Chemistry 125: Lecture 34December 2, 2009

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

Ernst Mohr Illustrations (1918)

Drawing chair cyclohexane rings:

opposite C-C bonds are parallel

axial bonds are parallel to 3-fold axis

equatorial bonds are (anti)parallelto next-adjacent C-C bonds

Whato’clock?

??

??Z

Cholic Acid(a Steroid)

Glucose(a Carbohydrate)

For such problems D.H.R. Barton Invents Conformational Analysis (1950)

Baeyer observed only one c-Hexyl-COOH, but in theseepimers, and OH groups have different reactivity!

“up” ; “down” (for molecule in conventional orientation,

old-fashioned configuration notation, like cis / trans)

Barton redraws Ring A

Intermediates in steroid hormone synthesis

A B

C D

(configurationally diastereotopic)

(e) “equatorial”

(p) “polar” (now axial)

Cf. ~1950 Stereochemistry:Bijvoet, Newman, CIP,(Molecular Mechanics)

(Nobel Prize 1969 for “development of the concept of conformation and its application in chemistry”)

ERRORS? “up” ; “down”

(for molecule in conventional orientation, old-fashioned configuration notation, like cis / trans)

3-fold axis

For such problems D.H.R. Barton Invents Conformational Analysis (1950)

)

Ring Flip?

Ernst Mohr Illustrations (1918)

Ring flip impossible for trans decalin!

N.B. During ring flip equatorials become axials

and vice versa.

anti

gauche

gauche, but not anti, is OK for the second ring of decalin.

fused chairs in "decalin"(decahydronaphthalene)

Try with modelsif you’re skeptical.

Mol4D(CMBI Radboud University, Nijmegen, NL)

Click for INDEX or go to http://cheminf.cmbi.ru.nl/wetche/organic/index.html

Conformational Jmol Animations

(see Wiki to install Jmol)

Mol4D(CMBI Radboud University, Nijmegen, NL)

Ethane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/ethane/jmindex.html

Eclipsed barrier ~5.2 kJ/mol 0.239 = 1.24 kcal/molShould be ~2.9 kcal/mol. Caveat emptor!

Step Keys

Click Points

Staggered

Mol4D(CMBI Radboud University, Nijmegen, NL)

Propane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/propane/jmproprot.html

Staggered

Eclipsed3.3 kcal/mol

Anti Gauche+

1013 10 -3/4 3.4 = 10 10.5 /sec

Mol4D(CMBI Radboud University, Nijmegen, NL)

Butane (central bond) Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/butane/jmindex.html

Gauche0.9 kcal/mol(tells how much)

eclipsed3.5 kcal/mol(tells how fast)

fully eclipsed~ 5.5 kcal/mol?

(experimentally irrelevant)

Anti

Gauche / Anti = 10 -3/4 0.9 = 10-0.68 = 1 / 4.7Gauche / Anti = 2 10 -3/4 0.9 = 2 10-0.68 = 1 / 2.4

+

+

Gauche-

H

H HH

H HH

H HH

H H

H

HH

H

H H

H

HH

H

H H

H

HH

H

H HH

H HH

H H

H

HH

H

H H

3 3 3

Conformational Energy of EthaneButane5.5

0.9(0.6?)

5.5

0.9(0.6?)

3.5

H

H HH

H HH

H HH

H H

H

HH

H

H H

H

HH

H

H H

H

HH

H

H HH

H HH

H H

H

HH

H

H H

CH3CH3 CH3

CH3

CH3 CH3

CH3

CH3 CH3 CH3CH3

CH3CH3

CH3

H H

3.5

0° 120° 240° 360°Torsional Angle

Ene

rgy

(kca

l/m

ole)

Mol4D(CMBI Radboud University, Nijmegen, NL)

Ring Flip of c-Hexane Click to Animate or go to http://cheminf.cmbi.ru.nl/wetche/organic/cyclohexane/jm/chxjmol.html

Flexible or Twist-Boat conformer

~5.5 kcal/mol

Barrier (Half-Chair)~ 11 kcal/mol

Chair conformer

Mol4D(CMBI Radboud University, Nijmegen, NL)

Flexible c-Hexane Click to Animate

or go to http://cheminf.cmbi.ru.nl/wetche/organic/cyclohexane/jm/twist_boat.html

Flexible or Twist-Boat Form

Barrier (Boat)~ 1 kcal/mol

The boat is not an isomer (an energy minimum), it is a barrier on the pleasantly smooth path between twist-boat isomers.

Shape,“Strain Energy”

&

Molecular Mechanics

“Hooke’s Law” for Strain Energy

Molecular Mechanics (1946)

Activation Energy for Racemizationobs. 19.5 kcal/mol

calc. 17.3 kcal/mol

At the barrier the C-C-Br angles

open by 12°.

t1/2 = 9 min at 0°C(1013 10-(3/4)*20 ~ 10-2/sec)

Question:How did having

COOH groups on the benzene rings

facilitate the experiment?

“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).

“MM2” Parameters66 different atoms types (including 14 different types of carbon)

138 different bond stretches (41 alkane carbon-X bonds)

“MM2” Parameters66 different atoms types (including 14 different types of carbon)

624 different bond bendings (41 alkane-alkane-X angles)

“MM2” Parameters66 different atoms types (including 14 different types of carbon)

1494 different bond twistings

(37 alkane-alkane-alkane-X twists)0

0.5

-0.5

Sum:1-1-1-1 Torsional Contribution to Butane

Overall Butane

kcal

/mol

e

120° 240° 360°

180° is low “because of” low van der

Waals repulsionjust tweaked a bit

by torsional energy in this scheme

Contrast with quantum mechanics, where there are

no arbitrary parameters. (just particle masses, integral charges & Planck's constant)

After simplification “MM3” has >2000 Arbitratily

Adjustable Parameters !

Catalogue of Molecular Mechanics Schemes

from Wikipedia: Force Fields (Chemistry)

We’ve come a long way from Couper,

Crum-Brown, and Dewar

“Ideal” Cyclohexane(by Molecular Mechanics)

0.33 Stretch 0.00

0.36 Bend 0.00

0.09 Stretch-Bend -0.000

2.15 Torsion 2.12

4.68 1,4 VDW 6.32-1.05 Non-1,4 VDW -0.55

6.56 TOTAL 7.89

Strain (kcal/mol)

1

2

3

4

5e.g. favorable C…H

e.g. (unfavorable)

1

2

3

4

e.g. gaucheC-C-C-C

Easier (or harder?)

to bend a stretched bond

Relaxation of Cyclohexane(by Molecular Mechanics)

0.33 Stretch 0.00

0.36 Bend 0.00

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

6 gauche butanes

Stretches and flattens slightly to reduce VDW

6 0.9 = 5.4 (mnemonic)

“Ideal”Minimized

gauche butane

End of Lecture 34Dec. 2, 2009

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