

Photoluminescence excitation and emission spectra, time-resolved photoluminescence data, and photoluminescence quantum yields were collected at room temperature on an Edinburgh Instruments FS5 spectrofluorometer featuring a 150 W CW ozone-free xenon arc lamp and EPL-375 ps pulsed diode laser excitation sources.

UV–Vis and Raman Spectroscopy

Diffuse reflectance spectra were collected at room temperature using a Shimadzu UV-2450 (Kyoto, Japan) spectrometer in a wavelength range of 200–800 nm. BaSO4 was employed as a nonabsorbing reflectance reference for calibration. Experimental reflection data were transformed into absorption spectra based on the Kubelka–Munk theory, and optical band gaps were extracted. The surface-enhanced Raman spectra were collected using a Renishaw inVia confocal Raman microscope system with a 785 nm laser and with a 9.5 mW laser power (Figure S6).

Thermogravimetric (TGA) and Differential Thermal Analysis (DTA)

Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) were performed on powder samples of pristine (Et2NH2)2TeCl6 and (Et2NH2)SnCl6 by using an SDT Q600 thermogravimetric analyzer. Samples were heated from room temperature to 600 °C at a rate of 10 °C/min under a nitrogen flow (100 mL/min) (Figure S6).

Energy-Dispersive Spectroscopy (EDS)

The elemental analysis of the (EtnNH4–n)2Sn1–xTexCl6 (n = 3 and 4) phases was performed on a Thermo Fisher Scientific Teneo field-emission scanning electron microscope at the Georgia Electron Microscopy facility.

DFT Calculations

First-principles calculations were performed using density functional theory (DFT) with the Vienna ab initio simulation package (VASP) planewave code, (84,85) generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE), (86) and projector-augmented wave (PAW) method. (87,88) The initial unit cells were converted to a primitive cell using VESTA software before geometry optimization. (89) The ground-state geometries at 0 K were optimized by relaxing the cell volume, atomic positions, and cell symmetry until the maximum force on each atom is less than 0.01 eV/Å. Nonspin-polarized calculations were performed, with a 520 eV cutoff energy for the plane wave basis set and 10–5 eV energy convergence criteria. The k-paths for band structure calculations were generated using the VASPKIT package. (90) Band structure visualization was performed using the Sumo package. (91)

Geometric Analysis of Crystal Structures Using Voronoi Tessellation

Crystal structure analysis was performed using the TOPOS 4.0 and ToposPro software packages. (92,94) The method of intersecting spheres was employed for coordination number determination using the AutoCN program. (74,92−94) Dirichlet and ADS programs were employed for Voronoi polyhedra construction and topological analysis, respectively.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c14554.

  • Selected crystallographic data and XRD experiment parameters, atomic displacement parameters, bond lengths, bond angles, characteristics of N–H···Cl hydrogen bonds, EDS results and SEM images, average PL lifetimes, PLQYs, parameters of TeCl62– octahedra distortion, synthesis details, Tauc plots, TGA/DTA, and Raman spectra (Tables S1–S28 and Figures S1–S6) (PDF)

Accession Codes

CCDC 23912912391295 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: + 44 1223 336033.

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Author Information

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  • Corresponding Author
  • Authors
    • Sergei A. Novikov - Department of Chemistry, University of Georgia, Athens, Georgia 30602, United StatesOrcidhttps://orcid.org/0000-0003-2007-3162
    • Hope A. Long - Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States
    • Aleksandra D. Valueva - Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States
  • Author Contributions

    The manuscript was written with the contributions of all authors. All authors have approved the final version of the manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the University of Georgia Department of Chemistry, Franklin College of Arts and Sciences, and the Office of Provost. The computational study was supported in part by resources and technical expertise from the Georgia Advanced Computing Resource Center, a partnership between the University of Georgia’s Office of the Vice President for Research and the Office of the Vice President for Information Technology. The authors thank Dr. Alevtina A. Maksimova (University of South Carolina) and Dr. Yanjun Yang (University of Georgia) for their assistance with DTA/TGA and Raman spectroscopy data collection.

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  • Abstract

    Figure 1

    Figure 1. Schematic representation of two major components of energy transfer and photoluminescence quenching in 0D organic–inorganic metal halides.

    Figure 2

    Figure 2. Views on the structures of hybrid tellurium halides of interest: (a) (EtNH3)2TeCl6, (b) (Et2NH2)2TeCl6, (c) m-(Et3NH)2TeCl6, and (d) (Et4N)2TeCl6. (53) The yellow octahedra are TeCl62–, Cl atoms are green, C atoms are gray, N atoms are blue, and H atoms (if located) are light blue.

    Figure 3

    Figure 3. (a,f) Schematic molecular orbital diagrams of octahedral SnCl6 and TeCl6 complexes. (b–e) Band structure diagrams of ((C2H5)nNH4–n)2SnCl6 and (g–j) ((C2H5)nNH4–n)2TeCl6 (n = 1–4). A1g MO orbitals (σ bonds formed by Sn/Te 5s and Cl 3p orbitals) are highlighted with blue, and T1u orbitals (σ and π bonds formed by Te 5p and Cl 3p orbitals) are highlighted with orange.

    Figure 4

    Figure 4. PXRD patterns of the (EtnNH4–n)2Sn1–xTexCl6 series: (a) (EtNH3)2Sn1–xTexCl6, (b) (Et2NH2)2Sn1–xTexCl6, (c) (Et3NH)2Sn1–xTexCl6, and (d) (Et4N)2Sn1–xTexCl6. Ref. stands for the reference line; (Et4N)2Sn1–xTexCl6 samples were collected with the Ge powder as an internal standard.

    Figure 5

    Figure 5. PLE and PL spectra of (EtnNH4–n)2Sn1–xTexCl6 series: (a) (EtNH3)2Sn1–xTexCl6 (x = 0.05–0.80, λex. = 388 nm, and λem. = 620 nm), (b) (Et2NH2)2Sn1–xTexCl6 (x = 0.05–1.00, λex. = 375 nm, and λem. = 600 nm), (c) (Et3NH)2Sn1–xTexCl6 (x = 0.05–0.80, λex. = 405 nm, and λem. = 650 nm), and (d) (Et4N)2Sn1–xTexCl6 (x = 0.1–1.0, λex. = 395 nm, and λem. = 600 nm).

    Figure 6

    Figure 6. Time-resolved PL spectra of (EtnNH4–n)2Sn1–xTexCl6 series, λex. = 372 nm: (a) (EtNH3)2Sn1–xTexCl6 (x = 0.05–0.80), (b) (Et2NH2)2Sn1–xTexCl6 (x = 0.05–1.00), (c) (Et3NH)2Sn1–xTexCl6 (x = 0.05–0.80), and (d) (Et4N)2Sn1–xTexCl6 (x = 0.1–1.0).

    Figure 7

    Figure 7. Photoluminescence quantum yield (PLQY) as a function of the organic cation and Te concentration.

    Figure 8

    Figure 8. A1g band dispersion energy as a function of (a) Te···Te or (b) Cl···Cl distances in chains of TeCl6 complexes. Two octahedral complex orientations are shown: linear (red plots) and rotated by 45° around the z-axis (blue plots).

    Figure 9

    Figure 9. Voronoi polyhedra (VP) analysis of intermolecular interactions in (EtnNH4–n)2TeCl6 structures. (a) View on the Te atom VP in a [TeCl6]2– complex. (b,c) Cl atom VPs show a strong interaction between two complexes. (d,e) Decreasing interaction between the octahedral TeCl6 complexes as d(Cl···Cl) and the corresponding solid angle decrease. (f) Electronically isolated TeCl6 complexes in (Et4N)2TeCl6.

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  • Supporting Information

    Supporting Information


    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c14554.

    • Selected crystallographic data and XRD experiment parameters, atomic displacement parameters, bond lengths, bond angles, characteristics of N–H···Cl hydrogen bonds, EDS results and SEM images, average PL lifetimes, PLQYs, parameters of TeCl62– octahedra distortion, synthesis details, Tauc plots, TGA/DTA, and Raman spectra (Tables S1–S28 and Figures S1–S6) (PDF)

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