Title: OCIV
1OCIV
Orbital Concepts and Their Applications in
Organic Chemistry
Klaus Müller
Script ETH Zürich, Spring Semester 2009
Chapter 5
psystems 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 sorbitals are orthogonal by symmetry
 there are no (s,p)orbital interactions
 there are no orbital splitting effects between
s and porbitals  hencethe porbital system can be treated
independently from the sorbital systemhowever  the orbital energies of the psystem are affected
by the selectron distribution  and viceversa
Hik
interaction energy between adjacent pp
orbitalsbCC b uniform interaction parameter
for Catoms in psystem
Hij
pp interaction energy involving heteroatomsin
simplest approach bCX b
Him
interaction energy between nonadjacent 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 selectron density modulated by
pelectron 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 ppAO of
Catoms in psystems
in refined HMO modelsHii ai hi bai
dependent on local topology hi numerical
parameter (small) b all energy corrections in
b units
3p
S1,2 0.25
poverlap 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 bparameters 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 xpolynomial
1
x
1
0
x4 x3 3x2 2x 1 0
the solutions x1, x2, , xn ofthe polynomial in
x provides the eigenvalues (pCMO 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
backsubstitution 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
4a  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 2center 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 multiorbital system
p(pCC) 1
p(pCO) 0.895
occ
Nel ? ni yi dv
2
?
i
occ
? ? ni qK
? qK
i
i
qK partial pAO population in yi at center K
i
K
K
qK total pelectron population at center K
occ
i
pKM ? ni pKM
i
pKM partial pbond order in yi between centers
K and M
pKM total pbond order between centers K and M
i
52center CX psystem 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 psystem
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 porbital of the
CX system  the increased amplitude at the
electrophilic C center in the porbital
Thus, towards a given nucleophile with a
relatively highlying occupied orbital, e.g.,
the nNdominated 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
porbital of the CX system increases with
decreasing energy gap DEHOMOp and increasing
porbital amplitude at the C center of the CX
system.
Protonation (or complexation by a Lewis acid) of
the Oatom in the splane of the CO system
results in a marked lowering the fO level and
concomitant increase of the pelectrophilicity of
the CO system.
The pMO systems of the CX units are useful
orbital building blocks for the derivation of
the porbital structures of more complex
psystems using the extended perturbation MO
(EPMO) method.
6Two approaches to the allyl system
A formal union of CC C
y3 pCC  0.52 fC 0.18 pCC
fCinduced 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 buildup of amplitude of equal absolute
size at allylic center
fCinduced 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
symmetryadapted group orbitals
fC2
de 1.41b
note that fC2 interacts exclusively with jCC
c 1.00
y1 ( jCC fC2 )
a 1.41 b
7chemical associations with allyl orbital
interaction schemes
pCC
pCC
pCC
pCC
pCC
pCC
repulsion in 2center4el sytem notcounted in
ZOA
symmetricsplitting in 2center3el 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
CCassisted solvolysis (45C, H2O/EtOH)
CCassistedhomolytic bond cleavage
B
CCpromotedCH acidity
94.5 kcal/mol
82.3 kcal/mol
CH acidity (DHº, gas)CH3CH2H
420.1 CH2CHH 407.5 CH2CHCH2H 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, CX
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 CX
sCC
sCC
no inter action by symmetry
sCX
disrotatory ring opening
conrotatory ring opening
8enamine and enolether psystems
de2
a  1.19 b
fNinduced pmixing 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
fNinduced pmixing 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
9the enol ether psystem
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
HOMOcontrolled 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 psystem arises from
polarization of the CC double bond by the Op
lonepair, not from pel.transfer!
(see next 2 slides)
10..
the enol ether psystem
how much pcharge transfer from X into CC
psystem?
generalized orbital interactions and mixing
effects assuming fX to lie below pCClevel
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 pcharge transfer arises only from the
interaction of the doubly occupied fX with the
unoccupied pCC orbital hence, net pcharge
transfer can be estimated to be 2d2 . For a
more quantitative estimate, the atomic pcharges
from the normalized porbitals y1 and y2 have to
be considered
11induced 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 pcharge 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 pcharge in CCpunit
(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
pcharge transfer is estimated to be
.
.
p
dq (X?CC) 2 0.2182 / (1 2 0.5182)
0.062 hence, not more than ca. 3
12comparison allyl anion carbanion a to CO
psystem
y3 pCC  0.52 fC 0.18 pCC
0.71
cpp 0.52
2.0
fCinduced 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
fCinduced 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 HMOsolution 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
fCinduced 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
fCinduced 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.
13comparison amide and ester psystems
net p energy stabilization 2 0.3 b 0.6
b net p charge shift from fN to CO  0.13
the CN torsion barrier disrupting NCO p
conjugationis typically 1820 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
fNinduced 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
fNinduced 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
..
fNinduced 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
fNinduced 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
141,3butadiene from 2 conjugated ethylene
psystems
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 penergy stabilization 2 2 de2 0.47 b
induced mixing
Note that the closedshell (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 1,3butadiene 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 buildup 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 EPMOestimated penergy 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 penergy stabilization 2 (de2 de3)
0.48 b
thus, essentially the same as for
1,3butadieneindeed, the trans ? cis torsional
barrier for acrolein is essentially the same as
for 1,3butadiene.
151,3butadiene from symmetryadapted 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