Transcript Chem 125 Lecture 10 9/26/07 Preliminary

Chemistry 125: Lecture 35
December 3, 2010
Understanding Molecular Structure
& Energy through Standard Bonds
The conformational energy of cyclic alkanes illustrates the use of
molecular mechanics, a useful, but highly empirical scheme for reckoning
conformational energy. Although molecular mechanics is imperfect, it is
useful for discussing molecular shapes in terms of standard covalent
bonds. The Cambridge Structural Database provides geometric details
for more that 50,000,000 bonds.
Preliminary
For copyright
notice see final
page of this file
Shape,
“Strain Energy”
&
Molecular Mechanics
“Hooke’s Law” for Strain Energy
Molecular Mechanics (1946)
Question:
How did having
COOH groups on
the benzene rings
facilitate the
experiment?
At the barrier
the C-C-Br angles
 open by 12°.
Activation Energy
for Racemization
obs.
19.5 kcal/mol
t1/2 = 9 min at 0°C
(1013  10-(3/4)*20 ~ 10-2/sec)
calc.
17.3 kcal/mol
“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” 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
3.5
3.5
66 different atoms types (including 14 different types of carbon)
0.9
Overall Butane
0.5
just tweaked a bit
by torsional energy
in this scheme
0.9
180° is low
“because of”
low van der
Waals repulsion
kcal/mole
1494 different bond twistings
0
120°
240°
(37 alkane-alkane
-alkane-X
twists)360°
-0.5
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)
Catalogue of Molecular
Mechanics Schemes
from Wikipedia: Force Fields (Chemistry)
We’ve come a long way
from Couper,
Crum-Brown, and Dewar
1
e.g.
e.g. gauche
C-C-C-C
(unfavorable)
21
43
4
5
23
e.g. favorable C…H
“Ideal” Cyclohexane
(by Molecular Mechanics)
Strain
(kcal/mol)
0.33
Stretch
0.00
0.36
Bend
0.00
0.09
2.15
-1.05
4.68
Stretch-Bend
Easier
Torsion
(or harder?)
Non-1,4
VDW
to
1,4bend
VDWa
-0.000
2.12
-0.55
6.32
bond 7.89
6.56 stretched
TOTAL
6 gauche butane
butanes
6  0.9 = 5.4
(mnemonic)
“Ideal”
Minimized
Stretches and flattens slightly
to reduce VDW
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
Relaxed
“Idealized
” 0.00
0.49
0.49
0.96
0.96
Stretch
Bend
0.00
0.14
0.14
3.08
3.08
Stretch-Bend
-0.00
Torsion
2.82
Axial Methylcyclohexane
-1.31
-1.31
5.31
5.31
Non-1,4 VDW
6.12
1,4 VDW
7.61
(by Molecular Mechanics)
8.66
8.66
TOTAL
16.55
Axial - Equatorial
= 1.7 kcal/mol
6 gauche
butanes
for CH3
H

[ ~2 gauche  2 anti ]
8 gauche
butanes !
“A-value”
a spectroscopic
CH3 measure of
group “size”
kcal/mol
Substituted Cyclohexanes
F
Cl
Br
I
8.66
0.3
0.6
0.6
0.6
VDW radius increase is offset
by increasing C-X distance.
Axial - Equatorial
= 1.7 kcal/mol
for CH3
“A-value”
a spectroscopic
measure of
group “size”
kcal/mol
Substituted Cyclohexanes
CH3
Et
i-Pr
t-Bu
1.7
1.8
2.2
4.8
no “good” torsional angle
Relaxed
Torsion vs. Bend
Cyclobutane Puckering
(by Molecular Mechanics)
Planar
0.77
Stretch
0.66
16.07
Bend
13.48
-0.92
Stretch-Bend
-0.78
11.23
Torsion
14.81
-0.26
Non-1,4-VDW
-0.28
2.35
1,4-VDW
2.27
29.24
TOTAL
30.16
Relaxed
"Envelope"
Cyclopentane Puckering
(by Molecular Mechanics)
Planar
0.31
Stretch
0.19
2.14
Bend
0.51
-0.09
Stretch-Bend
0.02
6.38
Torsion
11.53
-0.51
Non-1,4-VDW
-0.48
3.19
1,4-VDW
4.34
11.42
TOTAL
16.10
Like a plastic model, molecular
mechanics is satisfying because
not only does it say what a structure
should be, it can also say “why”.
two butane
gauche  eclipsed
(~7 kcal/mole)
e.g. why
What
is the
But
does
source
the barrier
plastic of
model
click?
to
c-hexane
ring
flip?
Baeyer
Angle
Strain
+7°
+5° +5°
-3°
(the actual transition state is
thought to be a “Half-
Are Molecular Mechanics
Programs Useful?
YES
As we work with more complex systems,
they become ever more indispensable.
Are They “True”?
NO
This is why Wikipedia alone lists 34 different
schemes of 11 types for various purposes.
Br•••Br
Contact
5Å
van der Waals
Radius
(1.9Å)
Br
C
Bonded
bromine
atoms
may not be
“spherical”!
Br•••Br
Contact
Br neighbor
positions <5Å
from many
crystals
(CSD)
Nyburg & Faerman,
Acta Crystallographica
B41, 274-279 (1985)
?
In order to balance attraction from
more distant atoms, the closest atoms
must be "too" close and repulsive.
•
Molecular
Mechanics
Programs
assume
they are!
Br
C
Despite its problems
MM is necessary
for complex
structures
Angiostatin
anti-cancer drug
largest
molecule
calculated by
quantum
mechanics
“We optimized kringle 1 with the AM1 method using Gaussian 03.
Plasminogen kringle 1 contains 1200 atoms, which are made up of
642 heavy atoms and 578 hydrogen atoms. The job takes about
650 optimization steps starting from the MM+ geometry.”
M. J. Frisch, Gaussian, Inc., 2003
Is the standard
Structural Model
realistic in
geometric detail?
X-Ray Diffraction
Cambridge Structural Database
Total X-Ray Structures
http://www.ccdc.cam.ac.uk
Atoms
per
Structure
>50,000,000
BONDS
Year
27
44
56
73
75
36,334,442
atomic
positions
Jan 2010
End of Lecture 35
Dec. 3, 2010
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0