Chemistry 125: Lecture 13 October 2, 2009 Overlap and Energy-Match Covalent bonding depends...
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Transcript of Chemistry 125: Lecture 13 October 2, 2009 Overlap and Energy-Match Covalent bonding depends...
Chemistry 125: Lecture 13October 2, 2009
Overlap and Energy-Match Covalent bonding depends primarily on two factors: orbital overlap and energy-match.
Overlap depends on hybridization. Bond strength also depends on the number of shared
electrons. So quantum mechanics shows that Coulomb’s law and kinetic energy answer
Newton’s query about what “makes the Particles of Bodies stick together by very strong
Attractions.” A re-vote shows that class has gained insight into the sources of bonding.
Energy mismatch between the constituent orbitals weakens the influence of their overlap.
Predictions of this theory are confirmed experimentally by measuring relative bond strengths of
H-H and H-F during heterolysis and homolysis. Because independent electron pairs must
have no net overlap, hybridization can be related simply to molecular structure, which will help
test our theory further.
For copyright notice see final page of this file
C-C Orbital Overlap (Clementi)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.15 1.25 1.35 1.45 1.55Angstroms
Orbital Overlap Integral
Curiosity:Over most of this range 2s overlaps with 2p
better than either 2s with 2s or 2p with 2p
1.0
0.8
0.6
0.4
0.2
0.0
Ove
rlap
Inte
gra
l
1.2 1.3 1.4 1.5 Å
s-p
p-p
s-sp-p
sp3-sp3
s2p-s2p
C C C C C C
sp3-sp3sp2-sp2sp-sp
xx
sp2-sp2
sp-sp
C-C Orbital Overlap (Clementi)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.15 1.25 1.35 1.45 1.55Angstroms
Orbital Overlap Integral
1.0
0.8
0.6
0.4
0.2
0.0
Ove
rlap
Inte
gra
l
1.2 1.3 1.4 1.5 Å
s-p
p-p
s-sp-p
sp3-sp3
s2p-s2p
C C C C C C
sp2-sp2
sp-sp
Hybrids overlap about twice as much as pure atomic orbitals.
sp gives best overlap, but only allows two orbitals (50% s in each)
sp3 can give four orbitals with nearly as much overlap (25% s in each)
(because they allow nearly full measure of s with p overlap plus s with s, and p with p.)
Degenerate
EnergyRising
EnergyFallingIncreasing Overlap
No SignificantEnergy Difference
Creates Splitting
Overlap Holds Atoms Together
A B
Ele
ctro
n E
nerg
y
separate separate
1/√2 (A+B)
1/√2 (A-B)
together
<
>
with greateroverlap
Electron Count and Bond Strength
•
•
•
•
A B
Ele
ctro
n E
nerg
y
separate separatetogether
•
•
•
•# Effect1 Bonding2 Strongly Bonding3 Weakly Bonding4 Antibonding
Why Doesn’t Increasing Overlap Make MolecularPlum Puddings Collapse?
H2 He?
Electrons do become 55% more stable (~650 kcal/mole)
But proton-proton repulsion increases much more dramatically (1/r)
(already increases by 650 kcal/mole from H-H to 0.3 Å)
Unless one uses neutron “glue” D2 He fusion fuels the Sun (200 million kcal/mole)
Finally we understand
the atom-atom ….
force law! … ….
Bonding Potential
Electron pair becomes more stable
with increasing overlap.
Nuclear repulsion becomes
dominant
All from Coulomb’s Lawand
Schrödinger Kinetic Energy of Electrons
(This curve provides the potential for studying molecular vibration.)
Atom-Atom Distance
Ene
rgy
Newton Opticks (1717)
Query 31
There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the business of experimental Philosophy to find them out.
shop
.rpg
.net
What Holds Atoms Together?Gravity Quarks
Kinetic Energy
Quantum Forces
Strange Attractors
Magnetic Forces
Electrical Forces The Strong Force
Shared Electron Pairs Exchange of Virtual Particles
Exchange of Photons
The Weak Force
Let’s Vote Again
0 0
59 50 (unanimous)
10 0 (plus sophisticated yesses)
5 50 (unanimous)
20 0 (no such thing)
58 50 (unanimous,
but sophisticated)
0 0
7 0
12 1 (holdout)
3 0 (plus a sophisticated yes))
5 0
5 0
What if partner is lower in energy than A?
A B
Ele
ctro
n E
nerg
y
separate separate
1/√2 (A+B)
1/√2 (A-B)
together
<
>
“Splitting” Overlap?B
*
*) approximately
Why use any of an“Inferior” Orbital?
The 1s “core” AOs did indeed remain pure and unmixed during creation
of molecular orbitals for CH3CHFOH :
Sorry, I was confused. The sound recording presents a discussion of Frame 21 while showing this Frame (14).Wikis should follow the frame numbers, not the sound recording.
Why use any of an“Inferior” Orbital?
but the valence-level AOs were heavily mixed.
The compact 1s “core”AOs did indeed remain pure and unmixed during creation
of molecular orbitals for CH3CHFOH,
a << b
B
A
(aA + bB)2 = a2 A2 + b2
B2 + 2abAB
Why use any of an“Inferior” Orbital?
Suppose the energy of the A orbital is muchhigher (less favorable) than that of the B orbital.
Can one profit from shifting electron density towardthe AB overlap region (from the “outside” region)
without paying too much of the high-energy“cost” of A?
Yes, because for a small amount (a) of A in the MO,the amount of A2 probability density (a2) is REALLY small,while the amount of shifted by overlap (2ab) is much larger.
e.g. a = 0.03, b = 0.98 means a2 = 0.001, b2 = 0.96, 2ab = 0.06(Incidentally, this is normalized, since the integral of AB is ~0.6, and 0.6 x 0.06 is ~0.04 = 1 - 0.96)
(Preliminary audio discussion of this frame appears out of order at 17:18-20:05 in the record lecture, and it exchanges A and B)
Degenerate
EnergyRising
EnergyFallingIncreasing Overlap
Splitting dueonly to
OriginalWell Offset
Fights Well Difference
Note Small Energy
Mismatch
still
Mixing non-degenerate
AOsNegligible
Mixing
StillBiased
MostlyLeft
MostlyRight
What if partner is lower in energy than A?What are the ultimate energies?
A B
Ele
ctro
n E
nerg
y
separate separate
1/√2 (A+B)
1/√2 (A-B)
together
<
>
?C
A-C
A+C
largerenergyshifts
smallerenergyshifts
looks mostly like C inshape & energy
looks mostly like A
B
A given overlapyields this
splitting forperfect E-match
How much smaller is the bonding shift when energy is mismatched?
C
A
Ele
ctro
n E
nerg
y
separate separatetogether
Averageof A and C
Energy-mismatch
B
How much smaller is the bonding shift when energy is mismatched?
C
A
Ele
ctro
n E
nerg
y
separate separatetogether
With E-mismatch larger splitting
for same overlapA given overlap
yields thissplitting for
perfect E-match Energy-mismatch
B
How much smaller is the bonding shift when energy is mismatched?
C
A-C
A+C
A
Ele
ctro
n E
nerg
y
separate separatetogether
(shift up a bit for >,< normalization)Splitting is less
sensitive to lesser contributor of
mismatch / overlap
For a given overlap,bonding shift is reduced
by energy mismatch.(Still A+C ends lower than
A+B, because C starts lower.)
e.g. when mismatch is relatively large, a given
amount of overlap doesn’t make much
difference
Important Generalizations
Mixing two overlapping orbitals gives one composite orbital that is lower in energy than either parent
and one that is higher in energy than either parent.
The lower-energy combination looks more like the lower-energy parent,
both in shape and in energy (ditto for higher-).
For a given overlap, increasing energy mismatch decreases the amount of mixing and
decreases the magnitude of energy shifts.
Which Bond is Stronger A-B or A-C?
A B
Ele
ctro
n E
nerg
y
separate separate
C
Compared to What?
••
••
••
••
A-B stronger if forming Ions (A+ B-)
together
A-C electrons clearly lower in energy,but…
Which Bond is Stronger A-B or A-C?
A B
Ele
ctro
n E
nerg
y
separate separate
C
Compared to What?
••
••
A-B stronger if forming Ions (A+ B-)
••
A-C stronger if forming Atoms (A C)• •
together
mismatch aids Heterolysis
mismatch hinders Homolysis
•
H-H vs. H-F
*
Homolysis to A• •Bkcal/mole
136104 HF Bondis Stronger
Heterolysis to A+ B-
kcal/mole (gas phase)
400 373HF Bondis Weaker
BigonF
BigonH
"Hydrofluoric Acid "
antibondingmolecular orbital
:
empty
(match) (mismatch)ABN
ABN(antibonding node)
AON(atomic orbital node)
sp1
sp3
There should be a relationship betweenHybridization and Structure
angle spm-spn = cos-1(mn)
1
m n angle
1 1
2 2
3 3
0
*
125.3°
* to avoid net overlap between different e-pairs (Pauli Principle)
1 3 125.3°
? 180° linear
120° trigonal
109.5° tetrahedral
90°
End of Lecture 13Oct. 2, 2009
Copyright © J. M. McBride 2009. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).
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The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0