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Chem 104A, UC, BerkeleyOrbital Interaction Diagram
1. Plot atomic valence orbital energies (or fragment orbitals forMore complex molecules).
2. Determine which orbitals can interact (those with S0).
3. Determine magnitude of each interaction: scales directly with magnitude of overlapscales inversely with orbital energy difference
4. Plot MO energies and draw orbitalsInteraction bonding + antibondingNone no change
5. Use Aufbau principle to fill in electrons
Chem 104A, UC, Berkeley
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2
Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
x
-40 eV
-18.7 eV
-13.6 eV
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3
Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
-19.5 eV
-10.7 eV
-32.4 eV
-15.9 eV
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4
Chem 104A, UC, Berkeley+ -- +
g1
u2Antibonding
+ +- -
- -+ +
- ++ -
u1
u1
g1
g2 Relative non-bondingOr Slightly bonding
Relative non-bondingOr Slightly antibonding
bonding
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
LUMO
HOMO
Frontier Orbitals
More carbon s character
More carbon p character
Chem 104A, UC, BerkeleyCO,
without C2s-O2pz interactionCO,
with C2s-O2pz interaction
C O
+
-Extra C2s character
Extra O2p character
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Chem 104A, UC, Berkeley
- -+ +
g1
g2 Relative non-bondingSlightly bonding
CO
N2LUMO
HOMO
+
_
+
+
+_
_C O
2
C O
Chem 104A, UC, Berkeley
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7
Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
Page 8
8
Chem 104A, UC, Berkeley
Chem 104A, UC, BerkeleyOrbital Interaction Diagram
1. Plot atomic valence orbital energies (or fragment orbitals forMore complex molecules).
2. Determine which orbitals can interact (those with S0).
3. Determine magnitude of each interaction: scales directly with magnitude of overlapscales inversely with orbital energy difference
4. Plot MO energies and draw orbitalsInteraction bonding + antibondingNone no change
5. Use Aufbau principle to fill in electrons
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Chem 104A, UC, Berkeley
Ligand Group OrbitalsLGOs
bu1
bg1
u1
*2 g
*2 u
Chem 104A, UC, Berkeley
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10
Chem 104A, UC, Berkeley
90° 180°HAH
1g
1u
1u
Walsh Diagram for AH2
+ +++ ++
+ +
+ -+ -+++
-
+ -+- Walsh’s correlation diagram:
Plot course of MO energies with change in geometry
Chem 104A, UC, Berkeley
Walsh’s Rules:
An AH2 molecule will be
Linear if it contains 3 or 4 valence elecronse.g. BeH2, BH2
+
Bent if it contains 1,2, or 5-8 valence electronse.g. BH2, CH2, NH2, H2O, H2S
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
H H
LGO
2pz
2px
2py
2s
O
1s
OH H
x
z
y
O
-15.9 eV
-32.4 eV
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
Ligand Group OrbitalsLGOs
bu1
bg1
u1
*2 g
*2 u
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Chem 104A, UC, Berkeley
)22(2
1xa ps
)22(2
1xb ps
p
character
s
character
Bonding
orbital
50% 50%
Chem 104A, UC, Berkeley
H H
LGO
2pz
2px
2py
2s
O
1s
OH H
x
z
y
O
-15.9 eV
-32.4 eV
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Chem 104A, UC, Berkeley
)2(2
1
)2(2
1
1
1
lpxlp
lpxlp
p
p
p
character
s
character
Bonding
orbital
80% 20%
lp
orbital
70% 30%
Chem 104A, UC, Berkeley
AH3 Molecule
BH3 vs NH3
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Chem 104A, UC, Berkeley
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
Chem 104A, UC, BerkeleyProjection Operator Method
1. Construct a reducible rep. using ligand orbitals as a basis.(any basis function that moves contribute nothing).
2. Apply reduction formula:
3. Apply projection operator:
to the basis orbitals to generate LGOs
)(1
# rirNh
RRh
lcP ii
i
)(
il Dimension of i
iR )( Character for operator R in i
Cotton, Chemical Applications of Group Theory, Wiley, 1990, chapt 6, 8
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Chem 104A, UC, Berkeley
Construct a reducible rep. Using ligand orbitals as a basis.(any basis function that moves contribute nothing).
Sa
Sb
Sc3h 3 0 1 3 0 1
Apply reduction formula:
''13 EAh
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
Chem 104A, UC, BerkeleyApply projection operator:
RRh
lcP ii
i
)(to the basis orbitals to generate LGOs
Sa
Sb
Sc
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
)(3
1
)(412
.............
)](1)(11.................
)(1)(11[12
)(
'1
'1
cbaa
cba
cbacba
cbacbaa
A
SSS
SSSc
SSSSSS
SSSSSSc
SP
LGO1
H
H H
'1a
?ˆ aSR
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Chem 104A, UC, BerkeleyApply projection operator:
RRh
lcP ii
i
)(to the basis orbitals to generate LGOs
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
Sa
Sb
Sc
)2(6
1
)224(12
2.............
)](0)()1(2.................
)(0)()1(2[12
2)(
'
'
cbae
cba
cbacba
cbacbaa
E
SSS
SSSc
SSSSSS
SSSSSSc
SP
LGO2
H
H H
'xe
LGO3
H
H H
'ye
)224()(
)224()('
'
bacc
E
cabb
E
SSScSP
SSScSP
)(2
1' cbe SS
subtraction
addition
Chem 104A, UC, Berkeley
BH H
H
y
X
LGOs
Orbitals from Boron: 2s, 2px, 2py, 2pz
H
H H
H
H H
H
H H
2s 2px 2py
LGO1
H
H H
'1a
LGO2
H
H H
'xe
LGO3
H
H H
'ye
'.........'1 EA
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Chem 104A, UC, Berkeley
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
S orbital
Chem 104A, UC, Berkeley
LGO1
LGO2
LGO3
2s
2px 2py 2pz
B 3 H
bs
bx b
y
nbz
*s
*x *
y
'11a
'11e
''21a
'1
'1
2
2
a
e
BH3
-14eV
-8.3 eV
~-13.6 eV
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Chem 104A, UC, Berkeley
90° 120°HAH
Walsh Diagram for AH3
Chem 104A, UC, Berkeley
Walsh’s Rules:
An AH3 molecule will be
pyramidal if it contains 1,2 or 8 valence electronse.g. NH3
planar if it contains 3-6 or 7 valence electronse.g. BH3, NH3
+
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Chem 104A, UC, BerkeleyWalsh Diagrams
from Gimarc, B. J. Acc. Chem. Research 1974, 7, 384.
AH2
AH3
AH4
Chem 104A, UC, Berkeley
Isolobal analogy
Two molecular fragments are isolobal if their frontierorbitals have the same symmetry, similar energies and bring in same No. of electron
..
..3 : XCHH
Pyramidal: NX3, PX3, AsX3, SbX3, NR3…..8ePlanar: BX3, GaI3, InMe3….6e
ClF3 ??
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Chem 104A, UC, Berkeley
LGO1
LGO2
LGO3
2s
2px
2py
2pz
B 3 H
bs
bx b
y
nbz
*s
*x *
y
'11a
'11e
''21a
'1
'1
2
2
a
e
BH3
Chem 104A, UC, Berkeley
LGO1
LGO2
LGO3
3s
3px
3py
3pz
Cl 3 H
bs
bx b
y
nbz
*s
*x *
y
ClF3 ClH3 10 e
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Chem 104A, UC, Berkeley
3s 3p
Cl
Cl*
3d
Valence bond theory treatment of bonding: a hypervalent molecule, ClF3
F Cl
F
F
3dCl* (sp3d)
F F F
The overlap of the sp3d hybrid orbitals on Cl with the 2p orbitals on the F atoms gives three P-F (sp3d)-2p bonds in two sets: the two axial bonds along the z-axis (less than 180° from each other because of the repulsion from the lone pairs) and the one equatorial bond halfway between the other Cl bonds. Again, the bond lengths will not be the same because there is more d contribution to the axial hybrid orbitals.
There are five “objects” around Cl so the geometry is trigonal bipyramidal and the shape is given by AX3E2 (T-shaped).
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
VSEPRValence Shell Electron Pair Repulsion
DG Chapt 2
Allows the prediction of molecular geometry
Sidgwick + Powell 1940
Gillespie + Nyholm 1957
Count up the number of steric contribution around the central atom. Steric number (SN) =# of attached atom + # of lone pairs
Rule 1: Assume that electron pairs around central atom repel each other, the most stable geometry corresponds to that obtained by maximizing the distance between SN points on the surface of a sphere, minimizing electron pair repulsion.
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
VSEPRValence Shell Electron Pair Repulsion
Rule 2: Lone pair electrons are held in closer to the nucleus. Most prohibitive repulsion is lp-lp, followed by lp-bp, then bp-bp…lps will spread out as much as possible.
Rule 3: lps occupy more space than bond pairs, ….large angle between lps than bps.
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
ClF3 ??
SN=5
Rule 1: Structure based on trigonal bypyramid.
Rule 2: LPs are on equatorial positions.
Rule 3. axial F atoms bend away from LPs.
87.5°
87.5°
ClF3
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Chem 104A, UC, Berkeley
LGO1
LGO2
LGO3
2s
2px
2py
2pz
B 3 H
bs
bx b
y
nbz
*s
*x *
y
'11a
'11e
''21a
'1
'1
2
2
a
e
Chem 104A, UC, Berkeley
87.5°
87.5°
ClF3
Note different energies for two LPs
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Chem 104A, UC, Berkeley
(xz, yz)(Rx, Ry)01-20-12E’’
z1-1-1-111A’’ 2
-1
-1
1
1
2 S3
1
0
-1
1
3 C2
-1-111A’’ 1
(x2 - y2, xy)
x2 + y2, z2
(x,y)
Rz
02-12E’
-1111A’2
1111A’1
3 vh2 C3ED3h
S orbital
Chem 104A, UC, Berkeley
E C2 v v’
1 1 1 1 z
1 1 -1 -1 Rz xy
1 -1 1 -1 x, Ry xz
1 -1 -1 1 y,Rx yz
C2v
A1
A2
B1
B2
222 ;; zyx
S Pz both become a1, mixing
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Chem 104A, UC, Berkeley
p
character
s
character
Bonding
orbital
75% 25%
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
214 TAH
E 8C3 3C2 6S4 6σdlinear,
rotationsquadratic
A1 1 1 1 1 1 x2+y2+z2
A2 1 1 1 -1 -1
E 2 -1 2 0 0 (2z2-x2-y2, x2-y2)
T1 3 0 -1 1 -1 (Rx, Ry, Rz)
T2 3 0 -1 -1 1 (x, y, z) (xy, xz, yz)
4 1 0 0 2H4
Chem 104A, UC, Berkeley
214 TAH
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Chem 104A, UC, Berkeley
“phase match”
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
8e Td molecules: 444 ,),,,,( BFARPbSnGeSiAAX
Chem 104A, UC, Berkeley
103°
Fax-S-Fax 179°
SF4
222244 ,,, TeClRSeClRSeClSCl
10e AH4
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Chem 104A, UC, Berkeley
XeFFF
Fsquareplanar
XeF4
44 , BrFICl
12e AH4