Lecture 18, March 2, 2015 graphene, bucky balls, bucky

Transcription

Lecture 18, March 2, 2015
graphene, bucky balls, bucky tubes
Elements of Quantum Chemistry with
Applications to Chemical Bonding and
Properties of Molecules and Solids
Course number: Ch125a; Room 115 BI
Hours: 11-11:50am Monday, Wednesday, Friday
William A. Goddard, III, [email protected]
316 Beckman Institute, x3093
Charles and Mary Ferkel Professor of Chemistry, Materials
Science, and Applied Physics,
California Institute of Technology
Special Instructor: Julius Su <[email protected]>
Teaching Assistants: Hai Xiao <[email protected]>
Mark Fornace <[email protected]>
Ch125-Goddard-L18
© copyright 2015 William A. Goddard III, all rights reserved
Ch125a1
Goddard-
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 = ½Ћ)
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)}.
(H =Ch125-Goddard-L18
E + pV assuming© an
ideal gas)
2
copyright 2015 William A. Goddard III, all rights reserved
Snap Bond Energy: Break bond without relaxing the fragments
Snap
Erelax = 2*7.3 kcal/mol
Adiabatic
D kcal/mol) De (95.0kcal/mol)
Desnap (109.6snap
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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  bond and a  bond.
3B
3B
1
1
3B
1
The HCH angle in CH2 was 132.3º, but Pauli Repulsion with
the new  bond, decreases this angle to 117.6º (cf with 120º
for CH3)
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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  bond. The
nonbonding l and r 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
(
on
same center)
Ch125-Goddard-L18
© copyright
2015 William A.
Goddard III, all
rights
reserved
5
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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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  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 of
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.
3B
57 kcal/mol
The experimental value is D298 ~ 75
kcal/mol, close to the prediction
Ch125-Goddard-L18
1
1A
1
8
CC triple bonds
Since the first CC bond is De=95 kcal/mol and the first CC
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 2 to 4-,
which costs 17 kcal each, weakening the
bond by 34 kcal/mol. Adding this to the 55
would lead to a total 2nd  bond of 89
kcal/mol comparable to the first
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2
4-
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Allyl radical
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Allyl Radical
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Allyl wavefunctions
It is about 12 kcal/mol
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Benzene resonance
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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
Pages from Ch120-Chap1-16-2
is a superposition of the VB structures in (2)
benzene as
≡
+
Pages from Ch120-Chap1-16-2
Ch125-Goddard-L18
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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
Ch125-Goddard-L18
© copyright
2015 William
A. Goddard
III, all rights
reserved
19
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: 2p orbitals per cell
2 bands of states each with N states
where N is the number of unit cells
2  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
Ch125-Goddard-L18
2nd band
1st band
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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  + 1/3 
Diamond: average CCs = 85 kcal/mol   = 3*27=81 kcal/mol
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energetics
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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
Ch125-Goddard-L18
Length =
1.4*sqrt(3)=
2.42A
23 kcal/mol/A
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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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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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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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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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1985-1990 Many papers on C60, no definitive proof that it had
fullerene structure, lots of skepticism
Ch125-Goddard-L18
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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
32
Ch125-Goddard-L18
copyright 2015
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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Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman
Sears arc welder with
flowing He, get soot of
C60. grams per hour
Ch125-Goddard-L18
34
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
Ch125-Goddard-L18
35
Polyyne
chain
precursors
fullerenes, all even
buck y ball ov erheads_Page_01
Ch125-Goddard-L18
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Ch125-Goddard-L18
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C540
All fullerens have 12
pentagonal rings
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Fullerene crystal structures
fcc structure C60
Ch125-Goddard-L18
hcp structure C70
C60 supercell with ordered C60-C60 interactions
Ch125-Goddard-L18

Lecture 18, March 2, 2015 graphene, bucky balls, bucky

Transcription

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