An axial tert-butyl group in strained cyclo­hexene: X-ray analysis and theoretical calculations of 2-(2-tert-butyl­cyclo­hex-3-en­yl)propan-2-ol

The structure of the title compound, C₁₃H₂₄O, (I), shows a sofa conformation of the ring with two pseudo-axial substituents. The dihedral angle between these substituents is 131.56 (12)°. Calculations using the B3LYP/6-31G* level of theory show two minima, one corresponding to the crystal structure and the other to a boat conformation of the ring with two equatorial substituents. The energy of this latter conformation is 17.4 kcal mol^-1 higher than that of (I). The mol­ecule forms an infinite co-operative hydrogen-bonded chain running in the b direction.

S1. Comment

Strained molecules have been known for about a century, but interest in these species is still relevant today. For six-membered ring molecules having strong interactions between a tert-butyl group and a vicinal substituent, the gauche interaction provides sufficient steric strain to produce unique conformational (Aycard & Bodot, 1975; Stolow, Groom & Lewis, 1969; Stolow, Gallo & Marini, 1969; Viani & Lapasset, 1981) and particular reaction stereoselectivities (Aycard & Bodot, 1973; Pizzala et al., 1978; Bouteiller-Prati et al., 1981). Thus, we have shown that cis-2-tert-butylcyanocyclohexane is more stable than its trans isomer by 1.5 kcal mol^-1 (Aycard & Bodot, 1973) (1 kcal mol^-1 = 4.184 kJ mol^-1). For cyclohexanones (Lafrance et al., 1976; Viani et al., 1978) and trans-3-tert-butyl-4-X-cyclohexenes in solution, large conformational heterogeneities have been detected and the existence of pseudo-axial tert-butyl has been postulated (Aycard & Bodot, 1975; Lafrance et al., 1977; Bouteiller-Prati et al., 1976). X-ray analysis of a series of congested 3-tert-butyl-4-X-cyclohexene derivatives (X = CN or CO₂CH₃) has shown that trans stereoisomers exhibit a sofa conformation which is expected to be only 0.8 kcal mol^-1 higher than for the half-chair (Bucourt, 1974) with a pseudo-equatorial tert-butyl group (Viani et al., 1978; Viani & Lapasset, 1981; Cossu et al., 1981). For the cis isomer, we have observed a half-chair conformation with a pseudo-equatorial tert-butyl group (Viani et al., 1981, 1985; Viani & Lapasset, 1981). We have never obtained a conformation with a pseudo-axial tert-butyl group.

In solution, the title compound, (I), which is similar to a 3,4-di-tert-butyl derivative, presents in its ¹H NMR spectrum a very small trans ³J_HH coupling constant value of 5.8 Hz between H atoms bonded to C atoms 4 and 5 (Bouteiller-Prati et al., 1976). This low value is indicative of a conformational heterogeneity with a majority of a pseudo axial tert-butyl conformer (>60%). To obtain structural data on this possible species, we carried out B3LYP calculations (GAUSSIAN03; Frisch et al., 2004) and X-ray analysis on a crystal obtained from the NMR solution of trans-3,6,6-trideuterio-3-tert-butyl 4-dimethylcarbinol cyclohexene, (I). The best way to describe the ring conformation is to use the endocyclic torsion angles Φ_ij (central bond ij). The values obtained from our X-ray data are reported in Table 3, and are compared with the classic half-chair and sofa values (Bucourt, 1974) and with those obtained from B3LYP calculations for the two expected possible conformers, (I) and (I').

We can see that the absolute value of the torsion angle Φ₂₃ [-6.6 (2)°] is smaller than the half-chair. In fact, the ring has a quasi-pure sofa conformation with a minor twisting of the double bond [-2.8 (3)°], as observed in other trans stereoisomers of 3-tert-butyl-4-X-cyclohexene derivatives (Viani et al., 1978, 1981). Atoms C1–C4 and C6 are coplanar to within 0.06 Å. There is also good agreement between the experimental and calculated values for all the torsion angles (ΔΦmax ≈ 2°). The value of the C1—C2—C3—C7 dihedral angle is a measure of the inclination of the C3—C7 bond with respect to the double-bond plane. The value obtained for (I) [-125.36 (19)°] is similar to that determined for trans-1-acetoxy 3-tert-butyl-4-cyanocyclohexene [-125.1 (3)°; Refererence?] and is indicative of a quasi-axial position of the tert-butyl substituent. The dihedral difference (Φ₃₄ - Φ₄₅) is a measure of the puckering of the ring in the C4 region (Viani et al., 1981).

A low value with respect to the half-chair value (109°) is indicative of an axial position and a large value of an axial position [Should one of these `axial' be `equatorial'?] (Chiang & Bauer, 1969; Scharpen et al., 1968). The value obtained for (I) (87°) shows that the dimethylcarbinol group adopts an isoclinal position as the tert-butyl. The C7—C3—C4—C11 torsion angle between the two substituents is 131.56 (12)° (130° theoretically), larger than the values obtained in other strained 3,4-cyclohexenes [84.4 (3), 77.4 (3) and 76.4 (3)°; Viani et al., 1979]. This value is indicative of an increasing axiality of the two substituents, as shown in Fig. 1, and allows the minimization of the gauche interaction between the two large substituents.

The bond lengths and the endocyclic valence angle values show moderate fluctuations (Δl ≈ 0.03 Å and ΔΘ ≈ 4°) compared with those obtained for similar compounds (Viani et al., 1978; Viani & Lapasset, 1981) and are similar to the values obtained from theoretical calculations. The exocyclic valence angles around the tert-butyl group are very close to the mean value observed in 3-tert-butylcyclohexenes (110.7°) and tert-butylcyclohexane (113°) compounds (Viani et al., 1978, 1981; Viani & Lapasset, 1981; Lectard et al., 1976).

Non-bonded interactions are the driving force of the geometric modifications which must give the best compromise between the different non-bonded distances. Short distances are associated with repulsive non-bonded energies. The short distances here have been selected on the basis of Allinger parametrizations; some of them must be considered as very short distances and are at the origin of the strongest non-bonded interactions (Handal et al., 1977; Allinger, 1976). Some of them are caused by the C9 methyl group of the tert-butyl [interacting?] with the ring atoms C2 and C4 and with the H atom bored [bonded?] by these atoms (Table 6).

Analysis of the packing shows an O—H···O hydrogen bond that links the molecules into infinite chains running in the b-axis direction (Fig. 2 and Table 2). These intermolecular bonds stabilize the position of the hydroxyl H atom in a gauche position. The C4—C11—O1—H11 dihedral angle is -65.2 (18)°. In the optimized structure of this conformer, similar to the gas phase, the C4—C11—O1—H11 dihedral angle is 180°.

The theoretical calculations for (I) give very good accuracy between the calculated geometric parameters and those obtained from the X-ray crystal data. For this, starting from a sofa conformation, we have modelled the structure for a diequatorial conformer. We obtain another energy minimum for the structure of (I'). This structure is 17.4 kcal mol^-1 less stable than (I). If the bond lengths and valence bond angles are similar for the two conformers (Tables 4 and 5), the values of the endocyclic torsion angles (Table 3) are very different and indicate a twist-boat conformation. In solution, this compound can be neglected.

Related literature

For related literature, see: Allinger (1976); Aycard & Bodot (1973, 1975); Bouteiller-Prati, Bouteiller & Aycard (1976, 1981); Bucourt (1974); Chiang & Bauer (1969); Cossu et al. (1981); Frisch (2004); Handal et al. (1977); Lafrance et al. (1976, 1977); Lectard et al. (1976); Parr & Yang (1989); Pizzala et al. (1978); Prince (1982); Scharpen et al. (1968); Stolow, Gallo & Marini (1969); Stolow, Groom & Lewis (1969); Viani & Lapasset (1981); Viani et al. (1978, 1979, 1985); Viani, Cossu & Lapasset (1981); Watkin (1994).

S2. Experimental

The synthesis of the title compound has been described previously by Bouteiller-Prati et al. (1981). The compound was obtained as white needles by crystallization from a solution in chloroform. The computational method to establish the molecular structure and the relative energy of the two conformations was that of ab initio calculations carried out using GAUSSIAN03 (Frisch et al., 2004). The different systems were optimized at the B3LYP/6–31G* level of theory (Parr & Yang, 1989).

S3. Refinement

Weighting was based on a Chebychev polynomial (Watkin, 1994; Prince, 1982). All H atoms were discernible in a difference Fourier map. The C—H distances were constrained to 0.95 and 0.98 Å for aryl and methyl H atoms, respectively, with U_iso(H) = 1.2U_eq(C). The positional parameter of atom H11 was refined freely and U_iso(H) = 1.5U_eq(O).

Computing details

Data collection: COLLECT (Nonius, 1997); cell refinement: DENZO/SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO/SCALEPACK (Otwinowski & Minor, 1997); program(s) used to solve structure: SIR92 (Altomare et al., 1994); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and PLATON (Spek, 2003); software used to prepare material for publication: CRYSTALS (Betteridge et al., 2003).

Figures

	Fig. 1. A view of the title molecule, with the atom-labelling scheme. Displacement ellipsoids are drawn at the 50% probability level and H atoms are shown as spheres of arbitary radii.
	Fig. 2. A motif of the O—H···O hydrogen bonds forming chains in the title structure.

2-(2-tert-butylcyclohex-3-enyl)propan-2-ol

Crystal data

C13H24O	F(000) = 440
Mr = 196.33	Dx = 1.042 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 15244 reflections
a = 13.0192 (4) Å	θ = 1.6–30.1°
b = 6.0581 (2) Å	µ = 0.06 mm^−1
c = 16.3514 (4) Å	T = 294 K
β = 103.915 (2)°	Needle, colourless
V = 1251.81 (7) Å^3	0.30 × 0.25 × 0.25 mm
Z = 4

Data collection

Nonius KappaCCD diffractometer	2533 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.040
Graphite monochromator	θmax = 30.1°, θmin = 1.6°
ϕ scans	h = −18→18
15244 measured reflections	k = −8→8
3625 independent reflections	l = −22→22

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.057	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.105	H atoms treated by a mixture of independent and constrained refinement
S = 0.91	Method, part 1, Chebychev polynomial (Watkin, 1994, Prince, 1982), [weight] = 1.0/[A0*T0(x) + A1*T1(x) ··· + An-1]*Tn-1(x)], where Ai are the Chebychev coefficients listed below and x = F /Fmax. Method = Robust Weighting (Prince, 1982), W = [weight] * [1-(δF/6*σF)^2]^2 Ai are: 430, 475, 362, 83.5.
2533 reflections	(Δ/σ)max = 0.000254
130 parameters	Δρmax = 0.19 e Å^−3
0 restraints	Δρmin = −0.17 e Å^−3
93 constraints

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. The reflections 1 1 0; 0 1 1 have been measured with too low intensities. It might be caused by some systematical error, probably by shielding by a beam stop of this diffraction. There were not used in the refinement.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
C1	0.60835 (13)	0.1174 (3)	0.27863 (12)	0.0627
C2	0.64613 (13)	0.1492 (3)	0.21159 (11)	0.0539
C3	0.73873 (10)	0.0307 (2)	0.19137 (8)	0.0399
C4	0.79559 (10)	−0.1201 (2)	0.26492 (8)	0.0357
C5	0.71811 (12)	−0.2177 (3)	0.31305 (9)	0.0467
C6	0.64943 (13)	−0.0505 (3)	0.34399 (11)	0.0595
C7	0.70934 (12)	−0.0792 (3)	0.10229 (9)	0.0480
C8	0.80774 (16)	−0.1728 (5)	0.08026 (11)	0.0861
C9	0.66458 (19)	0.0944 (4)	0.03570 (11)	0.0811
C10	0.62814 (17)	−0.2615 (4)	0.09684 (12)	0.0757
C11	0.89546 (10)	−0.0086 (3)	0.32095 (8)	0.0402
C12	0.87721 (14)	0.2158 (3)	0.35544 (12)	0.0586
C13	0.95169 (13)	−0.1590 (3)	0.39207 (9)	0.0546
O1	0.96826 (9)	0.0342 (2)	0.26814 (7)	0.0558
H1	0.5524	0.2056	0.2851	0.0756*
H2	0.6124	0.2548	0.1731	0.0656*
H3	0.7899	0.1467	0.1877	0.0487*
H4	0.8218	−0.2462	0.2384	0.0436*
H51	0.7591	−0.2966	0.3616	0.0566*
H52	0.6719	−0.3203	0.2759	0.0566*
H61	0.6912	0.0225	0.3938	0.0743*
H62	0.5904	−0.1265	0.3581	0.0743*
H81	0.8388	−0.2834	0.1208	0.1040*
H82	0.8577	−0.0559	0.0811	0.1040*
H83	0.7890	−0.2375	0.0251	0.1040*
H91	0.6466	0.0263	−0.0189	0.0950*
H92	0.7165	0.2075	0.0366	0.0950*
H93	0.6023	0.1587	0.0475	0.0950*
H101	0.6556	−0.3718	0.1385	0.0912*
H102	0.6135	−0.3271	0.0418	0.0912*
H103	0.5641	−0.2012	0.1069	0.0912*
H11	0.9871 (18)	−0.086 (4)	0.2534 (15)	0.0840*
H121	0.9429	0.2716	0.3890	0.0716*
H122	0.8271	0.2025	0.3897	0.0716*
H123	0.8502	0.3155	0.3097	0.0716*
H131	1.0129	−0.0851	0.4253	0.0646*
H132	0.9732	−0.2919	0.3689	0.0646*
H133	0.9044	−0.1952	0.4270	0.0646*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.0498 (9)	0.0728 (12)	0.0709 (11)	0.0143 (9)	0.0251 (8)	−0.0069 (10)
C2	0.0509 (8)	0.0517 (9)	0.0603 (9)	0.0152 (7)	0.0156 (7)	0.0057 (8)
C3	0.0369 (6)	0.0430 (7)	0.0409 (7)	0.0005 (6)	0.0119 (5)	0.0035 (6)
C4	0.0362 (6)	0.0376 (7)	0.0351 (6)	0.0001 (5)	0.0118 (5)	−0.0018 (5)
C5	0.0471 (8)	0.0504 (8)	0.0442 (7)	−0.0093 (7)	0.0138 (6)	0.0041 (7)
C6	0.0486 (9)	0.0820 (13)	0.0546 (9)	−0.0069 (9)	0.0260 (7)	−0.0022 (9)
C7	0.0422 (7)	0.0640 (10)	0.0372 (7)	0.0034 (7)	0.0083 (6)	0.0020 (7)
C8	0.0647 (11)	0.149 (2)	0.0447 (9)	0.0267 (13)	0.0142 (8)	−0.0209 (12)
C9	0.0946 (15)	0.0952 (17)	0.0473 (9)	0.0064 (13)	0.0048 (9)	0.0167 (10)
C10	0.0873 (14)	0.0804 (14)	0.0560 (10)	−0.0232 (12)	0.0104 (9)	−0.0137 (10)
C11	0.0372 (6)	0.0478 (8)	0.0381 (6)	−0.0034 (6)	0.0139 (5)	−0.0028 (6)
C12	0.0547 (9)	0.0522 (9)	0.0692 (11)	−0.0099 (8)	0.0160 (8)	−0.0167 (8)
C13	0.0507 (8)	0.0657 (11)	0.0430 (8)	−0.0016 (8)	0.0030 (6)	0.0004 (8)
O1	0.0414 (6)	0.0790 (9)	0.0515 (6)	−0.0096 (6)	0.0200 (5)	−0.0016 (6)

Geometric parameters (Å, º)

C1—C2	1.319 (2)	C8—H81	0.960
C1—H1	0.930	C8—H82	0.960
C2—C3	1.506 (2)	C8—H83	0.960
C2—H2	0.930	C9—H91	0.960
C3—C4	1.5493 (18)	C9—H92	0.960
C3—C7	1.563 (2)	C9—H93	0.960
C3—H3	0.980	C10—H101	0.960
C4—H4	0.980	C10—H102	0.960
C4—C5	1.5391 (17)	C10—H103	0.960
C4—C11	1.5534 (18)	C11—C12	1.512 (2)
C5—C6	1.517 (2)	C11—C13	1.520 (2)
C5—H51	0.970	C11—O1	1.4507 (15)
C5—H52	0.970	C12—H121	0.960
C6—C1	1.479 (3)	C12—H122	0.960
C6—H61	0.970	C12—H123	0.960
C6—H62	0.970	C13—H131	0.960
C7—C8	1.521 (2)	C13—H132	0.960
C7—C9	1.525 (2)	C13—H133	0.960
C7—C10	1.517 (2)	O1—H11	0.82 (2)
C1—C2—C3	126.23 (15)	C7—C8—H82	109.1
C2—C3—C4	111.64 (11)	C7—C8—H83	109.7
C2—C3—C7	112.21 (12)	C7—C9—H91	109.5
C3—C4—C5	111.96 (11)	C7—C9—H92	109.5
C3—C4—C11	112.17 (11)	C7—C9—H93	109.4
C3—C7—C8	110.37 (12)	C7—C10—H101	109.3
C3—C7—C9	109.72 (14)	C7—C10—H102	109.6
C3—C7—C10	112.08 (12)	C7—C10—H103	109.6
C4—C3—C7	115.88 (12)	C11—C4—H4	105.6
C4—C5—C6	115.16 (13)	C11—C12—H121	109.4
C4—C11—C12	115.25 (12)	C11—C12—H122	109.4
C4—C11—C13	111.81 (12)	C11—C12—H123	109.7
C4—C11—O1	107.49 (10)	C11—C13—H131	109.6
C5—C4—C11	115.09 (11)	C11—C13—H132	109.5
C5—C6—C1	110.99 (13)	C11—C13—H133	109.4
C6—C1—C2	123.94 (15)	C11—O1—H11	107.4 (16)
C8—C7—C9	106.68 (15)	C12—C11—C13	110.10 (13)
C8—C7—C10	109.22 (18)	C12—C11—O1	104.19 (12)
C9—C7—C10	108.60 (15)	C13—C11—O1	107.40 (12)
C1—C2—H2	116.9	H51—C5—H52	109.5
C1—C6—H61	109.0	H61—C6—H62	109.5
C1—C6—H62	109.2	H81—C8—H82	109.5
C2—C1—H1	118.1	H81—C8—H83	109.5
C2—C3—H3	105.3	H82—C8—H83	109.5
C3—C2—H2	116.9	H91—C9—H92	109.5
C3—C4—H4	105.6	H91—C9—H93	109.5
C4—C3—H3	105.4	H92—C9—H93	109.5
C4—C5—H51	108.0	H101—C10—H102	109.5
C4—C5—H52	108.1	H101—C10—H103	109.5
C5—C4—H4	105.5	H102—C10—H103	109.5
C5—C6—H61	109.1	H121—C12—H122	109.5
C5—C6—H62	109.0	H121—C12—H123	109.5
C6—C1—H1	118.0	H122—C12—H123	109.5
C6—C5—H51	108.0	H131—C13—H132	109.5
C6—C5—H52	108.1	H131—C13—H133	109.5
C7—C3—H3	105.4	H132—C13—H133	109.5
C7—C8—H81	109.6
C1—C2—C3—C4	−6.6 (2)	C4—C5—C6—C1	42.94 (19)
C1—C2—C3—C7	125.36 (19)	C4—C11—O1—H11	−65.2 (18)
C2—C3—C4—C5	32.81 (16)	C6—C1—C2—C3	−2.8 (3)
C2—C1—C6—C5	−15.2 (2)	C7—C3—C4—C11	131.56 (12)
C3—C4—C5—C6	−53.09 (16)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H11···O1^i	0.82 (2)	2.42 (2)	3.2320 (17)	170 (2)
C3—H3···O1	0.98	2.47	2.9499 (18)	110

Symmetry code: (i) −x+2, y−1/2, −z+1/2.