Chem 125 Lecture 10 9/26/07 Preliminary

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Transcript Chem 125 Lecture 10 9/26/07 Preliminary

Chemistry 125: Lecture 12
Overlap and
Atom-Pair Bonds
After applying the united-atom “plum-pudding” view of molecular orbitals, introduced in the
previous lecture, to more complex molecules, this lecture introduces the more utilitarian
concept of localized pairwise bonding between atoms. Formulating an atom-pair orbital as a
sum of atomic orbitals creates an electron difference density by means of the cross product
that enters upon squaring a sum. This “overlap” term is the key to bonding. The hydrogen
molecule is used to illustrate how close a simple sum of atomic orbitals comes to matching
reality, especially when the atomic orbitals are allowed to hybridize.
Synchronize when the speaker finishes saying
“…looked at methane and ammonia…”
Synchrony can be adjusted by using the pause(||) and run(>) controls.
For copyright
notice see final
page of this file
Ethane
&
Methanol
(Spartan 6-31G*)
H
H C H
H C H
7 Pairs of
Valence
Electrons
H
Compare MOs
to AOs of Ar
(7 electron pairs)
O H
H C H
H
Vacant
Rotated 90°
CH3CH3
Orbital
Energy
Occupied
HOMO-6
CH3OH
Orbital
Energy
Pedantic Note: with two
“heavy” atoms there are two
boring “core” orbitals.
For the purpose of making
atomic analogies to study
valence-level molecular
2s orbitals, we’ll use the atomic
1s orbital to stand for the set
Vacant of molecular core orbitals.
Thus we start with 2s rather
than 1s for valence-level
MOs, which will in truth
Occupied include tiny nodes around the
heavy nuclei.
CH3CH3
Orbital
Energy
2pz
HOMO-5
CH3OH
Orbital
Energy
CH3CH3
Orbital
Energy
2px
HOMO-4
CH3OH
Orbital
Energy
CH3CH3
Orbital
Energy
2py
CH3OH
Orbital
Energy
HOMO-3
CH3CH3
Orbital
Energy
3s
HOMO-2
CH3OH
Orbital
Energy
CH3CH3
Orbital
Energy
3dxz
HOMO-1
CH3OH
Orbital
Energy
CH3CH3
Orbital
Energy
3dyz
CH3OH
Orbital
Energy
HOMO
LUMO
CH3CH3
Orbital
Energy
3dz2
LUMO
CH3OH
Orbital
Energy
LUMO+1
CH3CH3
Orbital
Energy
3pz
LUMO+1
CH3OH
Orbital
Energy
LUMO+2
CH3CH3
Orbital
Energy
3py
CH3OH
Orbital
Energy
LUMO+3
LUMO+3
CH3CH3
Orbital
Energy
3px
LUMO+2
CH3OH
Orbital
Energy
LUMO+4
CH3CH3
Orbital
Energy
3dxy
LUMO+5
CH3CH3
Orbital
Energy
3dx2-y2
LUMO+6
CH3CH3
Orbital
Energy
4f
LUMO+4
CH3OH
Orbital
Energy
1-Fluoroethanol
Wire
Core 1
1s (F)
Core 2
1s(O)
Core 3
1s(C1)
Core 4
1s(C2)
1s(valence)
2px
2py
rotate
2py
rotate
2spz (up)
2spz(down)
3dxy
The Plum-Pudding View of Molecular Orbitals
Shows Generality of Kinetic-Energy-Based Clouds
But One Must Probe Harder to Gain a
Qualitative Understanding of Chemical Bonds
Single “United Atom”
e-density
contours
of H2
distorted by a
Atoms with
fragmented nucleus
weak bonding
Which
contour
should
we use?
“True” molecular orbitals
extend over entire molecules, but we
want to understand local bonds as
Pairwise LCAO MOs
1
Y(x1,y1,z1) = √2 ( AOa + AOb)
SUM (Linear Combination) of AOs
(like hybridization, but with two atoms)
Why is this form sensible?
H2 at Great Distance

Y (x
1,y1,z1)
=
1
2
2
2
( AOA + AOB )
negligible!
error? + AOA  AOB
Y(x1,y1,z1) =
1
√2
( AOA + AOB)
H2 at Bonding Distance?
Overlap (A  B) Creates Bonding
If we approximate a molecular orbital as a sum of atomic orbitals:
Looks very good
(normalization) < 1
 A  B
near nuclei
2
(A near A, B near B)
and square to find electron density:
A

2
<1
2
 B  2A  B
2
then subtract the average of the atom electron densities:
_

1 2
2
A B
2

Shifts e-density
from atoms
to overlap region.
we 
find bonding, the difference electron density due to overlap:
A completely different
“By-product” of
instance of multiplying!
squaring a sum.
(NOT two electrons)
AB
Black line is energy e-Density Shrinks
Blue line is Y
Antibonding
e-Density Grows
in A
Stabilzation
of Particle
Total Energy of Particle
"Mixing" localized Y s for double minimum
in B
Bonding!
Wells far
apart
in AB
Wells far
apart
Holds
Wells close A & B
together together
2 significant?
Where
Where
is Y
is AYAY
B significant?
At the center 2YAYB is as large as YA2 +YB2
Electron Density nearly Doubled!
2
a little
YB
2
YA
no!
yes
Yb small
yes!
Region of Significant Overlap
“Overlap Integral” (  YAYB)
measures net change from atoms.
no
Total e-Density
Difference Density
1s (atomic)
Bond
Energy
52%
Coutoured at
0.025 e/ao3
92.9% of
Total Electronic Energy
0.02 Coutoured at
e/ao3 0.004 e/ao3
(almost all of which was
already present in the atoms)
High accuracy is required to calculate correct value of the
Bond Energy, the difference between atoms and molecule.
(Cf. X-ray difference density)
State-of-the-art 40 years ago
Laws & Lipscomb, Isr. J. Chem. 10, 77 (1970)
Total e-Density
Difference Density
Very crudest model
shows most of bond.
1s (atomic)
Bond
Energy
shift from
atom to bond
52%
0.02
General spread increases
Adjust
molecular orbital to lower
thedensity/stabilization.
energy.
1s
(optimized exponent)
bonding
This makes it more realistic, because
the true energy is the lowestlarger
possible
shift from
according to the “variational
atomprinciple”.)
to bond
73%
0.04
Total e-Density
Hybridized + SCF
(96.7% 1s; 0.6% 2s; 2.7% 2p)
Difference Density
Directed spread improves
Helps
overlapdensity.
bonding
larger
but at the cost
of 3% n=2 character
shift from beyond
Bond nucleus to bond
Energy
76%
0.11
General spread increases
bonding density/stabilization.
1s (optimized exponent)
larger
shift from
Hybrid: 96.7%
100%1s
1s 0.6% 2s 2.7%2p
atom
to bond
73%
0.04
Total e-Density
Difference Density
Directed spread improves
bonding density.
Hybridized + SCF
(96.7% 1s; 0.6% 2s; 2.7% 2p)
Bond
Energy
76%
0.11
+ some correlation
Density ~unchanged
(How so?)
much
better
energy
90%
0.11
Pairwise LCAO-MO
Y(x1,y1,z1) =
<1
√2
( AOA + AOB)
Virtues: Easy to formulate and understand
Looks like atoms (especially near nuclei)
(the Main Event for electrons; ~ 6x larger than bond)
Builds up e-density between nuclei
(through Overlap - the source of Bonding)
Smooths Y to lower kinetic energy
[though ultimate contraction toward nuclei raises it again]
Hybridizing AOs provides flexibility
(unlimited if you use all H-like AOs in hybrid)
(but keep it simple - valence shell is fairly good)
Pairwise LCAO-MO
Y(x1,y1,z1) =
Y
=
>1
<1
2
>1
<1
√2
( AOA + AOB)
(AOA2 + AOB2 + 2 AOA AOB)
Atoms
Anti Bond
(overlap / product)
Overlap
&
Energy-Match
End of Lecture 12
Oct. 1, 2008
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J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0