Chemistry 125: Lecture 33

Conformational Energy and Molecular Mechanics

Understanding conformational relationships makes it easy to draw idealized chair structures

for cyclohexane and to visualize axial-equatorial interconversion. After quantitative

consideration of the conformational energies of ethane, propane, and butane, cyclohexane is

used to illustrate the utility of molecular mechanics as an alternative to quantum mechanics

for estimating such energies. To give useful accuracy this empirical scheme requires

thousands of arbitrary parameters. Unlike quantum mechanics, it assigns strain to specific

sources such as bond stretching, bending, and twisting, and van der Waals repulsion or

attraction.

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Ernst Mohr Illustrations (1918)confirm Sachse’s 1890 insight.

Ernst Mohr Illustrations (1918)

“chair” “boat”

bowsprit

flagpole

“ring flip” by 60° counter-rotation

of two parallel bonds

Red bonds rotate in & up. Blue bonds rotate in & down.

invertedchair

ww

w. d

ownu

nder

chic

ago.

com

/pic

s/ol

-la-

lafu

ma-

recl

iner

--pa

dded

--la

.jpg

http://beothic.blogspot.com/2007/01/dory_13.htm

l

Ernst Mohr Illustrations (1918)

Drawing chair cyclohexane rings:

opposite C-C bonds parallel

axial bonds parallel to 3-fold axis

equatorial bonds parallel (anti) to next-adjacent C-C bonds

Whato’clock?

??

??Z

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 OK within second ring of decalin, but not anti.

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 7.5 /sec OOPS!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)

eclipsed3.4 kcal/mol(tells how fast)

fully eclipsed~ 4.4 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-

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

Shape,“Strain Energy”

&

Molecular Mechanics

“Hooke’s Law” for Strain Energy

Conformational Energy of Ethane

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

0° 120° 240° 360°Torsional Angle

Ene

rgy

3 kcal/mol

Conformational Energy of Butane

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

0° 120° 240° 360°Torsional Angle

Ene

rgy

4.4 kcal/mol

0.9 kcal/mol

4.4 kcal/mol

0.9 kcal/mol

3.4 kcal/mol

CH3CH3 CH3

CH3

CH3 CH3

CH3

CH3 CH3 CH3CH3

CH3CH3

CH3

H H

Molecular Mechanics (1946)

“Molecular Mechanics” programs calculate (and can minimize) strain

assuming that molecules can be treated as 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” reduced anti

van der Waalsrepulsiontweaked by

torsional energy

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 !

“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

Axial Methylcyclohexane(by Molecular Mechanics)

0.49 Stretch 0.00

0.96 Bend 0.00

0.14 Stretch-Bend -0.00

3.08 Torsion 2.82

-1.31 Non-1,4 VDW 6.12

5.31 1,4 VDW 7.61

8.66 TOTAL 16.55

8 gauche butanes !

Axial - Equatorial= 1.8 kcal/mol

for CH3

[ 2 gauche 2 anti ]

Relaxed

H

CH3

“A-value”a measure of group “size”

“Idealized”

End of Lecture 33Dec. 1, 2008

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