Bingel–Hirsch Addition of Diethyl Bromomalonate to Ion-Encapsulated Fullerenes M@C60 (M=Ø, Li+, Na+, K+, Mg2+, Ca2+, and Cl−)

In the last 30 years, fullerene-based materials have become popular building blocks for devices with a broad range of applications. Among fullerene derivatives, endohedral metallofullerenes (EMFs, M@C_x) have been widely studied owing to their unique properties and reactivity. For real applications, fullerenes and EMFs must be exohedrally functionalized. It has been shown that encapsulated metal cations facilitate the Diels–Alder reaction in fullerenes. Herein, the Bingel–Hirsch (BH) addition of ethyl bromomalonate over a series of ion-encapsulated M@C₆₀ (M=Ø, Li⁺, Na⁺, K⁺, Mg²⁺, Ca²⁺, and Cl⁻; Ø@C₆₀ stands for C₆₀ without any endohedral metal) is quantum mechanically explored to analyze the effect of these ions on the BH addition. The results show that the incarcerated ion has a very important effect on the kinetics and thermodynamics of this reaction. Among the systems studied, K⁺@C₆₀ is the one that leads to the fastest BH reaction, whereas the slowest reaction is given by Cl⁻@C₆₀.     

DFT calculations on the structural stability and infrared spectroscopy of endohedral metallofullerenes

Endohedral metallofullerenes M@C₂₄ (M = Li^0/+, Na^0/+, K^0/+, Be^0/2+, Mg^0/2+ and Ca^0/2+) with different spin configurations have been systematically investigated using the hybrid DFT-B3PW91 functional in conjunction with 6-31G(d) basis sets. Our theoretical studies show that Li@C₂₄, Be@C₂₄, Be²⁺@C₂₄, and Mg²⁺@C₂₄ are energetically favorable. In these endohedral metallofullerenes, only the encapsulated Be and Ca atoms can donate the electrons to the cage. With exception of Be²⁺@C₂₄, the energy gaps of other charged compounds are larger than that of corresponding neutral compounds. We also find that some endohedral metallofullerenes have high energy gaps, but they are unlikely to show high thermodynamic stability. Additionally, the vibrational frequencies and active infrared intensities are also used as evidence to identify these endohedral metallofullerenes.     

He2@C60: Thoughts of the concept of a molecule and of the concept of a bond in quantum chemistry

We present a broad palette of discussions of the concepts of a molecule and a chemical bond that always lay down behind all computational modeling in quantum chemistry and of the endohedral fullerene He₂@C₆₀ in particular. For this purpose, we offer the definition of quantum chemistry as composed of three ingredients. Each of them is illustrated by its particular concept, either that of a molecule or a bond. The third, computational ingredient is tackled to resolve the bonding manifold of He₂@C₆₀ and to demonstrate that van‐der‐Waals binding of He? He is converted within He₂@C₆₀ into a stronger bond due to that C₆₀ acts as an electronic buffer and [He₂] moiety mimics a fractionally charged . Experimental fingerprints of He₂@C₆₀ are computed. © 2015 Wiley Periodicals, Inc.     

First Synthesis and Characterization of CH4@C60

The endohedral fullerene CH₄@C₆₀, in which each C₆₀ fullerene cage encapsulates a single methane molecule, has been synthesized for the first time. Methane is the first organic molecule, as well as the largest, to have been encapsulated in C₆₀ to date. The key orifice contraction step, a photochemical desulfinylation of an open fullerene, was completed, even though it is inhibited by the endohedral molecule. The crystal structure of the nickel(II) octaethylporphyrin/ benzene solvate shows no significant distortion of the carbon cage, relative to the C₆₀ analogue, and shows the methane hydrogens as a shell of electron density around the central carbon, indicative of the quantum nature of the methane. The ¹H spin‐lattice relaxation times (T₁) for endohedral methane are similar to those observed in the gas phase, indicating that methane is freely rotating inside the C₆₀ cage. The synthesis of CH₄@C₆₀ opens a route to endofullerenes incorporating large guest molecules and atoms.     

Identification of the Most Stable Sc2C80 Isomers: Structure,Electronic Property,and Molecular Spectra Investigations

A systematic density functional theory investigation has been carried out to explore the possible structures of Sc₂C₈₀ at the BMK/6‐31G(d) level. The results clearly show that Sc₂@C₈₀‐I_h, Sc₂@C₈₀‐D_5h, and Sc₂C₂@C₇₈‐C_2v can be identified as three isomers of Sc₂C₈₀ metallofullerene with the lowest energy. Frontier molecular orbital analysis indicates that the two Sc₂@C₈₀ isomers have a charge state as (Sc³⁺)₂@C₈₀^6?and the Sc₂C₂@C₇₈ has a charge state of (Sc³⁺)₂C₂^2?@C₇₈^4?. Moreover, the metal‐cage covalent interactions have been studied to reveal the dynamics of endohedral moiety. The vertical electron affinity, vertical ionization potential, infrared spectra and ¹³C nuclear magnetic resonance spectra have been also computed to further disclose the molecular structures and properties.     

Effect of substitution on the bonding in He dimer confined within dodecahedrane: A computational study

The effect of substitution in the dodecahedrane (C₂₀H₂₀) cage on bonding in the confined He dimer is analyzed. The He He distances inside the halogenated dodecahedrane C₂₀X₂₀ (X = F Br) cages are found to be less than half of that in the free He dimer. Comparing the equilibrium structure of He₂@C₂₀H₂₀ with He₂@C₂₀X₂₀ at ωB97XD/def2-TZVPP level, it is found that the He-He distances are relatively larger in the latter cases indicating the influence of halogen groups on the interaction between the cage and the trapped He pair. The viability of the He₂@C₂₀X₂₀ complexes is reflected in the presence of a very high activation energy barrier against the thermochemically feasible dissociation process producing free He₂ and C₂₀X₂₀. Quantum theory of atoms in molecules (QTAIM) approach reveals a partial covalent interaction between He pair.     

La2@Cs(17 490)‐C76: A New Non‐IPR Dimetallic Metallofullerene Featuring Unexpectedly Weak Metal–Pentalene Interactions

Although all the pure‐carbon fullerene isomers above C₆₀ reported to date comply with the isolated pentagon rule (IPR), non‐IPR structures, which are expected to have different properties from those of IPR species, are obtainable either by exohedral modification or by endohedral atom doping. This report describes the isolation and characterization of a new endohedral metallofullerene (EMF), La₂@C₇₆, which has a non‐IPR fullerene cage. The X‐ray crystallographic result for the La₂@C₇₆/[Ni^II(OEP)] (OEP=octaethylporphyrin) cocrystal unambiguously elucidated the C_s(17 490)‐C₇₆ cage structure, which contains two adjacent pentagon pairs. Surprisingly, multiple metal sites were distinguished from the X‐ray data, which implies dynamic behavior for the two La³⁺ cations inside the cage. This dynamic behavior was also corroborated by variable‐temperature ¹³⁹ La NMR spectroscopy. This phenomenon conflicts with the widely accepted idea that the metal cations in non‐IPR EMFs invariably coordinate strongly with the negatively charged fused‐pentagon carbons, thereby providing new insights into modern coordination chemistry. Furthermore, our electrochemical and computational studies reveal that La₂@C_s(17 490)‐C₇₆ has a larger HOMO–LUMO gap than other dilanthanum‐EMFs with IPR cage structures, such as La₂@D_3h(5)‐C₇₈ and La₂@I_h(7)‐C₈₀, which implies that IPR is no longer a strict rule for EMFs.     

Molecular modeling of hydration properties of hydrophobic ions Li<Superscript>+</Superscript>@C<Subscript>60</Subscript> and K<Superscript>+</Superscript>@C<Subscript>60</Subscript>

The Gibbs free energies of solvation (ΔG _s) and the electronic structures of endohedral metallofullerenes M⁺@C₆₀ (M⁺= Li⁺, K⁺) were calculated within the framework of the density functional theory and the polarizable continuum model. In water environment, the equilibrium position of K⁺ is at the center of the fullerene cavity whereas that of Li⁺ is shifted by 0.14 nm toward the fullerene cage. The Li⁺ cation is stabilized by interactions with both the fullerene and solvent. The equilibrium structures of both endohedral metallofullerenes are characterized by very close ΔG _s values. In particular, the calculated ΔG _s values for K⁺@C₆₀ are in the range from −124 to −149 kJ mol⁻¹ depending on the basis set and on the type of the density functional. Molecular dynamics simulations (TIP3P H₂O, OPLS force field, water sphere of radius 1.9 nm) showed that the radial distribution functions of water density around C₆₀ and M⁺@C₆₀ are very similar, whereas orientations of water dipoles around the endohedral metallofullerenes resemble the hydration pattern of isolated metal ions.     

Bonding in Endohedral Metallofullerenes as Studied by Quantum Theory of Atoms in Molecules

Metal–cage and intracluster bonding was studied in detail by quantum theory of atoms in molecules (QTAIM) for the four major classes of endohedral metallofullerenes (EMFs), including monometallofullerenes Ca@C₇₂, La@C₇₂, M@C₈₂ (M=Ca, Sc, Y, La), dimetallofullerenes Sc₂@C₇₆, Y₂@C₈₂, Y₂@C₇₉N, La₂@C₇₈, La₂@C₈₀, metal nitride clusterfullerenes Sc₃N@C_2n (2n=68, 70, 78, 80), Y₃N@C_2n (2n=78, 80, 82, 84, 86, 88), La₃N@C_2n (2n=88, 92, 96), metal carbide clusterfullerenes Sc₂C₂@C₆₈, Sc₂C₂@C₈₂, Sc₂C₂@C₈₄, Ti₂C₂@C₇₈, Y₂C₂@C₈₂, Sc₃C₂@C₈₀, as well as Sc₃CH@C₈₀ and Sc₄O_x@C₈₀ (x=2, 3), that is, 42 EMF molecules and ions in total. Analysis of the delocalization indices and bond critical point (BCP) indicators such as G_bcp/ρ_bcp, H_bcp/ρ_bcp, and |V_bcp|/G_bcp, revealed that all types of bonding in EMFs exhibit a high degree of covalency, and the ionic model is reasonable only for the Ca‐based EMFs. Metal–metal bonds with negative values of the electron‐density Laplacian were found in Y₂@C₈₂, Y₂@C₇₉N, Sc₄O₂@C₈₀, and anionic forms of La₂@C₈₀. A delocalized nature of the metal–cage bonding results in a topological instability of the electron density in EMFs with an unpredictable number of metal–cage bond paths and large elipticity values.     

Synthese,Kristallstruktur und thermischer Abbau von Mg(H2O)6[B12H12] · 6 H2O

Synthesis, Crystal Structure, and Thermal Decomposition of Mg(H₂O)₆[B₁₂H₁₂] · 6 H₂O By reaction of an aqueous solution of the free acid (H₃O)₂[B₁₂H₁₂] with MgCO₃ and subsequent isothermic evaporation of the resulting solution to dryness, colourless, bead‐shaped single crystals of the dodecahydrate of magnesium dodecahydro closo‐dodecaborate Mg(H₂O)₆[B₁₂H₁₂] · 6 H₂O (cubic, F4₁32; a = 1643.21(9) pm, Z = 8) emerge. The crystal structure is best described as a NaTl‐type arrangement in which the centers of gravity of the quasi‐icosahedral [B₁₂H₁₂]^2— anions (d(B—B) = 178—180 pm, d(B—H) = 109 pm) occupy the positions of Tl^— while the Mg²⁺ cations occupy the Na⁺ positions. A direct coordinative influence of the [B₁₂H₁₂]^2— units at the Mg²⁺ cations is however not noticeable. The latter are octahedrally coordinated by six water molecules forming isolated hexaaqua complex cations [Mg(H₂O)₆]²⁺ (d(Mg—O) = 206 pm, 6×). In addition, six “zeolitic” water molecules are located in the crystal structure for the formation of a strong O—H^δ+···^δ—O‐hydrogen bridge‐bonding system. The evidence of weak B—H^δ—···^δ+H—O‐hydrogen bonds between water molecules and anionic [B₁₂H₁₂]^2— clusters is also considered. Investigations on the dodecahydrate Mg[B₁₂H₁₂] · 12 H₂O (≡ Mg(H₂O)₆[B₁₂H₁₂] · 6 H₂O) by DTA/TG measurements showed that its dehydration takes place in two steps within a temperature range of 71 and 76 °C as well as at 202 °C, respectively. Thermal treatment eventually leads to the anhydrous magnesium dodecahydro closo‐dodecaborate Mg[B₁₂H₁₂].     

Theoretical study of association of acetylene,benzene, and carbonyl molecules “squeezed” inside fullerene cages

The equilibrium geometries, normal mode frequencies, magnetic shielding constants, and energetic characteristics of model endohedral 2(C₂H₂)@C₇₀, (C₄H₄)@C₇₀, 2(C₆H₆)C₈₄, (C₁₂H₁₂)@C₈₄, 6(CO)@C₈₄, and (C₆O₆)@C₈₄ clusters, mimicking the structure and properties of the guest molecules under “ultrahigh” pressures inside the fullerene cages, were calculated at the density functional theory B3LYP/6-31G and B3LYP/6-31G* levels. According to the calculations, all the structures under consideration correspond to local minima of the corresponding potential energy surfaces. The 2(C₂H₂)@C₇₀ isomer with two separated endohedral acetylene molecules turns out to be considerably less favorable than the (C₄H₄)@C₇₀ isomer with endohedral cyclobutadiene. The 2(C₆H₆)C₈₄ isomer with two separated endohedral benzene rings is almost 30 kcal/mol less favorable than the (C₁₂H₁₂)@C₈₄) isomer with distorted endohedral prismane. The 6(CO)@C₈₄ isomer with six separated carbonyl molecules is almost 45 kcal/mol less favorable than the (C₆O₆)@C₈₄ isomer in which the carbonyls are associated to form a more compact cyclic hexamer C₆O₆. The barriers separating the “associated” and “dissociated” (consisting of monomers) isomers are estimated at 10–15 kcal/mol. Calculations show that, in extremely tight endoclusters, the increase in compression and strain energy caused by the repulsion of the electronic shells of guest molecules and wall atoms is accompanied by a sharp energetic stabilization of compact associated isomers (including those poorly stable or unstable in the free state) as compared with the dissociated isomers, on the one hand, and by a sharp decrease in activation barriers, on the other hand. Both factors should favor the realization of association processes unlikely or impossible under common conditions.     

Synthesis and Isolation of the Titanium–Scandium Endohedral Fullerenes—Sc2TiC@Ih‐C80, Sc2TiC@D5h‐C80 and Sc2TiC2@Ih‐C80: Metal Size Tuning of the TiIV/TiIII Redox Potentials

The formation of endohedral metallofullerenes (EMFs) in an electric arc is reported for the mixed‐metal Sc–Ti system utilizing methane as a reactive gas. Comparison of these results with those from the Sc/CH₄ and Ti/CH₄ systems as well as syntheses without methane revealed a strong mutual influence of all key components on the product distribution. Whereas a methane atmosphere alone suppresses the formation of empty cage fullerenes, the Ti/CH₄ system forms mainly empty cage fullerenes. In contrast, the main fullerene products in the Sc/CH₄ system are Sc₄C₂@C₈₀ (the most abundant EMF from this synthesis), Sc₃C₂@C₈₀, isomers of Sc₂C₂@C₈₂, and the family Sc₂C_{2 n} (2 n=74, 76, 82, 86, 90, etc.), as well as Sc₃CH@C₈₀. The Sc–Ti/CH₄ system produces the mixed‐metal Sc₂TiC@C_{2 n} (2 n=68, 78, 80) and Sc₂TiC₂@C_{2 n} (2 n=80) clusterfullerene families. The molecular structures of the new, transition‐metal‐containing endohedral fullerenes, Sc₂TiC@I_h‐C₈₀, Sc₂TiC@D_5h‐C₈₀, and Sc₂TiC₂@I_h‐C₈₀, were characterized by NMR spectroscopy. The structure of Sc₂TiC@I_h‐C₈₀ was also determined by single‐crystal X‐ray diffraction, which demonstrated the presence of a short Ti=C double bond. Both Sc₂TiC‐ and Sc₂TiC₂‐containing clusterfullerenes have Ti‐localized LUMOs. Encapsulation of the redox‐active Ti ion inside the fullerene cage enables analysis of the cluster–cage strain in the endohedral fullerenes through electrochemical measurements.     

Do Carbon Nano-onions Behave as Nanoscopic Faraday Cages? A Comparison of the Reactivity of C60, C240, C60@C240, Li+@C60, Li+@C240, and Li+@C60@C240

From the analysis of the polarizability of carbon nano-onions (CNOs), it was concluded that CNOs behave as near perfect nanoscopic Faraday cages. If CNOs behave as ideal Faraday cages, the reactivity of the C₂₄₀ cage should be the same in Li⁺@C₂₄₀ and Li⁺@C₆₀@C₂₄₀. In this work, the Diels–Alder reaction of cyclopentadiene to the free C₂₄₀ cage and the C₆₀@C₂₄₀ CNO together with their Li⁺-doped counterparts were analyzed using DFT. It was found that in all cases the preferred cycloaddition is on bond [6,6] of type B of C₂₄₀. Encapsulation of Li⁺ results in lower enthalpy barriers due to the decrease of the energy of the LUMO orbital of the C₂₄₀ cage. When the Li⁺ is placed inside the CNO C₆₀@C₂₄₀, the decrease in enthalpy barrier is similar to that of Li⁺@C₂₄₀. However, the location of Li⁺ in Li⁺@C₂₄₀ (off-centered) and Li⁺@C₆₀@C₂₄₀ (centered) is quite different. When Li⁺ was placed in the center of the C₂₄₀ cage in Li⁺@C₂₄₀, the barriers increased significantly. Taking into account this effect, the barriers in Li⁺@C₂₄₀ and Li⁺@C₆₀@C₂₄₀ differ by about 4 kcal mol⁻¹. This result can be attributed to the shielding effect of C₆₀ in Li⁺@C₆₀@C₂₄₀. As a result, we conclude that this CNO does not act as a perfect Faraday cage.     

Préparation du complexe endoédrique hydrogène moléculaire fullerène C60, associé à du C60 hydrogéné

Preparation of endohedral complexes of molecular hydrogen-fullerene C_60, together with hydrogenated C₆₀. Using our new method described elsewhere, we have obtained the preparation of endohedral complexes H₂@C₆₀, together with hydrogenated C₆₀. Analyses by ¹H NMR, and by infrared and vacuum ultraviolet spectroscopies have been carried out, which proved the existence of these two kinds of compounds in our samples. A quantitative measurement has been done, giving values for the endohedral complexes of about 18%, and for the hydrogenated C₆₀ of about 35%. To cite this article: B. Oksengorn, C. R. Chimie 6 (2003).     

Unsupported Mg–Alkene Bonding

The first intermolecular early main group metal–alkene complexes were isolated. This was enabled by using highly Lewis acidic Mg centers in the Lewis base-free cations (^MeBDI)Mg⁺ and (^tBuBDI)Mg⁺ with B(C₆F₅)₄⁻ counterions (^MeBDI=CH[C(CH₃)N(DIPP)]₂, ^tBuBDI=CH[C(tBu)N(DIPP)]₂, DIPP=2,6-diisopropylphenyl). Coordination complexes with various mono- and bis-alkene ligands, typically used in transition metal chemistry, were structurally characterized for 1,3-divinyltetramethyldisiloxane, 1,5-cyclooctadiene, cyclooctene, 1,3,5-cycloheptatriene, 2,3-dimethylbuta-1,3-diene, and 2-ethyl-1-butene. In all cases, asymmetric Mg–alkene bonding with a short and a long Mg−C bond is observed. This asymmetry is most extreme for Mg–(H₂C=CEt₂) bonding. In bromobenzene solution, the Mg–alkene complexes are either dissociated or in a dissociation equilibrium. A DFT study and AIM analysis showed that the C=C bonds hardly change on coordination and there is very little alkene→Mg electron transfer. The Mg–alkene bonds are mainly electrostatic and should be described as Mg²⁺ ion-induced dipole interactions.     

[C5Li5]Mgn[C5Li5] (n?=?2–8): novel sandwich complexes containing –Mg–Mg– chain

A density functional theory (DFT) investigation on novel sandwich-type D ₅ [C₅Li₅]Mg _n [C₅Li₅] (n = 2–8) complexes containing –Mg–Mg– chain has been performed in this work. The equilibrium geometries, electronic structures, vibrational frequencies, and stabilities of these complexes are researched by B3LYP and BP86 methods at 6-311+G(d) levels of theory. The Mg _n ²⁺ sandwich complexes with D ₅ symmetry are all true minima on the potential energy surface. NBO analyses for the series of complexes reveal that the Mg–Mg bond is a weak σ covalent bond. There are mainly electrostatic interactions between C₅Li₅ ⁻ ligands and Mg _n ²⁺(n = 2–8) nuclear in these complexes. The NICS and NICS_zz computed with GIAO-B3LYP/6-311+G(d) indicates that the C₅Li₅ ⁻ rings in the series of complexes are aromatic. These novel complexes turn out to be strongly thermodynamically favored in the gas phases and may be targeted in future experiments to expand the structural domain of sandwich-type complexes.     

A computational study of the endohedral fullerene GeH4@C60

The structures, stabilities, and electronic properties of the endohedral fullerene GeH₄@C₆₀ have been systematically studied by using the hybrid DFT-B3PW91 functional in conjunction with 6-31G(d) basis sets. Our calculated results show that the GeH₄ molecule is more compact in the center of the C₆₀ cage and exists in molecular form inside the fullerene. The Zero-Point and BSSE corrected binding energy of GeH₄@C₆₀ is −1.77 eV. The calculated HOMO–LUMO energy gap, the vertical ionization potentials (VIP) and vertical electron affinities (VEA) are similar to that of C₆₀ cage. It is indicated that GeH₄@C₆₀ also seems to be very stable species. Natural population analysis on the GeH₄@C₆₀ reveals that the central GeH₄ only gain −0.06 charges from the C₆₀ cage. Additionally, the vibrational frequencies and active infrared intensities of GeH₄@C₆₀ are also discussed.     

Quantum chemical topology: The electronic structure of the alkaline nitrites MONO (M = Li,Na, K) studied by means of topological analysis of the electron localization function

In the search of the protocovalent bonding, previously recognized in the nitrous acid (HONO), a nature of the chemical bonds in the alkaline nitrites MONO (M = Li, Na, K) has been studied by means of the topological analysis of the Electron Localization Function (ELF) and Electron Localizability Indicator (ELI‐D). Calculations carried out with the B3LYP and MP2(full) methods, in conjunction with the aug‐cc‐pVTZ and 6‐311++G(3df,3pd) basis sets, revealed the cis (C_2v, more stable) and trans (C_s) isomers as minima on PES. Alkaline nitrites consist of the alkali metal cation M^δ+ interacting, mainly via electrostatic forces, with the nitrite anion [ONO]^δ− (δ ≈ 1e). The covalent N O bonds are characterized by disynaptic basins V(N,O) with the basin populations: 1.58÷1.62e for cis‐M^δ+[ONO]^δ− but 1.39÷1.49e for single N O bond and 1.81÷1.87e for formally double NO bond in trans M^δ+[O NO]^δ−. The protocovalent nitrogen–oxygen bond has not been observed. The N O bonds are slightly polarized towards the nitrogen atom with the polarity index p_NO ≤ 0.12. Two different sets of the hybrid (Lewis) structures are compared leading to different pictures of the bonding. According to NBO data there is a delocalization between the single N O and double NO type bonds, meanwhile results of the ELF analysis emphasize an electron delocalization between the single N O and ionic O⁻N⁺ hybrids. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Site Preference of Cations and Structural Variation in MgAl2–xGaxO4 (0 ≤ x ≤ 2) Spinel Solid Solution

The crystal structures of MgAl_2–xGa_xO₄ (0 ≤ x ≤ 2) spinel solid solutions (x = 0.00, 0.38, 0.76, 0.96, 1.52, 2.00) were refined using ²⁷Al MAS NMR measurements and single crystal X‐ray diffraction technique. Site preferences of cations were investigated. The inversion parameter (i) of MgAl₂O₄ (i = 0.206) is slightly larger than given in previous studies. It is considered that the difference of inversion parameter is caused by not only the difference of heat treatment time but also some influence of melting with a flux. The distribution of Ga³⁺ is little affected by a change of the temperature from 1473 K to 973 K. The degree of order‐disorder of Mg²⁺ or Al³⁺ between the fourfold‐ and sixfold‐coordinated sites is almost constant against Ga³⁺ content (x) in the solid solution. A compositional variable of the Ga/(Mg + Ga) ratio in the sixfold‐coordinated site has a constant value through the whole compositional range: the ratio is not influenced by the occupancy of Al³⁺. The occupancy of Al³⁺ is independent of the occupancy of Ga³⁺, though it depends on the occupancy of Mg²⁺ according to thermal history. The local bond lengths were estimated from the refined data of solid solutions. The local bond length between specific cation and oxygen corresponds with that expected from the effective ionic radii except local Al–O bond length in the fourfold‐coordinated site and local Mg–O bond length in the sixfold‐coordinated site. The local Al–O bond length in the fourfold‐coordinated site (1.92 Å) is about 0.15 Å longer than the expected bond length. This difference is induced by a difference in site symmetry of the fourfold‐coordinated site. The nature that Al³⁺ in spinel structure occupies mainly the sixfold‐coordinated site arises from the character of Al³⁺ itself. The local Mg–O bond length in the sixfold‐coordinated site (2.03 Å) is about 0.07 Å shorter than the expected one. Difference Fourier synthesis for MgGa₂O₄ shows a residual electron density peak of about 0.17 e/ų in height on the center of (Ga_0.59 Mg_0.41)–O bond. This peak indicates the covalent bonding nature of Ga–O bond on the sixfold‐coordinated site in the spinel structure.