Closed-shell Repulsion Research Articles

Machine-Learning Photodynamics Simulations Uncover the Role of Substituent Effects on the Photochemical Formation of Cubanes.

Photochemical [2 + 2]-cycloadditions store solar energy in chemical bonds and efficiently access strained organic molecular architectures. Functionalized [3]-ladderdienes undergo [2 + 2]-photocycloadditions to afford cubanes, a class of strained organic molecules. The substituents (e.g., methyl, trifluoromethyl, and cyclopropyl) affect the overall reactivities of these cubane precursors; the yields range from 1 to 48%. However, the origin of these substituent effects on the reactivities and chemoselectivities is not understood. We now integrate single and multireference calculations and machine-learning-accelerated nonadiabatic molecular dynamics (ML-NAMD) to understand how substituents affect the ultrafast dynamics and mechanism of [2 + 2]-photocycloadditions. Steric clashes between substituent groups destabilize the 4π-electrocyclic ring-opening pathway and minimum energy conical intersections by 0.72-1.15 eV and reaction energies by 0.68-2.34 eV. Noncovalent dispersive interactions stabilize the [2 + 2]-photocycloaddition pathway; the conical intersection energies are lower by 0.31-0.85 eV, and the reaction energies are lower by 0.03-0.82 eV. The 2 ps ML-NAMD trajectories reveal that closed-shell repulsions block a 6π-conrotatory electrocyclic ring-opening pathway with increasing steric bulk. Thirty-eight percent of the methyl-substituted [3]-ladderdiene trajectories proceed through the 6π-conrotatory electrocyclic ring-opening, whereas the trifluoromethyl- and cyclopropyl-substituted [3]-ladderdienes prefer the [2 + 2]-photocycloaddition pathways. The predicted cubane yields (H: 0.4% < CH3: 1% < CF3: 14% < cPr: 15%) match the experimental trend; these substituents predistort the reactants to resemble the conical intersection geometries leading to cubanes.

Computational Exploration of Ambiphilic Reactivity of Azides and Sustmann's Paradigmatic Parabola.

We examine the theoretical underpinnings of the seminal discoveries by Reiner Sustmann about the ambiphilic nature of Huisgen’s phenyl azide cycloadditions. Density functional calculations with ωB97X-D and B2PLYP-D3 reproduce the experimental data and provide insights into ambiphilic control of reactivity. Distortion/interaction-activation strain and energy decomposition analyses show why Sustmann’s use of dipolarophile ionization potential is such a powerful predictor of reactivity. We add to Sustmann’s data set several modern distortion-accelerated dipolarophiles used in bioorthogonal chemistry to show how these fit into the orbital energy criteria that are often used to understand cycloaddition reactivity. We show why such a simple indicator of reactivity is a powerful predictor of reaction rates that are actually controlled by a combination of distortion energies, charge transfer, closed-shell repulsion, polarization, and electrostatic effects.

Mono-, Di-, and Trifluoroalkyl Substituent Effects on the Torquoselectivities of Cyclobutene and Oxetene Electrocyclic Ring Openings.

The reactivities and torquoselectivities of electrocyclic ring opening reactions of fluoromethyl-substituted cyclobutenes and oxetenes were studied with M06-2X density functional theory. The torquoselectivities of a series of mono-, di-, and trifluoromethylcyclobutenes and oxetenes result from the interplay of favorable orbital interactions and closed-shell repulsions. When the substituent rotates inward, there can be a favorable interaction between the breaking σ(CO) bond and the σ(CF)* orbital (σ(CO) → σ(CF)*) of the fluoromethyl group in fluoromethyloxetenes. The preference for rotation of a fluoromethyl group is decreased in trifluoromethyloxetenes because closed-shell repulsions between the breaking σ(CO) bond and trifluoromethyl substituent orbitals compete with the σ(CO) → σ(CF)* interaction.

Activation-strain analysis reveals unexpected origin of fast reactivity in heteroaromatic azadiene inverse-electron-demand diels-alder cycloadditions.

Heteroaromatic azadienes, especially 1,2,4,5-tetrazines, are extremely reactive partners with alkenes in inverse-electron-demand Diels-Alder reactions. Azadiene cycloaddition reactions are used to construct heterocycles in synthesis and are popular as bioorthogonal reactions. The origin of fast azadiene cycloaddition reactivity is classically attributed to the inverse frontier molecular orbital (FMO) interaction between the azadiene LUMO and alkene HOMO. Here, we use a combination of ab initio, density functional theory, and activation-strain model calculations to analyze physical interactions in heteroaromatic azadiene-alkene cycloaddition transition states. We find that FMO interactions do not control reactivity because, while the inverse FMO interaction becomes more stabilizing, there is a decrease in the forward FMO interaction that is offsetting. Rather, fast cycloadditions are due to a decrease in closed-shell Pauli repulsion between cycloaddition partners. The kinetic-thermodynamic relationship found for these inverse-electron-demand cycloadditions is also due to the trend in closed-shell repulsion in the cycloadducts. Cycloaddition regioselectivity, however, is the result of differences in occupied-unoccupied orbital interactions due to orbital overlap. These results provide a new predictive model and correct physical basis for heteroaromatic azadiene reactivity and regioselectivity with alkene dieneophiles.

Reactivity for the Diels–Alder Reaction of Cumulenes: A Distortion-Interaction Analysis along the Reaction Pathway

Cumulenes, including allene, ketenimine, and ketene, can be employed as dienophiles in Diels-Alder type reactions. The activation energies of a Diels-Alder reaction between cyclopentadiene and either the C ═ C bond or the other C ═ X (X = C, N, or O) bond in cumulenes have been calculated by G3B3, CBS-QB3, M06-2X, and B3LYP methods. The reactivity trend for the C ═ C bond in cumulenes is allene > ketenimine > ketene and that of the C ═ X bond in cumulenes is ketene > allene > ketenimine. Application of distortion-interaction analysis only at transition states does not give a satisfactory explanation for these reactivities. By employing distortion-interaction analysis along reaction pathways, we found that the reactivity of the C ═ C and C ═ X bond in cumulenes is controlled by both of its distortion and interaction energies. The lowest distortion energy of allene leads to its highest reactivity; the higher interaction energy results in higher activation energy of ketene than that of ketenimine. Compared with the reactivity of the C ═ X bond in cumulenes, the C ═ O bond in ketene has the lowest activation energy to react with cyclopentadiene, due to its lowest interaction energy, whereas the lower distortion energy of ketenimine than that of allene leads to a higher reactivity. The distortion energy of the reactants can be attributed to folding ability and molecule strain. The corresponding interaction energy of the reactants is controlled by orbital interaction, closed-shell repulsion, and static repulsion.

Adsorption of Al, O, Hf, Y, Pt, and S Atoms on α-Al2O3(0001)

We use first-principles density functional theory to investigate adsorption of Al, O, Hf, Y, Pt, and S-atoms on the α-Al2O3(0001) surface. We identify stable adsorption sites and predict binding energies and structures. We find that Al, Hf, and Y preferentially adsorb on threefold-hollow sites, transfer electrons to the surface, and form ionic bonds to the three oxygen atoms. In contrast, the most stable adsorption site for Pt and S is ontop an oxygen atom, and we do not observe significant charge transfer. We find a binding order of S < Pt < O < Al ≪ Y < Hf, which reflects both the ease with which the early transition metals Hf and Y ionize, as well as the (nearly) closed-shell repulsions influencing the adsorption of O, Pt, and S. We use these results to rationalize some observations regarding the stability of thermal barrier coatings.

A Theoretical Study on the Reaction Mechanism for the Bergman Cyclization from the Perspective of the Electron Localization Function and Catastrophe Theory

The reaction mechanism associated with the Bergman cyclization of the (Z)-hexa-1,5-diyne-3-ene to render p-benzyne has been analyzed by means of a combined use of the electron localization function (ELF) and the catastrophe theory on the basis of density functional theory (DFT) calculations (B3LYP/6-31G(d)). The complex electronic rearrangements of this reaction can be highlighted using this novel quantum mechanical perspective. Five domains of structural stability of the ELF occurring along the intrinsic reaction path as well as four catastrophes (fold-cusp-fold-cusp) responsible for the changes in the topology of the system have been identified. The multiple factors that occur along the intrinsic reaction coordinate path are presented and discussed in a consistent way. The topological analysis of ELF and catastrophe theory reveals that mechanical deformation of the C1-C2-C3 unit and closed-shell repulsion between terminal acetylene groups lead to an early formation of diradicaloid character at C2 and C5 atoms. Immediately after the transition structure (TS) is reached, the open-shell-singlet biradical becomes stable. Meanwhile, C1 and C6 atoms are preparing to be covalently bonded; that will finally occur at a distance of 1.791 A. In addition, a separation of the ELF into in-plane (sigma) and out-of-plane (pi) contributions allows us to discuss the aromaticity profiles; sigma-aromaticity appears in the vicinities of the TS, while pi-aromaticity takes place in the final stage of the reaction path, once the ring has been formed.

Analysis of competing bonding parameters. Part 2. The structure of halosilanes and halogermanes (MH 4− nX n, n=1–4; M=Si, Ge; X=F, Cl, Br)

A qualitative rationalization of bonding patterns in halosilanes and halogermanes (MH 4− n X n , n=1–4; M=Si, Ge; X=F, Cl, Br) is presented. Geometrical and bonding properties in these molecules are discussed on the basis of ab initio molecular orbital calculations employing the natural bond orbital population analysis. The results have been compared with data derived previously for halomethanes. Differences in the n-dependence of the M–Cl and M–Br bond lengths for M=C, Si, Ge are explained by a significant reduction in the closed-shell repulsion between the halide atoms. As M gets larger, a continuous decrease in the X–M–X bond angle is observed. Small bond angles (for n=2, 3) are favoured by the p-rich M orbitals in the M–X bonds. They are opposed, however, by the X⋯X repulsion. As M gets larger, the X⋯X separation for a given bond angle increases. A reduction in the X–M–X bond angle is therefore accomplished without overcompensation due to the X⋯X repulsion energy. The variation in the charge density at M as a function of n has been rationalized by differences in the electronegativity of the terminal atoms H and X. Dipole moments have been computed for the molecules in the series. As in the fluoromethanes, a maximum in the dipole moments at n=2 is explained by a combination of geometric and electronic properties unique to the fluoro-compounds. These are, an n-independent charge density at the F sites and a significant decrease in the M–F bond distance as n increases.

Ab Initio High Pressure Investigations of InI

AbstractThe high pressure behaviour of InI is studied by DFT‐calculations and compared with experimental data. The existence of a 5s2 electron pair in In+ represents an unfavourable bonding situation for high symmetry structures because of effective closed shell repulsion. Since cations with a ns2 electron pair are highly polarizable and the electronic situation is more favourable in the low symmetry structure InI prefers a TlI‐type structure at ambient pressure. A pressure induced transition to the more densely packed high symmetry CsCl‐type structure takes place at about 19 GPa according to our calculations.At ambient pressure the interactions are predominantly ionic. However with increasing pressure the distances between In+ cations in the TlI‐type structure diminish drastically, mainly due to the changing space requirement of the lone electron pair. Apart from ionic interactions further bonding interactions between the In+ cations occur. At elevated pressure the electron localization function (ELF) as well as the band structure diagrams suggest metallic bonding between the In+ within the zigzag chain, i. e. increasing bonding interactions between the In+ cations due to the electron pair and its s‐p‐mixing. At ambient pressure In‐In interactions are rather weak and the space requirement of the lone electron pair mainly determines the characteristic arrangement of the ions. At elevated pressure the In‐In interactions become stronger and stabilise themselves additionally the specific structural arrangement.

Ligand close packing and the geometry of the fluorides of the nonmetals of periods 3, 4, and 5.

This paper discusses the geometry of the fluorides of the nonmetals of periods 3, 4, and 5 in terms of the ligand close packing (LCP) model according to which molecular geometry is determined primarily by ligand-ligand repulsions (Pauli closed shell repulsions) rather than by the bonding and lone pair Pauli repulsions of the VSEPR model. The LCP model becomes the dominant factor in determing geometry when the ligands are sufficiently crowded that they may be regarded as essentially incompressible. Ligand close packing is a modification of the VSEPR model in which ligand-ligand repulsion (Pauli closed shell repulsion) is given more emphasis than bonding and nonbonding electron pair Pauli repulsion. The nonmetals of period 3 are large enough to form octahedral six coordinated molecules in which the ligands are close packed. The larger nonmetals of period 4 also have a maximum coordination number of six and an octahedral geometry although the ligands are not close packed. Ligand radii derived from the interligand distances in the molecules of period 3 depend only on the charge of the fluorine ligands and are consistent with the previously derived radii obtained from the fluorides of the close packed tetrahedral molecules of the period 2 elements. Although the ligands in the molecules of the period 4 nonmetals are not close packed, these elements are not large enough to form molecules with a higher coordination number. However, the larger period 5 nonmetals may have coordination numbers of seven and eight. The seven coordinated molecules have a pentagonal bipyramidal geometry in which the equatorial ligands are close packed. The eight coordinated molecules have a square antiprism geometry, which is not a close packed geometry although the fluorine interligand distances are only a little larger than expected for close packing. The difference between the axial and equatorial bond lengths in the trigonal bipyramidal pentafluorides and the pentagonal bipyramidal pentafluorides can be understood on the basis of ligand close packing. Ligand packing prevents the lone pair in AF(6)E molecules from fully entering the valence shell and thereby exerting its full stereochemical effect so that these molecules have a C(3)(v)() distorted octahedral geometry rather than a geometry based on pentagonal bipyramidal seven coordination.

Importance of open-shell effects in adhesion at metal-ceramic interfaces

We demonstrate markedly enhanced adhesion between oxide ceramics and conducting metals via promoting open-shell electronic structure at the interface, by using a more covalent oxide or doping with early transition metals. Open-shell character suppresses closed-shell repulsions and permits local covalent and/or donor-acceptor bonding, even in the absence of a conventional reaction layer. The dramatic impact of such local bonding attractions, predicted from density-functional calculations, contradicts the idea of classical electrostatic forces dominating metal-oxide adhesion.

Lewis acidity of gallium halides.

The Lewis acidity of GaF(3), GaF(2)Cl, GaFCl(2), and GaCl(3) in acid-base interactions has been studied by taking ammonia as their electron-donating counterpart. We have derived an unoccupied reactive orbital that shows the maximum localization on the Ga atomic center for each species. The orbital is located lower in energy compared to those in the corresponding boron and aluminum halides. In contrast to boron halides, the unoccupied reactive orbital of the acid site tends to be delocalized considerably on the halogens as the fluorines are substituted by chlorines in gallium halides. The trend observed in the effects of fluorine and chlorine on the acidity of the gallium halides is opposite to those found in the boron halides. This cannot be interpreted solely in terms of the electron-accepting strength of the gallium center, but can be understood by including electrostatic interactions and closed-shell repulsion with ammonia in the adducts. The origin of the difference in Lewis acidity of BCl(3), AlCl(3), and GaCl(3) has been clarified.

Polarizable continuum model for lithium interface transitions between a liquid electrolyte and an intercalation electrode

A model is described and used to calculate the energy of lithium when crossing the interface between a liquid electrolyte and an electrode surface. The model is based on a classical treatment of the solute–solvent interactions in terms of a polarizable continuum model (PCM), and of the lithium crystal interactions by electrostatic (Madelung) energy calculations including short-range closed shell repulsion. In addition, the coupling of Li + with the charge compensating electron on a neighbour Mn 4+ site is taken into account. A first application of the model to the Li–Mn 2 O 4 (spinel) system shows that diffusion of Li from the surface to bulk of the electrode requires an activation energy, which is higher than the one for bulk diffusion. Surface charges, as deduced from electronegativity calculations are strongly reduced compared to the bulk ones. As a result, a barrier is also formed for the solvent to the surface Li + diffusion. On the basis of the calculated energy profiles we conclude that for Li/Mn 2 O 4 bulk diffusion is considerably faster than lattice incorporation. Our results are in qualitative agreement with fits of equivalent circuits to alternating current impedance measurements for Li + intercalation in cubic and layered TiS 2 and NiO 2 and potential jump kinetic experiments on Mn 2 O 4 :Li.

Theoretical Thermochemistry of Homolytic C−C and C−Cl Bond Dissociations in Unbranched Perchloroalkanes

Proper description of the dispersion interactions that attenuate the closed-shell repulsions among chlorine atoms in n-perchloroalkanes requires an accurate treatment of long-range electron correlation effects. The presently known density functionals, which do not correctly account for such effects, grossly underestimate thermodynamic stability of these molecules, yielding the standard enthalpy of C−C bond dissociation in n-C4Cl10 as low as 20 kcal/mol. In contrast, the predictions of the CBS-4 scheme fail to reproduce the weakening of the C−C bonds that is experimentally observed in the higher members of the CnCl2n+2 homologous series. For the CCl4 and C2Cl6 the most reliable estimates of and are provided by the G2 and G2MP2 methods. The MP2/6-311G** level of theory (without ZPEs and finite-temperature corrections) appears at present to be the only viable, though quite inaccurate, theoretical approach to theoretical thermochemistry of larger chlorocarbons. At that level of theory, is predicted to decrease by ca. 10 kcal/mol upon the addition of each −CCl2− unit, convincingly explaining the thermal lability of higher n-perchloroalkanes. Similar conclusions are reached by examining the estimates of derived from the CBS-4 standard enthalpies with the ECBS energy term excluded.

139La NMR Relaxation and Chemical Shift Studies in the Aqueous Nitrate and Chloride Solutions

139La NMR relaxations and chemical shifts in the aqueous nitrate and chloride solutions at 274−343 K were studied. The solutions in this study were La(NO3)3−LiNO3 or −HNO3, and LaCl3−LiCl3 or −HCl systems. The dependencies of the slope for the plot of 1/T1 (s-1) vs η/T (cP K-1) on the anion concentration showed that nitrate ions form inner-sphere complexes with lanthanum in a relatively low concentration but chloride ions scarcely form below about 4.3 mol/L. In the LaCl3−LiCl systems, the quadrupole coupling constants obtained by the temperature dependencies of 1/T1 below about 4.3 mol/L ranged from 3.1 to 3.4 MHz, which agreed well with the value of hydrated lanthanum. In the LaCl3−HCl systems, however, the quadrupole coupling constants slightly increased with an increase in chloride ion concentration even below about 4.3 mol/L, indicating that chloride ions possibly begin to form inner-sphere complexes. Activation energies for the rotational motion of lanthanum were determined in all of the solutions by the T1 analyses using the Arrhenius equation. The activation energies in the nitrate concentration range from 0 to 0.1 mol/L were about 14 kJ/mol and in that above 1 mol/L about 18 kJ/mol . On the basis of the quantitative analysis for the activation energies, these values were regarded as the energies for a breaking the hydrogen bond of H2O−H2O. While in the chloride ion systems, the activation energies gradually decreased above 0.6 mol/L, indicating that hydrated lanthanum ions are gradually removed from a net structure of the aqueous solution by being packed by chloride ions. Chemical shifts obtained from a series of experiments also showed that chloride ions do not form inner-sphere complexes with lanthanum below about 4.3 mol/L. Furthermore, the chloride ions induce downfield shifts and nitrate ions induce upfield relative to the value of hydrated lanthanum. It is likely that the downfield shifts in the chloride systems are due to the result of an overlapping closed-shell repulsion.

Electronic and structural properties of GaN by the full-potential linear muffin-tin orbitals method: The role of the d electrons.

The structural and electronic properties of cubic GaN are studied within the local density approximation by the full-potential linear muffin-tin orbitals method. The Ga $3d$ electrons are treated as band states, and no shape approximation is made to the potential and charge density. The influence of $d$ electrons on the band structure, charge density, and bonding properties is analyzed. It is found that due to the energy resonance of the Ga 3$d$ states with nitrogen 2$s$ states, the cation $d$ bands are not inert, and features unusual for a III-V compound are found in the lower part of the valence band and in the valence charge density and density of states. To clarify the influence of the Ga $d$ states on the cohesive properties, additional full and frozen--overlapped-core calculations were performed for GaN, cubic ZnS, GaAs, and Si. The results show, in addition to the known importance of non-linear core-valence exchange-correlation corrections, that an explicit description of closed-shell repulsion effects is necessary to obtain accurate results for GaN and similar systems. In summary, GaN appears to be somewhat exceptional among the III-V compounds and reminiscent of II-VI materials, in that its band structure and cohesive properties are sensitive to a proper treatment of the cation $d$ bands, as a result of the presence of the latter in the valence band range.

Effects of chemisorbed and substitutional 0, I, and II Ge, Sn, and Pb on CO adsorption on Pt(111): molecular orbital theory

Methanol oxidation rates on Pt anodes are increased by surface Sn adatoms apparently because of faster oxidation of CO, a surface poison, to CO 2. In an ASED-MO study using cluster models, Sn as well as Ge and Pb adatoms are found to reduce the chemisorption energy of CO at adjacent sites of Pt(111). Oxidation of these adatoms by OH only slightly reduces their effect on CO adsorption but oxidation by O nearly cancels it. When the atoms in their reduced and oxidized forms are placed substitutionally in the Pt surface they have very small effects on CO adsorption energies. The weakening caused by Sn adatoms stems in part from a CO4σ-Sn 5s closed-shell repulsion through the Pt surface atoms. The through-space repulsion is negligible. The weakening of the CO adsorption bond to Pt by Sn adatoms has been observed in recent high vacuum studies. During electrochemical oxidation of adsorbed CO this weakening may play a role, but other effects, such as the influence of Sn on the presence of active oxygen, need further examination.

Ethoxyacetylene and ethyl vinyl ether, dipolarophiles of opposite regiochemistry in diazomethane cycloadditions

Diazomethane adds to ethoxyacetylene to give a 96 : 4 mixture in favor of 4-ethoxypyrazole ( 3) which had been identified as the only product in a previous study. This result contrasts the behavior of ethyl vinyl ether which gives 3-ethoxy-1-pyrazoline ( 2). Transition structures for the four possible regioisomers are determined by MNDO-PM3 calculations. The regioselectivity is explained on the basis of the PM3 calculations and their perturbational analysis using the program PERVAL. Distortions of the dipolarophiles in the transition structures due to closed-shell repulsions lead to FMO interactions which favor the experimental regiochemistry.

Conformation study of helical main-group polymers: organic and inorganic, trans and gauche

In this paper electronic structures of some helical polymers, which range from typical organic polymers such as polyethylene and poly(oxymethylene) to standard inorganic polymers such as polymeric sulfur to main-group (P, B, etc.) atomic chains in crystals (such as NaP, CrB, etc.), have been investigated by means of our helical modifications of solid-state band theory programs based on modified neglect of diatomic overlap (MNDO) and extended Hueckel theory (EHT). The analysis of orbital interactions shows that the all-trans conformation for the polymer with either less or more than six valence electrons in the repeat unit is energetically favorable as compared with the gauche conformation while the polymers having valence electrons close to six in the repeat unit are more likely to be found in a gauche conformation, except for polyethylene and polysilane, for which both conformations are stable. The stability of all-trans-polyethylene and -polysilane is attributed to the weak repulsions between C-H and Si-H bonding electron pairs. A quadratic relationship between band width and the corresponding closed-shell repulsion for an energy band is established.

Segregation of substitutional bulk S to the Fe(100) surface and the Fe–Fe oxide interface: Molecular-orbital theory

A molecular-orbital study of the binding of S atoms in bulk iron and on the (100) surface is performed with ${\mathrm{Fe}}_{47}$ bulk and ${\mathrm{Fe}}_{41}$ surface cluster models to understand the commonly observed surface segregation of impurities. An atom-spin-polarization rule for ferromagnetic iron is suggested wherein each atom's contribution to the cluster-spin polarization is dependent on its coordination number. Its predictions are in satisfactory agreement with recent theoretically calculated values for Fe(100) and Fe(110) surfaces. The calculated binding energies are found to agree best with experiment when S is included in determining the Fe coordination number, thereby decreasing the spin polarization. The interaction of the filled S 3s orbital with occupied a-symmetry orbitals in a bulk substitutional site results in a closed-shell repulsion, while on the surface the S 3${p}_{z}$ orbital is symmetry allowed to mix with the S 3s orbital, reducing the repulsion. The S 3s orbital is largely responsible for sulfur bonding more strongly on the surface than to a bulk substitutional site; respective calculated values are 3.98 (4.20) eV and 3.10 eV, where the value in parentheses is experimental. Taking into account the predicted vacancy-formation energy of 0.79 eV, the calculated S dissolution energy 2.31 eV is close to the experimental value (2.56 eV). The difference, 1.67 eV, compares well with experimental estimates (1.64 and 1.71 eV). It is concluded that half of the S segregation energy is caused by the closed-shell repulsion and the other half by the bulk Fe-vacancy-formation energy. The fact that S dissolves substitutionally in Fe suggests an explanation for a recent experimental observation that S will not segregate to an Fe--Fe-oxide interface: doing so would break strong Fe-O bonds and might introduce repulsive ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$-${\mathrm{S}}^{2\mathrm{\ensuremath{-}}}$ interactions.