Li-F polarity-driven stabilization of −VII oxidation state of gold at high pressure

Domain: physics
Published: 2025-12-22
Editorial outcome: minor_revision

Abstract
The exploration of unconventional oxidation states is pivotal for expanding fundamental bonding paradigms and accessing exotic matter. Achieving highly negative oxidation states in transition metals remains a significant challenge. Here, we propose a dual-driven strategy combining a strong reductant (Li) and oxidant (F) under high pressure, stabilizing the oxidation state –VII of gold (Au) in a ternary electride Li10AuF. This insulating phase hosts paired interstitial anionic electrons and features an Au center nominally isoelectronic with the noble gas radon, governed by F-enhanced charge polarization, pressure-induced orbital reshuffling, and p-d hybridization that lowers the energy of Au 6p orbitals. Replacing F with I or P progressively reduces Au charge and interstitial electron localization, transforming semiconducting Li10AuF into semimetallic Li10AuI and ultimately superconducting Li10AuP. These results demonstrate how chemically polarized element combinations under compression can unlock unexpected oxidation states and charge distributions, guiding the design of quantum materials with emergent functionalities.

Introduction
The oxidation state (OS) of an element is a fundamental concept in chemistry and materials science, underpinning our understanding of charge distribution, electronic structure, and resulting material properties in both molecular and extended systems1–5. The emergence of nontraditional OSs is often associated with atypical structural motifs and unconventional charge-transfer mechanisms, which can lead to emergent physical phenomena and expand the accessible chemical space6–13. As such, the exploration of elemental OSs remains a central and enduring theme in chemical and materials research14–16, driven by the promise of discovering exotic bonding configurations and extraordinary functionalities. Traditionally, access to extreme OSs has relied on the use of strong oxidants to stabilize highly positive states8,11,17,18 or strong reductants to access deeply negative ones10,19. While these approaches have enabled landmark discoveries, such as the +IX state in [IrO4]+ cation1 and the –II state in Cs2Pt20, the stabilization of more negative oxidation states (NOSs), particularly for transition metals, remains highly restricted due to intrinsic electronic and structural constraints.

At ambient pressure, the most negative OS ever observed in isolated anionic species does not exceed –IV14,15, due to conflicting requirements. Achieving deeper NOSs necessitates central atoms that simultaneously exhibit strong electronegativity, large atomic radii, and high electron-accommodating capacity—an inherently contradictory set of criteria. For instance, electronegative p-block elements typically have small atomic radii and limited capacity to accept additional electrons, whereas transition metals offer extensive orbital availability (e.g., unfilled nd and unoccupied (n+1)p orbitals) but lack sufficient electronegativity. Ligand atoms also present trade-offs: strongly electropositive s-block metals tend to be large, limiting coordination due to steric hindrance, while smaller-radius ligands exhibit reduced electropositivity. Consequently, excess negative charge in known NOS-containing compounds is usually stabilized within the anionic framework itself14,21, leaving little room for more exotic bonding configurations such as electride states.

Electrides, where excess electrons are localized in interstitial voids and act as nuclear-free anions (IAEs)22, provide an alternative platform for hosting unconventional charge states23,24. However, these IAEs are typically weakly confined and spatially delocalized—characteristics unfavorable for stabilizing the highly localized electron density required for deep metal reduction. In such systems, excess electrons preferentially occupy lattice voids rather than being transferred to metal centers, impeding the formation of deeper reduced OSs. Nonetheless, electrides containing negatively charged metal species have exhibited remarkable physical properties under pressure,25–28, such as superionic conductivity and superconductivity, as exemplified by high-pressure Li6Al19. This apparent incompatibility—between the delocalized nature of IAEs and the localized requirements for deep transition-metal reduction—raises a fundamental question: can a condensed-phase system be designed in which reduced transition metals and IAEs coexist stably?

Here, we address this challenge by employing a contrasting design principle: rather than relying on a single reductive or oxidative agent, we introduce a chemically polarized combination of a strong reductant (Li) and a strong oxidant (F) under high pressure. This dual-driven framework enables significant charge redistribution, allowing simultaneous stabilization of a –VII OS of gold (Au–7) and the formation of paired IAEs—realizing a ternary electride state. Gold, a late transition metal with strong relativistic effects29,30, possesses the highest electronegativity among metals and a small energy gap between its 5d and 6s/6p orbitals. These features enable Au to access various OSs21,31–34 and unique hybridizations35–38 in condensed phases, making it a promising candidate for realizing unusual deep NOSs under suitable conditions.

Using this design principle and first-principles calculations, we identify a thermodynamically stable compound, Li10AuF, above 150 GPa, in which Au adopts an near-closed-shell configuration analogous to radon (Rn), while two excess electrons occupy well-defined interstitial voids. Comparative studies on related compounds, Li10AuI and Li10AuP, reveal tunable charge-transfer behavior, orbital delocalization, and even superconductivity in Li10AuP. These findings demonstrate the efficacy of combining strong redox elements to push the boundaries of oxidation-state chemistry and offer a promising platform for designing quantum materials with exotic charge states and functionalities.

Results
Stability and crystal structure of electride Li10AuF
Structure prediction based on first-principles swarm-intelligence algorithms was performed over 31 Li-/F-rich stoichiometries in Li-Au-F system, yielding two previously unreported Li-rich compounds—Li10AuF and Li6AuF—as well as an energetically more favorable phase of LiAuF6 at 200 GPa (Fig. 1a and Supplementary Figs. S1a and b and S2). Among these, Li10AuF was identified as the most Li-enriched composition and is thus the focus of this work. Li10AuF crystallizes into a monoclinic structure with P21 symmetry and contains two formula units (f.u.) per unit cell (Fig. 1b). Remarkably, the Au atom is encapsulated by 21 Li atoms, forming a highly coordinated AuLi21 polyhedron that is spatially separated from neighboring Au atoms by more than 4.1 Å, effectively suppressing Au–Au interactions. The AuLi21 polyhedra form a quasi-hexagonal arrangement within the ab plane and stack in an AA-like fashion along the c axis (Supplementary Fig. S3). The interstitial regions are filled by two distinct types of zigzag polyhedral chains (Fig. 1b): distorted FLi9 tri-capped trigonal prisms (violet) and hollow Li10 hexadecahedra (yellow), which face-share with each other and with the AuLi21 units to form a dense, close-packed framework. Notably, the Li10 hexadecahedron hosts two more vertices than the Na cube in Na2He electride24 and the Li8 cube in Li8Au electride39, reflect-ing its enhanced capacity for IAEs accommodation.

Given the structural similarity to known electrides, the presence of IAEs was rigorously examined. The calculated partial charge density clearly reveals ellipsoidal electron centered within the Li10 polyhedra (Fig. 1c), strongly suggesting the formation of an electride state. This is further corroborated by the highly localized features in the corresponding electron localization functions (ELF) map (Fig. 1d), and the presence of non-nuclear attractor (NNA) characterized by an electron density of ρNNA = 0.047 e/bohr3 and a negative Laplacian of ▽2ρNNA = –0.041 e/bohr5 (Supplementary Fig. S4), comparable to those of hP4-Na40. The ellipsoidal topology of the IAEs indicates s-like orbital character, stabilized via coulombic attraction to the surrounding Li+ framework. In addition, quasi-spherical electron localization features around the Au and F atoms (Supplementary Fig. S5) point to a dominantly ionic bonding character, consistent with the charge density distribution (Supplementary Fig. S6).

Phonon dispersion calculations confirm that Li10AuF is dynamically stable down to 50 GPa (Fig. 1e), and thermodynamically stable to at least 150 GPa (Fig. 1a). Finite-temperature ab initio molecular dynamics (AIMD) simulations in a 1×2×2 supercell indicate thermal stability up to 500 K, as evidenced by near-zero mean square displacements (MSD) of all atomic species (Fig. 1f and g). Upon heating beyond 1500 K, Li atoms diffuse significantly, while Au and F remain fixed near their equilibrium sites (Fig. 1f and Supplementary Fig. S7), indicating an incipient transition to a superionic phase. The optimized structure information and initial/final structures of AIMD are provided in the Supplementary Data 1.

Oxidation state of Li10AuF electride
For non-elemental electrides, their formation can be generally interpreted as a signature that the electronegative atoms in the compound have reached their lowest possible NOS. Conseqently, the excess electrons provided by the electropositive atoms become confined within lattice interstices, forming IAEs, as exemplified by N3− in Ca2N41, P3− in Li5P42, and C4− in Li6C43. On the other hand, electronic band structure analysis offers an effective approach to assessing formal OSs in ionic compounds21,44,45. The amount of fully occupied bands below the Fermi level (EF) directetly corresponds to the number of electron-filled atomic and intersitial orbitals. This principle, well illustrated in NaCl (Supplementary Fig. S8), provides a rigorous framework for quantifying the charge distribution in ionic solids. The meaning and scientific rationale for the theoretical investigation of high-pressure OSs are presented in Supplementary Note 1.

We therefore analyze the orbital-resolved electronic structure of Li10AuF to elucidate the electron occupation across atomic valence orbitals and IAE sites, enabling the assignment of formal OSs and a mechanistic understanding of IAEs formation. As shown in Fig. 2a, Li10AuF is a semiconductor with an indirect band gap of 0.56 eV at the PBE level (larger band gap under reduced pressure or within the the revised Heyd-Scuseria-Ernzerhof screened hybrid functional, Supplementary Fig. S9). Below the EF, the projected band structure reveals 6 bands primarily derived from Au 6p orbitals (–2.15 to 0.0 eV), 2 bands from IAEs (–2.80 to –2.15 eV), 10 bands from Au 5d orbitals, and 2 bands from Au 6s orbitals (–7.20 to –6.00 eV), while other bands appear at deeper energies (Supplementary Fig. S10). Notably, the number of these bands precisely matches the total number of corresponding orbitals per unit cell: 5×2=10 for Au 5d, 1×2=2 for Au 6s, 3×2=6 for Au 6p, and 1×2=2 for IAE-s orbitals in two formula units.

To further verify the orbital attribution, we analyze the band-decomposed charge density of the four highest-energy Au and IAE bands (labeled i-iv), which correspond the three quasi-orthogonal dumbbell-shaped distributions around Au (6p orbitals) and one ellipsoidal distribution at the IAE site (s-orbital character) (Fig. 2b), also illustrated by the band-resolved maximally-localized Wannier functions (supplementary Fig. S11). These features confirm the electronic occupation of Au 6p and IAE-s orbitals. The projected density of states (PDOS, Fig. 2c) also support this conclusion: Li 2s/2p and F 2p states show negligible contributions near EF, indicating near-complete electron donation by Li and full 2p occupancy for F (with F 2p states mainly below –11 eV, Fig. 2c). In contrast, the Au 6s, 5d, and 6p orbitals, as well as IAE-s states, exhibit strong localization below EF. Importantly, hybridization between Au 5d and its 6s/6p orbitals—enhanced by relativistic effects46, s-d orbital penetration36, and pressure-induced orbital reshaping—lowers the energy of the 6s/6p states, thereby promoting deep electron accommodation. From this analysis, we assign a formal OS of +I for Li, –I for F, and an unknown –VII for Au, reflecting essentially complete filling of its 6s and 6p orbitals. The IAEs appear as paired electrons confined in Li10 cages (Fig. 2e).

To corroborate this electron-counting scheme, we construct two hypothetical models. In Li10AuFO, one oxygen atom is introduced into each IAE site of Li10AuF. This lead to the disappearance of the 2 IAE bands and the appearance of 6 O 2p bands at deeper energy levels, while retaining semiconducting character (Fig. 2d). This confirms that each O atom receives two electrons at the IAE site to fill its 2p orbitals (Fig. 2e), further validating that IAEs exist as electron pairs in Li10AuF. Similar behavior is observed in hP4-Na and Na2He electrides and their oxygen-implanted counterparts24 (Supplementary Figs. S12 and S13). The second model, Li10XF (X=Po, At, and Rn), is created by replacing all Au with X and removing all Li and F atoms. Among them, Li10RnF0 display a PDOS profile for Rn 6p orbitals closely resembling that of Au 6p orbitals in Li10AuF (Fig. 2f), confirming the near-closed-shell configuration of Au 6p orbitals in the original compound.

As a result, a quasi-quantitative electron-counting scenario emerges: in Li10AuF per f.u., 10 electrons are donated by Li atoms, 1 is accepted by F to fill its 2p orbital, 7 are accommodated by Au atom (filling 6s and 6p orbitals), and 2 are localized as a pair within the Li10 cavity. This balanced electron distribution satisfies the octet rule for all species, supporting the semiconducting nature of Li10AuF. This insight aligns with known insulating electrides like Na2He24 and hP4-Na23. Crucially, unlike conventional 18-electron complexes47 and half-Heusler compounds14 with the only partial (n+1)s and (n+1)p filling, Li10AuF exhibits nearly complete occupation of Au 6p orbitals, establishing a –VII OS. This finding not only redefines the NOS limit of Au atom33,39 and other transition metals15, but also exceeds the previously accepted lower bound (–V) of IIIA-group elements based on atomic shell theory48. While Geng et al. recently proposed highly reduced states of Be8–, Mg8–, Fe8–, and Al7– in body-centered IAE sites of face-centered cubic Li framework49, their assignments are inconsistent with the actual stoichiometry (Li4X), undermining their validity. Lastly, the considerable electron gain by Au in Li10AuF leads to a significant increase in its atomic radius, reduces steric hindrance, and enables the observed hypercoordination, as further visualized in the expanded electronic shell structure of the Au 6p partial charge density (Supplementary Fig. S14).

Heteromorphic Li10AuX (X=F, I, P) electrides
To elucidate the role of fluorine in modulating charge transfer and stabilizing the crystal structure in Li10AuF, we substitute the F atoms with I and P atoms. These substitutions were motivated by the larger atomic radius and lower electronegativity of iodine, and the known larger electron-accepting of phosphorus. Although replacement of F in Li10AuF by I and P lead to dynamically unstable structures, extensive structure searches in the Li-Au-I and Li-Au-P systems uncover two heteromorphic electrides at 200 GPa: a stable Li10AuI with Pmc21 symmetry and a metastable Li10AuP with P-1 symmetry (Supplementary Figs. S1c-f, S15-S17), which are structurally heteromorphic to Li10AuF. Notably, in Li10AuP, the IAEs exhibit a dumbbell-like topology and form spatially extended bonds with extranuclear electrons from Au and P atoms (Fig. 3d), resembling the IAE characteristics observed in superconducting Li6P50 and Li9S51. The combination of electron-phonon coupling (EPC) calculations and the Allen-Dynes-McMillan equation52 gives a EPC parameter λ=0.84, and a logarithmic average frequency ωlog = 141.37 K, resulting in a predicted superconducting critical temperature of Tc = 7.1 K at 200 GPa (Coulomb pseudopotential parameter μ*=0.1). This Tc is comparable to measured 7 K of Bi-III and 8 K of Bi-V phase53. Based on the phonon density of states (PHDOS) (Fig. 3f), the low-frequency phonons dominated by Au atoms (below 6.3 THz) make a primary contribution of 62.5% to total λ, whereas the medium/high-frequency phonons associated to the coupled vibrations of Li and P atoms (above 6.3 THz) contribute 37.5%. Accordingly, metallized Au with 6p attribute dominates the superconductivity of Li10AuP.

Methods
Structure search and optimization
Using the CALYPSO structure search method in conjunction with first-principles calculations54,55, we systematically explored the crystal structures of LixAuyXz (X=F, P, and I, x=1–6, y=1-2, z=1–3; x=6-10, y=z=1) at 100 and 200 GPa. The structural relaxations and electronic properties calculations were performed within the framework of density functional theory as implemented in the VASP (version 5.4.4) code. The generalized gradient approximation (GGA)56 within the Perdew-Burke-Ernzerhof (PBE)57 framework was adopted for the exchange-correlation functional. The projector augmented wave (PAW) potentials58 were used to describe the electron-ion interaction, where the valence configurations were treated with 1s22s1, 5d106s1, 3s23p3, 5s25p5, 2s22p5 for Li, Au, P, I, and F atoms, respectively. The cutoff energy of 700 eV and the Monkhorst-Pack k-meshes with spacing of 2π × 0.03 Å−1 were used to ensure that all the enthalpy calculations with well convergence. The localized Wannier functions were through applying the WANNIER90 package59. The characterization of non-nuclear attractor (NNA) and its electron density (ρNNA) and Laplacian (▽2ρNNA) was performed in the Critic2 code60,61. Crystal structures were visualized with VESTA62.

Stability estimation
Phonon dispersion calculations were performed to determine the dynamical stability as done in the Phonopy code63. First-principles molecular dynamics simulations in NVT ensemble using the Nosé heat bath method64 lasted for 10 ps with a timestep of 1.0 fs.

IAE-related electronic structures
The IAE-projected density of states was calculated by projecting the charge density and wavefunction of the compounds onto empty spheres located at the IAE sites, as implemented in the VASP (version 5.4.4) code. To derive the IAEs-projected band structures, the electronic wavefunction of the pristine structure was firstly calculated, and then the volumes of IAEs were filled with random pseudoatoms with the same Wigner-Seitz radius of IAE blocks. The wavefunction is subsequently projected to the pseudoatoms. Notably, as the wavefunction is derived from the pristine structure, the choice of pseudo-atoms does not affect the electronic bands. They serve solely as atomic spacers to enable the projection of the wavefunction for IAEs.

Superconductivity estimation
The electron-phonon coupling (EPC) was calculated based on density functional perturbation theory, as implemented in the Quantum ESPRESSO (version 6.5) code65. The ultrasoft pseudopotentials were employed with 1s22s1, 5d106s1, and 3s23p3 as valence electrons for Li, Au, and P atoms, respectively. The kinetic energy cutoff for the wave-function expansion was chosen as 70 Ry. The dense k-meshes (16 × 9 × 8) for electronic Brillouin zone integration and enough q-meshes (4 × 3 × 2) for evaluating average contributions from the phonon modes were sampled for P-1 Li10AuP. The superconducting Tc is estimated from the McMillan-Allen-Dynes formula with Coulomb pseudopotential (μ*=0.1)66,67.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary: In this computational contribution, the authors explore the ternary phase diagram Li-Au-F at high pressure (as well as Li-Au-P and Li-Au-I). They report a stable high-pressure phase Li10AuF that features a very unusual Au(-VII) anion. They analyse the electronic properties of this compound in great detail, corroborating their oxidation state assignment by reciprocal space (band structure, DOS) and real space analyses (Bader charges, ELF). They also investigate the role of anion change (from F to P and I). They propose that the Li-F polarity drives the formation of this unusual gold oxidation state.\nRecommendation: High pressure can, amongst other things, change the order of electronic states, relative electronegativities, and induce unusual chemistry. The main result from this paper, as I see it, is the very neat discovery of the unusual highly negative oxidation state of gold, which I find well backed up by the different computational analyses. What is less clear to me is the proposed mechanism, especially the role of the F anions. This is a very complicated system: Li10AuF has Li+ cations, F- anions, interstitial electron pairs (electride character), and Au(7-) anions, in an overall complex low-symmetry crystal structure. It is difficult for me to disentangle the roles of the different ingredients and although the authors throw a lot of different analyses at this system, I am not necessarily wiser as to why this is happening in exactly this system. I feel that although the main result is interesting and noteworthy, the explanation needs to be sharpened up.\nDetailed comments:\n1. Is the reported Li10AuF a known structure type? I suppose one should treat the localised electrons as separate anions, hence look into structures of type A10B3 or A10BCD. If known, even if only approximately, can one draw parallels with the bonding and electronic structure of any prototype compound?\n2. Why does this system need to be so complicated? I notice that Li7Au is a stable binary compound - does this lead to a Au(7-) charge state? If instead high-Li content leads to electrides, do other LixAu compounds (x>7) feature highly negative Au anions?\n3. If none of the above work, what is the role of the F atoms? I could find only one statement in the manuscript, in the discussion, about a constructive role of fluorine: “F’s high electronegativity promotes strong Li ionization, thereby supplying additional electrons to the Au-IAE framework”. If one thinks about this, it makes no sense: F is highly electronegative, hence will draw electrons from Li, as well as Au, and the interstitial electrons; I see no direct process by which those electrons should end up on the Au atom instead. The F-2p states are much lower in energy than the Au or electride states (see DOS in Fig 3), so will not provide electrons to anything else. Could F- balance an overall ionic bonding framework; could it provide steric contribution to stabilise the Au-Li coordination; could it do something else? As it stands, the titular “Li-F polarity” mechanism is not clear to me.\n4. Since the authors are fond of numerical transmutation experiments, can I suggest one more? Could they replace the F atoms (and the corresponding amount of Li atoms) with inert species, e.g. He/Ne/Ar atoms, and test the resulting electronic structure? If the Au(7-) and the electride electron pair are retained, they are not caused by “Li-F polarity” or presence of F ions at all. (I leave it to the authors to find the suitably sized noble gas species, and choose appropriate Li site for these substitutions). However, as per my previous comment, F atoms might well play a role, for instance in stabilising the compound overall so it appears on the convex hull in the first place.", "reviewer_2": "The article \"Li-F polarity-driven stabilization of −VII oxidation state of gold at high pressure\" presents an interesting analysis of how to induce high oxydation states in ternary compounds under high pressure by a good admixture of high and low electronegavities with transition metals thanks to the differential change in their orbital ordering induced by pressure, higher coordinations and preferential redistribution of charge channels.\nThe article is overall very well written and studies are very thorough, including tests with different high electronegativity series, or the introduction of oxygen to verify electride nature.\nHowever, I do not completely agree with the analysis of the results:\n1) Electride characterization: Figure 1 shows apparently spherical IAEs. However, Figure S19 shows rather polymeric channels, with strong delocalization between the IAEs (which agrees with the semiconductor nature). And very different from the high pressure pictures in Figure S10 of Na. Furthermore, Table S1 gives approximately 1.2 electrons to each non nuclear attractor according to Bader theory (far from an electron pair). All these features suggest a non ionic electride, but rather a polymerized-delocalized channel. Maybe the authors could also provide ELF IAE charge to further verify the electride nature.\nELF 3D pictures for the I and P compounds as in S19 would also be appreciated in order to assert the nature of the electronic structure.\n2) On a more theoretical level: The delocalized nature as well as the semiconductor nature of the system (even boosted in the case of I and P, which go to semimetal and superconductor) poses theoretical questions in the attribution of oxydation states. In the case of metals, the localization of orbitals is not well defined, so I wonder on the meaning of assigning oxydation states at these high pressures where orbitals start to become delocalized. Also, on the technical level, how did authors assign orbitals to the IAE?\nI add a list of typos:\n-Traditionally, extreme OSs has have (verb is repeated)\n-Although dircted substitution (typo)\n-two new electrides at electride at (typo)"}, "author_response": "Response Letter to Reviewers\nResponses to the comments from Reviewer 1\nReviewer #1 (Remarks to the Author):\nSummary: In this computational contribution, the authors explore the ternary phase\ndiagram Li-Au-F at high pressure (as well as Li-Au-P and Li-Au-I). They report a stable\nhigh-pressure phase Li AuF that features a very unusual Au(-VII) anion. They analyse\n10\nthe electronic properties of this compound in great detail, corroborating their oxidation\nstate assignment by reciprocal space (band structure, DOS) and real space analyses\n(Bader charges, ELF). They also investigate the role of anion change (from F to P and\nI). They propose that the Li-F polarity drives the formation of this unusual gold\noxidation state.\nRecommendation: High pressure can, amongst other things, change the order of\nelectronic states, relative electronegativities, and induce unusual chemistry. The main\nresult from this paper, as I see it, is the very neat discovery of the unusual highly\nnegative oxidation state of gold, which I find well backed up by the different\ncomputational analyses. What is less clear to me is the proposed mechanism, especially\nthe role of the F anions. This is a very complicated system: Li AuF has Li+ cations, F-\n10\nanions, interstitial electron pairs (electride character), and Au(7-) anions, in an overall\ncomplex low-symmetry crystal structure. It is difficult for me to disentangle the roles of\nthe different ingredients and although the authors throw a lot of different analyses at\nthis system, I am not necessarily wiser as to why this is happening in exactly this system.\nI feel that although the main result is interesting and noteworthy, the explanation needs\nto be sharpened up.\nAuthors’ reply: We greatly appreciate the reviewer’s positive assessment and\nconstructive suggestions. Following the reviewer’s guidance, we have thoroughly\nanalyzed the essential role of F atoms in Li AuF in terms of structural modulation and\n10\nelectronic polarization. The insightful comments have significantly improved the\nclarity and readability of our manuscript. All the reviewer’s suggestions have been\ncarefully addressed and incorporated into in the revised manuscript, as detailed below.\nDetailed comments:\n1. Is the reported Li AuF a known structure type? I suppose one should treat the\n10\nlocalised electrons as separate anions, hence look into structures of type A B or\n10 3\nA BCD. If known, even if only approximately, can one draw parallels with the bonding\n10\nand electronic structure of any prototype compound?\nAuthors’ reply: We appreciate the reviewer’s insightful suggestion. We have examined\nwhether Li AuF corresponds to any known structure type but did not identify any\n10\nmatching prototypes. Considering that a Li-rich environment might stabilize Au in more\nnegative oxidation states (e.g., –7 with a formally closed 6p shell in Li AuF ), we\n9 2\nconstructed several model compounds—Li Au F, Li AuF , and Li Au—at various\n9 2 9 2 10\npressures. Their structural prototypes were inspired by reported hydrogen-rich or metal-\nhydride-type frameworks, such as K ReH [Inorg. Chem. 1964, 3, 558; J. Mater. Chem.\n2 9\nC 2022, 10, 14626] and LaH [Phys. Rev. Lett. 2017, 119, 107001; Proc. Natl. Acad.\n9 2\nLi AuF exhibit partially occupied Au 6p bands, while Li Au shows strong localized\n9 2 10\ninterstitial anionic electrons (IAEs), and isolated bands dominated by IAEs and Au 6p\norbitals. However, Li Au lies above the convex hull in the Li-Au phase diagram and\n10\nis dynamically unstable within 100-300 GPa. These results demonstrate that the specific\ncrystal framework of Li AuF plays a decisive role in stabilizing its unusual bonding\n10\nand electronic characteristics. The corresponding discussion has been added in current\nversion (Page 6 and Supplementary Note4).\nSupplementary Fig. S22| Constructed Li-Au-F/Li-Au structures based on known\ncompounds. (a-f) Crystal structures with ELF isosurfaces (0.75) and orbital-resolved\nband structures of six Li-Au-F/Li-Au models derived from reported compounds with\nstoichiometries comparable to Li AuF. (g) Formation enthalpy with respect to\n10\nelemental Li and Au, and (h) phonon dispersion curves of Li Au derived from Fm-3m\n10\n2. Why does this system need to be so complicated? I notice that Li Au is a stable binary\n7\ncompound - does this lead to a Au(7-) charge state? If instead high-Li content leads to\nelectrides, do other Li Au compounds (x > 7) feature highly negative Au anions?\nx\nAuthors’ reply: We sincerely appreciate the reviewer’s insightful comments and\nprofound understanding of the underlying physical chemistry, particularly concerning\nthe competition between the formation of IAEs and the filling of Au 6p orbitals.\nAssuming complete Li ionization, the Au atoms in Li Au can formally approach a\n7\nnegative oxidation state of Au7⁻. In Li Au, the additional Li atoms introduce excess\n8\nelectrons that cannot be fully accommodated by Au 6p orbitals, leading to the\ncoexistence of IAEs and negatively charged Au anions. However, the calculated\nelectron localization function (ELF) and orbital-resolved band structures\n(Supplementary Fig. S20) clearly reveal that in both Li Au and Li Au, IAEs coexist\n7 8\nwith partially occupied Au 6p states that cross the Fermi level, indicating incomplete\nLi ionization and hybridization between IAEs and Au 6p orbitals. Systematic\ncalculations across Li-Au binary compounds further clarify this evolution: As the Li\ncontent increases, Li atoms become less ionized, with more valence electrons remaining\nin interstitial regions rather than transferring to Au (Supplementary Table S2).\nConsequently, the charge transfer decreases, the IAE population grows, and the degree\nof Au reduction strengthens, following the sequence Li Au < Li Au < Li Au. This\n6 7 8\nanalysis indicates a delicate balance between electride formation and anionic Au states\nin Li-Au binaries. The corresponding discussion has been added in the revised\nmanuscript (Page 6 and Supplementary Note2).\nSupplementary Fig. S20| ELF and electronic structures of Li Au and Li Au.\n7 8\nELF isosurfaces (0.7) and orbital-resolved electronic band structures of (a) C2/c Li Au at\n7\nn\nGPa (+/- represent losing/gaining electrons).\nPhases Pressure (GPa) Li Au F IAEs\nPm-3m LiAu 200 +0.754 -0.754 —— ——\nImma Li Au 200 +0.723 -1.447 —— ——\n1 10\nNote: The structures are taken from previously reported Li-Au binaries (J. Am. Chem.\nSoc. 2016, 138, 4046; Phys. Rev. B 2023, 107, L100501), and all calculations were\nperformed under identical computational settings.\n3. If none of the above work, what is the role of the F atoms? I could find only one\nstatement in the manuscript, in the discussion, about a constructive role of fluorine:\n“F’s high electronegativity promotes strong Li ionization, thereby supplying additional\nelectrons to the Au-IAE framework”. If one thinks about this, it makes no sense: F is\nhighly electronegative, hence will draw electrons from Li, as well as Au, and the\ninterstitial electrons; I see no direct process by which those electrons should end up on\nthe Au atom instead. The F-2p states are much lower in energy than the Au or electride\nstates (see DOS in Fig 3), so will not provide electrons to anything else. Could F-\nbalance an overall ionic bonding framework; could it provide steric contribution to\nstabilize the Au-Li coordination; could it do something else? As it stands, the titular\n“Li-F polarity” mechanism is not clear to me.\nAuthors’ reply: We sincerely appreciate the reviewer’s insightful comments, which\nprompted us to further clarify the dual role of fluorine in the Li-Au-F system. Its\ninfluence can be understood from two complementary perspectives: (1) Structural\nmodulation The incorporation of F facilitates the formation of Li-F polyhedra, which\nspatially separate the Au-centered motifs and effectively increase the Li coordination\nnumber around Au. Compared with the binary Li-Au compounds, the presence of F\nenlarges the IAE-centered Li cavities, facilitating the formation of strong localized IAE\npairs. (2) Electronic polarization The introduction of F enhances the degree of Li\nionization, as confirmed by comparison with Li-rich binary Li-Au compounds\n(Supplementary Table S2 referenced in Comment 2). Although, as correctly pointed out\nby the reviewer, F itself gains one electron owing to its high electronegativity, its\nparticipation in Li–F bonding reinforces Li ionization and promotes internal charge\nredistribution within the framework. The combined effects of enhanced Li ionization\nand expanded Li coordination jointly facilitate the emergence of a highly negative Au\nspecies approaching the –7 charge state in Li AuF. The corresponding discussion\n10\nelucidating these dual structural and electronic roles of F has been incorporated into the\nrevised manuscript (Page 7).\n4. Since the authors are fond of numerical transmutation experiments, can I suggest\none more? Could they replace the F atoms (and the corresponding amount of Li atoms)\nwith inert species, e.g. He/Ne/Ar atoms, and test the resulting electronic structure? If\nthe Au(7-) and the electride electron pair are retained, they are not caused by “Li-F\npolarity” or presence of F ions at all. (I leave it to the authors to find the suitably sized\nnoble gas species, and choose appropriate Li site for these substitutions). However, as\nper my previous comment, F atoms might well play a role, for instance in stabilizing\nthe compound overall so it appears on the convex hull in the first place.\nAuthors’ reply: We sincerely thank the reviewer for the constructive suggestion.\nFollowing the advice, we replaced the F atoms in Li AuF with inert He, Ne, and Ar\n10\natoms at 150 GPa. Among the resultant structures, only Li AuNe was estimated to be\n10\ndynamically stable (Supplementary Fig. S21a-c), which can be rationalized by the fact\nthat the F⁻ ion and Ne atom possesses similar electron configurations and comparable\nionic/covalent radii. Intuitively, one might expect that replacing F with Ne atom could\nincrease the electron population on Au, since Ne is a close-shell species and could in\nprinciple redirect electrons that were previously associated with F to Au atom and\ninterstitial site. However, our calculations revealed a different outcome. The ELF maps\nand orbital-resolved band structures show that Ne substitution remarkably changes the\nelectronic distribution with respect to pristine Li AuF. Specifically, it induces the\n10\nformation of extra IAEs (marked with e′ in Supplementary Fig. S21d), enhances\nhybridization between Au 6p bands and the delocalized conduction states dominated by\nLi 2p and Au 5d, and drives a transition from semiconductor to metallic behavior\n(Supplementary Fig. S21e). These observations indicate a reduction of electron\npopulation on Au 6p orbitals rather than the expected increase. Bader charge analysis\nfurther confirms the decreased electron population on Au and also reveals a weakening\nof Li ionization (Supplementary Table S3). Therefore, although the same electron\nconfiguration between Ne and F-, F exhibits distinctive advantages in Li AuF: it\n10\nstrongly promotes Li ionization, facilitates the population of Au 6p electrons, and\nstabilizes the overall structure. The corresponding discussion has been added in the\ncurrent version (Page 6 and Supplementary Note3).\nSupplementary Fig. S21| Dynamical stability and electronic structures of Li AuX\n10\n(X = He, Ne, Ar). (a-c) Phonon dispersion curves of P2 Li AuX (X = He, Ne, and Ar)\n1 10\nwhich are constructed by substituting the F atoms in Li AuF with X atoms and being\n10\noptimized at 150 GPa. (d) ELF isosurfaces (0.7), and (e) electronic band structures\nprojected by partial atomic orbitals of P2 Li AuNe.\n1 10\nSupplementary Table S3. Bader charge comparison of Li AuF and Li AuNe at 150\n10 10\nGPa, highlighting the decreased electron population on Au and reduced Li ionization in\nthe Ne-substituted model.\nLi AuF +7.04 -4.91 -0.93 (F) -1.21\nReviewer #2 (Remarks to the Author):\nThe article \"Li-F polarity-driven stabilization of −VII oxidation state of gold at high\npressure\" presents an interesting analysis of how to induce high oxydation states in\nternary compounds under high pressure by a good admixture of high and low\nelectronegavities with transition metals thanks to the differential change in their orbital\nordering induced by pressure, higher coordinations and preferential redistribution of\ncharge channels.\nThe article is overall very well written and studies are very thorough, including tests\nwith different high electronegativity series, or the introduction of oxygen to verify\nelectride nature.\nAuthors’ reply: We greatly appreciate the reviewer’s careful evaluation of our work\nand the positive assessment of its novelty, presentation, and analysis. The reviewer’s\ninsightful comments have helped us clarify key aspects and motivated a deeper\ninvestigation into orbital localization in Li AuF. All the raised concerns have been\n10\nconsidered and properly implemented in the revised manuscript, as detailed below.\n1. Electride characterization: Figure 1 shows apparently spherical IAEs. However,\nFigure S19 shows rather polymeric channels, with strong delocalization between the\nIAEs (which agrees with the semiconductor nature). And very different from the high\npressure pictures in Figure S10 of Na. Furthermore, Table S1 gives approximately 1.2\nelectrons to each non nuclear attractor according to Bader theory (far from an electron\npair). All these features suggest a non ionic electride, but rather a polymerized-\ndelocalized channel. Maybe the authors could also provide ELF IAE charge to further\nverify the electride nature.\nELF 3D pictures for the I and P compounds as in S19 would also be appreciated in\norder to assert the nature of the electronic structure.\nAuthors’ reply: We appreciate the reviewer’s insightful comments. The distinct IAE\ntopologies observed in original Figures 1 and S19 originate from differences in pressure\nand atomic arrangement. Specifically, Figure S19 in the original manuscript\ncorresponds to a Li AuF phase by annealing from high to ambient pressure. During\n10\ndecompression, atomic rearrangements lead to the formation of polymeric IAE channels.\nHowever, this low-pressure phase is dynamically unstable, underscoring the crucial role\nof pressure in stabilizing the insulating Li AuF electride that hosts paired IAEs and the\n10\nunusual Au(–7) oxidation state. To improve clarity, the original Fig. S19 has been\nrevised and is now presented as Supplementary Fig. S24 in current version.\nWe acknowledge that conventional Bader charge analysis systematically\nunderestimates the charge associated with IAEs (J. Am. Chem. Soc. 2023, 145, 26472).\nFor instance, in the well-known electrides Y C:2e- and Ca N:1e-, it yields\n2 2\nunrealistically low interstitial electron charges of approximately 0.19e⁻ and 0e⁻,\nrespectively. Consistent evidence from the orbital-resolved band structure, the\nLi AuFO model, and the comparable IAE charge (~1.2e⁻) to those (~1.1e⁻) of Na He\n10 2\nand hP4-Na (Nat. Chem. 2017, 9, 440) collectively corroborate the presence of the\npaired IAEs in Li\nFollowing the reviewer’s recommendation, we have added ELF 3D isosurfaces for\nLi AuF, Li AuI, and Li AuP (Supplementary Fig. S18). These results clearly reveal\n10 10 10\na progressive enhancement in IAEs delocalization and a systematic topological\nevolution of the IAEs networks from F to I to P, demonstrating the strong dependence\nof electron distribution and bonding topology on the X element in Li AuX (X = F, I,\nSupplementary Fig. S24| Comparison of Li AuF at high and ambient pressures.\n10\n(a and d) The crystal structure with ELF isosurface (0.7), (b and e) orbital-resolved\nelectronic band structures and PDOS, and (c and f) phonon dispersion curves of\nLi AuF at 150 GPa and 0 GPa.\n10\n2D mappings corresponding to the planes where the IAEs are located in (a) P2 Li AuF,\n1 10\n(b) Pmc2 Li AuI, and (c) P-1 Li AuP. The blue spheres represent Li atoms for these\n1 10 10\nthree structures.\n2. On a more theoretical level: The delocalized nature as well as the semiconductor\nnature of the system (even boosted in the case of I and P, which go to semimetal and\nsuperconductor) poses theoretical questions in the attribution of oxidation states. In the\ncase of metals, the localization of orbitals is not well defined, so I wonder on the\nmeaning of assigning oxidation states at these high pressures where orbitals start to\nbecome delocalized. Also, on the technical level, how did authors assign orbitals to the\nIAE?\nAuthors’ reply: We thank the reviewer for raising this important point regarding\noxidation-state assignment under high pressure. Although oxidation state is an idealized\nconcept, defined based on complete electron transfer, it remains a useful framework for\ninterpreting electronic structures, even when orbitals are partially delocalized. Despite\npressure-induced changes in electronegativity and orbital energies, electron populations\nin atoms and interstitial sites generally follow fundamental quantum rules, including\nAufbau principle, Pauli exclusion principle, and Hund's rule. This allows a consistent\ndescription of electronic band gaps and a rational assignment of oxidation states with\nexperimental observations at high pressure, such as in hP4 Na at 300 GPa (Nature 2009,\n458, 182) and FeO and FeO H at 100 GPa (Nat. Commun. 2019, 10, 153; Phys. Rev.\n2 2 x\nLett. 2021, 126, 106001).\nBuilding on these advances, high-pressure theoretical studies of oxidation states and\nbonding mechanisms have provided deeper insights into element behavior and updated\nconventional views of chemical valence under extreme conditions (e.g., Nat. Chem.\n2013, 5, 846; Angew. Chem. Int. Ed. 2015, 54,9280; Nat. Commun. 2014, 5, 4861; Nat.\nRev. Chem. 2020, 4, 508; J. Am. Chem. Soc. 2025, 147, 33453). Within this framework,\nwe note that formal oxidation states become less well-defined in delocalized metallic\nsystems; therefore, for semimetallic or metallic Li AuX compounds (X = I, P), we\n10\nrefrain from assigning strict formal oxidation states and instead discuss electronic\npopulations and orbital contributions. In contrast, the insulating Li AuF presents ionic-\n10\nlike features, such as well-separated bands dominated by atomic orbitals, strong\nelectron localization, and a sizeable semiconductor gap, that justify a formal oxidation-\nstate assignment. The corresponding discussion has been added to Supplementary Note\n1 (Supplementary Information, Page S12).\nWe appreciate the reviewer’s attention to the technique of orbital assignment for IAEs.\nThe assigning of s-like orbital is based on their quasi-spherical symmetry, consistent\nwith the orbital-projection analyses of the electronic band structure and density of states\nperformed in VASP. Calculations of IAEs-related band structures and projected density\nof states are well-established functionality in VASP and have been validated in previous\nelectride studies. Detailed methodological descriptions have been provided in the\nSupplementary Information (Page S5).\nPrevious theoretical studies have systematically characterized IAE topologies, orbital\ncharacter, chemical tunability, formation mechanism, and their contributions to\nelectronic states and physical properties in layered and three-dimensional electrides\n(e.g., Nature 2013, 494, 336; Acc. Chem. Res. 2014, 47, 1311; Nat. Chem. 2017, 9, 440;\nJ. Am. Chem. Soc. 2017, 139, 13798; Phys. Rev. Lett. 2022, 129, 246403). These\nadvances establish a reliable framework for identifying and analyzing IAEs and provide\na solid foundation for computational electride research. Building on this foundation,\nour group has performed comprehensive studies on high-pressure Li-based electrides,\nrevealing their stabilization mechanisms, quantifying the correlation between IAE\npopulation and superconductivity, and elucidating the element-dependent modulation\nof IAE behavior (e.g., Phys. Rev. Lett. 2019, 122, 097002; Phys. Rev. B 2023, 107,\nL100501; Phys. Rev. B. 2023, 108, 104505; Phys. Rev. B. 2024, 109, 134505; Comput.\nMater. Today 2025, 5, 100020 [Invited review article]).\n3. I add a list of typos:\n-Traditionally, extreme OSs has have (verb is repeated)\n-Although dircted substitution (typo)\n-two new electrides at electride at (typo)\nAuthors’ reply: All typographical errors pointed out by the reviewer have been\ncorrected throughout the manuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Recommendation: The authors have responded extensively to my comments and made changes to the manuscript that give better insights into the mechanism that stabilises the Li10AuF compound, especially the role of the F anions. They have indulged my suggestion of additional numerical experiments and added those outcomes to the Supplementary. Overall I am satisfied with those changes and recommend the paper be accepted.", "reviewer_2": "The authors have adressed my main concerns based on previous publications. Although some of the arguments are not fully convincing to me, I believe that the public will be interested in these results, so I accept the publication"}, "author_response": ""}]

Decision letter