From polyanions to infinite chains: chemical bonding evolution in AX₃ polyhalides under pressure

Abstract

Polyhalides are molecular systems that defy conventional views of chemical bonding, with infinite linear halide chains being the most challenging systems. By studying CsI₃ under compression, we show how I₃⁻ polyanions, with electron-rich multicenter bonds, undergo progressive pressure-induced polymerization giving rise to infinite linear iodine chains, I_∞, and demonstrate that these chains, and, by extension, infinite linear halide chains, feature electron-deficient multicenter bonds that are in good agreement with the recently published unified theory of multicenter bonding. This result is in sharp contrast with previous assumptions that considered electron-deficient multicenter bonds to be impossible in valence electron-rich elements such as halogens. The pressure-induced formation of these unconventional bonds explains the decrease of the bandgap and the increase in electrical and photoelectrical conductivity in AX₃ polyhalides under compression.

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Introduction

Polyhalides are molecular systems that challenge conventional views of chemical bonding. Their electronic structures have created debates about the hypervalent nature of the halide atoms and challenged the applicability of Lewis diagrams.^1–9 Moreover, they present a wide range of structural arrangements that exhibit a fascinating interplay of covalent, ionic, and metallic properties, allowing them to act as versatile building blocks in molecular electronics, energy storage systems, and photonic materials.^10–15

Among the many types of polyhalides, infinite linear halide chains, X_∞, stand out as some of the most interesting and rare ones. First proposed by Colin and Gaultier de Claubry, and independently by Stromeyer over two centuries ago in a starch–iodine blue complex,^16,17 the existence of these structures remained theoretical for a long time. In 2013, the first infinite linear halide chain was reported in the Pm3̄n phase of NaCl₃, with high-pressure (HP) conditions necessary for its synthesis.⁶ It was only in 2016 that a room-pressure (RP) infinite linear iodine chain was synthesized and experimentally verified in a pyrroloperylene–iodine compound for the first time.¹⁸ Since then, many halide-containing compounds have been predicted and found to exhibit this linear atomic arrangement, particularly in nanometrically confined materials and/or under HP conditions.^18–30

Remarkably, infinite linear atomic chains are not limited to halides;^6,31–33 similar chains have been predicted and observed at both RP and HP in pseudo-halide atoms, such as P²⁻, Sb²⁻, Se⁻, and Te⁻.^34–41 These findings highlight the significance of infinite linear atomic chains as common yet understudied motifs in halide and pseudo-halide chemistry.

Despite the existence of infinite linear halide and pseudo-halide chains, the bonding in these chains remains poorly understood.^19,25,28,33 Even the most studied case, the infinite linear iodine chain, I_∞, challenges conventional models used to describe these systems. Unlike typical polyiodide frameworks composed of donor–acceptor interactions between I₂, I⁻, and I₃⁻ units,⁴ the I_∞ chain features equidistant iodine atoms with equivalent charges, making them difficult to ascribe to these models. A simple electron count yields a total of 7 electrons per atom in I_∞, thus exhibiting formally two-center one-electron (2c–1e) bonds.^4,42 This electron count suggests that the electronic structure of I_∞, as well as other infinite linear halide and pseudo-halide chains, features half-filled bands,^43,44 resembling the fascinating metallic 1D conductors with electron-deficient bonds, such as the infinite linear hydrogen chain.^45,46

The delocalized bonding perspective of infinite linear halide chains clashes with the generally accepted view that valence electron-rich elements (groups 15 to 18) primarily favor covalent bonding or electron-rich multicenter bonds (ERMBs), also known as three-center–four electron (3c–4e) bonds, hypervalent bonds, or hyperbonds.^42,47 In this classical view, it is also believed that electron-deficient multicenter bonds (EDMBs), also known as three-center–two-electron (3c–2e) bonds, could only occur in valence electron-deficient elements (e.g., hydrogen and groups 1, 2, and 13).⁴⁸

The conventional view of chemical bonding exposed in the preceding paragraph has recently been challenged by a unified theory of multicenter bonding, which explains the origin and formation process of ERMBs and EDMBs and their relationship with classical primary bonding (covalent, ionic, and metallic) and also with classical secondary non-covalent bonding (van der Waals and hydrogen bonding).^49,50 In this article, we aim to explore the chemical bonding and electronic delocalization within infinite linear halide and pseudo-halide chains. For this purpose, we have performed a joint HP experimental and theoretical study on the compound CsI₃. It is well known that HP conditions modify the chemical properties of the elements and induce remarkable changes in the chemistry of materials.^51–53 The ability of pressure to continuously modify the interatomic distances enables us to track the evolution of chemical bonding in a continuous way that would not be possible by comparing different compounds (atomic substitution) or by reducing the system, as already explained in the unified theory of multicenter bonding.⁵⁰ This is consistent with the view of Burdett that pressure could be used to study infinite linear chains by overcoming the typical Peierls distortion in these chains.⁴⁵ For this purpose, we have selected CsI₃ because it is one of the AX₃ halides that exists at RP^54–58 and forms I_∞ chains at HP.^6,19–25 CsI₃ can be considered a test bed model for the other AX₃ halides (A = Li, Na, K, Rb, Tl, and NH₄; X = F, Cl, Br, and I) and exhibits X_∞ chains at the lowest pressure within the AX₃ family, facilitating their experimental study. Details of experimental measurements and theoretical calculations can be found in sections 1 and 2 of the supplementary information (SI).

Our work demonstrates that pressure induces the formation of infinite linear halide chains in the cubic Pm3̄n HP phase of AX₃ halides and that the bonding in that chain is the EDMB, thereby revealing the bonding nature of infinite linear halide and pseudo-halide chains. Such a finding confirms that valence electron-rich elements can exhibit EDMBs in infinite linear atomic chains. This demonstration opens new avenues for designing materials with strong optical absorption, photovoltaic applications, thermoelectric properties, and data storage associated with this kind of unconventional bonding.⁵⁹ Moreover, the pressure-induced process of formation of EDMBs in the infinite linear chains in CsI₃ at HP fully agrees with the recently published unified theory of multicenter bonding.^49,50

Results and discussion

X-ray diffraction (XRD) measurements at RP allowed us to confirm that our CsI₃ samples contained only the Pnma phase (see Fig. S1 and structural data in Table S1 in the SI). It is known that CsI₃ undergoes the Pnma → P3̄c1 → Pm3̄n sequence of phase transitions at HP,^22–24 a similar sequence to that of other AX₃ halides.^6,25 The Pnma phase features isolated I₃⁻ anions in a herringbone motif (Fig. 1a); the P3̄c1 phase is characterized by linearly aligned I₃⁻ anions (showing secondary I₃⁻⋯I₃⁻ interactions) in three perpendicular directions (Fig. 1b); and the Pm3̄n phase exhibits I_∞ chains along the three perpendicular directions (Fig. 1c). All these phases show typical ionic bonds between Cs⁺ and I₃⁻ anions as well as homonuclear bonds between the I atoms themselves. Since the relevant change in chemical bonding occurs alongside the P3̄c1 → Pm3̄n phase transition during the polymerization of the I₃⁻ units to form I_∞ chains, we mainly focus our discussion on these two phases and their phase transition at HP.

Fig. 1 Details of the crystalline structure of the Pnma (a), P3̄c1 (b), and Pm3̄n (c) phases in CsI₃ at 0, 2, and 24 GPa, respectively. Cs, I(1), I(2), and I(3) indicate the four independent atoms in the Pnma phase. Cs(1), Cs(2), I(1), and I(2) indicate the four independent atoms in the P3̄c1 phase. I(1) and I(2) are the central and external atoms of the I₃⁻ units. The dashed line in the P3̄c1 phase indicates the intermolecular bonding (I₃⁻⋯I₃⁻) between aligned I₃⁻ units. In the Pm3̄n phase, there is only one Cs and one I independent atoms.

We did not perform HP-XRD measurements since they have been carried out in previous works and good data were previously obtained and reported, as discussed below. In particular, previous HP-XRD measurements showed that the Pnma → P3̄c1 phase transition in CsI₃ occurs at very low pressures (ca. 1.0 GPa) and that the P3̄c1 → Pm3̄n phase transition takes place at ca. 22.6 GPa.^22–24 These values agree with our ab initio calculations (Fig. S2 in the SI) and Raman measurements (Fig. S5–S11 in the SI). Moreover, our theoretical values for the unit cell volume, lattice parameters, atomic parameters, and I–I bond lengths in the three phases agree with experimental values²³ (see Tables S1–S3 in the SI) and previous calculations on CsI₃.^19,22–24 Furthermore, our simulated results accurately reproduce the experimental pressure dependence of the unit cell volume in the three phases (Fig. S3 and Table S4 in the SI) and of the interatomic bond distances (Fig. 2a). The good agreement between experimental and simulated results gives us confidence in: (i) the goodness of the experimental structural data previously reported, and (ii) the accuracy of our calculations, which we will use to study the change in chemical bonding in CsI₃ under compression.

Fig. 2 (a) Pressure dependence of the experimental (symbols) and theoretical (lines) primary (intramolecular I₍₁₎–I₍₂₎, I₍₁₎–I₍₃₎, and I–I) and secondary (intermolecular I₃⁻–I₃⁻) bond distances in CsI₃. Experimental values in (a) are taken from ref. 22 and 23. Dashed vertical lines indicate the experimental phase transition pressures. (b) Pressure dependence of the calculated number of electrons shared (ES) in the bonds of the P3̄c1 and Pm3̄n phases in CsI₃. ES values of the I₍₁₎–I₍₂₎ and I₍₁₎–I₍₃₎ bonds in the Pnma phase are not shown to avoid misunderstanding. Bold lines in (b) are a guide for the eye. The vertical dashed line indicates the theoretical phase transition pressure.

Before discussing the chemical bonding between the I atoms in the different crystalline phases of CsI₃, we need to comment on the pressure dependence of the I–I bond distances in these phases (Fig. 2a). The Pnma phase has two main I–I distances, I₍₁₎–I₍₂₎ and I₍₁₎–I₍₃₎, corresponding to the two bonds of the asymmetric I₃⁻ polyanion. They exhibit an expected decrease with increasing pressure, leading to a decrease in the total length of the I₃⁻ polyanion (see discussion in section 3.1 of the SI). On the other hand, the P3̄c1 phase features a symmetric I₃⁻ polyanion with a short (primary) intramolecular I–I (I(1)–I(2)) bond length of 2.945 Å at ca. 2.0 GPa.¹² In addition, we have to consider a long (secondary) intermolecular I–I bond distance that corresponds to the intermolecular I₃⁻⋯I₃⁻ (I(2)–I(2)) interaction between the external I atoms of neighbouring I₃⁻ polyanions arranged in a linear fashion (Fig. 1b). Interestingly, while the long secondary intermolecular I–I bond distance of the phase P3̄c1 strongly decreases upon compression, a small anomalous increase of the short primary intramolecular I–I bond distance is produced (see Fig. 5 in ref. 23). Importantly, these two distances equalize at HP, leading to the formation of I_∞ chains in the three dimensions in the cubic Pm3̄n phase, as a result of the pressure-induced polymerization (PIP) of the I₃⁻ units above 22 GPa. There is only a single I–I bond distance in the I_∞ chains of the cubic phase that shows a normal decrease with increasing pressure (Fig. 2a).

The changes in the I–I bond distances in CsI₃ under compression align with the three stages of the process of multicenter bond formation proposed in the unified theory of multicenter bonding (see discussion in section 3.2 of the SI)^49,50 and closely match the variations observed in the Raman vibrational modes (see discussion in section 4.4 of the SI, Fig. S5–S11 and Tables S5–S9). Regarding the vibrational properties and their relation to chemical bonding, here we just want to emphasize that the short primary bonds in the P3̄c1 phase, which exhibit an anomalous increase in bond distance, are associated with the softening of the high-wavenumber vibrational modes (related to stretching vibrations).^49,50 The soft behavior of these modes in the P3̄c1 phase is followed by their hardening in the Pm3̄n phase. This hardening is linked to the normal compression of the symmetric I–I bonds in the I_∞ chains above 22 GPa, as already pointed out. In summary, the sequence of equalization of the primary and secondary bond distances along with the anomalous increase of the short primary bond length and the softening of vibrational modes in the P3̄c1 phase, is characteristic of stage 2 (in which the multicenter interaction appears) in the process of formation of multicenter bonds.^49,50 This process culminates upon reaching the Pm3̄n phase, with the formation of multicenter bonds in I_∞ chains (stage 3).^49,50 At this point, we note that it is difficult to determine, relying only on the interatomic distances and vibrational data under compression, whether the bonds in I_∞ chains are EDMBs or ERMBs.

In this regard, it has been suggested that the homonuclear bonds in some infinite linear atomic chains, such as P–P bonds in infinite linear P²⁻ chains in the HP phase of Mo₂P³⁹ and Se–Se bonds in infinite linear Se⁻ chains in the HP phase of YSe₃,⁴⁰ are 2c–1e bonds (see the discussion of these bonds in relation to I–I bonds in I_∞ in CsI₃ in section 3.3 of the SI). More recently, Te–Te bonds in infinite linear Te⁻ chains, Te_∞⁻, in TlTe at RP, as well as in I_∞, have been classified as EDMBs;^4,49,50,58 however, to the best of our knowledge, no proof of the multicenter character of bonding in infinite linear atomic chains has been provided for any compound. Up to now, we have just shown that the trend in I–I bond distances and vibrational properties (see section 4.4 of the SI) under compression in the P3̄c1 phase of CsI₃ supports the multicenter character of symmetric I–I bonds in I_∞ in the Pm3̄n phase, according to the unified theory of multicenter bonding.^49,50 Hereon, we will focus on confirming the multicenter character of bonding in I_∞ with other bonding descriptors and also on determining the ERMB or EDMB nature of the bonds in I_∞ with the help of Fig. 2b.

According to the unified theory of multicenter bonding,^49,50 the distinction between ERMBs and EDMBs can be made by calculating the number of electrons shared (ES) and the normalized number of electrons transferred (ET) between two atoms using the density-based quantum theory of atoms in molecules (QTAIM)⁶⁰ (see details of these calculations in section 2 of the SI). In this density-based method, the ES value is derived as twice the delocalization index (DI) calculated between two atoms. While ERMBs usually feature ES values higher than 1.4 and ET values higher than 0.2, EDMBs usually exhibit ES values around 1.0 for ET = 0 and smaller values if ET ≠ 0.⁵⁰

It is well known that the X–X bonds within the X₃⁻ anions in the Pnma and P3̄c1 phases of AX₃ halides are ERMBs, i.e. three-center–four-electron (3c–4e) bonds.^{19,22,24,25,50} This is confirmed by our calculated ES (1.66) and ET (0.32) values for the short primary (intramolecular) I–I bond at 0 GPa in the P3̄c1 phase of CsI₃, which are comparable to those of the isolated I₃⁻ polyanion.⁵⁰ These bonding features change when pressure comes into play (see Fig. 2b, ES and ET values for I–I bonds in the different phases of CsI₃ are shown in Table S10 of the SI). Upon compression, the ES values of both intramolecular and intermolecular bonds in the P3̄c1 phase evolve inversely to the bond distances (Fig. 2b). While the short (long) intramolecular (intermolecular) bond distance increases (decreases), the corresponding ES value decreases (increases). This result indicates that as the short intramolecular bond lengthens, it loses electronic charge, whereas the long intermolecular bond gains electronic charge as it shortens. The overall process leads to an equalization of both I–I bond distances and ES values (around 1.1) in the Pm3̄n phase. In this context, the equalization of ES values gives further support to the multicenter character of the I–I bonds in I_∞.^49,50 Moreover, the ES value for the equalized I–I bonds in I_∞ is characteristic of EDMBs, indicating delocalized electron-deficient bonding in I_∞, in good agreement with previous suggestions.^4,49,50

Bader charges calculated with QTAIM (Fig. 3a and Table S11 in the SI) allow us to determine the ET values of the I–I bonds (Table S9 in the SI), which also provides information on the change of I–I chemical bonding under compression. In the P3̄c1 phase near RP, the average Cs atom shows a near +1 charge, while the I₃ unit carries a negative charge, consistent with the behavior of a monovalent alkali cation and an anion with a nominal charge –1, respectively. Specifically, the central I atom of the I₃⁻ polyanion at RP has a small Bader charge (ca. –0.07e), while the terminal I atoms have almost a –0.38e value. This result means that the terminal iodine atoms, I(2), share most of the electronic charge (0.83e) donated by the Cs cation. This accumulation of negative charge on the terminal I atoms is characteristic of the I₃⁻ polyanion and is a feature of ERMBs, as already discussed for this polyanion and other molecules with ERMBs, such as XeF₂ and HF₂⁻.⁵⁰

Fig. 3 (a) Pressure dependence of the Bader charges (q_Bader) of the average Cs and individual I atoms in the P3̄c1 (full circles) and Pm3̄n (open squares) phases of CsI₃. I₍₁₎ and I₍₂₎ indicate the central and the terminal atoms of the I₃⁻ anion in the P3̄c1 phase, respectively; I_(cub) indicates the iodine atoms in I_∞ in the Pm3̄n phase. (b) Scheme of the charge transfer processes taking place in the P3̄c1 phase at HP. The ERMB at the I₃⁻ polyanion exhibits two electrons between each pair of I atoms, but not equally distributed and shared, as explained in the unified theory of multicenter bonding.⁵⁰ Electrons are transferred from the I₃⁻ units to the Cs atom and also to the intermolecular bond as I₃⁻ polyanions approach each other. (c) Scheme of interatomic bonding at the Pm3̄n phase. EDMBs at I_∞ feature a single electron between each pair of I atoms.

With increasing pressure, the Bader charge of the Cs atom decreases from ca. +0.83e in the P3̄c1 phase to ca. +0.6e upon reaching the Pm3̄n phase at 22 GPa (Fig. 3a). This indicates that under compression, the I₃⁻ polyanion returns part of the electronic charge received from the Cs atom at RP; a behavior previously noted in ab initio calculations of CsI₃ at HP.^19,23 This process is also accompanied by a decrease in the Bader charge difference between the central and external I atoms of the I₃⁻ polyanion in the P3̄c1 phase, resulting in a gradual decrease of the ET value for the primary I–I bonds in the P3̄c1 phase from 0.32 near RP to 0.2 at 19 GPa. This trend culminates in a zero ET value for the symmetric I–I bond in I_∞ in the Pm3̄n phase, where all I atoms occupy the same Wyckoff site, further supporting our previous ES analysis and confirming that the bonding in the I_∞ chain should be considered as formed by an array of collinear (2c–1e) EDMBs or equivalently a concatenation of linear 3c–2e bonds.^49,50 In fact, the ES value of the I–I bonds in the Pm3̄n phase is slightly above 1 because the charge of each I atom in the I_∞ chain is not zero but ca. −0.2e above 22 GPa (the Bader charge of each I atom in the Pm3̄n phase). This means that there is an electronic charge of ca. 7.2e per iodine atom and ca. 1.2e per I–I bond in the I_∞ chain around 22 GPa (smaller values at higher pressures). Note that the other six electrons of each I atom in the I_∞ chain are located in three lone electron pairs located in the plane perpendicular to the chain (not plotted in Fig. 3c), as corresponds to the A(0,3,1) multicenter unit (see Fig. 10 in ref. 50).

The joint evolution of the calculated ES and ET values of the short (primary) I–I bond in the P3̄c1 phase with increasing pressure allows us to monitor the pressure-induced change in chemical bonding from ERMB in I₃⁻ to EDMB in I_∞, as shown in the ES vs. ET map (Fig. 4). The data reveal that the primary I–I bond in the P3̄c1 phase shifts from the ERMB region near RP towards the EDMB region as the Pm3̄n phase is reached at HP. This ERMB → EDMB chemical bonding transition seems to occur due to the charge depletion at the I₃⁻ polyanion. In contrast to previous calculations,^19,23 our results indicate that there are two mechanisms by which the polyanion charge is reorganized during the process of PIP of the I₃⁻ units in the P3̄c1 phase. First, a small fraction of the charge of the I₃⁻ polyanions is returned to the Cs atoms, as shown by the Bader charges (Fig. 3a). Second, an important fraction of the electronic charge of the I₃⁻ polyanions is transferred from the intramolecular bonds to the intermolecular I₃⁻⋯I₃⁻ interactions as the I₃⁻ units approach upon compression, as shown by the inverse behavior of the ES values of both bonds (Fig. 2b). This second mechanism has not been commented in previous HP works on AX₃ halides. The two charge-transfer processes are depicted schematically in Fig. 3b for CsI₃. As a consequence of the charge transfer, the I_∞ chain features ca. one electron shared between every two iodine atoms, i.e. a 2c–1e EDMB, as previously suggested for I_∞ and infinite linear Te⁻ chains in TlTe at RP.^4,50,58 This result is consistent with the 2c–1e bonds predicted in P²⁻ and Se⁻ atoms in MoP₂ and YSe₃ at HP, respectively.^39,40 Therefore, we can conclude that the P–P and Se–Se bonds along the P_∞ and Se_∞ chains in these compounds are also EDMBs.

Fig. 4 ES vs. ET map showing the evolution of the calculated ES and ET values of the hexagonal P3̄c1 phase (black rhombuses) at different pressures until the cubic Pm3̄n phase (black triangles) is attained above 19 GPa.

Once the EDMB nature of bonding in I_∞ has been clarified using a density-based method as QTAIM, we want to stress that the change in chemical bonding can also be traced with an orbital-based method (see details in section 2 in the SI). Within the orbital-based analysis with the LOBSTER software,^61,62 the ES value is obtained as twice the two-center integrated crystal orbital bond index, ICOBI(2c), and the normalized ET value is obtained from the Löwdin charge. The ICOBI(2c) values for the short primary and long secondary I–I bond distances in the P3̄c1 phase (Fig. S12 in the SI) show the same behavior as the ES, reinforcing that both the density-based and orbital-based analyses point towards the EDMB nature in the I_∞ chain.

The multicenter character of I_∞ is further supported by the integrated crystal orbital bond index for three centers, ICOBI(3c), which is the only known multicenter bond index available for solids, to our knowledge. Fig. 5a shows how the ICOBI(3c) for the I–I–I bond in the I₃⁻ polyanion of the P3̄c1 phase changes under compression. It changes from ca. −0.4 in the P3̄c1 phase at RP—a value typical of the isolated I₃⁻ polyanion and XeF₂—^{49,50,62–64} to −0.1 in the Pm3̄n phase. This last value is similar to that found for the octahedrally-coordinated phases of pnictogens, chalcogens, and phase change materials, such as rocksalt-like β-GeTe and PbTe, i.e. systems with EDMBs.^49,50,65 While previous studies have interpreted negative ICOBI(3c) values as indicative of ERMBs,^62–64 our results suggest that a value close to −0.1 is indicative of the presence of EDMBs. This conclusion is supported by the charge depletion and the PIP of I₃⁻ units in CsI₃, which aligns with the chemical picture of 2c–1e bonds, as confirmed by ELF analysis in other AX₃ halides.²⁵

Fig. 5 (a) Pressure dependence of ICOBI(3c) in the I₃⁻ units of the P3̄c1 phase (blue circles) and in the infinite linear iodine chain of the Pm3̄n phase (red squares). (b) Electronic density of states (DOS) for the P3̄c1 (Pm3̄n) phase at 8 GPa (32 GPa).

We propose that the negative value of ICOBI(3c) for the I–I bonds in I_∞ is consistent with EDMB formation, considering I_∞ as a resonant form (electron fluctuation) that accumulates charge with respect to the average population, as recently demonstrated by analyzing the statistics of the electron distributions.⁶⁶ In the I_∞ chain, the two resonant forms with alternating bonds (see Fig. 6) may act as charge reservoirs, potentially explaining its negative ICOBI(3c) value. To the best of our knowledge, this is the first report of bonding evolution from ERMBs to EDMBs in a material. Our findings underscore the role of pressure in resolving bonding controversies, such as the ones related to ERMBs and EDMBs.

Fig. 6 I_∞ can be considered as concatenated 2c–1e bonds (bottom) but also as a resonant structure of the three above chains. Violet balls represent I atoms and black dots represent the bonding electrons between the atoms.

The pressure-induced change in chemical bonding from ERMBs to EDMBs in CsI₃ correlates with the change in the electrical and photoelectrical properties of the material as experimentally measured,^19,23–25 and as shown by the electronic density of states (Fig. 5b). The hexagonal Pnma phase at 0 GPa is a semiconductor with an experimental bandgap of almost 1.79 eV.⁶⁷ Our calculations show that the bandgap at 8 GPa in the P3̄c1 phase reduces to ca. 0.7 eV and the cubic Pm3̄n phase at 30 GPa exhibits no gap. Our calculated pressure-induced decrease of the bandgap is consistent with experimental results.²⁴ Moreover, our calculations show that the cubic Pm3̄n has quasi-metallic conductivity that explains the pressure-induced increase in the electrical conductivity and photoconductivity in the Pnma → P3̄c1 → Pm3̄n sequence of phase transitions at HP.^19,23–25 The quasi-metallic conductivity of EDMBs in the cubic phase of CsI₃ is typical of semimetals with half-filled bands^43,44,49,50 and is characteristic of phase change materials that are considered incipient metals.^59,65 Moreover, the change in bonding agrees with the change in the electronic properties previously observed in similar pseudo-halide systems^34–41 and is consistent with the electrical properties found in starch–iodine and pyrroloperylene–iodine complexes exhibiting infinite linear iodine chains.¹⁸

We would like to finish by commenting on the optical properties of CsI₃ under compression. The experimentally measured decrease of the bandgap of CsI₃ with increasing pressure²⁴ is consistent with the increase of the calculated optical dielectric constant, ε_∞, in the P3̄c1 phase, as shown in Fig. S13 in the SI. It is shown that the optical dielectric constant is quite small (ca. 5) near RP when ERMBs are present in I₃⁻ units and increases in the hexagonal phase up to close to 100. Notably, the optical dielectric constant remains constant around a value close to 80 in the cubic phase above 22 GPa and does not diverge to infinity as expected in a metal. The increase of the optical dielectric constant from RP to 22 GPa explains why the Pm3̄n phase of CsI₃ shows metallic cluster. A feature that is consistent with the EDMB present in the I−I bonds of the Pm3̄n phase, since high values (but not infinite) of the optical dielectric constant and metallic luster have been measured in the phases of incipient metals, such as the simple cubic phase of cubic polonium and arsenic, as well as in the rocksalt phase of phase change materials.^49,65,68 The changes in chemical bonding in CsI₃ under compression are also traced by the increase of the chemical bond polarizability, leading to unusually high Born effective charges in the phase with EDMBs, as shown in Fig. S13. Clearly, the calculated Born effective charges of Cs atoms in the P3̄c1 phase show a negligible change with increasing pressure. In contrast, a notable increase of the calculated Born effective charges of I(1) atoms (double than of I(2)) has been obtained upon going from discrete I₃⁻ units to I_∞ chains. These high values of Born effective charges in the iodine atoms have been also found in the simple cubic phase of polonium and arsenic, as well as in the rocksalt phase of phase change materials, i.e., materials featuring EDMBs.^49,65,68

Conclusion

We have demonstrated that the pressure-induced Pnma → P3̄c1 → Pm3̄n sequence of phase transitions in CsI₃ leads to a pressure-induced polymerization (PIP) of the I₃⁻ units present in the original Pnma phase. The PIP drives a change in chemical bonding from ERMBs in discrete I₃⁻ polyanions (in the Pnma and P3̄c1 phases) to EDMBs in infinite linear iodine chains, I_∞ (in the Pm3̄n phase). This study confirms that EDMBs, as infinitely extended 2c–1e bonds (or equivalently as concatenated 3c–2e bonds) in one direction, are the characteristic bonding within the X_∞ chains in the Pm3̄n phases of all AX₃ halides. Therefore, this work supports the recent predictions of the presence of EDMBs in infinite linear atomic chains.^4,50,58 In this context, it must be mentioned that a pressure-induced polymerization of IO₃⁻ units has been recently reported in distorted AIO₃ perovskites leading to the formation of EDMBs in the polymerized units.⁶⁹

Noteworthily, the presence of EDMBs in the X_∞ chains is consistent with the prediction of 2c–1e EDMBs in infinite linear Sb²⁻ and Te⁻ chains in Li₂Sb and TlTe at RP, respectively,⁵⁰ and with the earlier proposals of 2c–1e bonds in infinite linear P²⁻ and Se⁻ chains in Mo₂P and YSe₃ at HP, respectively.^39,40 This conclusion is reasonable since P²⁻, Sb²⁻, Se⁻, and Te⁻ anions are isoelectronic to halide atoms. Consequently, EDMBs in the form of extended 2c–1e bonds are expected to be found not only in infinite linear halide chains but also in infinite linear pseudo-halide chains in many materials, e.g., in infinite linear Se⁻ and Te⁻ chains in isostructural β-ErSe₂⁷⁰ and UTe₂ at RP,⁷¹ respectively, and in the HP P6/mmm phase of Sc₂P.⁴¹ The discovery of EDMBs in infinite linear atomic chains and their related quasi-metallic conductivity opens new avenues for designing materials with novel optical, electronic, and optoelectronic properties.

We emphasize that the example of compressed AX₃ halides illustrates that EDMBs do actually occur in valence electron-rich elements, such as halogen atoms. Therefore, this work complements a previous study in which EDMBs were found in pnictogens and chalcogens at different pressures.⁴⁹ It is also worth highlighting that the pressure-induced change in chemical bonding in CsI₃ from the P3̄c1 phase to the Pm3̄n phase is consistent with: (i) the change from I–I bond elongation to compression; (ii) the change from phonon softening to hardening (in high-wavenumber vibrational modes), and (iii) the change in optical, electronic, and photoelectronic properties between phases with I₃⁻ and I_∞, as noted in previous HP works on AX₃ halides.^6,19–25 These changes are related to the three-stage process describing the formation of multicenter bonds in the recently formulated unified theory of multicenter bonding.^49,50 This theory challenges our current understanding of chemical bonding in materials and offers insights into important technological materials for enhanced applications.^4,59

We should finally note that during the finalization of this manuscript, we have been aware of a manuscript which has addressed the nature of chemical bonding in 1D iodine chains in the [Na(DMSO)₃]_n(I₂)_n solid.⁷² In that work, authors make a nice historical revision of the 1D iodine chains in different systems, such as the 200 year-old starch–iodine blue complex, leading to a potato stagnation procedure with the KI/I₂ starch test, and herapathite, whose unique optical properties led to the foundation of the Polaroid Corporation. These systems evidence the technological importance of 1D iodine chains, like those found in the Pm3̄n phase of AX₃ polyhalides for possible iodine-based conductors, superconductors, batteries, data storage, and optical materials with strong optical absorption for photovoltaic applications associated with unconventional EDMBs.⁵⁹

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: experimental and theoretical details; structural properties of the three phases of CsI₃ including the discussion of the total bond length of the I₃⁻ polyanion in different phases of CsI₃, of the three stages of multicenter bond formation in CsI₃ from the point of view of interatomic distances, and the discussion about the electron-deficient multicenter (2c–1e) bonds in infinite linear atomic chains; vibrational properties of the three phases of CsI₃, including the discussion of the three stages of multicenter bond formation in CsI₃ from the point of view of the vibrational properties; and data for the analysis of the electron density topology.^73–94 See DOI: https://doi.org/10.1039/d5tc01566a.

Acknowledgements

This publication is financed by Spanish Ministerio de Ciencia e Innovación (MCIN) and the Agencia Estatal de Investigación MCIN/AEI/10.13039/501100011033 as part of the project MALTA Consolider Team network (RED2022-134388-T), and I + D + i projects PID2021-122585NB-C22 and PID2022-138076NB-C42/C44 co-financed by EU FEDER funds, by project PROMETEO CIPROM/2021/075 (GREENMAT) financed by Generalitat Valenciana and co-financed by EU FEDER. This study also forms part of the Advanced Materials programme supported by MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat Valenciana through project MFA/2022/025 (ARCANGEL). We would like to express our gratitude to Giulia Longo for providing us with the experimental XRD patterns of CsI₃ under room temperature conditions and to Matteo Savastano and Ángel Vegas for their insightful and engaging discussions on our findings. Their input and feedback greatly enriched the development of this article.

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Footnote

† These authors contributed equally to this work.

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