Chem 125 Lecture 13 10/3/08 This material is for the exclusive use of Chem 125 students at Yale and...
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Transcript of Chem 125 Lecture 13 10/3/08 This material is for the exclusive use of Chem 125 students at Yale and...
Chem 125 Lecture 1310/3/08
This material is for the exclusive use of Chem 125 students at Yale and may
not be copied or distributed further.
It is not readily understood without
reference to notes from the lecture.
Consider how theOverlap Integral
(the “sum” of A x B over all space)
depends on the Distancebetween two Carbon Atomsand on Hybridization
of their Atomic Orbitals
2s 2s
C Overlap Scale
Diameter of node for 2sC is 0.7 Å
Sliding together to1.4Å
(~CC bond distance)superimposesthe two 'X's
xx
2s
x
C Overlap Scale
2s
x
2s
x
2s
x
2s
x
2s
x
2s
x
2s
x
Sliding together to1.4Å
superimposesthe two 'X's
Overlap Integral = 0.41!
Guess the overlap integral, A B(remember that A A = 1)
C Overlap
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
Overlap Integral
1.2 1.3 1.4 1.5 Å
s-
p
2s2p
2s2p
2p2p
+ x -
+ x +
2p
xx
s-sp-
p
C C C C C C
and are“orthogonal”(net overlap = 0)
to -1 atD = 0
to 0 atD = 0
to 1 atD = 0
p-
p
(sigma) is Greek “s” MO
analogue of s AO.(no node
through nuclei)
(pi) is Greek “p”
MO analogue of p AO.
(nodal planethrough nuclei)
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
Overlap Integral
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-sp3
sp2-sp2
sp-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
Overlap Integral
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 gives 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.)
Degenera
te
EnergyRising
EnergyFallingIncreasing Overlap
No SignificantEnergy Difference
Creates Splitting
Overlap Holds Atoms Together
A B
Electron Energy
separate separate
1/√2 (A+B)
1/√2 (A-B)
together
<
>
with greateroverlap
Electron Count and Bond Strength
•
•
•
•
A B
Electron Energy
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 repulsio
n becomes dominant
All from Coulomb’s Lawand
Schrödinger Kinetic Energy of Electrons(This curve provides the potential for studying
molecular vibration.)
Atom-Atom Distance
Energy
Newton Opticks (1717)
Query 31There 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 if partner is lower in energy than A?
A B
Electron Energy
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 :
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,
(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 toward
the internuclear AB 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 AB shifting (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)
Degenera
te
EnergyRising
EnergyFallingIncreasing Overlap
Splitting dueonly toOriginal
Well Offset
Fights Well Difference
Note Small Energy Mismatch
still
Mixing non-
degenerate AOsNegligible
Mixing
StillBiased
What if partner is lower in energy than A?
What are the ultimate energies?
A B
Electron Energy
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 thissplitting forperfect E-match
How much smaller is the bonding shift when
energy is mismatched?
C
A
Electron Energy
separate separatetogether
Averageof A and C
Energy-mismatch
B
How much smaller is the bonding shift when
energy is mismatched?
C
A
Electron Energy
separate separatetogether
With E-mismatch larger
splittingfor same overlap
A given overlapyields thissplitting forperfect E-matchEnergy-
mismatch
B
How much smaller is the bonding shift when
energy is mismatched?
C
A-C
A+C
A
Electron Energy
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
Electron Energy
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
Electron Energy
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)