Lecture 5 January 11, 2012
CC Bonds
Nature of the Chemical Bond
with applications to catalysis, materials
science, nanotechnology, surface science,
bioinorganic chemistry, and energy
William A. Goddard, III, wag@wag.caltech.edu
316 Beckman Institute, x3093
Charles and Mary Ferkel Professor of Chemistry,
Materials Science, and Applied Physics,
California Institute of Technology
Teaching Assistants:
Caitlin Scott <cescott@caltech.edu>
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1
Now combine Carbon fragments to form larger molecules
(old chapter 7)
Starting with the ground state of CH3 (planar),
we bring two together to form ethane, H3C-CH3.
As they come together to bond, the CH bonds
bend back from the CC bond to reduce overlap
(Pauli repulsion or steric interactions between
the CH bonds on opposite C).
At the same time the 2pp radical orbital on each
C mixes with 2s character, pooching it toward
the corresponding hybrid orbital on the other C
120.0º
1.086A
107.7º 1.095A
1.526A
111.2º
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Bonding (GVB) orbitals of ethane (staggered)
Note nodal planes
from
orthogonalization
to CH bonds on
right C
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Staggered vs. Eclipsed
There are two
extreme cases for the
orientation about the
CC axis of the two
methyl groups
The salient difference between these is the overlap of the CH
bonding orbitals on opposite carbons.
To whatever extent they overlap, SCH-CH Pauli requires that they
be orthogonalized, which leads to a repulsion that increases
exponentially with decreasing distance RCH-CH.
The result is that the staggered conformation is favored over
eclipsed by 3.0 kcal/mol
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Alternative interpretation
The bonding electrons are
distributed over the molecule, but it
is useful to decompose the
wavefunction to obtain the net
charge on each atom.
This leads to qH ~ +0.15 and qC ~ -0.45.
qH ~ +0.15
qC ~ -0.45
These charges do NOT indicate the electrostatic energies
within the molecule, but rather the electrostatic energy for
interacting with an external field.
Even so, one could expect that electrostatics would favor
staggered.
The counter example is CH3-C=C-CH3, which has a rotational
barrier of 0.03 kcal/mol (favoring eclipsed). Here the CH bonds
are ~ 3 times that in CH3-CH3 so that electrostatic effects would
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William A. Goddard
III, all rights reserved
decrease
by only 1/3.©However
decreases
exponentially.
5
Propane
Replacing an H of ethane with CH3,
leads to propane
Keeping both CH3 groups staggered
leads to the unique structure
Details are as shown. Thus the bond
angles are
HCH = 108.1 and 107.3 on the CH3
HCH =106.1 on the secondary C
CCH=110.6 and 111.8
CCC=112.4,
Reflecting the steric effects
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Trends: geometries of alkanes
CH bond length = 1.095 ± 0.001A
CC bond length = 1.526 ± 0.001A
CCC bond angles
HCH bond angles
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Bond energies
De = EAB(R=∞) - EAB(Re)
e for equilibrium)
Get from QM calculations. Re is
distance at minimum energy.
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Bond energies
De = EAB(R=∞) - EAB(Re)
Get from QM calculations. Re is
distance at minimum energy
D0 = H0AB(R=∞) - H0AB(Re)
H0=Ee + ZPE is enthalpy at T=0K
ZPE = S(½Ћw)
This is spectroscopic bond energy from
ground vibrational state (0K)
Including ZPE changes bond distance
slightly to R0
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Bond energies
De = EAB(R=∞) - EAB(Re)
Get from QM calculations. Re is
distance at minimum energy
D0 = H0AB(R=∞) - H0AB(Re)
H0=Ee + ZPE is enthalpy at T=0K
ZPE = S(½Ћw)
This is spectroscopic bond energy from
ground vibrational state (0K)
Including ZPE changes bond distance
slightly to R0
Experimental bond enthalpies at 298K and atmospheric pressure
D298(A-B) = H298(A) – H298(B) – H298(A-B)
D298 – D0 = 0∫298 [Cp(A) +Cp(B) – Cp(A-B)] dT =2.4 kcal/mol if A and
B are nonlinear molecules (Cp(A) = 4R). {If A and B are atoms D298
– D0 = 0.9 kcal/mol (Cp(A) = 5R/2)}.
(HCh120a-Goddard-L07,08
= E + pV assuming© an
ideal gas)
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copyright 2011 William A. Goddard III, all rights reserved
Bond energies, temperature corrections
Experimental measurements of bond energies, say at 298K,
require an additional correction from QM or from spectroscopy.
The experiments measure the energy changes at constant
pressure and hence they measure the enthalpy,
H = E + pV (assuming an ideal gas)
Thus at 298K, the bond energy is
D298(A-B) = H298(A) – H298(B) – H298(A-B)
D298 – D0 = 0∫298 [Cp(A) +Cp(B) – Cp(A-B)] dT =2.4 kcal/mol
if A and B are nonlinear molecules (Cp(A) = 4R).
{If A and B are atoms D298 – D0 = 0.9 kcal/mol (Cp(A) = 5R/2)}.
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Snap Bond Energy: Break bond without relaxing the fragments
Snap
DErelax = 2*7.3 kcal/mol
Adiabatic
D
Desnap (109.6snap
kcal/mol) De (95.0kcal/mol)
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Bond energies for ethane
D0 = 87.5 kcal/mol
ZPE (CH3) = 18.2 kcal/mol,
ZPE (C2H6) = 43.9 kcal/mol,
De = D0 + 7.5 = 95.0 kcal/mol (this is calculated from QM)
D298 = 87.5 + 2.4 = 89.9 kcal/mol
This is the quantity we will quote in discussing bond breaking
processes
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The snap Bond energy
In breaking the CC bond of ethane the geometry changes from
CC=1.526A, HCH=107.7º, CH=1.095A
To CC=∞, HCH=120º, CH=1.079A
Thus the net bond energy involves both breaking the CC bond
and relaxing the CH3 fragments.
We find it useful to separate the bond energy into
The snap bond energy (only the CC bond changes, all other
bonds and angles of the fragments are kept fixed)
The fragment relaxation energy.
This is useful in considering systems with differing substituents.
For CH3 this relation energy is 7.3 kcal/mol so that
De,snap (CH3-CH3) = 95.0 + 2*7.3 = 109.6 kcal/mol
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Substituent effects on Bond energies
The strength of a CC bond changes from 89.9 to 70 kcal/mol as
the various H are replace with methyls.Explanations given include:
•Ligand CC pair-pair
repulsions
•Fragment relaxation
•Inductive effects
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Ligand CC pair-pair repulsions:
Each H to Me substitution leads to 2 new CH bonds gauche to
the original CC bond, which would weaken the CC bond.
Thus C2H6 has 6 CH-CH interactions lost upon breaking the
bond,
But breaking a CC bond of
propane loses also two addition
CC-CH interactions.
This would lead to linear changes
in the bond energies in the table,
which is approximately true.
However it would suggest that the
snap bond energies would
decrease, which is not correct.
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Fragment relaxation
Because of the larger size of Me compared to H, there will be
larger ligand-ligand interaction energies and hence a bigger
relaxation energy in the fragment upon relaxing form
tetrahedral to planar geometries.
In this model the snap bond enegies are all the same.
All the differences lie in the relaxation of the fragments.
This is observed to be approximately correct
Inductive effect
A change in the character of the CC bond orbital
due to replacement of an H by the Me.
Goddard believes that fragment relaxation is the correct
explanation
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Bond energies: Compare to CF3-CF3
For CH3-CH3 we found a snap bond energy of
De = 95.0 + 2*7.3 = 109.6 kcal/mol
Because the relaxation of tetrahedral CH3 to planar gains
7.3 kcal/mol
For CF3-CF3, there is no such relaxation since CF3 wants
to be pyramidal, FCF~111º
Thus we might estimate that for CF3-CF3 the bond energy
would be De = 109.6 kcal/mol, hence D298 ~ 110-5=105
Indeed the experimental value is D298=98.7±2.5 kcal/mol
suggesting that the main effect in substituent effects is
relaxation (the remaining effects might be induction and
steric)
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Stopped L4, January 11, 2012
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CH2 +CH2  ethene
Starting with two methylene radicals (CH2) in the
ground state (3B1) we can form ethene
(H2C=CH2) with both a s bond and a p bond.
The HCH angle in CH2 was 132.3º, but Pauli Repulsion with
the new s bond, decreases this angle to 117.6º (cf with 120º
for CH3)
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Comparison of The GVB
bonding orbitals of ethene
and methylene
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Twisted ethene
Consider now the case where the plane of one CH2 is rotated by
90º with respect to the other (about the CC axis)
This leads only to a s bond. The
nonbonding pl and pr orbitals can be
combined into singlet and triplet states
Here the singlet state is referred to as N (for Normal) and the
triplet state as T.
Since these orbitals are orthogonal, Hund’s rule suggests that T is
lower than N (for 90º). The Klr ~ 0.7 kcal/mol so that the splitting
should be ~1.4 kcal/mol.
Voter, Goodgame, and Goddard [Chem. Phys. 98, 7 (1985)] showed that N is
below
T by 1.2 kcal/mol, due
to Intraatomic
Exchange
(s,p
same center) 22
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Goddard III, all
rightson
reserved
Twisting potential surface for ethene
The twisting potential surface for ethene is shown below. The
N state prefers θ=0º to obtain the highest overlap while the T
state prefers θ=90º to obtain the lowest overlap
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geometries
For the N state (planar) the CC bond
distance is 1.339A, but this increases to
1.47A for the twisted form with just a
single s bond.
This compares with 1.526 for the CC bond of ethane.
Probably the main effect is that twisted ethene has very little CH
Pauli Repulsion between CH bonds on opposite C, whereas
ethane has substantial interactions.
This suggests that the intrinsic CC single bond may be closer to
1.47A
For the T state the CC bond for twisted is also 1.47A, but
increases to 1.57 for planar due to Orthogonalization of the
triple coupled pp orbitals.
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CC double bond energies
The bond energies for ethene are
De=180.0, D0 = 169.9, D298K = 172.3 kcal/mol
Breaking the double bond of ethene, the HCH bond angle
changes from 117.6º to 132.xº, leading to an increase of 2.35
kcal/mol in the energy of each CH2 so that
Desnap = 180.0 + 4.7 = 184.7 kcal/mol
Since the Desnap = 109.6 kcal/mol, for H3C-CH3,
The p bond adds 75.1 kcal/mol to the bonding.
Indeed this is close to the 65kcal/mol rotational barrier.
For the twisted ethylene, the CC bond is De = 180-65=115
Desnap = 115 + 5 =120. This increase of 10 kcal/mol compared to
ethane might indicate the effect of CH repulsions
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bond energy of F2C=CF2
The snap bond energy for the double bond of ethene od
Desnap = 180.0 + 4.7 = 184.7 kcal/mol
As an example of how to use this consider the bond energy
of F2C=CF2,
Here the 3B1 state is 57 kcal/higher than 1A1 so that the
fragment relaxation is 2*57 = 114 kcal/mol, suggesting that
the F2C=CF2 bond energy is Dsnap~184-114 = 70 kcal/mol.
The experimental value is D298 ~ 75 kcal/mol, close to the
prediction
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Bond energies double bonds
Although the ground state of CH2 is 3B1 by 9.3 kcal/mol,
substitution of one or both H with CH3 leads to singlet ground
states. Thus the CC bonds of these systems are weakened
because of this promotion energy.
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C=C bond energies
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CC triple bonds
Starting with two CH radicals in the 4S- state we can form
ethyne (acetylene) with two p bonds and a s bond.
This leads to a CC bond length of 1.208A compared to 1.339
for ethene and 1.526 for ethane.
The bond energy is
De = 235.7, D0 = 227.7, D298K = 229.8 kcal/mol
Which can be compared to De of 180.0 for H2C=CH2 and
95.0 for H3C-CH3.
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GVB orbitals of HCCH
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GVB orbitals of CH 2P and 4S- state
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CC triple bonds
Since the first CCs bond is De=95 kcal/mol and the first CCp
bond adds 85 to get a total of 180, one might wonder why the
CC triple bond is only 236, just 55 stronger.
The reason is that forming the triple bond
requires promoting the CH from 2P to 4S-,
which costs 17 kcal each, weakening the
bond by 34 kcal/mol. Adding this to the 55
would lead to a total 2nd p bond of 89
kcal/mol comparable to the first
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2P
4S-
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32
Bond energies
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Diamond
Replacing all H atoms of ethane and with methyls, leads to with a
staggered conformation
Continuing to replace H with methyl groups
forever, leads to the diamond crystal
structure, where all C are bonded
tetrahedrally to four C and all bonds on
adjacent C are staggered
A side view is
This leads to the diamond crystal structure. An expanded view
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35
Infinite structure from tetrahedral bonding plus staggered bonds
on adjacent centers
2nd layer
3
1
1
1st layer
1
2
02
2
2nd layer
0
0
1c
1st layer
1
1
1
1
2nd layer
1st layer
Chair
configuration
of cylcohexane
Not shown: zero layer just like 2nd layer but above layer 1
rd layer just like the 1st layer but below layer 2
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36
c
The unit cell of diamond crystal
An alternative view of the
diamond structure is in terms of
cubes of side a, that can be
translated in the x, y, and z
directions to fill all space.
c
f
c
i
c
i f
f
f
f
i c
i
Note the zig-zag chains c-i-f-i-c
f
and cyclohexane rings (f-i-f)-(i-f-i) c
c
There are atoms at
•all 8 corners (but only 1/8 inside the cube): (0,0,0)
•all 6 faces (each with ½ in the cube): (a/2,a/2,0), (a/2,0,a/2),
(0,a/2,a/2)
•plus 4 internal to the cube: (a/4,a/4,a/4), (3a/4,3a/4,a/4),
(a/4,3a/4,3a/4), (3a/4,a/4,3a/4),
Thus each cube represents 8 atoms.
All other atoms of the infinite crystal are obtained by translating
this
cube by multiples©of
a in 2011
theWilliam
x,y,zA. Goddard
directions
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c
37
Diamond Structure
Now bond one of these
atoms, C2, to 3 new C
so that the bond are
staggered with respect
to those of C1.
5a
3a
1a
4b
2b
5
6
3
4
2
1b
4a
2a
1
Start with C1 and
make 4 bonds to form
a tetrahedron.
5b
3b
1c
7
Continue this process.
Get unique structure:
diamond
Note: Zig-zag chain
1b-1-2-3-4-5-6
Chair cyclohexane
ring: 1-2-3-3b-7-1c
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Properties of diamond crystals
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Properties of group IV molecules (IUPAC group 14)
1.526
There are 4 bonds to each atom, but each bond connects two
atoms.
Thus to obtain the energy per bond we take the total heat of
vaporization and divide by two.
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William
Goddard III,
all rights reserved
Note
for Si, that the average
bond
isA.much
different
than for Si H40
Comparisons of successive bond energies SiHn and CHn
p
lobe
lobe
lobe
p
lobe
p
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p
41
Redo the next sections
Talk about heats formation first
Then group additivity
Then resonance etc
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Benzene and Resonance
referred to as Kekule or VB structures
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Resonance
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Benzene wavefunction
is a superposition of the VB structures in (2)
benzene as
≡
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+
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45
More on resonance
That benzene would have a regular 6-fold symmetry is not
obvious. Each VB spin coupling would prefer to have the
double bonds at ~1.34A and the single bond at ~1.47 A (as
the central bond in butadiene)
Thus there is a cost to distorting the structure to have equal
bond distances of 1.40A.
However for the equal bond distances, there is a
resonance stabilization that exceeds the cost of distorting
the structure, leading to D6h symmetry.
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Cyclobutadiene
For cyclobutadiene, we have the same situation, but here the
rectangular structure is more stable than the square.
That is, the resonance energy does not balance the cost of
making the bond distances equal.
1.34 A
1.5x A
The reason is that the pi bonds must be orthogonalized,
forcing a nodal plane through the adjacent C atoms, causing
the energy to increase dramatically as the 1.54 distance is
reduced to 1.40A.
For benzene only one nodal plane makes the pi bond
orthogonal
to both other
bonds,
leading
to lower
cost
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A. Goddard
III, all rights
reserved
47
graphene
Graphene: CC=1.4210A
Bond order = 4/3
Benzene: CC=1.40 BO=3/2
Ethylene: CC=1.34 BO = 2
CCC=120°
Unit cell has 2 carbon atoms
1x1 Unit cell
This is referred to as graphene
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Graphene band structure
1x1 Unit cell
Unit cell has 2 carbon atoms
Bands: 2pp orbitals per cell
2 bands of states each with N states
where N is the number of unit cells
2 p electrons per cell  2N electrons for
N unit cells
The lowest N MOs are doubly occupied,
leaving N empty orbitals.
The filled 1st band touches
the empty 2nd band at the
Fermi energy
Get semi metal
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2nd band
1st band
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49
Graphite
Stack graphene layers as ABABAB
Can also get ABCABC Rhombohedral
AAAA stacking much higher in energy
Distance between layers = 3.3545A
CC bond = 1.421
Only weak London dispersion
attraction between layers
De = 1.0 kcal/mol C
Easy to slide layers, good lubricant
Graphite: D0K=169.6 kcal/mol, in plane bond = 168.6
Thus average in-plane bond = (2/3)168.6 = 112.4 kcal/mol
112.4 = sp2 s + 1/3 p
Diamond: average CCs = 85 kcal/mol  p = 3*27=81 kcal/mol
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energetics
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Allyl Radical
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Allyl wavefunctions
It is about 12 kcal/mol
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Cn
What is the structure of C3?
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Cn
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Energetics Cn
Note extra stability of odd Cn by 33 kcal/mol, this is because odd
Cn has an empty px orbital at one terminus and an empty py on the
other, allowing stabilization of both p systems
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Stability of odd Cn
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Bond energies and thermochemical calculations
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Bond energies and thermochemical calculations
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Heats of Formation
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Heats of Formation
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Heats of Formation
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Heats of Formation
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Bond energies
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Bond energies
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Bond energies
Both secondary
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Average bond energies
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Average bond energies
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Real bond energies
Average bond
energies of little
use in predicting
mechanism
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Group values
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Group functions of propane
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Examples of using
group values
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Group values
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Strain
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Strain energy cyclopropane from Group values
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Strain
energy
c-C3H6
using real
bond
energies
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Stained GVB orbitals of cyclopropane
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Benson Strain energies
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Resonance in thermochemical Calculations
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Resonance in thermochemical Calculations
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Resonance energy butadiene
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Allyl radical
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Benzene resonance
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Benzene resonance
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Benzene resonance
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Benzene resonance
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Benzene resonance
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Graphene: generalize benzene in all directions
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Have to terminate graphene: two simple cases
Armchair edge
Zig-zag edge
For each edge
atom break two
sp2 sigma bonds
but form bent pi
bond in plane
For each edge
atom break sp2
sigma bond,
maybe not break
pi bond?
111.7 – 20 = 92
kcal/mol
111.7/2 = 56
kcal/mol per
dangling bond
Length =
3*1.4=4.2A
22 kcal/molA
Thus both
graphene
ribbon surfaces
(edges) have
similar
energies
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Length =
1.4*sqrt(3)=
2.42A
23 kcal/mol/A
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91
C60 flat sheet
Cut from graphene
6 arm chair pairs @92
5 zig-zag atoms @56
Total cost 832 kcal/mol!
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92
C60 fullerene
No broken bonds
Just ~11.3 kcal/mol
strain at each atom
678 kcal/mol
Compare with 832
kcal/mol for flat sheet
Lower in energy than flat
sheet by 154 kcal/mol!
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93
First observation
Heath, Smalley, Krotos
Laser evaporation of carbon + supersonic nozzle
Observe various sized clusters in mass spect
Change various conditions found peak at C60!
Smalley and Krotos each independently postulated futball
(soccer ball structure) ~1986
^ H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl and R.
E. Smalley (1985). "C60: Buckminsterfullerene". Nature
318: 162–163. doi:10.1038/318162a0.
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94
Nature 1985: discovery of C60
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10 torr He
Evidence for C60, Nature 1985
maximize clustercluster reactions
in integration cup
760 torr He
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96
1985-1990 Many papers on C60, no definitive proof that it had
fullerene structure, lots of skepticism
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1985-1990 Many papers on C60, no definitive proof that it had
fullerene structure, lots of skepticism
In 1990 physicists W. Krätschmer and D.R. Huffman for the first
time produced isolable quantities of C60 by causing an arc
between two graphite rods to burn in a helium atmosphere and
extracting the carbon condensate so formed using an organic
solvent.
Then, Nature 347, 354 - 358 (27 September 1990)
W. Krätschmer, Lowell D. Lamb, K. Fostiropoulos & Donald
R. Huffman; Solid C60: a new form of carbon
A new form of pure, solid carbon has been synthesized
consisting of a somewhat disordered hexagonal close
packing of soccer-ball-shaped C60 molecules.
Infrared spectra and X-ray diffraction studies of the molecular
packing confirm that the molecules have the anticipated
'fullerene' structure.
Mass spectroscopy shows that the C70 molecule is present
98
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Goddard
III, all rights reserved
at ©levels
of aWilliam
fewA. per
cent.
Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman
Sears arc welder with
flowing He, get soot of
C60. grams per hour
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100
Carbon 13 NMR spectrum of C60
1 peak
NMR the key
experiment
Definitive proof that
C60 is fullerene
Carbon 13 NMR spectrum of C70
5 peaks, definitive proof of fullerene structure
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101
C540
All fullerens have 12
pentagonal rings
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102
Polyyne
chain
precursors
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fullerenes, all even
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103
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Mechanism for formation of fullerenes
Heath 1991: Fullerene road. Smaller fullerenes and C3 etc
add on to pentagonal sites to grow C60
Contradicted by He chromatography and high yield of
endohedrals
Smalley 1992: Pentagonal road. Graphtic sheets grow and
curl into fullerenes by incorporating pentagonal C3 etc add
on to pentagonal sites to grow C60
Contradicted by He chromatography
Arc environment: mechanism goes through atomic species
(isotope scrambling)
He chromatography Go through carbon rings and form
fullerenes
Has high temperature gradients
Ring growth road. Jarrold 1993. based on He chromatography
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105
He chromatography (Jarrold)
Relative abundance of the isomers and
fragments as a function of injection
energy in ion drifting experiments
Conversion of bicyclic ring to fullerene
when heated
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Energies from QM
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Force Field for sp1 and sp2 carbon clusters
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108
4n vs 4n+2 for Cn Rings
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109
Population of various ring and fullerene species with Temperature
Based on free energies from QM and FF
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Bring two C30 rings together
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111
Energetics (eV) for isomerizations converting bicyclic ring to
monocyclic or Jarrold intermediates for n = 30, 40, 50
TS to Bergman cyclization
singlet (leads to Jarrold
ring
mechanism)
2 rings
TS to form tricyclic
E tricyclic
TS convert
C40
C34
E tricyclic
C60
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Energetics (eV) for initial steps of Jarrold
Jarrold
pathway
If get here, then get
fullerene
Modified
Jarrold
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Number pi bonds
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113
energetics (eV)
Downhill race from tricyclic to bucky ball
30 eV of energy gain as
form Fullerene
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Number
sp2
centers
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III, all rights reserved
114
Structures in Downhill race from tricyclic to bucky ball
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115
energetics (eV)
Energy contributions to downhill race to fullerene
Number sp2 bonded centers
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116
C60 dimer
Prefers packing of 6 fold face
De = 7.2 kcal/mol
Face-face=3.38A
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117
Crystal structure C60
Expect closest packing: 6 neighbors in plane
3 neighbors above the plane and 3 below
But two ways
ABCABC face centered cubic
ABABAB hexagonal closet packed
Predicted crystal structure 3 months before experiment
Prediction of Fullerene Packing in C60 and C70 Crystals
Y. Guo, N. Karasawa, and W. A. Goddard III
Nature 351, 464 (1991)
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118
C60 is face centered cubic
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119
C70 is hexagonal closest packed
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120
Vapor phase grown Carbon fiber,
R. T. K. Baker and P. S. Harris, in Chemistry and Physics of
Carbon, edited by P. L. Walker, Jr. and A. Thrower (Marcel
Dekker, New York, 1978), Vol. 14, pp. 83–165;
G. G. Tibbetts, Carbon 27, 745–747 (1989);
R. T. K.Baker, Carbon 27, 315–323 (1989).
M. Endo, Chemtech 18, 568–576 (1988).
Formed carbon fiber from 0.1 micron up
Xray showed that graphene planes are
oriented along axis but perpendicular to
the cylindrical normal
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121
Multiwall nanotubes
"Helical microtubules of graphitic carbon". S. Iijima, Nature
(London) 354, 56–58 (1991).
Ebbesen, T. W.; Ajayan, P. M. (1992). "Large-scale synthesis of
carbon nanotubes". Nature 358: 220–222.
Outer diameter of MW NT
inner diameter of MW NT
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122
Single wall carbon nanotubes, grown catalytically
S. Iijima and T. Ichihashi, "Single-shell carbon nanotubes of 1-nm
diameter".Nature (London) 363, 603–605 (1993) used Ni
D. S. Bethune, C.-H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazquez,
and R. Beyers, "Cobalt-catalyzed growth of carbon nanotubes with singleatomic-layer walls".Nature (London) 363, 605–607 (1993). used Co
Ching-Hwa Kiang grad student with wag on leave at IBM san Jose
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123
Single wall carbon nanotubes, grown catalytically
S. Iijima and T. Ichihashi, "Single-shell carbon nanotubes of 1-nm
diameter".Nature (London) 363, 603–605 (1993) used Ni
D. S. Bethune, C.-H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazquez,
and R. Beyers, "Cobalt-catalyzed growth of carbon nanotubes with singleatomic-layer walls".Nature (London) 363, 605–607 (1993). used Co
Ching-Hwa Kiang grad student with wag on leave at IBM san Jose
Catalytic Synthesis of Single-Layer Carbon Nanotubes with a Wide Range of Diameters C.- H.
Kiang, W. A. Goddard III, R. Beyers, J. R. Salem, D. S. Bethune, J. Phys. Chem. 98, 6612–6618
(1994).
Catalytic Effects on Heavy Metals on the Growth of Carbon Nanotubes and Nanoparticles C.-H.
Kiang, W. A. Goddard III, R. Beyers, J. R. Salem, and D. S. Bethune, J. Phys. Chem. Solids 57, 35
(1995).
Effects of Catalyst Promoters on the Growth of Single-Layer Carbon Nanotubes; C.-H. Kiang, W. A.
Goddard III, R. Beyers, J. R. Salem, and D. S. Bethune, Mat. Res. Soc. Symp. Proc. 359, 69 (1995)
Carbon Nanotubes With Single-Layer Walls," Ching-Hwa Kiang, William A. Goddard III, Robert
Beyers and Donald S. Bethune, " Carbon 33, 903-914 (1995).
"Novel structures from arc-vaporized carbon and metals: Single-layer carbon nanotubes and
metallofullerenes," Kiang, C-H, van Loosdrecht, P.H.M., Beyers, R., Salem, J.R., and Bethune,
D.S., Goddard, W.A. III, Dorn, H.C., Burbank, P., and Stevenson, S., Surf. Rev. Lett. 3, 765-769
124
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(1996).
Kiang CNT
form 1993
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125
Kiang CNT form 1993
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126
Distribution of
diameters for carbon
SWNT, Kiang 1993
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128
Examples Single wall carbon nanotubes
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129
Some bucky tubes
(8,8)
armchair
(14,0)
zig-zag
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(6,10)
chiral
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130
Contsruction for (6,10) edge
1
2
3
6
4
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5
131
13.46A diameter
(10,10) armchair carbon
SWNT
40 atoms/repeat
distance
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132
(14,0) zig-zag Bucky tube
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133
Crystal packing
of (10,10) carbon
SWNT
13.5A
Density
SWNT: 1.33 g/cc
Graphite 2.27 g/cc
Ec Young’s modulus
SWNT 640 GPa
Graphite 1093 GPa
16,7A
Heat formation
Graphite 0
C60 11.4
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(10,10)
CNT 2.72
Ea Young’s modulus
SWNT 5.2 GPa
Graphite 4.1 GPa
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Vibrations in (10,10)
armchair CNT
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135
Carbon fibers and tubes
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136
Vibrations in (10,10)
armchair CNT
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137
Vibrations in (10,10)
armchair CNT
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138
Mechanism for gas phase CNT
formation
Polyyne Ring Nucleus Growth
Model for Single-Layer Carbon
Nanotubes
C-H. Kiang and W. A. Goddard III
Phys. Rev. Lett. 76, 2515 (1996)
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139
Mechanism for gas phase CNT formation
A two-stage mechanism of bimetallic catalyzed growth of singlewalled carbon nanotubes Deng WQ, Xu X, Goddard WA
140
Nano Letters
42011
(12):
2331-2335
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William
A. Goddard III, all(2004)
rights reserved
But mechanism of gas phase C SWNT, no longer important
The formation of Carbon SWNT by CVD growth on
a metal nanodot on a support is now the preferred
mechanism for forming SWNT
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141
Mechanisms Proposed for Nanotube Growth
Stepwise Process
Adsorption
Dehydrogenation
Saturation
Diffusion
Nucleation
Growth
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142
Vapor-Liquid-Solid (Carbon Filament)
Mechanism
• Vapor carbon feed stock adsorbs unto
liquid catalyst particle and dissolves.
Dissolved carbon diffuses to a region of
lower solubility resulting in supersaturation and precipitation of the solid
product.
• Originally developed to explain the growth
of carbon whiskers/filaments.
• Temperature, concentration or free energy
gradient is implicated as the driving force
responsible for diffusion.
Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89. Bolton, et al. J. Nanosci.
Nanotechnol. 2006, 6, 1211.
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143
Yarmulke Mechanism
Dai, et al. Chem. Phys. Lett. 1996, 260, 471.
Raty, et al. Phys. Rev. Lett. 2005 95, 096103.
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• Carbon-carbon bonds form
on the surface (either
before or as a result of
super-saturation).
• Diffusion of carbon to
graphene coating can be
an important rate limiting
step.
• Coating of more than a
complete hemisphere
results in poisoning of
catalyst.
• New layers can start
beneath the original layer
after/as it lifts off the
surface resulting in MWNT.
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144
Experimental Confirmation of a Yarmulke
Mechanism
Atomic-scale, video-rate environmental transmission
microscopy has been used to monitor the nucleation and
growth of single walled nanotubes.
Hofmann, S. et al. Nano Lett. 2007, 7, 602.
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145
Role of the Catalyst Particle in Nanotube
Formation
• Size of catalyst particles is related to the
diameter of the nanotubes formed.
• Catalyst nanoparticles are known to deform
(elongate) during nanotube growth.
• Structural properties of select catalyst
surfaces (Ni111, Co111, Fe1-10) exhibit
appropriate symmetry and distances to
overlap with graphene and allow thermally
forbidden C2 addition reaction.
• Graphene is believed to stabilize the high
energy nanoparticle surface. MWNT have
been observed growing out of steps, which
they stabilize.
•
•
•
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Hong, S.; et al. Jpn J. Appl. Phys.
2002, 41, 6142.
Vinciguerra, V.; et al. Nanotechnol.
2003, 14, 655.
Hofmann, S. et al. Nano Lett.
2007, 7, 602
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146
Tip vs. Base Growth Mechanisms
Same initial reaction step: absorbtion,
diffusion and precipitation of carbon
species.
Strength of interaction between catalyst
particle and catalyst support determines
whether particles remains on surface or
is lifted with growing nanotube.
Huang, S.; et al. Nano Lett. 2004 4, 1025.
Kong, J.; et al. Chem. Phys. Lett. 1998, 292, 567.
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Images of nanotubes show catalyst
particles trapped at the ends of
nanotubes in the case of tip growth, or
nanotubes bound to catalysts on
support in the case of base growth.
Alternatively capped nanotube tops
show base growth.
A kite (tip) growth mechanism has been
used to explain the growth of long (order
147
of mm),
well III,
ordered
SWNTs.
© copyright 2011 William
A. Goddard
all rights reserved
Limiting Steps for Growth Rates
Diffusion of reactive species either
through the catalyst particle bulk or across
its surface can play an important role in
determining the rate of nanotube growth.
In the case of carbon species which
dissociate less readily the rate of carbon
supply to the particle can act as the rate
limiting step.
The rate of growth must also take into
account a force balance between the
friction of the nanotube moving through
the surrounding feedstock gas and the
driving force for/from the reaction.
Vinciguerra, V.; et al. Nanotechnol. 2003, 14, 655.
Hofmann, S. et al. Nano Lett. 2007, 7, 602.
Hafner, J. H.; et al. Chem. Phys. Lett. 1998, 296, 195.
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