Scheme 1. Model for explaining regioselectivity in intramolecular g-hydroxypropyl bromonium ion-opening directed by strain- (top) and charge effects (bottom; E = CO₂Et; R = H or CH₃, R’ = H, CH₃, or phenyl; R’’ = H, CH₃).

Results: For computing a consistent set of relative Gibbs free energies of dimethyl tetrahydropyrans I–VI, we used Becke’s 3 parameter hybrid functional in combination with the 6-31+G** basis set. The chosen computational method reproduces A-values of alkyl substituted tetrahydropyrans within a precision that is close to the experimental accuracy for determing such data, for example, from NMR-spectroscopy. The A-value reflects the degree of steric interaction between a substituent and the (hetero)cyclic core, the substituent is attached to and therefore poses a benchmark for assessing theoretical methods for conformational analysis.

Figure 1. Structure formulas, indices, and calculated (B3LYP/6-31+G**//B3LYP/6-31+G**) DG_298.15-values in kJ mol^–1 (numbers in brackets) of dimethyltetrahydropyrans I–VI.

In the computational study, dimethyltetrahydropyran minimum structures were obtained from gradient searches. Minima were verified as such by computing second derivatives of wavefunctions by diagonalizing Hessian matrices. Minimum structures lacked in negative eigenvalues and imaginary frequencies. Approximate Gibbs free energies (G_298.15) were computed from thermochemical analysis at 298.15 K, using unscaled frequency calculations, including zero-point vibrational energy corrections, thermal corrections, and entropy.

The lowest in energy isomer from the computed set of compounds (Figure 1), and from all possible dimethyltetrahydropyrans, is the stereoisomer of 2,6-dimethyltetrahydropyran Ia having both methyl groups attached equatorially. Theory predicts for the remaining stereoisomers of I higher DG_298.15-values as the number of axial methyl groups increases (Ib and Ic), and the distance between methyl carbons becomes smaller (Figure 2). Both observations are consistent with the basics of conformational analysis. The computed value of +34.9 kJ mol^–1 for Ic is larger than twice the computed A-value for the methyl group in 2-methyltetrahydropyran (14.9 kJ mol^–1 for 298.15 K; experimental: 12.0 ± 0.8 kJ mol^–1 at 188–173 K) on the same level of theory, pointing to notable steric repulsion between axial methyl groups at C2 and C6 in cis-2,6-dimethyltetrahydropyran Ic. In the equilibrium structure, axial methyl carbons of Ic are separated 3.332 Å apart, which is less than the sum of 3.40 Å for two carbon van der Waals-radii. The carbon-carbon distance of substituents in diaxial isomers of cis-2,4- and cis-3,5-dimethyltetrahydropyran is larger (3.499 Å for IId, and 3.329 Å for IIIc) but still expected to induce strain, because the van der Waals radius of a methyl group is by the distance of the carbon-hydrogen bond larger than the van der Waals radius of a carbon atom. Since close contacts between methyl groups cause steric repulsion, and the structural response to repulsion is strain, we refer to the computed DG_298.15-values as strain energy. Strain, particularly in compounds I–III is evident from a flattening of tetrahydropyran puckering (Figure 3), and an offset of methyl substituents from idealized axial positions to the periphery.

To quantify the effect of 1,3-dimethyl substitution on puckering, we subtracted the sum of absolute values of the six endocyclic torsion angles [S(|w_ijⁿ|) for compounds I–III from the respective value S(|w_ij^thp|) of the parent heterocycle tetrahydropyran (thp) (Figure 3). A plot of this puckering parameter versus computed relative Gibbs free energies is linear for I–III, indicating that the effect of axial methyl substitution on flattening of the heterocyclic core is additive. The effect of substituents in positions 2,6 thereby is smaller than in positions 2,4 and largest in positions 3,5.

Figure 2. Correlation between methyl carbon distances (d_C,C) and calculated DG_298.15-values (cf. Figure 3) of Ia–c [●; d_C,C = –0.04(G_298.15) Å mol kJ^–1+ 4.84 Å; R2 = 0.978], IIa–d [○; d_C,C = –0.05(DG_298.15) Å mol kJ^–1+ 5.75 Å; R2 = 0.978], and IIIa–c (◊; d_C,C = –0.08(G_298.15) Å mol kJ^–1+ 6.85 Å; R2 = 0.997).

Figure 3. Correlation of a parameter describing puckering changes in dimethyltetrahydropyrans Ia–c, referenced toward tetrahydropyran (thp) on the basis of endocyclic dihedral angles [S(Dw_ij) = S(|w_ij^thp|) – S(|w_ij^I–III |)] and DG_298.15-values (Figure 3), whereby S(|w_ij^thp|) – S(|w_ij^I–III |) denotes summation of absolute values of endocyclic torsion angles between atoms i and j in tetrahydropyran (thp) minus S(|w_ij^I–III |) for compounds I–III [for Ia–c (●): Dw_ij = –0.80(DG_298.15) deg mol kJ^–1 + 0.47 deg; R2 = 0.986; for IIa–c (○): Dw_ij = –0.61(DG_298.15) deg(rees) mol kJ^–1 + 6.82 deg, R2 = 0.983; for for IIIa–c (◊): Dw_ij = 0.36(DG_298.15) deg mol kJ^–1– 8.19 deg; R2 = 0.904].

A second structural motif leading to strain in tetrahydropyran is geminal dimethyl substitution (see IV–VI, Figure 1). If geminal dimethyl substitution is already part of the alkenol used for constructing the tetrahydropyran nucleus, this backside strain is less relevant for describing regioselectivity of C,O-cyclization. If carbons 2 and 6 in tetrahydropyran both bear two methyl substituents, and one dimethyl substitution is newly formed in the course of the cyclization, the situation becomes less favorable. Geometric changes arising from backside strain, for example, between methyl groups at carbon 2 intensify repulsion between the axially positioned methyl group at C2 and a second axial methyl group, for example, located at C6 (cf. section 2.4.2).

On the thermochemistry of alkenol cyclization

To find out whether methyl substitution guides regioselectivity in cyclization of tertiary prenyl type alkenols, we calculated thermochemistry for the isomerization of substrate VII into 2,2-dimethyl-5-isopropyl tetrahydrofuran (VIII) and 2,2,6,6-tetramethyl tetrahydropyran (IX) (Scheme 2). Equilibrium structures of alkenol VII and tetrahydrofuran VIII  thereby were obtained from usage directed conformational searches (force field) leading to minima, which served as input for density functional theory calculations. The heterocyclic core of the minimum structure of tetrahydrofuran VII adopts a ₃T⁴ twist conformation, similar to the heterocyclic core found in the solid state structure of cis-3d. The isopropyl substituent and one of the methyl groups in this conformation are bound pseudoequatorially, and the second methyl group pseudoaxially. The distances between the secondary isopropyl carbon and the two methyl carbons at C2 are larger than the distances between methyl carbons at positions 2 and 6 in tetrahydropyran IX. In a reversible reaction, B3LYP-theory thus favors tetrahydrofuran formation from alkenol VII. MP2-theory leads to the same result, although the driving force for tetrahydrofuran formation is less pronounced.