OC-IV

1
OC-IV
Orbital Concepts and Their Applications in
Organic Chemistry
Klaus Müller
Script ETH Zürich, Spring Semester 2009
Chapter 4
symmetry-adapted group orbitals
Lecture assistants Deborah Sophie MathisHCI
G214 tel. 24489mathis_at_org.chem.ethz.ch Alexey
FedorovHCI G204 tel. 34709 fedorov_at_org.chem.et
hz.ch
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Consider the following case of an enol ether
p-LMO
spn nO-LMO f1
The p-, p-LMOs and the two symmetrically
equivalent nO-LMOs would represent a valid
starting point for the discussion of the orbital
structure of the enol ether.

spn nO-LMO f2
However, the two equivalentnO-LMOs f1 and f2
are not symmetry-adapted to the planar symmetry
of the enol ether unit.
p-LMO
p nO p-type LMO
Therefore, it is more convenient to consider the
mutual interaction between the two nO-LMOs
firstand, by this, generate symmetry-adapted
lone pair orbitals.
spm nO s-type LMO
Since f1 and f2 are symmetrically related,
orthogonal spn hAOs, they are energetically
degenerate their interaction results a
symmetrical split intoan spm-type (s-type) lone
pair orbital and an anti-symmetrical (p-type)
pure p lone pair orbital
pp
(f1 - f2)
pp
f1
pure pp-type AO
ps
ps
s
s
f2
-pp
(f1 f2)
ps
s
AO decomposition of the two symmetry
equivalent orthonormal spn-type lone pair LMOs
spm-hAO in s-plane
3
pp
(f1 - f2)
pp
f1
pure pp-type AO
ps
ps
s
s
f2
(f1 f2)
-pp
ps
s
spm-hAO in s-plane
What is the nature of the s-type (spm) hAO by
mixing of two symmetry-equivalent spn hAOs?
s-char
p-char
spn hAO
the s-type spm hAO collects all s-character from
the two spn-hAOs, while the total p-character is
reduced by 1 p-AO that is consumed by the p-type
orbital of the minus-linear combination of the 2
spn hAOs
spm hAO
s-char
p-char
- 1
hence m (n -1)/2
sp3
p
sp
sp3
symmetry-equivalent sp3-hAOs (equal energy)
symmetry-adapted sp-hAO (s-type, lower
energy) and p-AO (p-type, higher energy)
sp2
sp0.5
p
sp2
symmetry-equivalent sp2-hAOs (equal energy)
symmetry-adapted sp0.5-hAO (lower energy) and
p-AO (higher energy)
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The same principles hold true for
symmetry-equivalent s-LMOs or s-LMOs
sCH1-LMO
sp3
sp3
p
sp
sCH2-LMO
symmetry-adapted s-type CH2 group orbital (lower
energy) and p-type CH2 group orbital (higher
energy)
symmetry-equivalent sCH-LMOs (equal
energy) involving sp3-hAOs at central atom

sCX1-LMO
sp3
sp3
p
sp

sCX2-LMO
symmetry-adapted s-type CX2 antibonding group
orbital and p-type CH2 antibonding group orbital
symmetry-equivalent sCX-LMOs (equal
energy) involving sp3-hAOs at central atom

IPp - ep (eV)
8
ep calculated byPRDDO SCF MOmethod using STO
minimal basis set
stabilization of p-orbital by small (1,3)-type
interactions betweenp-type CH3 group orbitals
by ca 0.1 eV per (1,3)p-interaction
IPp
-ep(yp)
9
dep 1.2 eV
dep 1.2 eV
dep 1.1 eV
dep 1.7 eV
dep 2.2 eV
dep 0.6 eV
10
-ep-LMO
IPp
11
C slightly more electronegative than H pulling
effect in s-system lowers p-LMOby ca 0.1-0.2 eV
per CH3 group
hyperconjugative upshift of p-LMO by p-type CH3
group orbitalsby ca 0.6 eV per CH3 group
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The same principles also hold for the reverse
processgeneration of symmetry-equivalent LMOs
from symmetry-adapted LMOs e.g. t-LMOs for a
CC double bond by linear combination of s- and
p-LMOs
sp5
sp5
sp5
sp5
sp2
sp2
pp
pp
t1,CC-LMO by LC
t2,CC-LMO by -LC
sCC-LMO
pCC-LMO
rationalization of allylic torsion potential
using t-LMOs
anticlinal to CC
synclinal to CC
antiplanar to CC
eclipsed to CC
preferred conformation
corresponds to torsional transition state
torsional energy barrier depends on substitution
pattern DE 1-3 kcal/molfor propene DE 2.0
kcal/mol
t1-LMO
Newman projection
in terms of t-LMO description of CC double
bond, the preferred conformation has a
staggered arrangement of doubly occupied LMOs
t2-LMO
X-ray structures from the CSD
ZZZDDJ02
ZIZCOA
QIMHUP
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R
R
sp3
hAO involved in s- and s-LMO
(1)
sp3
(4)
sp3
(2)
sp3
(3)
f1
sp3 (2)
symmetry-equivalent orthonormal lone pair
hAOs(e.g., assuming sp3 hybridization, see
slide 1, Chapter 2)
sp3 (3)
f2
sp3 (4)
f3
To transform these 3 symmetry-equivalent lone
pair orbitals, f1, f2, f3, back
into (orthonormal) lone pair orbitals j1, j2, j3,
that are adapted to the axial C3-symmetry, we
take the following linear combinations
j1
(f1 f2 f3)
(3/2 s - 3 pz)
j2
( f2 - f3)
1/2 px - (1/2 px) px
j3
(2f1 - f2 - f3)
R
Regarding orbital energies and interactions, the
symmetry-equivalent sp3 lone pair hAOs exhibit
strong geminal interactions.
R
e
j3 py
de2 de3
de1
j2 px
j1
This results in a split into the
C3-symmetrical (s-type) hAO j1 at low energy (75
s-character!) and the two energetically
degenerate j2 and j3 orbitals (identical to the
pure px and py orbitals, p-type lone pair
orbitals) note that these two pp-orbitals, as a
group together, represent the C3-axial symmetry.
Note that de1 2de2 ( 2de3) since the lone
pair orbitals are all doubly occupied, the total
energy of the lone pairs remains unaffected.
sp1/3 hAO pointing along C3 symmetry axis
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3 symmetry-adapted lone pair orbitals
3 equivalent lone pair spn-hAOs
pp
spms
pp
the orthogonal pp(F) pp(F) lone pair orbitals
interact exclusively with the orthogonal pCC- and
pCC-LMOs, resp.,
all 3 lone pairs at F interact with both the p-
and s-systems of acetylene
whereas the spm(F) lone pair orbital interacts
exclusively within the axial sCC-system of the
acetylene unit.
Analogous transformations convert 3
symmetry-equivalent s-LMOs (or s-LMOs) into
symmetry-adapted (s)3-group orbitals (or
(s)3-group orbitals)
p-typeCH3 group orbital by (0)(1)(-1)-mixing
orthogonal p-typeCH3 group orbitalby
(2)(-1)(-1)-mixing
2 orthogonal equivalent pCN-LMOs
3 symmetry- equivalent sCH-LMOs
2 degenerate orthogonal p-typeCH3 group orbitals
e
de2 de3
e ltlt 0
s-typeCH3 group orbitalby (1)(1)(1)-mixing
de1
sCH-LMOs
s-type CH3 group orbital
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A particular important application of group
orbitals of trigonal symmetry are the generation
of group orbitals for the cyclopropane unit
(Walsh-orbitals)
H
sp2 hAOs are taken here for simplicity if exact
orientation along the bond axes(interorbital
angle of 115) were desired, the hAOs would be
of type sp2.37however, the arguments below are
not affected by a change in hybridization.
115º
sp2 hAOs
H
symmetry-equivalent sp5 hAOs
radial sp2 hAO
peripheral p-AO

cyclopropane CC bond system described by 3
equivalent bent sCC-LMOs (and sCC-LMOs)
cyclopropane CC bond system described by LCs of
3 symmetry- adapted radial sp2 hAOs and 3
peripheral p-AOs
e

WA
note for
e
IPp 10.5 eV
IPp 10.85 eV
WA
WS
e
e
Jahn-Teller splitting
9

pCC
pCC
WA
WA
similar DE for
DE 3 kcal/mol
compare to 1,3-butadiene
essentially the same E-profile
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2
pCC
pCC
pCC
pCC

WA
p
CO
antibonding
compare tolmax 160-180 nmfor aliphatic
CO lmax220-240 nm for CC-CO
bathochromic shift of p-p UV band
bonding
antibonding
lmax190-210 nm
WA
WS
e
p
CO
Nu-
Nu-
compare to Michael addition to a,b-unsaturated
carbonyl