Information • Textbooks • Media • Resources
A Comparison of the ab Initio Calculated and Experimental Conformational Energies of Alkylcyclohexanes Fillmore Freeman* and Zufan M. Tsegai Department of Chemistry, University of California, Irvine, Irvine, CA 92697-2025; *
[email protected] Marc L. Kasner Department of Chemistry and Biochemistry, Montclair State University, Upper Montclair, NJ 07043 Warren J. Hehre Department of Chemistry, University of California, Irvine, Irvine, CA 92697, and Wavefunction, Inc., Irvine, CA 92612
The conformations of cyclohexane (1–11) and heterocycles (11–21) are important in the teaching of stereochemistry and are of active mechanistic, pharmacological, synthetic, and theoretical interest. Computational chemistry can play a central role in delineating the structures of conformers and rotamers of molecules. Indeed, computational chemistry can provide greater insight into the conformer population and into the nonbonded interactions in structures than an experimental technique such as 1H NMR. The conformation of a molecule has a critical effect on bioactivity and reactivity, and on the stereochemical outcome of many reactions. An understanding of relative energies and conformation populations will enable more reasonable predictions to be made concerning reactivity, stereochemistry, and product distribution in reactions. Substituents in the chair conformation of monosubstituted cyclohexane (1) or in the 4-monosubstituted half-chair conformation of cyclohexene (13) generally prefer the equatorial position. In substituted cyclohexanes, the axial substituents have steric interactions with the synaxial hydrogens at C3 and C5 (1,3-diaxial interactions, eq 1). The difference in energy between the axial and equatorial conformers can be measured and is designated the conformational energy (᎑∆G ° or A value) (22). The larger the conformational energy, the greater the preference for the equatorial position. R H
H
H H
4
H
H H
5
H H
H H 1a
4
H
1
2
3
6
H
H
H
1
2
3
H
H
H
H 6
5
H
H
R
(1)
H 1b
Although conformational energy values for simple alkyl groups have been determined many times, the methods employed have mostly involved the study of cyclohexanes (model compounds) which contained not only the alkyl group of interest but other substituents. It is sometimes difficult to evaluate the influences of the other substituents on the experimental parameters being measured. It has been difficult to obtain a reliable experimental conformational energy value for the tert-butyl group and there does not appear to be an experimental ᎑∆G ° value for the n-propyl or neo-pentyl group. Although much consideration has been given to the nonbonded axial substituent–synaxial hydrogen interactions as the major factors for the equatorial preference, much less attention has been paid to the gauche (synclinal) effects and to the repulsive nonbonded interactions in the corresponding equatorial conformers (22, 23).1 This study was undertaken in order to use ab initio methods to investigate the geometries and relative energies of the conformers and rotamers of
alkylcyclohexanes (1). Another objective of this study is to compare the calculated conformational energies of alkylcyclohexanes (1, R = CH3, C2H5, C3H7, C3H7, iso-C3H7, t-C 4 H 9 , neo-C5H11) and trimethylsilylcyclohexane (Si(CH3)3) to their experimental values (24–32).2 Computational Methods The energies (1 kcal/mol = 4.184 kJ/mol; 1 hartree = 627.51 kcal/mol) and optimized geometries for the conformers of cyclohexane and substituted cyclohexanes were calculated with the MacSpartan Plus 1.1.6, Spartan 4.0, and Spartan 5.0 computational programs using the 6-31G(d) and MP2/631G(d)//6-31G(d) ab initio molecular orbital methods (33– 36 ).3 Although most of these calculations were done on Silicon Graphics workstations, many of the 6-31G(d) geometry optimizations were done very quickly on a desktop Macintosh computer with MacSpartan Plus 1.1.6. Ab initio MP2/631G(d)//6-31G(d) calculations can also be performed on desktop computers using Spartan PC Pro3 and Gaussian 98. The necessary thermochemical corrections have not been made to these calculated energy differences (∆E ), since it is approximated that the differences between ∆E and ᎑∆G ° is negligible. Results and Discussion Tables 1 and 2 show that the equatorial conformer (2b, Cs point group, zero gauche butane interactions) of methylcyclohexane (2a) is more stable than the axial conformer (2a, Cs point group, two gauche butane interactions, Table 3). The MP2/6-31G(d)//6-31G(d) calculated conformational energy of 1.96 kcal/mol is larger than the experimental value of 1.74 kcal/mol (Table 1) (24, 25, 32). Since there are two 1,3-diaxial interactions for each axial methyl group (2a), one would predict the axial conformer to be less stable than the equatorial conformer (2b) by approximately 1.8 kcal/mol, which is close to the experimental value (1.74 kcal/mol) and to the MM4 calculated (1.85 kcal/mol) (6 ) and ab initio calculated values (1.96 kcal/mol; Table 2, Figs. 1, 2) (32, 37–40). However, the gauche interactions in cyclohexane may not be comparable to those of gauche butane because the nonbonded hydrogen– hydrogen repulsive interactions are minimized in cyclohexane (see structures below) (38, 39). 2.401
H
Ha
H
4
H
2.480 2.453
H H H
H
H
H 2a
H
4
H
1
2
3
H
6
5
H H
1
2
3
Hb
H
H
H
H
Hc
H 6
5
H
H
Hc Ha Hb
H 2b
JChemEd.chem.wisc.edu • Vol. 77 No. 5 May 2000 • Journal of Chemical Education
661
Information • Textbooks • Media • Resources Table 1. Calculated and Conformational Energies and Dipole Moments of Alkylcyclohexanes MP2/6-31(d)//6-31(d)
᎑∆G° a/ µ/D Energy/hartree (kcal/mol)
Energy/hartree
᎑∆G° a/ (kcal/mol)
H
1
D3d
᎑234.208007
—
0.00
᎑234.991630
—
CH3 ax
2a
Cs
᎑273.239998
—
0.05
᎑274.157686
—
CH3 eq
2b
Cs
᎑273.243664
0.09
᎑274.160811
C2H5 ax
3a
C1
᎑312.272625
—
0.03
᎑313.322470
—
C2H5 ax
3b
C1
᎑312.265866
(᎑4.24)
0.09
᎑313.315761
(᎑4.21)
C2H5 eq
3c
C1
᎑312.276375
2.35
0.04
᎑313.325338
1.80
C2H5 eq
3d
C1
᎑312.274627
[᎑1.10]
0.07
᎑313.323971
[᎑0.86]
2.30
1.96
n-C3H7 ax
4b
C1
᎑351.307151
—
0.06
᎑352.488231
—
n-C3H7 ax
4a
C1
᎑351.305525
(᎑1.02)
0.03
᎑352.487330
(᎑0.57)
n-C3H7 ax
4d
C1
᎑351.300372
(-4.25)
0.07
᎑352.481749
(᎑4.07)
n-C3H7 ax
4c
C1
᎑351.294854
(᎑7.72)
0.09
᎑352.477115
(᎑6.98)
n-C3H7 eq
4e
C1
᎑351.310914
2.36
0.09
᎑352.490995
1.73
n-C3H7 eq
4f
Cs
᎑351.309076
[᎑1.15]
0.09
᎑352.489643
[᎑0.85]
n-C3H7 eq
4g
C1
᎑351.306314
[᎑2.89]
0.10
᎑352.487049
[᎑2.48]
n-C3H7 eq
4h
C1
᎑351.304121
[᎑4.26]
0.09
᎑352.485541
[᎑3.42]
i-C3H7 ax
5a
Cs
᎑351.303464
—
0.07
᎑352.488546
—
i-C3H7 ax
5b
C1
᎑351.298127
(᎑3.35)
0.09
᎑352.482652
(᎑3.70)
i-C3H7 eq
5c
Cs
᎑351.307379
2.46
0.08
᎑352.491096
1.60
i-C3H7 eq
5d
C1
᎑351.307182
[᎑0.12]
0.06
᎑352.490953
[᎑0.09]
t-C4H9 ax
6a
C1
᎑390.327629
—
0.05
᎑391.649839
—
t-C4H9 ax
6b
Cs
᎑390.319798
(᎑4.91)
0.05
᎑391.641767
(᎑5.07)
t-C4H9 eq
6c
C1
᎑390.337397
0.05
᎑391.658526
neo-C5H11 ax 7a
C1
᎑429.370192
—
0.03
᎑430.822759
—
neo-C5H11 ax 7b
C1
᎑429.367614
(᎑1.62)
0.07
᎑430.820400
(᎑1.48)
neo-C5H11 eq 7c
C1
᎑429.373401
2.01
0.04
᎑430.824863
1.32
neo-C5H11 eq 7d
C1
᎑429.366444
[᎑4.37]
0.11
᎑430.818788
[᎑3.81]
SiMe3 ax
8a
C1
᎑641.413220
—
0.11
᎑642.678744
—
SiMe3 eq
8b
C1
᎑641.418844
0.08
᎑642.683024
6.13
3.53
5
4 t 4H10 t-C
3
C2H5
1
0
2
3
H H
4
H
5
H
1 H
H
H
2
3
6
H
H
H H H
4
5
H
H
H
MM (Ref)
6
5
4
3
t-C4H10
C 2H 5 2
i-C3H7
CH3 1
y = 1.114x - 0.189 r = .982
Experimental ᎑∆G°/ (kcal/mol)
T/ °C
Ref
2
1.85 (6, 30)
2.30
1.96
1.74
27
25
3
1.87 (6, 30)
2.35
1.80
1.79
27
25
n-C3 H7
4
—
2.36
1.73
i -C3H7
5
2.05 (6, 30)
2.46
1.60
t -C4H9
6
4.7 (31)
6.13
5.45
neo-C5 H1 1 7
—
2.01
1.32
8
—
3.53
2.69
— 2.21 >5.4 4.9
27 ᎑120
1
33
3
4
5
Figure 2. A plot of MP2/6-31G(d)//6-31G(d) calculated conformational energies (᎑∆ G °) of alkylcyclohexanes versus the experimental conformational energies (᎑∆G°) of the corresponding alkylcyclohexanes.
25 23c 28
— 2.5
2
Experimental conformational energies (-∆G °) of alkylcyclohexanes
C2 H5
662
5
Si(CH3)3
0
H
CH3
SiMe3
4
R
6
H
MP2/6-31G(d) 6-31G(d) //6-31G(d)
3
Figure 1. A plot of 6-31G(d) calculated conformational energies (᎑∆G°) of alkylcyclohexanes versus the experimental conformational energies (᎑∆G°) of the corresponding alkylcyclohexanes.
0 1
Calculated ᎑∆G°/(kcal/mol) R
2
H
H
H
1
Experimental conformational energies (-∆G °) of alkylcyclohexanes
R H
y = 1.253x + 0.052 r = .993
H 0
2.69
Table 2. Comparison of Calculated and Experimental Conformational Energies for Alkylcyclohexanes H
i-C3H7
CH3
2
5.45
aThe conformational energy (᎑∆G° = E – E ) refers to the energy difference beax eq tween the most stable axial conformer and the most stable equatorial conformer. The other values are the energy differences between the most stable axial conformer and the other axial conformers in parentheses and the energy differences between the most stable equatorial conformer and the other equatorial conformers in brackets.
H
Si(CH3)3
6
6-31(d) calculated conformational energies (-∆G °) of alkylcyclohexanes
6-31G(d)
MP2/6-31(d) calculated conformational energies (-∆G °) of alkylcyclohexanes
Substituent, Numbered Structure, and Point Group
29
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources Table 3. Calculated Torsion Angles in Alkylcyclohexanes in 6-31G(d) Optimized Geometries Angle (°)
Substituent
C3᎑C2᎑C1᎑C7 C5᎑C6᎑C1᎑C7
C2᎑C1᎑C7᎑C8
C6᎑C1᎑C7᎑C8
H
1
—
—
—
—
CH3 ax
2a
73.5
73.5
—
—
CH3 eq
2b
179.1
179.1
—
—
C2 H5 ax
3a
73.6
72.4
170.2
65.1
C2 H5 ax
3b
88.3
88.3
65.5
65.5
C2 H5 eq
3c
178.3
179.9
64.4
171.8
C2 H5 eq
3d
176.0
176.0
63.2
63.2
n - C3H7 ax
4a
71.8
73.8
60.3
175.3
n - C3H7 ax
4b
72.3
73.5
66.1
169.2
n - C3H7 ax
4c
86.9
87.9
56.5
74.8
n - C3H7 ax
4d
88.7
88.7
65.5
65.6
n - C3H7 eq
4e
176.2
179.9
65.0
171.2
n - C3H7 eq
4f
175.7
175.7
63.3
63.3
n - C3H7 eq
4g
179.3
178.5
174.5
61.2
n - C3H7 eq
4h
173.7
174.3
47.9
80.3
i - C3H7 ax
5a
71.2
71.2
56.7/179.2
56.7/179.2
i - C3H7 ax
5b
88.3
87.8
76.6/157.3
54.2/71.9
i - C3H7 eq
5c
178.7
178.7
56.5/179.7
56.5/179.7
i - C3H7 eq
5d
176.2
174.9
t - C4H9 ax
6a
85.0
88.0
57.3/68.9
69.1/164.8
42.8/80.0/159.5
50.8/69.7/173.5
t - C4H9 ax
6b
86.6
86.6
56.7/65.6/172.1
56.7/65.6/172.1
t - C4H9 eq
6c
174.9
174.9
58.0/63.2/175.7
57.9/63.2/175.6
neo- C5H11 ax 7a
72.4
73.0
125.8
109.9
neo- C5H11 ax 7b
69.6
74.1
66.8
169.3
neo- C5H11 eq 7c
179.7
179.5
134.6
102.2
neo- C5H11 eq 7d
170.5
169.6
53.0
77.5
SiMe3 ax
8a
82.4
81.4
55.7/65.0/178.0
57.7/63.2/176.3
SiMe3 eq
8b
177.6
177.6
57.4/63.2/176.3
57.4/63.2/176.3
In the axial conformation 2a there are four nonbonded distances, which are comparable to the sum (2 × 1.20 Å = 2.40 Å) of the van der Waals radii for hydrogen (41– 49).4 There are two repulsive nonbonded distances in the equatorial conformer 2b. Table 4 shows that the C6–C1–C7 angle in the axial conformer 2a is slightly larger (0.9°) than the corresponding angle in the equatorial conformer 2b. This suggests that the methyl group in the axial conformer 2a is tilted away from the ring to minimize nonbonded interactions with the synaxial C3 and C5 hydrogens. Although steric effects are considered to be responsible for equatorial preferences in cyclohexanes, natural bond orbital analysis (NBO) (50–53) suggests that bond–anti-bond interactions of the exocyclic C1–C7 bond in methylcyclohexane (2) with σ * C–C and σ * C–H bonds are mainly responsible for the equatorial preference (11). In ethylcyclohexane (3) the axial conformer has three rotamers: 3a (C1 point group, three gauche butane interactions) and its mirror image, and 3b, a high-energy rotamer with the methyl group pointing toward the ring (C1 point group, three gauche butane interactions). The equatorial conformer of 3 also has three rotamers: conformer 3c (C1 point group, one gauche butane interaction) and its mirror image, and conformer 3d (C1 point group, two gauche butane interactions). Table 1 shows that the equatorial conformer 3c is more stable than the axial conformer 3a (᎑∆G ° = 1.80 kcal/mol) and 0.86 kcal/mol more stable than the other equa-
torial conformer 3d. The MP2/6-31G(d)//6-31G(d) calculated conformational energy for 3 (᎑∆G° = 1.80 kcal/mol) agrees with the experimental value of ᎑∆G ° = 1.79 kcal/mol (24, 25 ) and calculated energy difference between the equatorial conformers 3b and 3c (0.86 kcal/mol) is approximately the value of one gauche butane interaction. H
2.286
Hc
2.396 2.370
Ha
H
H
H
H H
4
Hb
2.471
H H
H 3a
Hb
H
H
H H
H H 6
5
4
2.336
1
2
3
H H
H
2.175
Hd
Ha H
6
5
H
Hc
2.207
2.391 1
2
3
H 2.206
H
2.475
H
H
H 3b
The conformational energy (᎑∆G °) of propylcyclohexane is 1.73 kcal/mol. The lower energy axial conformer 3a, has five repulsive nonbonded interactions. There are six such interactions in 3b. There are three repulsive nonbonded interactions in the chiral equatorial conformer 3c, and four in the symmetrical equatorial conformer 3d. Thus, the additional nonbonded interaction and the additional gauche butane interaction contribute to the higher energy of conformer 3d relative to that of 3c. In addition, the similarity of the calculated conformational energies for methylcyclohexane (2) and ethylcyclohexane (3) is consistent with rotation about the
JChemEd.chem.wisc.edu • Vol. 77 No. 5 May 2000 • Journal of Chemical Education
663
Information • Textbooks • Media • Resources Table 4. Calculated Bond Angles in Alkylcyclohexanes in 6-31G(d) Optimized Geometries Angle (°)
Substituent
C2᎑C1᎑C6
C1᎑C2᎑C3
C1᎑C6᎑C5
C2᎑C3᎑C4
C6᎑C5᎑C4
C3᎑C4᎑C5
H
1
111.4
111.4
111.4
111.4
111.4
111.4
—
—
CH3 ax
2a
110.0
113.2
113.2
111.3
111.3
111.3
112.5
112.5
CH3 eq
2b
110.3
112.2
112.2
111.5
111.5
111.2
111.6
111.6
C2H5 ax
3a
109.3
113.2
113.1
111.3
111.3
111.4
114.1
111.9
C2H5 ax
3b
111.1
115.4
115.4
111.4
111.4
110.7
115.0
115.0
C2H5 eq
3c
110.0
112.2
112.5
111.7
111.4
111.0
110.7
112.9
C2H5 eq
3d
110.1
111.6
111.6
111.4
111.4
111.3
113.3
113.3
n-C3H7 ax
4a
109.2
113.1
113.2
111.4
111.3
111.4
111.9
114.1
n-C3H7 ax
4b
109.3
113.1
113.4
111.2
111.4
111.4
111.4
114.2
n-C3H7 ax
4c
111.1
115.5
115.5
111.4
111.4
110.7
115.1
115.1
n-C3H7 ax
4d
110.5
115.0
115.6
111.4
111.2
110.9
114.8
116.4
n-C3H7 eq
4e
109.9
112.3
112.5
111.7
111.4
111.0
110.6
113.0
n-C3H7 eq
4f
110.1
111.6
111.6
111.4
111.4
111.3
113.5
113.5
n-C3H7 eq
4g
110.0
112.6
112.2
111.4
111.8
111.0
113.8
110.4
n-C3H7 eq
4h
110.3
111.6
111.3
111.5
111.5
111.3
111.4
113.5
i-C3H7 ax
5a
107.6
113.0
113.0
111.3
111.3
111.6
114.0
114.0
i-C3H7 ax
5b
110.4
115.9
115.4
111.2
111.6
110.8
116.2
114.7
i-C3H7 eq
5c
109.4
112.9
112.9
111.8
111.8
110.4
112.3
112.3
i-C3H7 eq
5d
109.7
111.6
111.8
111.6
111.4
111.2
112.6
114.8
t-C4H9 ax
6a
108.6
115.7
115.7
112.0
110.8
110.9
117.6
115.8
t-C4H9 ax
6b
108.4
116.0
116.0
111.5
111.5
111.6
117.1
117.1
t-C4H9 eq
6c
108.8
112.1
112.1
111.8
111.8
110.7
114.4
114.4
neo-C5H11 ax
7a
109.4
113.2
113.0
111.5
111.1
111.1
112.5
112.8
neo-C5H11 ax
7b
108.2
113.2
113.4
111.1
111.4
111.5
110.2
116.8
neo-C5H11 eq
7c
109.4
112.4
112.3
111.6
111.4
111.1
112.4
111.4
neo-C5H11 eq
7d
109.9
111.3
111.2
111.4
111.5
111.3
114.8
116.5
SiMe3 ax
8a
109.6
113.3
113.3
111.6
111.2
111.5
116.5
116.0
SiMe3 eq
8b
110.0
112.2
112.2
111.6
111.6
111.2
113.4
113.5
C1–C7 bond in 3 in such a way that the ethyl group adopts a conformation that minimizes the effects of the additional methyl group (cf. 3a). That is, the allyl group points away from the interior of the ring. In addition, the numerous repulsive nonbonded hydrogen–hydrogen interactions in the equatorial conformers 3c and 3d help to reduce the magnitude of the equatorial preference in 3. 2.491
H
H
H
2.365
3
H
H
H 2
3
H
5
4
H
H H
H
H H
H
H
H H
3c
H 2.384
H
H
H
H
4
Hd
2.352 2.447
2
H
H
2.410
6
5
H
H
H
H
H
Ha
4b
H H H
H
H
H
Hc
H
3 H
6
Hb
H 1
4a
2.353 3d
Hd
2.281
H
Among the rotamers of axial propylcyclohexane are 4a, 4b, 4c, and 4d. The lower-energy rotamers include two structures with C8 oriented away from the ring (4a, C1 point group and 4b, C1 point group) and two structures with C8 directed toward the interior of the ring (4c, C1 point group and 4d, C1 point group). The rotamers 4c and 4d are considerably less stable (4.07 kcal/mol and 6.98 kcal/mol, Table 1) than the most stable axial conformer, 4a. Each of the lower-energy axial configurations, 4a and 4b, has three gauche interactions and each of the higher-energy axial conformers, 4c and 4d, has four gauche interactions. Each of the four axial rotamers has six repulsive nonbonded interactions. 664
4
H H
H H
H
1 6
5
4
Hb
2
3
2.424
H
5
H
2.478
H 1
H
Hc
Ha
2.399 2.540
2.476
H
H 6
Hd Hb
Ha
2.402
H H Ha
1
2
H
2.269 Hc
2.276
Hb
H
H
2.260
H
2.315
H
H
H
H
C6᎑C1᎑C7 C2᎑C1᎑C7
H 2.275 2.198
Hc
2.397
Ha
2.155 H
2
H H
H 6
5
4
2.374
H 1
H
3
H
H
2.334
Hb
Hd
2.190
Ha
2.454
2.476
Hc
Hb
H
H 2.369
2
H H
H
2.476
H
H
H
H 6
5
4
2.335
H 1
H
3
H
H
H 4c
4d
Among the rotamers of equatorial propylcyclohexane are 4e (C1 point group, one gauche interaction), 4f (Cs point group, two gauche interactions), 4g (C1 point group, one gauche interaction), and 4h (C1 point group, two gauche interactions). The equatorial conformer 4e is more stable than 4f (0.85 kcal/mol), 4g (2.48 kcal/mol), and 4h (3.42 kcal/mol). Both equatorial conformers 4e and 4f are more stable than
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources
the most stable axial conformer 4a, while conformers 4g and 4h are less stable than 4a (Table 1). 2.495 2.287
H
H
H
4
H
H 2.418 H
H
1
4
H
H
H
2.276
H H
H
4
H
H
H
4
H
2.386
Hd
H
H
2.185
H
2.361
2.300 2.432
Ha
H
H
H
H
H H
2
3
H H
2.166
H H
H
2
3
H
5
4
H
Hb
1
H 6
H H
H 5c
5
4
H
H
Hd
H
H Hb
H H
Hc
2.364 2.287
2.049
6 H
H
H
H
7a
Hd
H
H
5
4
1
2
H H
2.359
H
H 3
6
H
H H
2.433
2.385
H
H
Hb
1
2.381H
H Ha
H 6
H
H
2.393
H
Hd Hc
2.290
5d
The calculated conformational energy (᎑∆G °) of tertbutylylcyclohexane (6) is 5.45 kcal/mol, which is comparable to the experimental value of approximately 5.45 kcal/mol (Tables 1, 2). An axial tert-butyl group cannot avoid the stringent steric repulsion of the 1,3-diaxial interactions with a methyl group. The two axial conformers (6a, C1 point group; 6b Cs point group) of 6 each has four gauche interactions. Although there are only minor differences in the geometrical parameters of 6a and 6b, 6b is 5.07 kcal less stable than 6a.
H
H 2
3 H
H
H
2.212
5b
2
3
H
H
H H
H Ha
2.338 2.413
H
H
H
H
H H
H
H
H
H
2.322
H
Hc
Ha
H
H
H
1
1
2.439
H HH
H
2.391 Hc
H 2.404 Hb
6
H
H
H
2.304
7b
H H
2 5
4
5a
H
H
H
H
H He Hf
2.308
H
3
H
H
H
2.158
6
H H
Hb H
H
5
Ha
H
H
6
5
4
H
2.160
1
H
2
4
H
Hc
H
H
Hd
H
H
H
H
Hc
1
2 5
4
H
H
Hb
Hc
Hb
The calculated conformational energy of neopentylcyclohexane (7) is 1.32 kcal/mol. The more stable axial rotamer (7a, C1 point group) has more nonbonded repulsive interactions (five vs four) and fewer gauche butane interactions (two vs three) than the higher-energy axial rotamer (7b, C1 point group). The equatorial conformer 7c (C1 point group) does not have any gauche interactions.
H 2.271 2.160
H
6c
H
H
Ha
H
3
H
H
3
The calculated conformational energy (᎑∆G °) of isopropylcyclohexane (5) is 1.60 kcal/mol, which is smaller than the value of 2.21 kcal/mol obtained from NMR studies (25, 32) and the value of 2.05 kcal/mol from molecular mechanics calculations (Figs. 1, 2; Tables 1, 2). The lowerenergy axial conformer (5a, Cs point group, four gauche butane interactions) of isopropylcyclohexane (5) has the methyl groups oriented away from the ring. The higher-energy axial conformer (5b, C1 point group, five gauche interactions) has one of the methyl groups is oriented over the ring. Both axial conformers (5a, 5b) have four repulsive nonbonded hydrogen–hydrogen interactions (41–49). Equatorial isopropylcyclohexane (5) has three high population rotamers (5c, Cs point group and 5d, C1 point group, and its enantiomer). The more stable equatorial conformer 5c has two repulsive nonbonded interactions and the less stable conformer 5d and its mirror image each has five such interactions.
Ha Hd
H
H
H
H
4h
HH
4
2.361
H 6b
H
Hc
H
H H 6
5
H 2.442
H
H
4g
2.161
H
H
Ha
6
H H
H
H
H
5
2.411
H
H
H
H
H
2.159
1
2
3
6
1
2
H
H
Hd Hc H e
H
H
3
6a
Hb
H
H
H
H
H H
5
4
2.483
H
H
Ha
1 6
5
H
Hb
2
H
H
2.306
1
2
H
2.116
He Hd H
H
H
Ha
2.107
H
H Hb
H
Hc
Hb
3
4f
H
3
H
H
H
H
2.187
2.329
2.479
H
H
Hc Hd
H
4e
H
2.202
H
H
H
H
2.448
H
6
5
Ha
2.209
2
3 H
H
H
H
H
6
5
H Hb Ha
H H
1
2
3 H
2.384 H
Ha
H
H
H
Hb
H
The equatorial conformer (6c, C1 point group) has four gauche butane interactions and six repulsive nonbonded interactions.
4
H H
Ha H
H
2.394 2.498
H
H
H
H
4
H
6
5 H
7c
H 2.405 H
H
H
H
H
7d
H
Ha H
1
2
3 H
H
H
Hb
H H
1 H
6
5 H
H
2.259 2.396
H
2.207
H 2.243
H H H H
The calculated conformational energy for the trimethylsilyl group (᎑∆G° = 2.69 kcal/mol) is close to the experimental value of 2.5 kcal/mol (Table 4) (29). Table 1 shows that the equatorial conformer (8b, C1 point group, four gauche interactions) of trimethylsilylcyclohexane (8) is more stable than the axial conformer (8a, C1 point group, six synclinal interactions). In the axial conformation 8a, there are two repulsive nonbonded hydrogen–hydrogen interactions; there are no repulsive nonbonded interactions in the equatorial conformer 8b because there are no hydrogen–hydrogen distances less than 2.500 Å. The carbon–silicon bond lengths in 8a and 8b are 1.918 and 1.909 Å, respectively (Table 5). A smaller conformation energy for the trimethylsilyl group than for the tert-butyl group is
JChemEd.chem.wisc.edu • Vol. 77 No. 5 May 2000 • Journal of Chemical Education
665
Information • Textbooks • Media • Resources
reasonable because the C1–Si bond length in 8 is longer than the C1–C7 bond length in 6. H 2.385 2.441
H
Ha Hb
H
H
H Si
H
H
H
Notes H
H
H
H
H
H 8a
Acknowledgment is made to the National Science Foundation (NSF CHE-9015849 and CHE-9311713) for partial support of this work.
H
H
6
5
4
H
H
H
1
2
3
H H
H H
H
H
H
H
H
H
6
5
4
HH
H
H
1
2
3
H
H Si
H
H
H
Acknowledgment
8b
Conclusions The results above show that ab initio calculations on the six alkyl monosubstituted cyclohexanes and trimethylsilylcyclohexane reveal reliable information regarding the conformations of these species, quite consistent with experimental observations in those cases where data are available. Although stereoelectronic effects may also be involved, the MP2/6-31G(d)//6-31G(d) calculated conformational energies of alkylcyclohexanes (1) are determined primarily by steric effects, which include gauche interactions and repulsive nonbonded interactions in both the axial and equatorial conformers.
1. Gauche: In A–B–C–D, ligands A and D are gauche if the torsion angle (ABCD) about the B–C bond is near +60° or ᎑60°. Synclinal (sc): In X–A–B–Y, ligands X and Y are synclinal if the torsion angle (XABY) about the A–B bond is between +30° and +90° or between ᎑30° and ᎑90° (1, 23). 2. In solution, the entropy and enthalpic terms must be considered. For example, in alkylcyclohexanes, the increase in the ᎑∆G ° values (kcal/mol) for Me (1.74), Et (1.79), i-Pr (2.21) is due to diminished entropy in the axial conformers as the rotamer population is reduced to those rotamers with C7–H inside [Me (3); Et (2); i-Pr (1)] (24–27 ). 3. The MacSpartan Plus and Spartan computational programs are available from Wavefunction, Inc., 18401 Von Karman Avenue, Suite 370, Irvine, CA 92612. 4. The van der Waals radius, which is determined from interatomic distances in crystals, is the effective size of the atomic cloud around a covalently bonded atom as perceived by another atom. The van der Waals radius is not the distance at which repul-
Table 5. Calculated Bond Lengths in Alkyacyclohexanes in 6-31G(d) Optimized Geometries Bond Length/Å
Substituent
666
C1᎑C2
C1᎑C6
C2᎑Hax
C2᎑Heq
C1᎑H
C4᎑C3
C4᎑C5 C1᎑C7
H
1
1.532
1.532
1.089
1.087
—
1.532
1.532
—
CH3 ax
2a
1.539
1.539
1.089
1.087
1.088
1.531
1.531
1.534
CH3 eq
2b
1.534
1.534
1.089
1.087
1.091
1.531
1.531
1.529
C2H5 ax
3a
1.540
1.540
1.089
1.087
1.089
1.531
1.531
1.540
C2H5 ax
3b
1.545
1.545
1.089
1.088
1.088
1.529
1.529
1.544
C2H5 eq
3c
1.536
1.536
1.090
1.086
1.092
1.530
1.530
1.535
C2H5 eq
3d
1.536
1.536
1.088
1.088
1.091
1.531
1.531
1.538
n-C3H7 ax
4a
1.540
1.541
1.089
1.086
1.087
1.531
1.531
1.541
n-C3H7 ax
4b
1.540
1.540
1.089
1.085
1.089
1.531
1.531
1.540
n-C3H7 ax
4c
1.543
1.536
1.089
1.087
1.088
1.530
1.530
1.548
n-C3H7 ax
4d
1.545
1.547
1.089
1.088
1.088
1.529
1.529
1.544
n-C3H7 eq
4e
1.536
1.536
1.090
1.086
1.091
1.530
1.530
1.536
n-C3H7 eq
4f
1.536
1.536
1.088
1.088
1.091
1.531
1.531
1.539
n-C3H7 eq
4g
1.536
1.536
1.090
1.087
1.091
1.530
1.530
1.537
n-C3H7 eq
4h
1.535
1.537
1.088
1.088
1.091
1.531
1.531
1.543
i-C3H7 ax
5a
1.542
1.542
1.089
1.084
1.090
1.531
1.531
1.551
i-C3H7 ax
5b
1.547
1.546
1.089
1.087
1.088
1.529
1.529
1.554
i-C3H7 eq
5c
1.540
1.540
1.090
1.084
1.092
1.528
1.528
1.548
i-C3H7 eq
5d
1.537
1.537
1.088
1.086
1.091
1.530
1.530
1.547
t-C4H9 ax
6a
1.549
1.548
1.089
1.085
1.088
1.529
1.529
1.570
t-C4H9 ax
6b
1.549
1.549
1.089
1.083
1.088
1.530
1.530
1.569
t-C4H9 eq
6c
1.541
1.541
1.088
1.084
1.091
1.528
1.528
1.563 1.552
neo-C5H11 ax 7a
1.541
1.540
1.089
1.087
1.085
1.531
1.530
neo-C5H11 ax 7b
1.540
1.543
1.089
1.087
1.087
1.531
1.531
1.546
neo-C5H11 eq 7c
1.537
1.538
1.090
1.087
1.088
1.530
1.530
1.548
neo-C5H11 eq 7d
1.536
1.539
1.087
1.087
1.091
1.531
1.531
1.549
SiMe3 ax
8a
1.546
1.545
1.090
1.087
1.093
1.530
1.530
1.918
SiMe3 eq
8b
1.543
1.543
1.090
1.087
1.094
1.530
1.530
1.909
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources sive interactions of the electrons on two atoms outweigh the attractive forces between them, as is often assumed (48). However, hydrogen–hydrogen distances less than approximately 2.500 Å are considered to be repulsive in the discussion. Although many sets of van der Waals radii are available, the values from ref 41 are used in this study.
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