Type-I dyotropic rearrangement for 1,2-disubstituted cyclohexanes: substitution effect on activation energy

Abstract

For an array of judiciously selected 1,2-disubstituted cyclohexane motifs, the migratory aptitude and contribution of specific structural features of synthetically valuable functional groups and halogen atoms in type-I dyotropic rearrangement are reported by employing quantum chemical calculations. This double migration process requires higher activation barriers for carbon, silicon and nitrogen bearing substituents, however, it is thermally allowed and a feasible approach for several important moieties including oxygen, sulphur, phosphorous and halogen atoms bearing migrating fragments. Strong positive correlations are observed by plotting representative activation energy trends against inductive sigma (σ_I), field (σ_F), steric substituent (E_s) and polar substituent (σ*) constants. Also, an effect of the asymmetric combinations of substituents is presented which provides an interesting insight into such substitution patterns.

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Introduction

Type-I dyotropic rearrangement¹ is a highly stereo- and regioselective pericyclic process, which proceeds reversibly through a cyclic transition state in a concerted manner.² A distinctive feature of this rearrangement involves one pi (π) system and a simultaneous intramolecular exchange of two sigma (σ) bonds (Fig. 1). Based on molecular-orbital and valence-bond analyses, this double migration process for 1,2-disubstitued ethane has been explicitly proposed to proceed either via an ethylenic scaffold or a diradical species.³ Contrary to this, type-II dyotropic rearrangement⁴ occurs via migration of two substituents to new sites in a molecule. In addition to a usual C–C⁵ stationary scaffold, dyotropic reaction has been successfully applied to C–B,⁶ C–N,⁷ C–O,⁸ C–Al,⁹ C–Si,¹⁰ C–S,^8,11 C–Cu,¹² C–Zn,¹³ C–Zr,¹⁴ C–Pd,¹⁵ C=Si,¹⁶ N–N,¹⁷ O–N,¹⁸ Si=Si,¹⁹ Fe–Pt,²⁰ and Ge=Sn,²¹ used as static frameworks.

Fig. 1 Generic representation of type-I dyotropic rearrangement.

This double migration approach has been articulately incorporated to construct structurally complex molecules of synthetic and biological relevance such as lacrimin A (1),²² jaspamide (2),²³ zoapatanol (3),²⁴ and azafenestrane (4, Fig. 2).²⁵ Moreover, several other bioactive natural products such as milbemycin β₃,²⁶ discodermolide,²⁷ xanthanolides,²⁸ cephalostatin analogues²⁹ and a number of synthetically significant building blocks³⁰ have also been prepared through this methodology. Additionally, type-II dyotropic rearrangement has also found its applications towards the synthesis of bioactive derivatives including cyclic peptide TCM-95A and B.³¹

Fig. 2 Synthetic applications of type-I dyotropic rearrangement towards representative bioactive molecules.

Chemical reactions proceed through one or more transition states and the rate of the reaction depends on the activation energy (E_a), which is the free energy difference between the transition state (TS) and the reactants. It is a measure of chemical reactivity and provides a very useful information about the reaction profile. Also, it is directly linked with stability of the TS, which relies on several decisive factors, not just limited to (a) electronic interactions between the reacting centres, (b) charge distributions, (c) steric hindrance caused by substituents, (d) mesomeric, inductive and anomeric effects. In case of type-I dyotropic rearrangement, hybridization of the atoms of the migrating groups directly attached with the stationary scaffold has a pronounced influence on E_a due to associated electronic nature and steric effect. In general, sp³ hybridized atoms are electron donating moieties whereas both sp² and sp hybridized atoms tend to withdraw electronic density from a molecule. In case of substituted aromatic systems, the electronic influence is controlled by the substituent attached with the aromatic system. The transition states are stabilized/destabilized as a result of all these factors, which have a direct impact on the E_a; greater the stability of the TS, lower will be the E_a. Quantum chemical calculations provide an insightful information towards the elucidation of reaction mechanisms and chemical reactivity descriptors.³² Application of computational investigations in synthesis has emerged as an indispensable research element and indeed, is a time and cost effective approach. It has been eloquently applied to dyotropic rearrangement and is reported for several structural units such as dithienylethenes,³³ arene/allene cycloadducts,³⁴ phosphate and sulphate anions,³⁵ azines,³⁶ pentalenene,³⁷ vicinal dibromides,³⁸ β-lactones,³⁹ dimethylaurate,⁴⁰ organocuprates and organoargentates,⁴¹ and nitroso acetals.⁴²

Undoubtedly, cyclohexane is regarded as one of the most privileged cycloalkane due to associated structural features. It exists in several interconvertible conformations along with a perfectly unstrained and highly stable chair conformation. It is a fairly unreactive molecule with limited applications⁴³ however, substituted cyclohexane is of substantial synthetic utility and acts as a precursor to numerous organic transformations. Moreover, replacement of hydrogen atoms with larger substituents in cyclohexane skeleton can prevent the interconversion between different conformations and this phenomenon is a common observation in cyclohexane containing structures of biological importance. Considering its significance, a comprehensive investigation towards the migratory aptitude of synthetically significant functional groups/atoms in type-I dyotropic rearrangement for variously functionalized 1,2-disubstituted cyclohexane structures is described.

Results and discussion

In general, type-I dyotropic rearrangement occurs at high temperatures as reported for thermal mutarotation of 2,3-dibromo-tert-butylcyclohexane,⁴⁴ and vicinal dibromides in steroidal structures.⁴⁵ The results obtained from this study are in agreement with this experimental observation and 1,2-shifts for the considered groups proceed via high energy barriers up to 126 kcal mol⁻¹. Such high barriers have also been reported for the type-I dyotropic model systems studied for 1,2-disubstituted ethane structures.^3b The results for 1,2-disubstituted cyclohexanes bearing migratory groups with sp³-hybridized atoms and halogen atoms directly attached with the cyclohexane skeletons are summarized in Table 1 and the optimized structures of the corresponding four-membered transition states are provided in the ESI† (Fig. 1).

Table 1 Type-I dyotropic reactions for migratory substituents with sp³-hybridized atoms and halogen atoms directly attached with the cyclohexane unit

Entry	Substituents (R and R′)	Activation energy^a (Ea), kcal mol^−1	Bond distance^b (r), Å	Average bond distance^a^,^b (r), Å	Average bond angle^a^,^b (θ)
			C^α–C^β	C^α/C^β–R/R′	C^α–R–C^β and C^α–R′–C^β
a For a detailed information about energies, bond distances and bond angles (see ESI).b The values are for the corresponding transition states.
1	CH3	120.9	1.368	2.425	32.77
2	NH2	92.02	1.445	2.065	43.15
3	OH	76.85	1.416	1.973	42.04
4	F	58.56	1.423	1.909	43.77
5	SiH3	88.62	1.371	2.879	27.52
6	PH2	63.67	1.376	2.814	28.28
7	SH	49.00	1.418	2.492	33.04
8	Cl	36.24	1.434	2.384	35.00
9	CH2CH3	120.2	1.362	2.541	31.28
10	CH(CH3)2	109.4	1.353	2.700	29.03
11	C(CH3)3	95.83	1.345	3.107	25.00
12	CH2CHCH2	90.16	1.353	3.039	25.54
13	Si(CH3)3	97.00	1.362	3.010	26.13
14	P(CH3)2	68.22	1.361	2.934	26.81
15	OCH3	71.29	1.418	1.967	42.25
16	SCH3	50.14	1.417	2.461	33.45
17	OC(CH3)3	89.28	1.431	2.011	41.67
18	OCH2Ph	79.10	1.422	2.000	41.65
19	OCH2OCH3	77.53	1.422	2.033	40.90
20	OSi(CH3)3	71.10	1.424	1.975	42.27
21	OC(O)CH3	63.88	1.420	2.059	40.32
22	OPh	60.99	1.420	2.021	41.14
23	OC(O)Ph	50.42	1.432	2.084	40.20
24	Br	31.50	1.428	2.506	33.11

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It is evident that 1,2-migration for carbon bearing groups requires higher energy barriers; the maximum for CH₃ groups (entry 1) and it gradually decreases when CH₃ motifs are replaced by NH₂ (entry 2), OH (entry 3) and F (entry 4) substituents. In the transitions states, the bond distance between the carbon atoms (C^α and C^β) bearing CH₃ groups is 1.368 Å, which is an indication of an olefinic bond. However for NH₂, OH and F migrating groups, it is in the range of 1.416–1.445 Å.⁴⁶ Also, the average bond distance for C^α/C^β–R/R′ is comparatively higher for CH₃ groups (2.425 Å) as compared to NH₂, OH and F moieties (1.909–2.065 Å).

This decrease in the computed activation barrier in going from CH₃ to F substituents may be ascribed to the increase in the bond polarity or inductive effect, which is in an order of CH₃ < NH₂ < OH < F. It significantly influences to stabilize the transition states and decreases the E_a. Also, it has been proposed for 1,2-disusbstituted ethane molecules that halogen atoms as migrating groups provide better stabilization to the transition states through an additional donor–acceptor orbital interaction between the lone pairs of halogen atoms and the newly formed ethylenic π* LUMO.^3b This additional stabilization completes the pericyclic circuit and consequently, a lower activation barrier is observed. In addition to this, linear free-energy correlations for the energy barriers and inductive sigma (σ_I) and field (σ_F) constants for CH₃, NH₂, OH and F groups/atoms are shown in Fig. 3.⁴⁷ From the positive correlation coefficients obtained, it can be concluded that the energy barrier has a strong relationship with the corresponding Hammett constants. Replacing with the substituents bearing the atoms belonging to the third period of the periodic table (entries 5–8), a similar trend is observed; E_a is in an order of SiH₃ > PH₂ > SH > Cl. Also, the presence of a weaker C–R bond in the reactants corresponds to a lower E_a and it has been noticed for the pairs SiH₃ and CH₃, PH₂ and NH₂, OH and SH, F and Cl. Similar observations for the type-I dyotropic rearrangement barrier have been reported for the pairs CH₃ and SiH₃, F and Cl substituted ethane molecules and explained in terms of activation-strain and molecular-orbital analyses.^3b

Fig. 3 The correlation between the activation energy (E_a) of CH₃, NH₂, OH and F as migrating groups with their corresponding (a) inductive sigma constants (σ_I) and (b) field constants (σ_F).

Interestingly, sequential exchange of hydrogen atoms with CH₃ groups in CH₃ substituents significantly reduces the energy barrier (entries 9–11). For this particular case of carbon bearing migrating fragments, an increase in the steric crowding (by replacing hydrogen atoms with CH₃ groups) results in an increase in the average bond distances (2.541–3.107 Å) between the carbon atoms (C^α and C^β) and the substituents (R and R′) involved in the transition states. It is conceivable to infer that this increase in the bond distances leads to lower the steric interactions between the substituents and the carbon atoms, which consequently stabilize the corresponding transition states and result in decreasing the E_a for this double migration process. Notably, the bond angles between carbon atoms (C^α and C^β) and the substituents (R and R′) seem to be related with the steric crowdedness as a gradual decrease in the bond angles is recorded from CH₂CH₃ to C(CH₃)₃ substituents (31.28–25.00°). These results are also supported by linear free-energy relationship described by the Taft equation and strong positive correlations are observed between the activation energy and steric substituent (E_s) and polar substituent (σ*) constants for CH₃, CH₃CH₂, CH(CH₃)₂ and C(CH₃)₃ as shown in Fig. 4.⁴⁸

Fig. 4 The correlation between the activation energy (E_a) of CH₃, CH₃CH₂, CH(CH₃)₂ and C(CH₃)₃ as migrating groups with their corresponding (a) steric substituent constants (E_s) and (b) polar substituent constants (σ*).

In addition to this, the migrating ability of allyl group (entry 12) requires higher E_a, which is probably because of the repulsive interaction between the π-bonds present in the allylic substituents and the newly formed π-bond in the corresponding transition state (TS12, Fig. 1, ESI†). Such a repulsion leads to destabilize the TS and causes an increase in the energy barrier. However, the steric effect becomes more pronounced when there is a slight increase in the bond distances between the carbon atoms (C^α and C^β) and the substituents (R and R′) involved in the transition states. It is the case when SiH₃ (entry 5) is substituted with Si(CH₃)₃ (entry 13); the difference for average bond distance is of 0.131 Å and for CH₃ and C(CH₃)₃ groups, it is 0.682 Å. It is plausible that an increase in the steric crowding by replacing H atoms with CH₃ groups result in an enhanced steric repulsion between the substituents and the stationary scaffold, which destabilizes the resultant transition states. This explains why rearrangement of Si(CH₃)₃ substituents is linked with a higher E_a than the corresponding [1,2]-shifts for SiH₃ groups. Comparing to their respective hydrogenated equivalents, similar effect towards an increase in E_a has been computed for P(CH₃)₂ (entry 14), OCH₃ (entry 15) and SCH₃ (entry 16).

At this juncture, an investigation was carried out to understand the behaviour of commonly used OH protecting groups for this [1,2]-shifts approach and a regular pattern can be envisaged. From OH (entry 3) to OC(CH₃)₃ (entry 17), introduction of the steric bulk significantly increases the energy barrier and this agrees well with other findings of this study, where the steric factor is a dominant contributor. The functional groups OCH₂Ph (entry 18) and OCH₂OCH₃ (entry 19) have E_a values similar to OH groups (entry 3). For OSi(CH₃)₃ substituents (entry 20), a lower energy barrier of 71.10 kcal mol⁻¹ is calculated as compared to OH migrating fragments (76.85 kcal mol⁻¹). This decrease in the E_a may be ascribed to the presence of a more polarized O–Si bond than an O–H bond. A significant decrease in the activation barrier is computed for OC(O)CH₃ migrating units (entry 21), where the TS receives better stabilization due to the presence of carbonyl groups. Stabilization of the TS caused by delocalization of the lone pairs of oxygen substituents over aromatic system renders a lower barrier (60.99 kcal mol⁻¹) and it has been noticed for OPh groups (entry 22). As anticipated, the energy barrier for OC(O)Ph (entry 23) substituents is remarkably lower than the corresponding OH groups by 26.43 kcal mol⁻¹ due to additional stabilization, which is clear from the TS23 (Fig. 1, ESI†). It is the lowest activation barrier for the considered OH protecting groups, which is a consequence of more stabilized TS due to the presence of improved delocalization. The most feasible migrating fragments for the type-I dyotropic rearrangement among the considered systems are Br atoms (entry 24) with a reaction barrier of 31.5 kcal mol⁻¹. This is due to weaker C–Br bonds in the reactant and it is one of the consistent aspects of this study; weaker the C–R bond in the reactants, lower will be the energy barrier.

For comparative purposes and to comprehensively document this investigation, the migratory aptitude for the groups bearing sp²- and sp-hybridized carbon atoms was explored. A range of valuable functional moieties were selected, which provides an important information about the specific behaviour of the substituents in this double migration process and the results are summarized in Table 2. In the presence of these functional groups, type-I dyotropic rearrangement for cyclohexanes as stationary scaffolds proceeds via high activation barriers (more than 100 kcal mol⁻¹) with an exception of C(O)Cl groups. Vinyl groups as migrating substituents require the highest energy barrier (126.1 kcal mol⁻¹, entry 1) that is probably due to an increased electronic interaction between the olefinic bonds of the substituents and the newly formed π-bond in the corresponding TS (TS25, Fig. 1, ESI†). A significant decrease of 8.9 kcal mol⁻¹ is observed when H atoms of the carbon atoms of vinyl groups attached with the cyclohexane unit are swapped by CH₃ groups. By doing this, the steric crowdedness is increased, which generally results in higher E_a. However, the average distance between the newly formed π-bond in the TS and the substituents increases from 2.31 to 2.372 Å. Probably, this increase stabilizes the TS by reducing the interactions, which would lead to a lower E_a. The net effect of this replacement is a decrease in the activation barrier and it is in accordance with the findings for other carbon bearing groups such as going from CH₃ to C(CH₃)₃ substituents, entries 1 and 11 of Table 1 respectively.

Table 2 Type-I dyotropic reactions for migratory fragments with sp²- and sp-hybridized atoms directly attached with the cyclohexane unit

Entry	Substituents (R and R′)	Activation energy^a (Ea), kcal mol^−1	Bond distance^b (r), Å	Average bond distance^a^,^b (r), Å	Average bond angle^a^,^b (θ)
			C^α–C^β	C^α/C^β–R/R′	C^α–R–C^β and C^α–R′–C^β
a For a detailed information about energies, bond distances and bond angles (see ESI).b The values are for the corresponding transition states.
1	CHCH2	126.1	1.378	2.310	34.73
2	C(CH3)CH2	117.3	1.375	2.372	33.70
3	C(O)H	111.6	1.364	2.582	30.64
4	C(O)CH3	104.5	1.362	2.697	29.24
5	C(O)NH2	109.4	1.369	2.539	31.27
6	C(O)NHPh	105.1	1.369	2.597	30.57
7	C(O)OCH3	111.1	1.378	2.421	33.06
8	C(O)OH	110.6	1.380	2.410	33.27
9	C(O)OC(O)CH3	108.6	1.381	2.417	33.18
10	C(O)F	108.5	1.387	2.372	34.00
11	C(O)Cl	92.50	1.385	2.417	33.31
12	Ph	119.8	1.379	2.328	34.44
13	CCH	115.1	1.431	2.197	40.40
14	CN	106.9	1.410	2.183	37.69

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The presence of carbonyl groups as migrating substituents withdraw the electronic density from the newly formed π-bonds in a TS, which promotes destabilization of the TS and increases the E_a. Another factor is steric hindrance offered by bulky substituents attached with the carbonyl groups, which leads to an increased bond distances between the carbon atoms (C^α and C^β) and the substituents (R and R′) involved in the transition states. This results in lowering the steric interactions hence a decrease in activation barrier as observed for carbon bearing groups as migrating substituents. So, the carbonyl substituents behave differently and the resultant energy barrier is directly linked with the extent of electron withdrawal and the steric hindrance. The computed activation barriers for C(O)H (entry 3) and C(O)CH₃ (entry 4) are 111.6 and 104.5 kcal mol⁻¹ respectively. These values are lower than vinyl groups (entry 1) due to increased bond distances and lower repulsive interactions for carbonyl bearing groups as compared to vinyl substituents. The average computed bond distance for C(O)CH₃ substituents is 2.697 Å, while for C(O)H groups is 2.582 Å. Also, CH₃ groups tend to reduce the electron withdrawing ability of the carbonyl group due to hyperconjugation, which leads to stabilize the TS and consequently E_a is decreased. In case of nitrogen containing substituents like C(O)NH₂ (entry 5) and C(O)NHPh (entry 6), there is a difference of 4.3 kcal mol⁻¹. This may be ascribed to a possible extended delocalization of electronic cloud through the involvement of π-electrons from the Ph ring, which can reduce the electron withdrawing ability of the carbonyl group (TS30, Fig. 1, ESI†). This can assist to stabilize the TS as compared to the situation when no Ph group is present and consequently, E_a is significantly decreased.

For oxygen bearing carbonyl groups such as C(O)OCH₃ (entry 7), C(O)OH (entry 8) and C(O)OC(O)CH₃ (entry 9), the energy barriers are 111.1, 110.6 and 108.6 kcal mol⁻¹ respectively. Moving from C(O)OC(O)CH₃ substituents to C(O)OCH₃, a difference of 2.5 kcal mol⁻¹ is observed that is probably related to better stabilization of newly formed π-bond in the TS by the oxonium species through hyperconjugation. A significant difference of 16.0 kcal mol⁻¹ in the energy barrier is observed for C(O)F (entry 10) and C(O)Cl (entry 11), which seems to be due to the repulsive interaction of lone pairs on F and Cl atoms with the newly formed π-bond. The average bond distances between the substituents and the carbon atoms (C^α–C^β) suggest that these interactions are higher for C(O)F substituents as it is 2.372 Å compared to 2.417 Å for C(O)Cl migrating groups. In addition to this, higher electronegativity of F over Cl atom can destabilize the corresponding TS by withdrawing electronic density from the newly formed π-bond, and causes a higher E_a for C(O)F substituents.

An installation of Ph groups (entry 12) as migrating substituents show higher value of E_a, 119.8 kcal mol⁻¹, which is significantly lower than the vinyl substituents (entry 1). This seems to be as a result of delocalized π-bonds in the aromatic system, which renders lower electronic interactions between the newly formed π-bond and the π-bonds in the Ph rings. For other synthetic transformations, the existence of ortho/para and/or meta directing groups on an aromatic ring plays a decisive rule to determine the reactivity and selectivity. In case of type-I dyotropic rearrangement for 1,2-disubstituted cyclohexane, there seems to be a very minor contribution offered by these ortho/para and meta directors located on Ph substituents.⁴⁹ For CCH (entry 13) and CN (entry 14) groups, activation barriers of 115.1 and 106.9 kcal mol⁻¹ and bond distances (C^α–C^β) of 1.431 and 1.41 Å are observed respectively.⁴⁶ This decrease in E_a in going from CCH to CN may be rationalized on the basis of their optimized transition state structures (TS37 and TS38, Fig. 1, ESI†). It is reasonable to suggest that in the case of CN as migrating groups, planarity of the substituents in the TS renders better stabilization and lower repulsive interactions in the TS as compared to CCH groups. Consequently, a lower activation barrier is noticed for CN migrating groups in type-I dyotropic rearrangement of cyclohexanes.

Finally, an investigation towards the energy barriers for asymmetric combinations of substituents was carried out and the results are summarized in Table 3. It provides an interesting information towards captodative substitution, which demonstrates a combined effect of electron withdrawing (captor) and electron donating (dative) substituents attached to the same substrate.⁵⁰

Table 3 Effect of asymmetric combinations of substituents on the activation barriers of 1,2-disubstituted cyclohexanes

Entry	Substituents		Activation energy^a (Ea), kcal mol^−1	Bond distance^b (r), Å
	R	R′		C^α–C^β
a For a detailed information about energies, bond distances and bond angles (see ESI).b The values are for the corresponding transition states.
1	CH3	NH2	105.0	1.399
2	CH3	OH	90.5	1.388
3	CH3	F	77.2	1.385
4	NH2	OH	72.7	1.449
5	NH2	F	57.3	1.443
6	OH	F	62.0	1.421
7	CH3	C(O)CH3	113.2	1.367
8	NH2	C(O)CH3	99.3	1.404
9	OH	C(O)CH3	86.9	1.389
10	F	C(O)CH3	73.8	1.385
11	CH3	CN	94.7	1.394
12	NH2	CN	73.5	1.463
13	OH	CN	86.4	1.427
14	F	CN	81.5	1.415
15	C(O)CH3	CN	93.0	1.387
16	F	Cl	47.5	1.432
17	F	Br	45.2	1.430
18	Cl	Br	33.9	1.431

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Certain captodative substitution patterns have been found effective in decreasing the activation barriers for several pericyclic transformations.⁵¹ An explanation of the results presented in Table 3 appear somewhat intricate however, couple of aspects can be clearly seen:

(1) For most of the substitution patterns studied, the activation energies for unsymmetrical disubstituted cyclohexanes are in between the barrier values obtained for the corresponding individual symmetrical disubstituted cyclohexane systems.

(2) An acceleration effect is observed for certain combinations where the energy barriers of asymmetric 1,2-disubstituted cyclohexanes are significantly lower than the analogous symmetrical disubstituted cyclohexanes. These combinations include the presence of two mesomerically electron donating substituents such as NH₂ and OH (entry 4), an electron donating and an electron withdrawing species like CH₃ and CN (entry 11) and both electron withdrawing migrating fragments such as C(O)CH₃ and CN (entry 15).

Conclusions

A comprehensive investigation towards type-I dyotropic rearrangement for a range of 1,2-disubstituted cyclohexane molecules is presented. The results obtained for the considered groups/atoms are in good agreement with the experimental observations and reported DFT based calculations for the related systems. To establish a free-energy linear relationship, representative activation energy trends are plotted against inductive sigma (σ_I), field (σ_F), steric substituent (E_s) and polar substituent (σ*) constants, which provide a strong positive correlation. The salient conclusions drawn from this double migration process include:

(a) Inductive effect of the substituents plays a substantial role in determining the feasibility of this approach and it is a thermally allowed process for 1,2-dihalogenated cyclohexanes due to added stabilization by the interaction of halogen lone pairs with the newly formed π-bond.

(b) Oxygen, sulphur and phosphorus bearing migrating fragments require moderate levels of activation barriers and these have also been computed for the most common OH protecting groups. The most convenient OH protecting group for type-I dyotropic reaction of 1,2-disubstituted cyclohexane is O(CO)Ph with an activation barrier of 50.42 kcal mol⁻¹, which is 26.43 kcal mol⁻¹ lower than the corresponding OH substituted system.

(c) Installation of carbon, silicon and nitrogen bearing migrating groups proceed via higher energy barriers; the maximum is for carbon atom.

(d) The presence of carbonyl groups as migrating units result in higher activation energies for the considered groups because of enhanced destabilization of the transition states.

(e) Phenyl (Ph) rings as migrating substituents have higher energy barriers and there is a slight difference in the E_a caused by the synergistic effect of electron donating and withdrawing groups.

(f) Increase in steric bulk of the substituents lead to higher energy barriers and increase in the bond distances between the carbon atoms (C^α and C^β) and the substituents (R and R′) involved in the transition states decreases the activation barrier.

(g) Asymmetric combinations of substituents usually proceed with an energy barrier related to the corresponding individual symmetrically disubstituted systems however for certain unsymmetrical combinations, such as NH₂ and OH, CH₃ and CN, and C(O)CH₃ and CN, an extra acceleration effect is observed which leads to a significant decrease in the activation energy of 1,2-asymmteric disubstituted cyclohexane molecules.

Methods

All calculations were performed with the Gaussian 09W programme⁵² and the results were produced with GaussView 5.0. Density functional theory (DFT)⁵³ calculations using the B3LYP functional⁵⁴ were used to locate all the stationary points involved. Geometries were optimized at B3LYP/6-31+G(d,p) level of theory, which has been successfully applied to related dyotropic reactions.^37,42 The frequency calculations were run at the same level of theory to confirm each stationary point to be either a minimum or a transition structure. The transition states were also linked to their corresponding minima through the intrinsic reaction coordinate (IRC)⁵⁵ calculations (see ESI for details†), which confirm the connection of transition structures with the reactants and products. Zero-point energy (ZPE) values were computed from the optimized geometries at 298.15 K and are not corrected.

Acknowledgements

The author gratefully acknowledges the support offered by the King Faisal University, Saudi Arabia. Also, D. Leonori (University of Manchester, UK) is thanked for the technical discussions.

Notes and references

1. M. T. Reetz, Angew. Chem., Int. Ed. Engl., 1972, 11, 129–130.
2. For a selection of reviews concerning dyotropic rearrangement, see: (a) M. F. Croisant, R. van Hoveln and J. M. Schomaker, J. Org. Chem., 2015, 27, 5897–5907; (b) I. Fernandez and F. M. Bickelhaupt, Chem. Soc. Rev., 2014, 43, 4953–4967; (c) E. M. Greer and C. V. Cosgriff, Annu. Rep. Prog. Chem., Sect. B: Org. Chem., 2013, 109, 328–350; (d) O. Gutierrez and D. J. Tantillo, J. Org. Chem., 2012, 77, 8845–8850; (e) D. J. Tantillo and J. K. Lee, Annu. Rep. Prog. Chem., Sect. B: Org. Chem., 2011, 107, 266–286; (f) I. Fernandez, F. P. Cossio and M. A. Sierra, Chem. Rev., 2009, 109, 6687–6711; (g) I. D. Gridnev, Coord. Chem. Rev., 2008, 252, 1798–1818; (h) M. T. Reetz, Adv. Organomet. Chem., 1977, 16, 33–65.
3. (a) H. M. Buck, Open J. Phys. Chem., 2013, 3, 119–125; (b) I. Fernandez, F. M. Bickelhaupt and F. P. Cossío, Chem.–Eur. J., 2012, 18, 12395–12403.
4. M. T. Reetz, Angew. Chem., Int. Ed. Engl., 1972, 11, 131–132.
5. For C–C stationary scaffold, see selected examples: (a) D. C. Braddock, D. Roy, D. Lenoir, E. Moore, H. S. Rzepa, J. I.-C. Wu and R. Schleyer, Chem. Commun., 2012, 48, 8943–8945; (b) J. G. Buchanan, G. D. Ruggiero and I. H. Williams, Org. Biomol. Chem., 2008, 6, 66–72; (c) F. Stöckner, R. Beckert, D. Gleich, E. Birckner, W. Günther and H. Görls, J. Org. Chem., 2007, 8, 1237–1243; (d) F. Stöckner, C. Käpplinger, R. Beckert and H. Görls, Synlett, 2005, 643–645; (e) G. D. Ruggiero and I. H. Williams, Chem. Commun., 2002, 732–733; (f) K. Sato, Y. Yamashita and T. Mukai, Tetrahedron Lett., 1981, 22, 5303–5306.
6. (a) E. Hupe, D. Denisenko and P. Knochel, Tetrahedron, 2003, 59, 9187–9198; (b) G. Zweifel and H. Arzoumanian, J. Am. Chem. Soc., 1967, 89, 5086–5088.
7. J. W. Davies, J. R. Malpas and M. P. Walker, Chem. Commun., 1985, 686–687.
8. (a) M. T. Reetz, M. Kliment, M. Plachky and N. Greif, Chem. Ber., 1976, 108, 2728–2742; (b) M. T. Reetz, M. Kliment and M. Plachky, Chem. Ber., 1976, 108, 2716–2727; (c) M. T. Reetz, M. Kliment and M. Plachky, Angew. Chem., Int. Ed. Engl., 1974, 13, 813–814.
9. A. Alexakis, J. Hanaizi, D. Jachiet, J.-F. Normant and L. Toupet, Tetrahedron Lett., 1990, 31, 1271–1274.
10. (a) W. Uhl, J. Bohnemann, M. Layh and E.-U. Wuerthwein, Chem.–Eur. J., 2014, 20, 8771–8781; (b) A. Naka, S. Ueda, J. Ohshita, A. Kunai, T. Miura, H. Kobayashi and M. Ishikawa, Organometallics, 2008, 27, 2922–2928; (c) Y. Yu and S. Feng, Int. J. Quantum Chem., 2007, 107, 105–115; (d) Y. Yu and S. Feng, J. Phys. Chem. A, 2006, 110, 12463–12469; (e) Y. Yu, S. Feng and D. Feng, J. Phys. Chem. A, 2005, 109, 3663–3668; (f) L. Claes, J.-P. François and M. S. Deleuze, J. Am. Chem. Soc., 2003, 125, 7129–7138; (g) H. Bürger and P. Moritz, Organometallics, 1993, 12, 4930–4939; (h) R. Köster, G. Seidel, R. Boese and B. Wrackmeyer, Chem. Ber., 1990, 123, 1013–1028; (i) M. T. Reetz and N. Greif, Angew. Chem., Int. Ed. Engl., 1977, 16, 712–713; (j) W. I. Bevan, R. N. Haszeldine, J. Middleton and A. E. Tipping, J. Organomet. Chem., 1970, 23, C17–C19.
11. A. Haas, Angew. Chem., Int. Ed. Engl., 1965, 4, 1014–1023.
12. N. J. Rijs, B. F. Yates and R. A. J. O'Hair, Chem.–Eur. J., 2010, 16, 2674–2678.
13. T. Harada, D. Hara, K. Hattori and A. Oku, Tetrahedron Lett., 1988, 29, 3821–3824.
14. (a) G. Erker and R. Petrenz, Organometallics, 1992, 11, 1646–1655; (b) G. Erker and R. Petrenz, Chem. Commun., 1989, 345–346; (c) E. Negishi, K. Akiyoshi, B. O'Corner, K. Takagi and G. Wu, J. Am. Chem. Soc., 1989, 111, 3089–3091; (d) A. S. Ward, E. A. Mintz and M. P. Kramer, Organometallics, 1988, 7, 8–12; (e) G. Erker and F. Rosenfeldt, J. Organomet. Chem., 1980, 188, C1–C4; (f) G. Erker and F. Rosenfeldt, Angew. Chem., Int. Ed. Engl., 1978, 17, 605–606.
15. J. Faessler and S. Bienz, Organometallics, 1994, 13, 4704–4707.
16. K. M. Baines, A. G. Brook, R. R. Ford, P. D. Lickiss, A. K. Sexana, W. J. Chatterton, J. F. Sawyer and B. A. Behnam, Organometallics, 1989, 8, 693–709.
17. E. Gellermann, U. Klingebiel, T. Pape, F. Dall'Antonia, T. R. Schneider and S. Schmatz, Z. Anorg. Allg. Chem., 2001, 627, 2581–2588.
18. (a) C. Ekber, S. Schamatz, F. Diedric and U. Klingebiel, Silicon Chem., 2003, 2, 117–123; (b) F. Diedric, U. Klingebiel and M. Schäfer, J. Organomet. Chem., 1999, 588, 242–246; (c) T. Albercht, G. Elter and A. Meller, Z. Anorg. Allg. Chem., 1999, 625, 1453–1456.
19. (a) H. B. Yokelson, D. A. Siegel, A. J. Millevolte, J. Maxka and R. West, Organometallics, 1990, 9, 1005–1010; (b) H. B. Yokelson, D. A. Siegel and R. West, J. Am. Chem. Soc., 1986, 108, 4239–4241.
20. (a) P. Braunstein, M. Knorr, G. Reinhard, U. Schubert and T. Stährfeldt, Chem.–Eur. J., 2000, 6, 4265–4278; (b) P. Braunstein, M. Knorr, B. Hirle, G. Reinhard and U. Schubert, Angew. Chem., Int. Ed. Engl., 1992, 104, 1583–1585.
21. A. Sekiguchi, R. Izumi, V. Y. Lee and M. Ichinohe, Organometallics, 2003, 22, 1483–1486.
22. A. Takle and P. Kocienski, Tetrahedron, 1990, 46, 4503–4516.
23. P. Kocienski and C. Barber, Pure Appl. Chem., 1990, 62, 1933–1940.
24. P. Kocienski, C. J. Love, R. J. Whitby, G. Costello and D. A. Roberts, Tetrahedron, 1989, 45, 3839–3848.
25. (a) S. E. Denmark, J. I. Montgomery and L. A. Kramps, J. Am. Chem. Soc., 2006, 128, 11620–11630; (b) S. E. Denmark and J. I. Montgomery, Angew. Chem., Int. Ed., 2005, 44, 3732–3736.
26. (a) P. Kocienski, C. Yates, S. D. A. Street and S. F. Campbell, J. Chem. Soc., Perkin Trans. 1, 1987, 2183–2187; (b) P. Kocienski, S. D. A. Street, C. Yates and S. F. Campbell, J. Chem. Soc., Perkin Trans. 1, 1987, 2189–2194.
27. E. Lemos, F.-H. Poŕee, A. Commercon, J.-F. Betzer, A. Pancrazi and J. Ardisson, Angew. Chem., Int. Ed., 2007, 46, 1917–1921.
28. W. Ren, Y. Bian, Z. Zhang, H. Shang, P. Zhang, Y. Chen, Z. Yang, T. Luo and Y. Tang, Angew. Chem., Int. Ed., 2012, 51, 6984–6988.
29. W. Li, T. G. LaCour and P. L. Fuchs, J. Am. Chem. Soc., 2002, 124, 4548–4549.
30. (a) V. C. Purohit, A. S. Matla and D. Romo, J. Am. Chem. Soc., 2008, 130, 10478–10479; (b) I. Arrastia, B. Lecea and F. P. Cossío, Tetrahedron Lett., 1996, 37, 245–248; (c) J. Mulzer, A. Pomtner, R. Strasser, K. Hoyer and U. Nagel, Tetrahedron Lett., 1995, 36, 3679–3682; (d) T. H. Black and T. S. McDermott, J. Chem. Soc., Chem. Commun., 1991, 184–185; (e) T. H. Black, S. A. Eisenbeis, T. S. McDermott and S. L. Maluleka, Tetrahedron, 1990, 46, 2307–2316; (f) T. H. Black, J. A. Hall and R. G. Sheu, J. Org. Chem., 1988, 53, 2371–2374; (g) T. H. Black and J. D. Fields, Synth. Commun., 1988, 29, 1747–1750; (h) J. Mulzer and G. Brütrup, Angew. Chem., Int. Ed. Engl., 1979, 18, 793–794.
31. S. Lin and S. J. Danishefsky, Angew. Chem., Int. Ed., 2002, 41, 512–515.
32. S. M. Bachrach, Computational Organic Chemistry, Wiley, 2nd edn, 2014.
33. T. Mahmood, M. Arshad, M. A. Gilani and K. Ayub, J. Mol. Model., 2015, 21, 1–9.
34. H. V. Pham, A. S. Karns, C. D. Vanderwal and K. N. Houk, J. Am. Chem. Soc., 2015, 137, 6956–6964.
35. S. Yamabe, G. Zeng, W. Guan and S. Sakaki, J. Comput. Chem., 2014, 35, 2195–2204.
36. Maria, M. Hanif, T. Mahmood, R. Ludwig and K. Ayub, J. Mol. Model., 2014, 20, 2304–2307.
37. M. W. Lodewyk, D. Willenbring and D. J. Tantillo, Org. Biomol. Chem., 2014, 12, 887–894.
38. I. Fernandez, M. A. Sierra and F. P. Cossio, Chem.–Eur. J., 2006, 12, 6323–6330.
39. (a) C. A. Leverett, V. C. Purohit, A. G. Johnson, R. L. Davis, D. J. Tantillo and D. Romo, J. Am. Chem. Soc., 2012, 134, 13348–13356; (b) R. L. Davis, C. A. Leverett, D. Romo and D. J. Tantillo, J. Org. Chem., 2011, 76, 7167–7174.
40. N. J. Rijs, G. B. Sanvido, G. N. Khairallah and R. A. J. O'Hair, Dalton Trans., 2010, 39, 8655–8662.
41. N. J. Rijs and R. A. J. O'Hair, Organometallics, 2010, 29, 2282–2291.
42. R. L. Davis and D. J. Tantillo, J. Org. Chem., 2010, 75, 1693–1700.
43. A major application of cyclohexane is an industrial scale preparation of adipic acid and caprolactam, which are used to manufacture nylon.
44. D. H. R. Barton and A. J. Head, J. Chem. Soc., 1956, 932–937.
45. C. A. Grob and S. Winstein, Helv. Chim. Acta, 1952, 35, 782–802.
46. This exceptional increase in the bond distance is due to higher synchronicity values and computed synchronicity values for NH₂, OH and CN are 0.61, 0.85 and 0.63 a.u. respectively.
47. C. Hansch, A. Leo and R. W. Taft, Chem. Rev., 1991, 91, 165–195.
48. E. V. Anslyn and D. A. Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006, p. 455.
49. Compared to Ph groups substituted cyclohexane, a slight difference in the energy barriers is noticed for the CH₃, NH₂, OH, OCH₃, Cl, C(O)H, C(O)CH₃ and COOH groups bearing Ph substituted cyclohexanes, both at meta and para positions separately.
50. For a selection of reviews concering captodative substitution effect, see: (a) H. G. Viehe, Z. Janousek, R. Merenyi and L. Stella, Acc. Chem. Res., 1985, 18, 148–154; (b) R. Sustmann and H. G. Korth, Adv. Phys. Org. Chem., 1990, 26, 131–178.
51. For selected examples of captodative substitution in pericyclic transformations, see: (a) T. J. Greshock and R. L. Funk, J. Am. Chem. Soc., 2006, 128, 4946–4947; (b) T.-Q. Yu, Y. Fu, L. Liu and Q.-X. Guo, J. Org. Chem., 2006, 71, 6157–6164; (c) N. A. Magomedov, P. L. Ruggiero and Y. Tang, J. Am. Chem. Soc., 2004, 126, 1624–1625; (d) J. Mertes and J. Mattay, Helv. Chim. Acta, 1988, 71, 742–748; (e) J. L. Boucher and L. Stella, Tetrahedron, 1986, 42, 3871–3885; (f) J. L. Boucher and L. Stella, Tetrahedron Lett., 1985, 26, 5041–5044; (g) J. L. Boucher and L. Stella, Tetrahedron, 1985, 41, 875–887.
52. M. J. Frisch, et al., GAUSSIAN09, (Revision D.01), Gaussian, Inc., Wallingford CT, 2013; the full reference can be found in the ESI.†.
53. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules; Oxford University Press, U.K., 1989.
54. (a) P. J. Stephens, F. J. Devlin, C. F. Chabalowski and M. J. Frisch, J. Chem. Phys., 1994, 98, 11623–11627; (b) A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652; (c) A. D. Becke, J. Chem. Phys., 1993, 98, 1372–1377; (d) C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 785–789.
55. (a) C. Gonzalez and H. B. Schlegel, J. Phys. Chem., 1990, 94, 5523–5527; (b) C. Gonzalez and H. B. Schlegel, J. Phys. Chem., 1989, 90, 2154–2161; (c) K. Fukui, Acc. Chem. Res., 1981, 14, 363–368; (d) Due to unsuccessful IRC calculations for some cases, the transition state structures were linked to their corresponding minima via perturbing their structures in the direction along the vibrational coordinate linked with the imaginary frequency, followed by optimization.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra25482e

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