1. For copyright notice see final page of this file
Chemistry 125: Lecture 34 December 2, The Conformation of Cycloalkanes
Understanding conformational relationships makes it easy to draw idealized chair structures for cyclohexane and to visualize axial-equatorial interconversion. The conformational energy of cyclic alkanes illustrates the use of molecular mechanics, a useful, but highly empirical scheme for reckoning conformational energy.
For copyright notice see final page of this file

2. Ernst Mohr Illustrations (1918)
What
o’clock? ? Z ? ? ?
Drawing chair cyclohexane rings:
opposite C-C bonds are parallel
axial bonds are parallel to 3-fold axis
equatorial bonds are (anti)parallel
to next-adjacent C-C bonds

3. Cholic Acid
(a Steroid)
Glucose
(a Carbohydrate)

4. For such problems D.H.R. Barton Invents Conformational Analysis (1950)
 “up” ;   “down”
(for molecule in conventional orientation,
old-fashioned configuration notation, like cis / trans)
Intermediates in steroid hormone synthesis
Barton redraws Ring A A B C D  
Baeyer observed only one c-Hexyl-COOH, but in these
epimers,  and  OH groups have different reactivity!
(configurationally diastereotopic)

5. For such problems D.H.R. Barton Invents Conformational Analysis (1950)
 “up” ;   “down”
(for molecule in conventional orientation,
old-fashioned configuration notation, like cis / trans)
ERRORS? )
(e) “equatorial”
(p) “polar” (now axial)
Ring Flip?
Cf. ~1950 Stereochemistry:
Bijvoet, Newman, CIP,
(Molecular Mechanics)
3-fold axis
(Nobel Prize 1969 for “development of the concept of conformation and its application in chemistry”)

6. Ernst Mohr Illustrations (1918)
gauche, but not anti, is OK for the second ring of decalin.
anti
N.B. During ring flip equatorials become axials
and vice versa.
gauche
fused chairs in "decalin"
(decahydronaphthalene)
Try with models
if you’re skeptical.
Ring flip impossible for trans decalin!

7. Mol4D (CMBI Radboud University, Nijmegen, NL)
Conformational Jmol Animations
Click for INDEX or go to
(see Wiki to install Jmol)

8. Mol4D (CMBI Radboud University, Nijmegen, NL)
Ethane Click to Animate or go to
Click Points
Staggered
Step Keys
Eclipsed barrier ~5.2 kJ/mol  = 1.24 kcal/mol
Should be ~2.9 kcal/mol. Caveat emptor!

9. Mol4D (CMBI Radboud University, Nijmegen, NL)
Propane Click to Animate or go to
Eclipsed
3.3 kcal/mol
Staggered

10. Mol4D (CMBI Radboud University, Nijmegen, NL)
Butane (central bond) Click to Animate or go to
Anti Gauche+
1013 10 -3/4  3.4 = /sec
fully eclipsed
~ 5.5 kcal/mol?
(experimentally irrelevant)
eclipsed
3.5 kcal/mol
(tells how fast) +
Anti
Gauche
0.9 kcal/mol
(tells how much)
Gauche-
Gauche / Anti = 10 -3/4  0.9 = = 1 / 4.7
Gauche / Anti = 2  10 -3/4  0.9 = 2  = 1 / 2.4

11. Conformational Energy of Ethane
Butane
5.5
0.9
(0.6?)
3.5
CH3 H 0°
120°
240°
360°
Torsional Angle
Energy (kcal/mole) 3
e.g. Journal of Molecular Structure: THEOCHEMVolume 814, Issues 1-3, 15 July 2007, Pages 43-49

12. Mol4D (CMBI Radboud University, Nijmegen, NL)
Ring Flip of c-Hexane Click to Animate or go to
Barrier (Half-Chair)
~ 11 kcal/mol
Flexible or
Twist-Boat conformer
~5.5 kcal/mol
Chair conformer

13. Mol4D (CMBI Radboud University, Nijmegen, NL)
Flexible c-Hexane Click to Animate or go to
Barrier (Boat)
~ 1 kcal/mol
Flexible or
Twist-Boat Form
The boat is not an isomer (an energy minimum), it is a barrier on the pleasantly smooth path between twist-boat isomers.

14. Shape, “Strain Energy” & Molecular Mechanics
“Hooke’s Law” for Strain Energy

15. Molecular Mechanics (1946)
N. E. Searle and Roger Adams, JACS, 56, 2112 (1935)
At the barrier
the C-C-Br angles
 open by 12°.
Activation Energy for Racemization
obs kcal/mol
Question:
How did having COOH groups on the benzene rings facilitate the experiment?
t1/2 = 9 min at 0°C
(1013  10-(3/4)*20 ~ 10-2/sec)
calc kcal/mol

16. to make energies match experiment (or reliable quantum calculations).
“Molecular Mechanics” programs calculate (and can minimize) strain assuming that molecules can be treated as (electro)mechanical entities.
To achieve useful precision they require a very large set of empirical force constants adjusted arbitrarily
to make energies match experiment
(or reliable quantum calculations).

17. 138 different bond stretches (41 alkane carbon-X bonds)
“MM2” Parameters
66 different atoms types (including 14 different types of carbon)
138 different bond stretches (41 alkane carbon-X bonds)

18. 624 different bond bendings (41 alkane-alkane-X angles)
“MM2” Parameters
66 different atoms types (including 14 different types of carbon)
624 different bond bendings (41 alkane-alkane-X angles)

19. “MM2” Parameters 1494 different bond twistings
66 different atoms types (including 14 different types of carbon)
Overall Butane
180° is low “because of”
low van der
Waals repulsion
0.5
-0.5
just tweaked a bit
by torsional energy in this scheme
1494 different bond twistings
(37 alkane-alkane-alkane-X twists)
kcal/mole
120°
240°
360°
Sum:
Torsional Contribution to Butane

20. After simplification “MM3” has >2000 Arbitratily Adjustable Parameters !
Contrast with quantum mechanics, where there are no arbitrary parameters. (just particle masses, integral charges & Planck's constant)

21. We’ve come a long way from Couper,
Catalogue of Molecular Mechanics Schemes from Wikipedia: Force Fields (Chemistry)
We’ve come a long way from Couper,
Crum-Brown, and Dewar

22. “Ideal” Cyclohexane (by Molecular Mechanics)
e.g. (unfavorable) 1 2 3 4
e.g. gauche
C-C-C-C 1 2 3 4 5
Strain (kcal/mol)
0.33
Stretch
0.00
0.36
Bend
0.09
Stretch-Bend
-0.000
e.g. favorable C…H
Easier
(or harder?)
to bend a stretched bond
2.15
Torsion
2.12
-1.05
Non-1,4 VDW
-0.55
“Ideal” Cyclohexane (by Molecular Mechanics)
4.68
1,4 VDW
6.32
6.56
TOTAL
7.89

23. Relaxation of Cyclohexane (by Molecular Mechanics)
6 gauche butanes
gauche butane
6  0.9 = 5.4
(mnemonic)
Minimized
“Ideal”
0.33
Stretch
0.00
0.36
Bend
0.09
Stretch-Bend
-0.000
2.15
Torsion
2.12
-1.05
Non-1,4 VDW
-0.55
4.68
1,4 VDW
6.32
6.56
TOTAL
7.89
Stretches and flattens slightly to reduce VDW
Relaxation of Cyclohexane (by Molecular Mechanics)

24. End of Lecture 34 Dec. 2, 2009
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