1. 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.
For copyright notice see final page of this file
Preliminary

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

3. 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

4. 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).

5. 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)

6. 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)

7. “MM2” Parameters 1494 different bond twistings
3.5
66 different atoms types (including 14 different types of carbon)
0.9
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

8. 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)

9. 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

10. “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
e.g. favorable C…H
Stretch-Bend
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

11. 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)

12. Axial Methylcyclohexane (by Molecular Mechanics)
Relaxed
“Idealized”
0.49
0.96
0.14
3.08
-1.31
5.31
8.66
0.49
Stretch
0.00
0.96
Bend
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
Axial Methylcyclohexane (by Molecular Mechanics)

13. Substituted Cyclohexanes
CH3
Axial - Equatorial
= 1.7 kcal/mol
for CH3
6 gauche butanes 
8 gauche butanes !
[ ~2 gauche  2 anti ]
“A-value”
a spectroscopic measure of group “size” F Cl Br I
0.3
0.6
kcal/mol
values from Eliel, Wilen, & Mander, Stereochemistry of Organic Compounds (1994)
0.6
Substituted Cyclohexanes
8.66
VDW radius increase is offset
by increasing C-X distance.

14. Substituted Cyclohexanes
Axial - Equatorial
= 1.7 kcal/mol
for CH3
“A-value”
a spectroscopic measure of group “size”
CH3 Et
i-Pr
t-Bu
1.7
1.8
2.2
kcal/mol
values from Eliel, Wilen, & Mander, Stereochemistry of Organic Compounds (1994)
Substituted Cyclohexanes
4.8
no “good” torsional angle

15. Cyclobutane Puckering (by Molecular Mechanics)
Relaxed
0.77
16.07
-0.92
11.23
-0.26
2.35
29.24
Planar
0.66
13.48
-0.78
14.81
-0.28
2.27
30.16
Stretch
Bend
Stretch-Bend
Torsion
Non-1,4-VDW
1,4-VDW
TOTAL
Torsion vs. Bend
Cyclobutane Puckering (by Molecular Mechanics)

16. Cyclopentane Puckering (by Molecular Mechanics)
Relaxed
0.31
2.14
-0.09
6.38
-0.51
3.19
11.42
Planar
0.19
0.51
0.02
11.53
-0.48
4.34
16.10
Stretch
Bend
Stretch-Bend
Torsion
Non-1,4-VDW
1,4-VDW
TOTAL
"Envelope"
Cyclopentane Puckering (by Molecular Mechanics)

17. 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)
+7°
+5°
-3°
e.g. What is the source of the barrier to c-hexane ring flip?
But why does the plastic model click?
Baeyer Angle Strain
(the actual transition state is thought to be a “Half-Chair”)

18. 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.

19. "allowed" locus for Br neighbors within 5Å
Br•••Br Contact
van der Waals
Radius
(1.9Å) C Br 5Å

20. ? • Br•••Br Contact Br C "allowed" locus for Br neighbors within 5Å
positions <5Å
from many
crystals
(CSD)
Nyburg & Faerman, Acta Crystallographica B41, (1985)
"allowed" locus for Br neighbors within 5Å
Br•••Br Contact
Bonded
bromine
atoms
may not be
“spherical”! ?
Molecular
Mechanics
Programs
assume
they are! C Br •
S.C. Nyburg and C.H. Faerman,A Revision of van der Waals Atomic Radii for Molecular Crystals - N, O, F, S, Cl, Se, Br, and I Bonded to Carbon.Acta Crystallographica B41, (1985).
In order to balance attraction from more distant atoms, the closest atoms must be "too" close and repulsive.

21. Angiostatin anti-cancer drug
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

22. Is the standard Structural Model realistic in geometric detail?
X-Ray Diffraction

23. Cambridge Structural Database
>50,000,000
BONDS
Total X-Ray Structures
36,334,442
atomic
positions
Jan 2010
Atoms
per
Structure 27 44 56
Year 73 75

24. End of Lecture 35 Dec. 3, 2010
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0