OCIV

1
OC-IV
Orbital Concepts and Their Applications in
Organic Chemistry
Klaus Müller
Script ETH Zürich, Spring Semester 2009
Chapter 5
p-systems HMO and extended PMO method
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
2

• For planar unsaturated systems
• the p- and s-orbitals are orthogonal by symmetry
• there are no (s,p)-orbital interactions
• there are no orbital splitting effects between
  s- and p-orbitals
• hencethe p-orbital system can be treated
  independently from the s-orbital systemhowever
• the orbital energies of the p-system are affected
  by the s-electron distribution
• and vice-versa

Hik
interaction energy between adjacent pp
orbitalsbCC b uniform interaction parameter
for C-atoms in p-system
Hij
pp interaction energy involving heteroatomsin
simplest approach bCX b
Him
interaction energy between non-adjacent pp
orbitalsin simplest approach bCC 0
in refined approach bCX kCX b typically kCX
lt 1 (prop. SCX/SCC)
p
p
refined approach bim kim b e.g. kim
typically b1,3 0.3 b b1,4 0
Hjj
pp orbital energy for heteroatom Hjj a hj b
Hii
pp orbital energies
Hkk
- characteristic for given atom- modulated by
local s-electron density- modulated by
p-electron density

• - specified with reference to aC
• modulation in units of b- hi numerical
  parameter hi gt 0 atom more el.neg. than C
• hi lt 0 atom less el.neg. than C

in simplest HMO approachHii Hkk aC aa
uniform energy parameter for pp-AO of
C-atoms in p-systems
in refined HMO modelsHii ai hi bai
dependent on local topology hi numerical
parameter (small) b all energy corrections in
b units
3
p
S1,2 0.25
p-overlap integrals are relatively small
therefore, they are neglected in the eigenvalue
problem
p
S1,3 0.08
the typical eigenvalue problem of the LCAO MO
approach is

H11 - e
H12 - eS12
H1n - eS1n

H21 eS21
H22 - e
H2n eS2n
0
. . .




Hn1 eSn1
Hn2 eSn2
Hnn e
this simplifies in the ZOA to

H11 - e
H12
H1n

H21
H22 - e
H2n
0
. . .




Hn1
Hn2
Hnn e
with a- and b-parameters of the HMO schemethis
transforms into

a - e
b
0

b
a - e
0
0
. . .




0
0
a e
dividing by the universal b parameter
andsubstituting x (a e) / b, results in

b
-x
b
1
0
b
e.g., for acrolein (above) in the standard
(simple) approximation

1
2
1
-x
0
3
4
a
0
aO
. . .
a
a



-x1
1
0
0
aO a b

-x
0
1
0
1
0
-x
0
giving the x-polynomial
1
-x
1
0
x4 x3 3x2 2x 1 0
the solutions x1, x2, , xn ofthe polynomial in
x provides the eigenvalues (p-CMO energies) via
ei a xi b
0
0
-x
1
with the solutions
x1 1.88 e1 a 1.88 b
x2 1.00 e1 a b
back-substitution of xi into the above linear
equations provides the relative expansion
coefficients for CMO yi
x3 -0.35 e1 a - 0.35 b
x4 -1.53 e1 a - 1.53 b
4
a - b
a - b
0.707
-0.707
a 0.618b
de 1b
de 0.618b
0.851
-0.526
symmetrical orbital splitting in ZOA
a
DE 0
a
H 1b
symmetrical orbital splitting in ZOA
DE 1b
H 1b
de 1b
pCC
a b
a b
de 0.618b
0.707
0.707
pCO
a 1.618b
a 2b
0.526
0.851
electron distribution in 2-center LCAO MO in the
ZOA
yp c1 f1 c2 f2
2
2
2
2
2
yp c1 f1 2c1c2 f1f2 c2 f2
2
2
2
2
2
?
?
?
?
yp dv c1 f1 dv 2c1c2 f1f2 dv c2 f2 dv
1
0 (ZOA)
1
2
2
2
yp c1 c2 1
hence
normalization condition in the ZOA
note
there is no overlap population in the ZOA!
in its place, one has to resort to bond orders
to discuss bonding or antibonding character
bond order p12 2c1c2
for example (for CC and CO)


p(pCC) -1
p(pCO) -0.895
for multi-orbital system
p(pCC) 1
p(pCO) 0.895
occ
Nel ? ni yi dv
2
?
i
occ
? ? ni qK
? qK
i
i
qK partial p-AO population in yi at center K
i
K
K
qK total p-electron population at center K
occ
i
pKM ? ni pKM
i
pKM partial p-bond order in yi between centers
K and M
pKM total p-bond order between centers K and M
i
5
2-center CX p-system with varying aX a hX b
-0.707
0.707
0.788
-0.615
0.851
-0.526
0.894
-0.447
0.924
-0.383
a - b
0.944
-0.331
de 1.00b
de 0.78b
de 0.62b
de 0.50b
de 0.41b
de 0.35b
a
DE 0b
DE 0.5b
DE 1.0b
DE 1.5b
a b
DE 2.0b
DE 2.5b
0.707
0.707
a 2b
0.788
0.615
0.851
0.526
0.894
0.447
a 3b
..
0.924
0.383
..
0.944
0.331
Note
The electrophilic character of the CX p-system
increases with increasing electronegativity of
X, i.e. decreasing energy of the fX AO.
The increased electrophilicity manifests itself
through
- the increased lowering of the p-orbital of the
CX system - the increased amplitude at the
electrophilic C center in the p-orbital
Thus, towards a given nucleophile with a
relatively high-lying occupied orbital, e.g.,
the nN-dominated CMO of an amine or highest
occupied MO (HOMO) of an enamine (see below),
the possible coupling effect through
intermolecular interaction of this HOMO with the
p-orbital of the CX system increases with
decreasing energy gap DEHOMO-p and increasing
p-orbital amplitude at the C center of the CX
system.
Protonation (or complexation by a Lewis acid) of
the O-atom in the s-plane of the CO system
results in a marked lowering the fO level and
concomitant increase of the p-electrophilicity of
the CO system.
The p-MO systems of the CX units are useful
orbital building blocks for the derivation of
the p-orbital structures of more complex
p-systems using the extended perturbation MO
(EPMO) method.
6
Two approaches to the allyl system
A formal union of CC C

y3 pCC - 0.52 fC 0.18 pCC
fC-induced mixing of p into p
pCC

DE 1bH 0.707b
de 0.37b
c 0.52

y2 fC - 0.52 pCC 0.52 pCC
fC
note exact cancellation of orbital amplitude
DE 1bH 0.707b
de 0.37b
pCC
c 0.52
note build-up of amplitude of equal absolute
size at allylic center
fC-induced mixing of p into p

y1 pCC 0.52 fC 0.18 pCC

B formal union of C1 C3 Ccentral

y3 ( jCC - fC2 )
a - 1.41 b
symmetry-adapted group orbitals
fC2
de 1.41b
note that fC2 interacts exclusively with jCC

c 1.00

y1 ( jCC fC2 )
a 1.41 b
7
chemical associations with allyl orbital
interaction schemes
pCC
pCC
pCC



pCC
pCC
pCC
repulsion in 2-center-4-el sytem notcounted in
ZOA
symmetricsplitting in 2-center3-el sytem in ZOA
stabilization of anion by allyl resonance
stabilization of cation by allyl resonance
stabilization of radical by allyl resonance
in ZOA
DEp 2 0.4 b
DEp 2 0.4 b
DEp 2 0.4 b
CC-assisted solvolysis (45C, H2O/EtOH)
CC-assistedhomolytic bond cleavage
B
CC-promotedC-H acidity
94.5 kcal/mol
82.3 kcal/mol
C-H acidity (DHº, gas)CH3CH2-H
420.1 CH2CH-H 407.5 CH2CH-CH2-H 390.8
(via SN2 not SN1 ?)
disrotatory process thermally allowed
stereochemistry experimentally confirmed at low
temperature.
sCC
sCC


sCX


conrotatory process thermally forbidden experim
entally not observed
SbF5, SO2ClF
-100ºC, by NMR
pC2
pC2
Experimentally, no cyclopropyl cation
intermediate can be observed thus, C-X
solvolysis and ring opening may occur in a
synchronous fashion for transparent orbital
analysis, the two processes are treated
sequentially.
ground state correlates with doubly excited state
nX
nX
solvolysis of C-X

sCC
sCC


no inter- action by symmetry
sCX
disrotatory ring opening
conrotatory ring opening
8
enamine and enolether p-systems
de2
a - 1.19 b

fN-induced p-mixing into p reduces amplitude at
Ca and augments amplitude at Cb
DE 2.5 b
de2 0.19b
c 0.26
H 0.707 b
y2 pCC - 0.71 fN - 0.25 pCC

a 0.5 b
de1
pCC
DE 0.5 b
de1 0.50b
fN
a 1.5 b
H 0.707 b
c 0.71
de1
de2

a 2.19 b
y1 fN 0.71 pCC 0.26 pCC
Note CMOs approximated by EPMO method
are unnormalized to show mixing effects
de2
a - 1.16 b

DE 3.0 b
de2 0.16b
c 0.22
H 0.707 b
fN-induced p-mixing into p reduces amplitude at
Ca and augments amplitude at Cb
y2 pCC - 0.52 fO - 0.18 pCC
a 0.63 b

pCC
de1
DE 1.0 b
de1 0.37b
H 0.707 b
c 0.52
fO
a 2.0 b
de1
de2
a 2.53 b

y1 fO 0.52 pCC 0.22 pCC
9
the enol ether p-system
orbital interactions and mixing effects
0.707
cpp 0.224
2.0
pCC mixes from belowinto pCC, thus enhancingthe
antibonding characterwith fO
a 1.16 b

y3 p 0.22 fO 0.08 p
a b
a - b
Hfp 0.707 b
de2 0.16 b
c 0.22
DEfp 3.0 b
0.707
a
cpp 0.518
2.0
DEpp 2 b

pCC mixes from above into pCC, thus
enhancingthe bonding characterwith fO
a 0.63 b
y2 p 0.52 fO 0.18 p
pcc
a b
Hfp 0.707 b
de1 0.37 b
a b
c 0.52
DEfp 1.0 b
a 2.0 b
fO
a 2b
a 2.53 b
y1 fO 0.52 p 0.22 p
polarization of y2 by admixture of p in a
bonding mode to fO as p admixes from above
polarization of y2
0.51
0.45
0.73
normalized amplitudes in y2 prior to
polarization
0.63
0.46
0.63
normalized amplitudes in y2 after to polarization
HOMO-controlled electrophilic attack (by soft
electrophile) occurs at Cb of enol ether.
Note that the large amplitude at Cb in the HOMO
of the enol ether p-system arises from
polarization of the CC double bond by the O-p
lonepair, not from p-el.transfer!
(see next 2 slides)
10
..
the enol ether p-system
how much p-charge transfer from X into CC
p-system?
generalized orbital interactions and mixing
effects assuming fX to lie below pCC-level
induced mixing effects
y3 p d fX b p
a - b
a b
direct mixing effects
a
induced mixing effects
y2 p c fX a p
pcc
a b
direct mixing effects
a b
fX
a 2b
y1 fX c p d p
direct mixing effects
Net p-charge transfer arises only from the
interaction of the doubly occupied fX with the
unoccupied pCC orbital hence, net p-charge
transfer can be estimated to be 2d2 . For a
more quantitative estimate, the atomic p-charges
from the normalized p-orbitals y1 and y2 have to
be considered
11
induced mixing effects
y3 p d fX b p
direct mixing effects
a b
induced mixing effects
a
2
y2 p c fX a p
N2 1 c2 a2
pcc
a b
direct mixing effects
fX
2
y1 fX c p d p
N1 1 c2 d2
direct mixing effects
total p-charge in fX unit
(1) (c2)


2
2
(1 2c2 a2)
(1 c2 a2 c2 )
2
2
2
2
N1
N2
N1
N2
2
2
N1
N2
(1 2c2 a2) -
p
dqX - 2
2
net charge transfer from fX


2
2
N1
N2
(1 2c2 a2) -
(1 2c2 a2 d2)
- 2d2
2

(1 2c2 a2 d2)
(1 2c2)
total p-charge in CC-p-unit
(c2 d2) (1 a2)


2
2
(1 2c2 a2 2d2)
(c2 d2 1 a2 c2 d2 )
2
2
2
2
N1
N2
N1
N2
2
2
(1 2c2 a2 2d2) -
N1
N2
p
2
dqCC - 2

net charge transfer into CCp
2
2
N1
N2
(1 2c2 a2 2d2) -
(1 2c2 a2 d2)
2d2
2

(1 2c2)
(1 2c2 a2 d2)
for the specific example of the enol ether, net
p-charge transfer is estimated to be
.
.
p
dq (X?CC) 2 0.2182 / (1 2 0.5182)
0.062 hence, not more than ca. 3
12
comparison allyl anion carbanion a to CO
p-system
y3 pCC - 0.52 fC 0.18 pCC

0.71
cpp 0.52
2.0
fC-induced mixing of p into p
pCC

DE 1bH 0.707b
de 0.37b
c 0.52
..
0
fC
y2 fC - 0.52 pCC 0.52 pCC

DE 1bH 0.707b
de 0.37b
fC-induced mixing of p into p
pCC
c 0.52
0.71
cpp 0.52
2.0
y1 pCO 0.52 fC 0.18 pCO

from exact HMO-solution of allyl system
net p energy stabilization 2 0.4 b 0.8
bnet p charge shift from fC to CC - 0.5
Note CMOs approximated by EPMO method
are unnormalized to show mixing effects
net p energy stabilization 2 0.6 b 1.2
b net p charge shift from fC to CO - 0.57
y3 pCO - 0.70 fC 0.17 pCO

0.53
0.85
a - 1.22 b
cpp 0.70
2.24
fC-induced mixing of pCO into pCO
-0.53
DE 0.62bH 0.85b
de 0.60b

a 0.62 b
c 0.70
..
fC
a 0.44 b
y2 fC - 0.30 pCO 0.70 pCO

DE 1.62bH 0.53b
de 0.16b
c 0.30
fC-induced mixing of pCO into pCO
pCO

a 1.62 b
0.85
cpp 0.30
a 1.78 b
2.24
0.53
0.85
y1 pCO 0.30 fC 0.11 pCO



Note the pCO orbital lies at a lower energy and
has a larger amplitude at C than the pCC
likewise, the energy pCO is lower and its
amplitude at C is smaller compared to the pCC
these combined factors result in a net
downshift of the fC a to CO to produce the CMO
y2 with net bonding amplitudes (positive
partial p bond order) between the two C atoms.
13
comparison amide and ester p-systems
net p energy stabilization 2 0.3 b 0.6
b net p charge shift from fN to CO - 0.13
the C-N torsion barrier disrupting NCO p
conjugationis typically 18-20 kcal/mol
..
0.85
-0.53
a 0.92 b
y3 pCO - 0.35 fN 0.08 pCO

de2
a - 0.62 b
0.53
pCo

cpp 0.35
2.24
DE 2.12 b
de 0.30 b
fN-induced mixing of pCO into pCO
H 0.85 b
c 0.35

DE 0.12 b
de 0.47 b
H 0.53 b
c 0.89
de2
y2 fN - 0.89 pCO 0.35 pCO

fN-induced mixing of pCO into pCO
a 1.33 b
de1

a 1.5 b
pCO
0.85
fN
a 1.62 b
cpp 0.89
de1
2.24
a 2.09 b
0.53
y1 pCO 0.89 fN 0.34 pCO

0.85
Note CMOs approximated by EPMO method
are unnormalized to show mixing effects
..
fN-induced mixing of pCO into pCO
net p energy stabilization 2 0.25 b 0.5
b net p charge shift from fO to CO - 0.11

0.53
cpp 0.30
2.24
y3 pCO - 0.30 fO 0.07 pCO

0.85
-0.53
de2
a 0.87 b
fN-induced mixing of pCO into pCO
a - 0.62 b
pCo


de 0.25 b
DE 2.62 b
0.85
c 0.30
H 0.85 b
cpp 0.70
2.24
y2 pCO - 0.70 fO - 0.27 pCO

DE 0.38 b
de 0.37 b
H 0.53 b
c 0.70
a 1.25 b
de1
pCO
a 1.62 b
a 2.0 b
fO
0.53
de1
0.85
de2
a 2.62 b
y1 fO 0.70 pCO 0.30 pCO

14
1,3-butadiene from 2 conjugated ethylene
p-systems
y4
induced mixing
de2
a - 1.62 b
de1
y3
p1,CC
p2,CC


de1
a - 0.62 b
de2

pCC - pCC
DE 2.0 b
de2 0.12 b
induced mixing
H 0.5 b
c 0.24
DE 0.0 b
de1 0.50 b
induced mixing
pCC - pCC
H 0.5 b
c 1.00
de2
a 0.62 b
p2,CC
de1
p1,CC
de1
de2
y2
a 1.62 b
net p-energy stabilization 2 2 de2 0.47 b
induced mixing
Note that the closed-shell (overlap) repulsion
effect due to the pCC pCC interaction is
neglected in the ZOA hence the net p energy
stabilization is overestimated the trans ? cis
torsional barrier is ca. 5 kcal/mol.
y1
PE spectrum of 1,3-butadiene IP1 9.03 eV, IP2
11. 46 eV hence b 2.4 eV
Note that b parameter cannot be transferred from
spectroscopy to thermodynamic properties
Note the build-up of a large LUMO amplitude at
the Cb position to the OC group in acrolein
(Michael addition)
de3
a - 1.49 b
de4
0.851
0.65
-0.58
p2,CC

DE 0.38 b
de4 0.44 b


pOC - pCC
H 0.60 b
c 0.73
p1,OC

de4
a - 0.37 b
DE 2.62 b
de3 0.05 b

pOC - pCC
de2
H 0.37 b
c 0.14
y3 pOC 0.73 pCC - 0.33 pCC - 0.03 pOC


DE 1.62 b
de2 0.19 b

pOC - pCC
H 0.60 b
c 0.33


y2 pCC - 0.47 pOC 0.33 pOC - 0.00 pCC
DE 0.62 b
de1 0.18 b
de1
pOC - pCC
p2,CC
de2
H 0.37 b
c 0.47
a 0.99 b
0.526
The EPMO-estimated p-energy levels may be
compared to the exact HMO- energies given on
slide 2 of this Chapter
de1
p1,OC
de3
a 1.85 b
net p-energy stabilization 2 (de2 de3)
0.48 b
thus, essentially the same as for
1,3-butadieneindeed, the trans ? cis torsional
barrier for acrolein is essentially the same as
for 1,3-butadiene.
15
1,3-butadiene from symmetry-adapted group
orbitals
0.372
0.602
y4 jin - 0.62 jout
-
-
A
a - 1.62 b
-0.372
y3 jout - 0.62 jin


A
0.602
j- (f2 - f3)
j- (f1 f4)
a - 0.62 b
in
S
out
A
DE 1.0 b
de2 0.62 b
H 1.0 b
c 0.62
S
A
j (f2 f3)
j (f1 f4)
a 0.62 b
in
out
0.602
S
-
-
y2 jout 0.62 jin
-0.372
a 1.62 b
S
y1 jin 0.62 jout


0.372
0.602
chemical association thermal ring opening of
cyclobutene occurs in conrotatory mode
sCC

A
S
y4
S
pCC

A
y3
175 ºC
pCC
j-
S
out
j
A
out
175 ºC
S
y2
C2
pCC
A
y1
A
pCC

C2
sCC
sCC
conrotatory ring opening
S