Substituent effect on local aromaticity in mono and di‐substituted heterocyclic analogs of naphthalene

A quantitative study on local aromaticity has been performed on a series of mono‐ and di‐substituted biheterocycles (quinoline, isoquinoline, quinoxaline, quinazoline). Three electronically based indices (PDI, ATI, and FLU) have been employed to investigate the substituent effect on the π‐electron delocalization in both heterocycle and benzenoid rings. Three typical substituents (Cl, OCH₃, and CN) with different inductive and resonance power have been selected. Generally, substituent causes a reduction in aromaticity irrespective of whether it is electron attracting or electron donating. It is shown that the maximum aromaticity exhibits a similar trend of Cl > CN > OCH₃ for all the studied rings. Moreover, it is found that the substituent situation with respect to the heteroatom has a significant influence on the aromaticity. It results from our study that in di‐substituted derivatives, irrespective of whether the two substituents form a meta or para isomer, they preferably choose the position which leads to the maximum aromaticity character. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical investigation of an unusual substituent effect on the dienophilicity of >CP? functionality present in 2‐phosphaindolizines

Effect of the number and positions of the methoxycarbonyl substituents in 2‐phosphaindolizine on the feasibility of its Diels–Alder (DA) reaction with 1,3‐butadiene has been investigated theoretically at the density functional theory (DFT) level. Among the series of four differently substituted 2‐phosphaindolizines, 3‐methoxycarbonyl‐2‐phosphaindolizine does not undergo the DA reaction due to the highest activation barrier (29.49 kcal mol^?1) and endothermicity, whereas the activation barrier of the corresponding reaction of 1,3‐bis(methoxycarbonyl)‐2‐phosphaindolizine is lowest (22.43 kcal mol^?1) with exothermicity making it possible to occur. This reactivity trend is corroborated by FMO energy gaps as well as by global electrophilicity powers of the reactants. Copyright © 2008 John Wiley & Sons, Ltd.     

Substituent effect investigation of 3‐(2, 4‐dichlorophenyl)‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one. Part 1. Correlation analysis of 13C NMR chemical shifts

A series of substituted chlorinated chalcones namely, 3‐(2,4‐dichlorophenyl)‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one, have been synthesized, X being H, NH₂, OMe, Me, F, Cl, CO₂Et, CN, and NO₂. Dual substituent parameter (DSP) models of ¹³C NMR chemical shift (CS) have revealed that π‐polarization concept could be utilized to explain the reverse field effect at CO, the enhanced substituent field effect at CO, C‐2, and C‐5, and the decreased sensitivity of substituent field effect at C‐6. Chlorine atoms dipole direction at the benzylidene ring either enhances or reduces substituent effect depending on how they couple with the substituent dipole at the probe site. The correlation of ¹³C NMR CS of C‐2, C‐5, and C‐6 with σ and σ indicates that chlorine atoms in the benzylidine ring deplete the ring from charges. Both MSP of Hammett and DSP of Taft ¹³C NMR CS models give similar trends of substituent effects at C‐2, C‐5, and C‐6. However, the former fail to give a significant correlation for CO and C‐6 ¹³C NMR CS. MSP of σ_q and DSP of Taft and Reynolds models significantly correlated ¹³C NMR CS of C_β. MSP of σ_q fails to correlate C‐1′ ¹³C NMR CS. Investigation of ¹³C NMR CS of non‐chlorinated chalcones series: 3‐phenyl‐1‐(4′‐X‐phenyl)‐2‐propen‐1‐one has revealed similar trends of substituent effects as in the chlorinated chalcones series for C‐1′, CO, C_α, and C_β. In contrast, the substituent effect of the non‐chlorinated chalcone series at C‐2, C‐5, and C‐6 did not correlate with any substituent constant. Copyright © 2010 John Wiley & Sons, Ltd.     

The β‐silicon effect. 4: substituent effects on the solvolysis of 1‐alkyl‐2‐(aryldimethylsilyl)ethyl trifluoroacetates

Solvolysis rates of 2‐(aryldimethylsilyl)‐1‐methylethyl and 2‐(aryldimethylsilyl)‐1‐tert‐butylethyl trifluoroacetates were determined conductimetrically in 60% (v/v) aqueous ethanol. The effects of aryl substituents at the silicon atom on the solvolysis rates at 50 °C were correlated with parameters of r⁺ = 0.15 with the Yukawa–Tsuno equation, giving ρ values of ?1.5 for both secondary α‐Me and α‐tert‐Bu systems. The ρ values for those secondary systems are less negative than ?1.75 for the 2‐(aryldimethylsilyl)ethyl system that proceeds by the Eaborn (non‐vertical) mechanism, while they are distinctly more negative than ?0.99 for 2‐(aryldimethylsilyl)‐1‐phenylethyl system that should proceed by the Lambert (vertical) mechanism. There was a fairly linear relationship between the reaction constants (ρ) for the β‐silyl substituent effects and the solvolysis reactivities for a series of β‐silyl substrates. The solvolyses of the α‐Me and tert‐Bu substrates proceed through the transition state (TS) with an appreciable degree of the β‐silyl participation, close to the Eaborn (non‐vertical) TS rather than to the Lambert (vertical) TS. Copyright © 2010 John Wiley & Sons, Ltd.     

Transmission of polar substituent effects across the cubane ring system: 19F substituent chemical shifts (SCS) of 4‐substituted (X) cub‐1‐yl fluorides revisited

¹⁹F NMR shieldings of 4‐substituted (X) cub‐1‐yl fluorides ( 4 ) for a set of substituents (X?H, NO₂, CN, NC, CF₃, COOH, F, Cl, HO, NH₂, CH₃, Si(CH₃)₃, Li, O^? and NH) covering a wide range of electronic substituent effects were calculated using the DFT‐GIAO theoretical model. The level of theory, B3LYP/6‐311+G(2d,p), provided ¹⁹F substituent chemical shifts (SCS) in good agreement with experimental values where known. By means of NBO analysis, various molecular parameters were obtained from the optimized geometries. Linear regression analysis was employed to explore the relationship between the calculated ¹⁹F SCS and polar field, resonance and group electronegativity substituent constants (σ_F, σ_R and σ_x, respectively) and also the NBO derived molecular parameters (fluorine natural charges (Q_n), electron occupancies on fluorine of lone pairs (n_F) and occupation number of the C? F antibonding orbital (σ_CF*)). The key determining parameters appear to be n_F and σ_CF*(occup). Both factors are a function of the electrostatic field influence of the substituent (σ_F effect) but are counteractive in their influence on the shifts. No evidence for a significant resonance effect influence on the shifts could be identified. Copyright © 2009 John Wiley & Sons, Ltd.     

A computational study (DFT,MP2, and GIAO‐DFT) of substituent effects on protonation regioselectivity in β,β‐disubstituted vinyldiazonium cations: formation of highly delocalized carbenium/diazonium dications

Protonation reactions were studied by quantum‐chemical theoretical methods (DFT and MP2) for a series of β,β‐disubstituted vinyldiazonium cations ( 1 ⁺ – 14 ⁺ ), bearing stabilizing electron‐releasing groups (H₃CO? , (H₃C)₂N? , H₃C? , (H₃C)₃Si? , as well as halogens F, Cl). Taking into account the various mesomeric forms that these species can represent, protonations at C_α, at the β‐substituent, and at N_β were considered. The energetically most favored pathway in all cases was C_α protonation, which formally corresponds to trapping of the mesomeric diazonium ylid. Based on the computed properties (optimized geometries, NPA‐charge densities, and multinuclear GIAO‐NMR chemical shifts), the resulting dications can best be viewed as carbenium/diazonium dications, in which the carbocation is further delocalized into the β‐substituent. For the α‐nitro derivative 15 , protonation of the nitro group was predicted to be the most favored reaction, while C_α‐ and N_β‐protonation resulted in the loss of the nitronium ion. Copyright © 2009 John Wiley & Sons, Ltd.     

Substituent effects in the Baeyer–Villiger reaction of acetophenones: a theoretical study

This paper reports the first complete theoretical study of substituent effects on the mechanism of the Baeyer– Villiger (BV) reaction in non‐polar solvents taking into account the lowest‐energy mechanism that has been proposed for this rearrangement which is non‐ionic and fully concerted. The BV reaction of p‐substituted acetophenones, p‐XC₆H₄COCH₃ (X = NO₂, CN, H, CH₃, OCH₃), with performic (PFA) and trifluoroperacetic (TFPAA) acids, catalyzed by formic (FA) and trifluoroacetic (TFAA) acids, respectively, using the MPWB1K functional and the 6‐311G(d,p) and 6‐311++G(d,p) basis sets, are studied. Solvent effects are taken into account by means of the PCM continuum model using dichloromethane as solvent. Electron‐donating substituents on the aryl group have a relatively small activation effect on the first step, but a pronounced activation effect on the second to the point of being able to change the rate‐determining step (RDS) of the reaction, as observed in the case of p‐methoxyacetophenone with TFPAA acids. After analyzing the changes in Gibbs free energy of activation, geometrical parameters, and charge distributions of the transition states (TSs), explanations are provided for the two distinct effects that substituents on the ketone have on the kinetics of the addition and migration steps of the BV oxidation. The effect of the acid/peracid pair used is also discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

UV filter 2‐ethylhexyl 4‐methoxycinnamate: a structure,energetic and UV–vis spectral analysis based on density functional theory

2‐Ethylhexyl 4‐methoxycinnamate (EHMC) is a very commonly used UVB filter that is known to isomerize from the (E) to the (Z) isomer in the presence of light. In this study, we have performed high level quantum chemical calculations using density functional theory (DFT) with the B3LYP density functional and extended basis sets to study the gas‐phase molecular structure of EHMC and its energetic stability. Calculations were also performed for related smaller molecules cinnamic acid and 4‐methoxycinnamic acid. Charge delocalization has been analyzed using natural charges and Wiberg bond indexes within the natural bond orbital analysis and using nucleus independent chemical shifts. Density functional theory calculations reveal that the (E) isomer of EHMC is more stable than the (Z) by about 20 kJ mol^?1 in both the gas and aqueous phases. The enthalpy of formation in the gas phase of (E)‐EHMC was derived from an isodesmic bond separation reaction. Long‐range corrected DFT calculations in implicit water were made in order to understand the excited state properties of the (E) and (Z) isomers of EHMC. Copyright © 2013 John Wiley & Sons, Ltd.     

Calculated polar substituent effects on the stability of 4‐substituted(X) ‐ cub‐1‐yl and ‐bicyclo[2.2.2]oct‐1‐yl cations: a DFT study

The effects of substituents on the stability of 4‐substituted(X) cub‐1‐yl cations ( 2 ), as well as the benchmark 4‐substituted(X) bicyclo[2.2.2]oct‐1‐yl cation systems ( 7 ), for a set of substituents (X = H, NO₂, CN, NC, CF₃, COOH , F, Cl, HO, NH₂, CH₃, SiH₃, Si(CH₃)₃, Li, O^?, and NH) covering a wide range of electronic substituent effects were calculated using the DFT theoretical model at the B3LYP/6‐311 + G(2d,p) level of theory. Linear regression analysis was employed to explore the relationship between the calculated relative hydride affinities (ΔE, kcal/mol) of the appropriate isodesmic reactions for 2 / 7 and polar field/group electronegativity substituent constants (σ_F and σ_χ, respectively). The analysis reveals that the ΔE values of both systems are best described by a combination of both substituent constants. This highlights the distinction between through‐space and through‐bond electronic influences characterized by σ_F and σ_χ, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Tuning the absorption spectra and nonlinear optical properties of D‐π‐A azobenzene derivatives by changing the dipole moment and conjugation length: a theoretical study

The optical properties of several azobenzene derivatives were modulated by varying the dipole moments and conjugation lengths of the D‐π‐A systems. The relationship between the structure and absorption spectrum and polarizability was studied in the gas phase, THF and MeOH solutions, respectively, by using the density functional theory. The calculated absorption spectra and second‐order polarizabilities are in good agreement with the available experimental observations. In comparison with the D‐π‐A monomer, the H‐shaped D‐π‐A dimer almost doubles the dipole moments and hence increases the second‐order polarizabilities, without a significant shift in the maximum absorption bands. The addition of another azobenzol group between electron‐donating and ‐accepting groups increases the second‐order polarizabilities by 4–6 times, but leads to an evident red‐shift of about 65–80 nm in spectra. The relative second‐order polarizability of the halogen‐substituted derivatives is in the sequence of ? CF₃ > ? F > ? Cl > ? Br, without obvious substituent effects on the optical transparency. The D‐π‐A chromophores with the strong electron‐donating (amino) and ‐accepting (acetyl) substituent present the larger second‐order polarizabilities, at the cost of about 20 nm red‐shift of the maximum absorption lengths relative to the halogen‐substituted species. It is also demonstrated that both the linear and nonlinear optical properties augment with the increase in solvent polarity, accompanied by a red‐shift in the wavelengths of maximum absorption by about 18 and 23 nm, respectively, in THF and MeOH solutions. The changes in optical properties upon the structural modifications are further rationalized by the electronic structures of various H‐shaped dimers. Copyright © 2010 John Wiley & Sons, Ltd.     

The quest for a better system for evaluating pi‐electron substituent constant: a comparison of benzoic,acrylic and tria‐, penta‐, heptafulvene‐based carboxylic acids. A computational study

Carboxylic acids based on exo‐substituted tria‐, penta‐, heptafulvenes and ethylene (acrylic acids) were examined in order to determine if they are more sensitive to the substituent effect than benzoic acid – the system originally employed by Hammett. In order to accomplish this task, all possible structural isomers of benzoic acid, tria‐, penta‐ and heptafulvene‐based carboxylic acids, acrylic and methacrylic acids substituted by 13 substiuents (BH₂, CHO, CN, COCN, NO₂, CF₃, Me, Cl, F, OH, OMe, NH₂ and NMe₂) were optimized at the B3LYP/6‐311++G(d,p) level of theory, and Gibbs free energies of carboxylic group dissociation (ΔG_dis) were calculated. These energies were subsequently intercorrelated, and from the slopes of linear regressions, it was estimated which system is associated with greatest changes of ΔG_dis due to substitution and thus is most sensitive to the substituent effect. It was found that all fulvene‐based carboxylic acids have greater range of ΔG_dis change than benzoic acid, but the largest range of change was observed in the case of acrylic and methacrylic acids. The acrylic acid as the most sensitive system to substitution could replace benzoic acid for an improved version of substituent constant used to measure pi‐electron substituent effect. Copyright © 2013 John Wiley & Sons, Ltd.     

Electron reorganization in allowed and forbidden pericyclic reactions: multicenter bond indices as a measure of aromaticity and/or anti‐aromaticity in transition states of pericyclic electrocyclizations

The multicenter bond indices (MCI), recently proposed as quantitative measures of cyclic delocalization in aromatic systems, have been applied to characterize the differences in the nature of the electron reorganization in a series of allowed and forbidden electrocyclic reactions of linear neutral polyenes of general formula C_nH_n+2 and related charged systems of formula C_nH_n+2(+) and C_nH_n+2(?) for n ranging from 4 to 7. The proposed methodology, which is based on the monitoring of the variation of the extent of cyclic delocalization along the concerted reaction paths, is shown to be completely consistent with the empirical Evans/Dewar classification anticipating aromatic transition states for allowed and anti‐aromatic transition states for forbidden electrocyclic reactions. Although the study reports the results of the analysis of electron reorganization just for the above‐mentioned particular class of electrocyclic reactions, the proposed approach is completely general and its conclusions remain valid for any pericyclic reaction. Copyright © 2009 John Wiley & Sons, Ltd.     

Substituent effect study on 13Cβ SCS of styrene series. A Yukawa–Tsuno model and Reynolds dual substituent parameter model investigation

The Yukawa–Tsuno (Y–T) and Reynolds dual substituent parameter (DSP) models have been used to model ¹³C substituent chemical shift (SCS) of the C_β atom of 19 series of para‐substituted styrenes (X‐C₆H₄CR?CYW) with variable electronic and structural demands in the side‐chain. The best fit of the Y–T model was better than that of the Reynolds DSP model for most of the studied series. A high correlation was found between the ρ value of the Y–T model and ρ_F value of the Reynolds DSP model. The ρ value, which reflects the sensitivity of ¹³C_β SCS to the substituent field effect, was found to be influenced by the group W on the C_β atom. A W group that enhances the para‐substituent π‐polarization of the side‐chain has a higher ρ value than its counterpart W groups that induce counter π‐polarization in the side‐chain. The series with W in an E‐configuration to the aryl ring has higher ρ value than corresponding Z series. A lower ρ value is observed when W induces a counter π‐polarization of the side‐chain (as with NO₂ and COMe) or when the R substituent imposes a 65° dihedral angle between the side‐chain and the para‐substituted benzene ring (as with t‐Bu). When the W group is a heterocyclic ring, the closer the heteroatom is to C_β, the lower the ρ value is due to the greater counter π‐polarization. The two components of the substituent effect on ¹³C _β SCS, namely the field effect and resonance effect, behave inversely. The resonance demand (r⁺ value) increases, as the Y and/or W groups become more electron‐withdrawing (EW). The series with W as a hetrocyclic ring develop negative charge at the carbon atom of the hetrocyclic ring adjacent to C_β (and to which the styryl moiety is attached) and has a lower r⁺ value than those which fail to do so. The lowest r⁺ value was for those series with a 65° dihedral angle. Copyright © 2007 John Wiley & Sons, Ltd.     

Structure and properties of α‐cyclo[N]thiophenes as potential electronic materials – a theoretical study

Density functional theory (DFT) calculations of ring‐shaped α‐cyclo[N]thiophenes with N = 2 to N = 18 have been performed for ideal structures of high symmetry (point groups C_nv and D_nh) and for optimum energy structures of lower symmetry (D_2d, C_s, C_2v, C_i or C₁). Whereas the first three members of the series behave exceptionally the higher members are typical cyclothiophenes consisting of weakly interacting thiophene rings. In contrast to neutral compounds, cations and dications of cyclothiophenes with N ≥5 exhibit pronounced electron delocalizations along the carbon backbone. However, if the functional B3LYP is replaced by BH cations of large ring‐size cations show polaron‐type charge defects. According to broken symmetry DFT calculations dications with N = 14 and N = 18 have biradical character. These structures correspond to two‐polaron‐type structures rather than to dipolarons. The calculated vertical ionization energies of cyclo[N]thiophene are comparable with those of oligo[N]thiophenes of the same number of thiophene rings but the calculated absolute energies are probably too low at large ring size. Cyclothiophenes absorb light of lower energies than the related oligothiophenes. Cyclothiophenes belong to the strongly absorbing organic chromophores. In case of high molecular symmetry some of the excited states of cyclothiophenes are degenerate. The degeneracy is lifted with lower symmetries but the general absorption feature remains. The theoretical results are discussed with respect to recent experimental findings. Copyright © 2007 John Wiley & Sons, Ltd.     

Tuning HOMO–LUMO levels: trends leading to the design of 9‐fluorenone scaffolds with predictable electronic and optoelectronic properties

Highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) tuning is an important consideration in the development of organic‐based semiconducting materials. A study of the specific effects and overall trends for the HOMO–LUMO tuning of a diverse series of 9‐fluorenones by means of extended conjugation and substituent effects is described. Trends were explored in a range of compounds, beginning with structures having highly electron‐withdrawing substituents and progressing to structures having highly electron‐donating substituents. Compounds with an incremental increase in conjugation were also examined. Electrochemical and optical measurements were used to calculate the HOMO–LUMO levels and HOMO–LUMO bandgap (HLG) for each structure. Results from both methods were compared and correlated with the differences in molecular structure. Increasing the electron‐donating character of the substituents was observed to decrease the HLG and increase the energy levels of the HOMO and the LUMO, whereas an increase in the electron‐withdrawing character produced the opposite results. Increasing conjugation decreased the HLG, increased the HOMO energy level, but decreased the LUMO energy level. Spectroscopic evidence of substituent influence on the carbonyl suggests that substituents directly impact the HLG by influencing the availability of nonbonding electrons within the carbonyl, which impacts the probability of an nπ* transition. The data presented not only elaborate on the HOMO–LUMO tuning of 9‐fluorenone systems but also enable the consideration of 9‐fluorenones as analogous models for HOMO–LUMO tuning in other more complex polyaromatic systems such as bifluorenylidenes. These trends may provide insight into developing materials with specifically tuned HLGs and HOMO–LUMO levels for a variety of applications. Copyright © 2011 John Wiley & Sons, Ltd.     

Initiation of petroleum formation and antioxidant function – a DFT study of sulfur?sulfur bond dissociation enthalpies

Experimental studies showed that sulfur radicals play the vital role in petroleum formation. 1 Sulfur‐ centered radicals also exhibit activities in antioxidant functions. Here we conduct a theoretical investigation of their precursor‐disulfides. By investigation into substituent effect on sulfur? sulfur bond dissociation enthalpies (S? S BDEs), we would like to find the most effective provider for sulfur radicals. In the present work, 50 alpha‐substituted disulfides and 16 para‐substituted aryl disulfides are studied systematically, with the general formula XS‐SX or HS‐SX. The substituent effect on S? S BDEs is found to be very eminent, ranging from 33.2 to 75.0 kcal/mol for alpha‐substituted disulfide, and from 43.7 to 59.7 kcal/mol for para‐substituted phenyl disulfides. We also evaluate the performance of 44 density functional methods to get an accurate prediction. A further study indicates that substituents play a major role in radical energies, instead of molecule energies, which is substantiated by the good linearity between XS‐SX bond dissociation enthalpy (BDE) and HS‐SX BDE. Copyright © 2007 John Wiley & Sons, Ltd.     

Calculated polar substituent effects on the stability of 3‐substituted(X) bicyclo[1.1.1]pent‐1‐yl cations and 4‐substituted(X) bicyclo[2.2.1]hept‐1‐yl cations: a DFT study

The effects of substituents on the stability of 3‐substituted(X) bicyclo[1.1.1]pent‐1‐yl cations (3) and 4‐substituted(X) bicyclo[2.2.1]hept‐1‐yl cations (4), for a set of substituents (X = H, NO₂, CN, NC, CF₃, CHO, COOH , F, Cl, HO, NH₂, CH₃, SiH₃, Si(CH₃)₃, Li, O^?, and NH₃⁺) covering a wide range of electronic substituent effects were calculated using the DFT theoretical model at the B3LYP/6‐311 + G(2d,p) and B3LYP/6‐31 + G (d) levels of theory, respectively. Linear regression analysis was employed to explore the relationship between the calculated relative hydride affinities (ΔE, kcal/mol) of the appropriate isodesmic reactions for 3/4 and polar field/group electronegativity substituent constants (σ_F and σ_χ, respectively). The analysis reveals that the ΔE values for both systems are best described by a combination of both substituent constants. The result highlights the importance of the σ_χ dependency of charge delocalization in these systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Relationship between electronic and crystal structure in Cu–Ni–Co–Mn–O spinels: Part A: Temperature-induced structural transformation

Local atomic and crystal structures around Cu and Mn atoms in Mn_1.68Cu_0.6Ni_0.48Co_0.24O₄ spinel samples fabricated by metal–organic decomposition synthesis at different annealing temperatures were investigated by X-ray absorption fine structure analysis. There are two distinct copper cations, Cu¹⁺ and Cu²⁺, both of which maintain tetrahedral coordination. The bond-length distances are Cu¹⁺–O = 2.00 Å and Cu²⁺–O = 1.80 Å. The manganese cations are for the most part octahedral. The spinels prepared at low temperature (600 °C) contain smaller (Mn⁴⁺–O = 1.88 Å) undistorted MnO₆ octahedrons corresponding to Mn⁴⁺ valence, whereas the manganese octahedrons in high-temperature materials (800 °C and higher) were larger and had a pronounced tetragonal distortion pertaining to Mn³⁺ oxidation state (Mn³⁺–O = 1.93 Å and 2.11 Å). By rising the fabrication temperatures, relative concentration of the species of Mn⁴⁺ and Mn³⁺ varies as a result of the reaction represented by Cu¹⁺ + Mn⁴⁺  Cu²⁺ + Mn³⁺, implying irreversible temperature-induced structural transformation. Atomic coordinates in the low-temperature phase are similar to those found in the ideal cubic spinel with oxygen parameter u = 0.27, whereas local environments of the Cu and Mn atom correspond to the tetragonal CuMn₂O₄ phase (space group I4₁/amd). Unlike in CuMn₂O₄, orientation of the lattice distortions is random, however, the long-range cubic spinel structure is retained at all time.