The discovery and description of ionic bonding may be traced back to the late eighteenth century, when pioneering electrochemistry experiments conducted by Humphry Davy and Michael Faraday1 and theories established by Walther Kossel2 unveiled the intricate process of electron transfer between atoms during compound formation. The transfer of electrons defines ions and the subsequent emergence of ionic compounds. The formation of ionic compounds is governed by electrostatic interactions. The concept of electronegativity was introduced soon after.3,4 It is an essential concept for comprehending the polarity of chemical bonds. Notably, electronegativity has been employed to describe the intrinsic origin of the hardness of superhard materials.5 Electronegativity also emerges as an important factor in modulating the energetics of bonding between transition metals and oxygen, determining their chemical interactions.6 For example, the electronic structure of ZnCo₂O₄ has been tailored through the strategic incorporation of low-electronegativity anions, improving its water oxidation activities.7 In the field of surface chemistry, the electronegativities of atoms influence the capability of electron surface scattering on thin metal layers.8 In general, when two atoms form a chemical bond, the atom with higher electronegativity tends to fully acquire the valence electrons from the other atom, resulting in electron transfer and the formation of ionic bonds. Under ambient conditions, it is widely accepted that the pairing of alkali metals with highly electronegative nonmetals forms stable ionic compounds.

However, ionic compounds under pressure may violate the conventional rule of electronegativity. Noble gases, traditionally deemed inert and of weak electronegativity, have been found to exhibit reactivity and even to form ionic bonds9 under pressures of tens of gigapascals. For instance, noble gases have demonstrated reactivity with alkali metals,10 alkaline earth metals,11 iron,9,12 iron peroxide,13 and alkali oxides or sulfide compounds14 under high pressure. Pressure also generates multiple or fractional valence states, in, for example, cesium, forming complex ionic compounds like CsI_y15,16 and Cs_xI.17 Pressure even enforces electron transfer between Mg and Fe to form Fe–Mg compounds, whose chemistry involves two elements that are almost immiscible under ambient conditions.18,19 In short, applying pressure may bypass the rule of electronegativity and create ionic compounds that were previously considered inconceivable under ambient pressure.20,21

In particular, Dong et al.22 established profound correlations between pressure, electronegativity, and chemical hardness over the entire Periodic Table. They suggested that transition metals such as Ag, Zn, and Cd shift toward high electropositivity at elevated pressures. The chemical behavior of those elements, according to conventional wisdom, should be such that they are more amenable to forming ionic compounds with other nonmetallic elements, particularly those from the halogen group. We therefore focus on silver halides in this study. Under ambient conditions, the crystal structures of silver halides predominantly exhibit characteristics akin to the rock salt structure. The ionicity of Ag–X (X = F, Cl, Br, and I) is key to determining their mechanical properties, such as plasticity.23 In addition, silver halides have extensive applications in chemical processes such as photography, photochemistry, and electrochemistry.24,25 Their exceptional photocatalytic performance has attracted a substantial amount of interest in recent years.26–28 However, it has been reported that silver iodide decomposes to single element members under high pressure, despite the enhanced difference in the electronegativity of the ions.29 This intriguing contradiction has motivated us to investigate the evolution of ionic bonds in silver halides under pressure, possibly ruling out an ionic chemical behavior upon compression.

In our study, we systematically investigate the polymorphism and stoichiometry of Ag–X (X = F, Cl, Br, and I) systems up to 500 GPa. Notably, we observe that the electropositivity of cations is enhanced within this pressure range. Furthermore, our research reveals an abnormal decomposition behavior of Ag–X compounds and elucidates the underlying causes of this phenomenon. Specifically, we focus on the evolution of ionic bonding and antibonding states of Ag–X compounds under pressure, aiming to identify the fundamental mechanism governing the reactivity of ionic bonds.

A comprehensive global structure search for Ag_xX_y (x, y = 1–4) compounds is employed to simulate unit cells containing 1–8 formula units between 1 atm and 500 GPa pressure. To predict stable structures for a given chemical composition, we utilize the CALYPSO code30,31 along with the particle swarm optimization algorithm. This approach is based on ab initio total-energy calculations and implemented within the framework of density functional theory.32 Geometrical optimization and electronic property calculations are conducted using the Vienna Ab initio Simulation Package (VASP),33 employing an exchange–correlation functional within the Perdew–Burke–Ernzerhof (PBE)34 generalized gradient approximation (GGA). The projector-augmented-wave (PAW) method35 is employed with appropriate Ag, F, Cl, and Br potentials, considering their respective valence electrons: 4d¹⁰5s¹, 2s²2p⁵, 3s²3p⁵, and 4s²4p⁵. Additionally, we also test the effect of another Ag pseudopotential with valence electrons 4p⁶4d¹⁰5s¹. These potentials have been adopted from the VASP potential library. To ensure good convergence within 1 meV/atom, we use a plane-wave energy cutoff of 600 eV and a Monkhorst–Pack36k-point grid with a spacing of 0.02 Å. Charge transfer is calculated using Bader’s quantum theory.37 Crystal orbital Hamilton populations38 (COHPs) are calculated using the LOBSTER program39 to analyze interatomic interactions. Finally, the Madelung energy is generated using VESTA software. Computational results in the AgI binary system are taken from our previous work29 for comparison.

Structural searches under specified pressure conditions help us to constrain the thermodynamic stability of silver halides. This step refines the stoichiometry and selects stable polymorphic phases that will be addressed. Figures S1(a)–S1(d) (supplementary material) illustrate the enthalpies of various Ag–X structures relative to Ag and X as functions of pressure.

Among Ag–F compounds, AgF₂ is the most stable, adopting the Pbca phase structure (AgF₂-I) under ambient pressure. It undergoes a transformation to the Pca2₁ structure (AgF₂-II) at 10 GPa, and then to Pbcn (AgF2-III) at 15 GPa.40,41 Under ambient pressure, AgF adopts a rocksalt structure (AgF-I), transforming to the CsCl-type structure (AgF-II) at 2.7 GPa and remaining stable over a wide pressure range.40–43

Among Ag–Cl compounds, AgCl adopts a rocksalt structure (AgCl–I) at ambient pressure.44,45 At 6.6 GPa, it transforms to a KOH structure (AgCl-II, space group P2₁/m), and further undergoes a structural phase transition from P2₁/m to Cmcm (AgCl-III) at 10.8 GPa.44 Previous work has also predicted a CsCl-type structure for AgCl (AgCl-IV).46

Among Ag–Br compounds, AgBr-I and AgBr-II phases adopt rocksalt and KOH structures, respectively, with a phase transition occurring at 7.9 GPa.44 The Pm-3m phase of AgBr is found to be stable.47

Among Ag-I compounds, AgI exists in both wurtzite-type (AgI-I) and zinc-blende-type (AgI-II) phases under ambient conditions44 and then transforms to a rocksalt structure (AgI-III, space group Fm-3m) at 76 K and 0.3 GPa.48 Additionally, powder neutron diffraction experiments have observed an intermediate structure, AgI-IV, with a P4/nmm structure, during the transformation from AgI-II to AgI-III within a narrow pressure range of 0.28–0.38 GPa.49 Using angular-dispersive X-ray diffraction (XRD), Hull and Keen44,49 identified a reconstructive transition of AgI-III to the KOH-type structure (AgI-V, space group P2₁/m) at 11.3 GPa, and predicted further orthorhombic TlI-type and CsCl-type phases at higher pressures.

We show some high-pressure structures of Ag–X compounds in Fig. S2 (supplementary material). Additionally, we have selected the AgBr system to test the effect of another Ag pseudopotential with valence electrons 4p⁶4d¹⁰5s¹. Our results show that the phase transition sequences and pressure, as well as the decomposition pressure of the AgBr system, exhibit only slight differences from our previous findings, as shown in Fig. S3 (supplementary material). Moreover, our results indicate that the 4p electrons of Ag have a very minimal impact on our findings, leading us to infer that the influence of the 4s electrons would be even more negligible. This test further validates our findings. Our simulations have not only reproduced previously reported structures and the sequence of phase transformations in Ag–X compounds,40,43–50 but also calculated the enthalpy differences ΔH for Ag–Cl, Ag–Br, and Ag–I, which abnormally increase at higher pressures. Specifically, at above 41 GPa for AgI, 116 GPa for AgBr, and 323 GPa for AgCl, ΔH becomes positive, indicating chemical decomposition to Ag and halogen elements (Fig. 1). Notably, the dashed line in Fig. 1 suggests that the decomposition pressure for AgI29 will be much lower even when the temperature increases from 0 K (static condition) to room temperature. In stark contrast, the thermodynamic stabilities of Ag–F ionic compounds are improved with pressure. The evolution of stable phases and their formation enthalpy for binary Ag_xX_y are shown in Figs. S1(e)–S1(h) (supplementary material). It is worth noting that AgF₂ is predicted as the stable phase, owing to the potent oxidizing nature of F, while other silver halides remain in the conventional AgX stoichiometry throughout the pressure range we have investigated. In the following subsections, only the most stable structures of silver halides under the corresponding pressure regime have been selected for in-depth analysis.

The formation enthalpies of compressed silver halides imply their chemical stability under pressure. For AgF, the enhanced stability stems from the decrease in the P∆V term. By contrast, for AgCl, AgBr, and AgI, the increase in the P∆V term results in greater ∆H, and the elemental components become more thermodynamically stable [Figs. 2(a)–2(d)]. Notably, variation of the internal energy ∆U exerts extra influence on ∆H for all studied silver halides. The evolutions of the volume differences ∆V for all investigated materials are depicted in Figs. 2(e)–2(h) and S4 (supplementary material). In AgF, ∆V reveals a negative under-pressure, decreasing P∆V. This is completely opposite to the behavior of the other silver halides AgCl, AgBr, and AgI.

In parallel, we calculate the electronegativity differences between Ag and halogen under varying pressure conditions, aiming to assess the impact of ionization on the stabilities of the Ag–X systems [Figs. 2(a)–2(d)]. Our findings confirm the main conclusion drawn by Dong et al.22 that the electronegativities of Ag and halogen elements are reduced under pressure. Furthermore, taking into account the influence of the crystal structure and ion spacing within silver halides, we also perform Bader charge analysis and calculate the Madelung energy to quantify the interatomic interactions within Ag–X compounds. In ionic crystals, ions charged at ±q engage in long-range interactions that encompass both electrostatic attraction between oppositely charged ions and electrostatic repulsion between ions of the same charge. The binding energy of ionic crystals is predominantly derived from this electrostatic interaction, commonly referred to as Madelung energy. At ambient pressure, the charge transfer per Ag ion approximates 0.7e, 0.55e, 0.45e, and 0.25e for AgF, AgCl, AgBr, and AgI, respectively. Applying pressures may reduce charge transfer between ions, but this effect is not prominent with variations below 0.1e [Figs. S5(a)–S5(d), supplementary material]. This is also reflected by the weak dependence of the Madelung energies on pressure, which represents the ionic electrostatic interactions [Figs. S5(e)–S5(h), supplementary material]. In short, our calculation of ionization suggests that the electronegativity and ionic interaction are not the leading factors in controlling the stability of silver halides under high pressure.

Hybridization of molecular orbitals is an important factor in controlling the stability of compounds, and it becomes stronger when chemical bonds are shortened. Another critical factor here is the extent of electron occupancy in antibonding orbitals, which is known to affect both bonding at solid surfaces51 and the weakening of the stability of a compound.52 In our Ag–X binary systems, the orbitals of Ag and halogen elements intermingle, giving rise to both lower-energy bonding orbitals and higher-energy antibonding orbitals. In general, occupation of antibonding orbitals increases a system’s energy and destabilizes ionic compounds. Through COHP analysis, we quantify the orbital overlap strength and covalent bond strength. Furthermore, we calculate the integrated COHP (ICOHP) and the partial density of states (PDOS) to explore the bonding properties of silver halides. The evolution of the projected ICOHP (pICOHP) between silver and halogens under pressure reveals that the attenuation of covalent interaction in AgCl, AgBr, and AgI is mainly due to weakening of the covalent interactions between Ag-4d and halogen orbitals, whereas it is negligible in AgF, as illustrated in Figs. 3(a)–3(d). The effects of pressure on the occupation of antibonding states in AgF and AgCl are illustrated in Figs. 3(e) and 3(f), and those for AgBr and AgI are shown in Fig. S6 (supplementary material). We find that the electronic structures of AgCl, AgBr, and AgI exhibit similar trends under pressure.

Further examination of the evolution of the COHP of Ag-4d and Cl-3p orbitals under pressure reveals the filling and spreading of antibonding states beneath the Fermi level, as depicted in Fig. 3(f). This is also corroborated by the PDOS, which suggests that the electrons of Ag-4d will be transferred into an antibonding state. In addition, the pressure-induced metallization in silver halides, for instance in AgCl,53 facilitates this process. By contrast, the evolution of the electronic structure of AgF is distinct from that of the other silver halides. For example, its antibonding states only exhibit a moderate broadening, while the occupation of antibonding states beneath the Fermi level largely remains consistent [Fig. 3(e)]. The d-band center model, originally proposed by Hammer and Nørskov,54 is useful in providing an understanding of the catalytic behavior of transition metal-based compounds. This model demonstrates that the d-band position is crucial for comprehending metal–adsorbate interactions, since it influences the occupation and filling of bonding and antibonding states. Generally, an upshift of the d-band center facilitates adsorbate binding, while a downshift hinders adsorption or even promotes desorption due to the diffusion of the antibonding states.55,56 However, there are several strategies to influence transition metal–adsorbate interactions by optimizing the d-band center position, including doping, creating vacancies, adjusting the coordination number, and applying tensile or compressive strains.57–59 Notably, we believe this model is also valuable for interpreting the pressure-induced decomposition of binary silver halide compounds. As pressure increases, Ag–X compounds undergo structural phase transformations and compressive strain, leading to changes in their electronic structure. Specifically, under pressure, the center of the Ag-4d band in Ag–X compounds downshift, affecting the occupation of antibonding states below the Fermi level and promoting decomposition of the compounds.

Figure 4 illustrates the behavior of the Ag-4d band center under varying pressure. The results show dramatic downshifts of 2.4, 2.9, and 3.5 eV in the position of the Ag-4d band center for AgCl, AgBr, and AgI, respectively. From a joint consideration of Figs. 3(f) and S6 (supplementary material), we observe that the antibonding states below the Fermi level diffuse as the d-band center is downshifted. In contrast to the other Ag–X compounds, the center of the Ag-4d band in AgF undergoes only a weak downshift of ∼0.8 eV. Similarly, as shown in Fig. 3(e), there is no significant diffusion of the antibonding states below the Fermi surface in AgF.

Our computational study has brought together two perspectives on the intricate decomposition phenomenon within Ag–X ionic compounds, namely, the energy contributions from ionic bonds controlled by electronegativity and the occupation of antibonding states. These compete under pressure and exhibit distinct chemical behaviors for different systems. Here, AgF is confirmed to exhibit the highest Madelung energy, signifying robust ionic bonds and superb stability. As a result, pressurizing AgF only makes it denser and more stable. For the other halides AgCl, AgBr and AgI, despite their lower Madelung energies, their dependences on pressure are relatively weak. By contrast, the variation of free energy is mainly controlled by the mechanism of filling antibonding states below the Fermi level. It is reasonable to conclude that the heightened occupation of antibonding orbitals beneath the Fermi level will prevail over the Coulomb interaction between Ag and halide ions under pressure. This has demonstrated a unique example of pressure-engineered electronic structure and associated reactivity.

The uniqueness of silver halides also stems from the combination of highly electropositive Ag and highly electronegative halogens. It is well established that the reactivities of ionic compounds of neighboring Au and other Group IIB metals (e.g., Cd and Hg) are mainly controlled by electron transfer between ions.60,61 For instance, pressure hinders electron transfer between Hg and I, gradually transforming ionic into covalent bonding.60 For those main group metals and transition metals with completely filled d-electrons, their ionic bonding is conventionally through s-electrons. However, the d-states of silver halides have a strong influence on their chemical reactivity under pressure. In contrast to the aforementioned metals, the charge transfer in silver halides is even strengthened under pressure, but it plays a secondary role in the formation of ionic compounds. Instead, pressure-induced downshifting of d-states makes a greater contribution to enthalpy, resulting in the elemental Ag and halogens being more stable than the compounds.

In summary, our results suggest that electron transfer is no longer a primary signature of ionic silver halides. Even though the differences in electronegativity between the constituent ions in these compounds are high, the ionic force will eventually be overcome by filling of antibonding states. Electron transfer and molecular orbital hybridization compete in governing the reactivity of ionic compounds. As has been well documented in the literature, charge transfer is dominant under ambient conditions. The reactivity of silver halides, however, is governed by shifts of d-states. Our model may shed new light on the electronic structures of transition metals and reveal the complexity of chemistry under extreme conditions.

The supplementary material includes figures illustrating the convex hull, enthalpy, volume, and PDOS calculated at various pressures for Ag–X systems.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974154, 12304278, and T2425016), the Taishan Scholars Special Funding for Construction Projects (Grant No. TSTP20230622), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2022MA004 and ZR2023QA127), and the Special Foundation of Yantai for Leading Talents above Provincial Level.