Transcript Chem 125 Lecture 10 9/26/07 Preliminary
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)
flagpole bowsprit “chair” Red bonds rotate in & up. “boat” Blue bonds rotate in & down. “ring flip” by 60° counter-rotation of two parallel bonds inverted chair
What o’clock?
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
For such problems D.H.R. Barton Invents
Conformational Analysis
(1950) Intermediates in steroid hormone synthesis “up” ; “down” (for molecule in conventional orientation, old-fashioned configuration notation, like
cis / trans
) Barton redraws Ring A C D A B
Baeyer observed only one c-Hexyl-COOH, but in these epimers,
and
OH groups have different reactivity!
(configurationally diastereotopic)
For such problems D.H.R. Barton Invents
Conformational Analysis
(1950)
ERRORS?
“up” ; “down” (for molecule in conventional orientation, old-fashioned configuration notation, like
cis / trans
)
Ring Flip?
) (e)
“equatorial”
(p)
“polar”
(now
axial
) 3-fold axis
Cf
. ~1950 Stereochemistry: Bijvoet, Newman, CIP, (Molecular Mechanics)
(Nobel Prize 1969 for “development of the concept of conformation and its application in chemistry”)
Ernst Mohr Illustrations (1918)
gauche
OK within second ring of decalin, but not
anti .
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!
Mol4D
(CMBI Radboud University, Nijmegen, NL) Conformational
Jmol
Animations
Click for INDEX
or go to http://cheminf.cmbi.ru.nl/wetche/organic/index.html
(see Wiki to install Jmol)
Mol4D
(CMBI Radboud University, Nijmegen, NL) Click Points Ethane Click to Animate http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/ethane/jmindex.html
or go to
Staggered Eclipsed
barrier ~5.2 kJ/mol 0.239 = 1.24 kcal/mol Should be ~2.9 kcal/mol.
Caveat emptor!
Step Keys
Mol4D
(CMBI Radboud University, Nijmegen, NL) Propane Click to Animate http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/propane/jmproprot.html
or go to Eclipsed 3.3 kcal/mol Staggered
Mol4D
(CMBI Radboud University, Nijmegen, NL) Butane (central bond) or go to Click to Animate http://cheminf.cmbi.ru.nl/wetche/organic/nalkanesconf/butane/jmindex.html
Anti
10 13 10 -3/4
Gauche +
3.4
= 10 7.5
eclipsed
3.4 kcal/mol (tells how fast) OOPS!
fully eclipsed
~ 4.4 kcal/mol?
(experimentally irrelevant)
Gauche
-
Anti Gauche
+ 0.9 kcal/mol (tells how much)
Gauche / Anti
= 10 -3/4
0.9
= 2 10 -3/4 = 10
0.9
-0.68
= 2 = 1 / 4.7
10 -0.68
= 1 / 2.4
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
Barrier (
Half-Chair
) ~ 11 kcal/mol
Chair
conformer
Flexible
or
Twist-Boat
conformer ~5.5 kcal/mol
Mol4D
(CMBI Radboud University, Nijmegen, NL)
Flexible c
-Hexane Click to Animate go to http://cheminf.cmbi.ru.nl/wetche/organic/cyclohexane/jm/twist_boat.html
or Barrier (
Boat
) ~ 1 kcal/mol
Flexible Twist-Boat
or Form
Shape, “Strain Energy”
&
Molecular Mechanics
“Hooke’s Law” for Strain Energy
Conformational Energy of Ethane 3 kcal/mol 0° H H H H H H H H H H 120° H H Torsional Angle H 240° H H H H H H H H H H H H H H H 360° H H H H
Conformational Energy of Butane 4.4 kcal/mol 4.4 kcal/mol 3.4 kcal/mol 0° CH CH 3 H H 0.9 kcal/mol H CH 3 CH 3 H H H 0.9 kcal/mol 120° CH 3 H Torsional Angle 240° H CH 3 H CH 3 H CH 3 H CH 3 H CH H 3 H H CH 3 CH 3 H H H H 360° H CH 3 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” Parameters
66 different atoms types (including 14 different types of carbon)
138
different bond stretches (41 alkane carbon-X bonds)
“MM2” Parameters
66 different atoms types (including 14 different types of carbon)
624
different bond bendings (41 alkane-alkane-X angles)
“MM2” Parameters
66 different atoms types (including 14 different types of carbon) 0.5
-0.5
Overall Butane
1494
tweaked by torsional energy 180° is low “because of” reduced anti van der Waals
different bond twistings (37 alkane-alkane
-
alkane-X twists) Sum: 1-1-1-1 Torsional Contribution to Butane
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)
e.g.
gauche C-C-C-C 4
e.g.
(unfavorable) 1 5
e.g.
favorable C
…
H “Ideal” Cyclohexane (by Molecular Mechanics) 0.33
0.36
0.09
2.15
-1.05
4.68
6.56
Stretch Bend Stretch-Bend Easier (or harder?) to bend a
TOTAL
Strain (kcal/mol) 0.00
0.00
-0.000
2.12
-0.55
6.32
7.89
6
gauche
butanes 6 0.9 =
5.4
(mnemonic) Stretches and flattens slightly to reduce VDW Relaxation of Cyclohexane (by Molecular Mechanics) Minimized 0.33
0.36
0.09
2.15
-1.05
4.68
Stretch Bend Stretch-Bend Torsion Non-1,4 VDW 1,4 VDW
6.56
TOTAL
“Ideal” 0.00
0.00
-0.000
2.12
-0.55
6.32
7.89
Axial Methylcyclohexane (by Molecular Mechanics) H 8 Axial - Equatorial
gauche
butanes !
3 [ 2
gauche
2 anti
] CH 3 Relaxed 0.49
“
A-value
” a measure of group “size”
“Idealized” Stretch 0.00
0.96
0.14
3.08
-1.31
5.31
8.66
Bend Stretch-Bend Torsion Non-1,4 VDW 1,4 VDW
TOTAL
0.00
-0.00
2.82
6.12
7.61
16.55
End of Lecture 33 Dec. 1, 2008
Copyright © J. M. McBride 2009.
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