Chemistry 125: Lecture 35December 4, 2009

Understanding Molecular Structure and Energy

through Standard Bonds Although molecular mechanics is imperfect, it is useful for discussing molecular shapes in

terms of standard covalent bonds. Analysis of the Cambridge Structural Database shows that

predicting bond distances to within 1% requires detailed categorization of bond types. Early

attempts to predict heats of combustion in terms of composition proved adequate for physiology,

but not for chemistry. Group- or bond-additivity schemes are useful for understanding heats of

formation, especially when corrected for strain. Heat of atomization is the natural target for bond-

energy schemes, but experimental measurement requires spectroscopic determination of the heat

of atomization of elements in their standard states.For copyright

notice see final page of this filePRELIMINARY

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.

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

“Idealized”0.49

0.96

0.14

3.08

-1.31

5.31

8.66

Relaxed

H

CH3

Substituted Cyclohexanes

6 gauche butanes

8 gauche butanes !

Axial - Equatorial= 1.7 kcal/mol

for CH3

[ ~2 gauche 2 anti ]

“A-value”a spectroscopic

measure of group “size”

8.66

0.60.6

FClBrI

0.30.6

kcal/mol

VDW radius increase is offset by increasing C-X distance.

Axial - Equatorial= 1.7 kcal/mol

for CH3

Substituted Cyclohexanes

“A-value”a spectroscopic

measure of group “size”

4.8

CH3

Eti-Prt-Bu

1.71.82.2

kcal/mol

no “good” torsional angle

Stretch

Bend

Stretch-Bend

Torsion

Non-1,4-VDW

1,4-VDW

TOTAL

Cyclobutane Puckering(by Molecular Mechanics)

Torsion vs. Bend

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

Cyclopentane Puckering(by Molecular Mechanics)

"Envelope"

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

e.g. What is the source of the barrier

to c-hexane ring flip?

two butanegauche eclipsed

(~7 kcal/mole)

But why does the plastic model click?Baeyer Angle Strain

+7°+5°

-3°

+5°

Like a plastic model, molecular mechanics is satisfying because

not only does it say what a structure should be, it can also say “why”.

(the actual transition state is thought to be a “Half-Chair”)

Are They “True”?

YES

Are Molecular MechanicsPrograms Useful?

NO

As we work with more complex systems, they become ever more indispensable.

This is why Wikipedia alone lists 34 different schemes of 11 types for various purposes.

C

Brvan der WaalsRadius(1.9Å)

Br•••BrContact

5Å

Br neighborpositions <5Å

from manycrystals(CSD)

Nyburg & Faerman, Acta Crystallographica B41, 274-279 (1985)

C

Br

•

•In order to balance attraction from

more distant atoms, the closest atoms must be "too" close and repulsive.

Bondedbromineatoms

may not be“spherical”!

MolecularMechanicsProgramsassume

they are!

?

Br•••BrContact

Angiostatinanti-cancer drug

“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 about650 optimization steps starting from the MM+ geometry.”

M. J. Frisch, Gaussian, Inc., 2003

largest molecule

calculated byquantum

mechanics

Despite its problemsMM is necessaryfor complex structures

Is the standard Structural Model

realistic in geometric detail?

X-Ray Diffraction

Cambridge Structural DatabaseT

otal

X-R

ay S

truc

ture

s

YearAtomsper

Structure 27 44 56 73

>500,000predictedby 2010

33,532,769atomic

positionsJan 2009

http://www.ccdc.cam.ac.uk

>50,000,000BONDS

75

CSD1

CSD1

Number ofMean BondLengths Tabulated.(specialized because ofinfluence of neighborson precise bond distance)

175CC

97CN

119CO

119 different types of CO bonds27 different typesof Csp3-Csp3 bonds

CSD1

mean high1/4

median low1/4

#obs

stddev

3

C* meansC bearingC,H only

C# meansany Csp3

crowdingstretches bond

evenmoreso

shortlong

R2CH CR3

R2CH CHR2

R3C CR3

RCH2 CH3

R2CH CH3

R3CH CH3

~1%

C C bond lengths

single 1.53 Ådouble 1.32triple 1.18

aromatic 1.38(one-and-a-half bonds)

single: sp3-sp2 1.50 sp2-sp2 1.46

N to

Caromatic

BondLengths

N Planar N Pyramidal

N

N+

_

poor overlap

Twist

Bimodal?

N

:

••

How Complex Must a Model beto Predict Useful Structures?

To get standard deviations in bond distance of 0.015Å(~1%) the Cambridge crew defined:

682 kinds of bonds altogether

175 different kinds of CC bonds(differing in multiplicity, hybridization,

attached groups, rings, etc.)

97 different types of CN bonds

119 different types of CO bonds

We want to understand all “Stuff”

Its Properties & Transformations

Keys:Structure (Bonds)

(Bonds?)& Energy

How Standard are Bond Energies?

Obviously there will be correction for conformation and strain,

but is there an underlying energy for composition or constitution?

Adolph Oppenheim: On the Relationship of Heat of Combustion with the Constitution of Substances.

1868

Ludimar Hermann: On the Regularity and Calculation of Heat of Combustion of Organic Compounds. By a frequently expressed need of physiology to be able to calculate heats of combustion, I have been led to study the current situation…

HCombustion by C / H Content?

SubstanceCarbons

atoms/moleHydrogensatoms/mole

Theory Hcombust

kcal/moleError

kcal/moleError

%

Graphite [1] 0 -94.05 - -

Hydrogen 0 2 -57.8 - -

c-Hexane 6 12 -911.1 -881.6 -29.5 -3

c-Hexanol 6 12 -911.1 -842.7 -68.4 -8

Ethene 2 4 -303.7

Glucose 6 12 -911.1 -670.4 -240.7 -36

Not too bad for fuel purposes, especially if one were to include some kind of correction for partial oxidation.

[-57.8] per H2

[-94.05] per C

= 2 94.05 + 2 57.8

H2C=CH2 has extra energy to give off. One of its bonds () is not very stabilizing,

so it starts unusually high in energy.

O1

O6

partially"pre-oxidized"

-316.2 +12.5 +4

Composition:Atom Additivity

How Complex Must a Model be to Predict Chemically Useful Energies?

For physiology purposes you might be content with ± 5% in heat of combustion.

But for predicting the equilibrium constant between c-hexane + 1/2 O2 and c-hexanol, being off by 1% (9 kcal/mole) means being

off in Keq by a factor ofA useful model must go beyond composition.

How about constitution?

107!

End of Lecture 35Dec. 4, 2009

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