OCIV. Orbital Concepts and Their Applications in Organic Chemistry. Klaus Müller. Script ETH Zürich, Spring Semester 2009. Lecture assistants: Deborah Sophie Mathis HCI G214 – tel. 24489 [email protected] Alexey Fedorov HCI G204 – tel. 34709 [email protected] Chapter 2.
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Orbital Concepts
and
Their Applications in Organic Chemistry
Klaus Müller
Script
ETH Zürich, Spring Semester 2009
Lecture assistants:
Deborah Sophie MathisHCI G214 – tel. [email protected]
Alexey FedorovHCI G204 – tel. 34709 [email protected]
hybrid atomic orbitals (hAO’s)
and their use in qualitative LMO pictures
see also document:“Basic Features of MO Theory”
on http://www.chen.ethz.ch/course/
√3/2
= 1/2 s  1/√2 px  1/√6 py  √3/6 pz
= 1/2 s + √2/√3 py  √3/6 pz)
= 1/2 s + 1/√2 px  1/√6 py  √3/6 pz
hAO’s for tetrahedral centers
for an atom with a tetrahedral configuration,
4 equivalent valence sp3 hybridAO’s are used
sp3
sp3
sp3
sp3
(1)
(2)
(3)
(4)
 sp3hAO’s have 25% scharacter and 75% pcharacter; hence the squared mixing coefficients for the sAO and pAO components are, 1/4 and 3/4, respectively, and the linear mixing coefficients are 1/2 and .
 proper vector components for the px, py, pzAO’s ensure that the sp3hAO’s
are correctly oriented and remain orthogonal and normalized:
example:
z
sp3 (1) =
1/2 s + √3/2 (√8/3 ( √3/2 px  1/2 py)  1/3 pz)
g = tetrahedral; cos g = 1/3
sin g = √8/3
sp3 (4)
y
1/2 s + √3/2 (√8/3 py  1/3 pz)
x
1/2 s + √3/2 (√8/3 (+ √3/2 px  1/2 py)  1/3 pz)
sp3 (2)
sp3 (3)
√2 √3
z
z
z
1/√3
y
y
y
x
x
x
1/√3 s + √2/√3 (1/2 py + √3/2 px)
sp2(1)
sp2(3)
= 1/√3 s + √2/√3 py
= 1/√3 s  1/√6 py  1/√2 px
hAO’s for trigonal planar centers
for an atom with a planar trigonal configuration,
3 equivalent valence sp2 hybridAO’s are defined
sp2
sp2
sp2
p
(1)
(2)
(3)
(4)
 proper vector components for the px, pyAO’s ensure that the sp2hAO’s
are correctly oriented and remain mutually orthogonal and normalized;
this is illustrated below for the case where the three sp2HOA’s are defined
in the (xy)plane; the pzAO remains unused:
sp2
sp2
sp2
(1)
(2)
(3)
1/√3 s + √2/√3 (1/2 py  √3/2 px)
sp2(2)
= 1/√3 s  1/√6 py + 1/√2 px
sp(2)
= 1/√2 s + 1/√2 py
= 1/√2 s  1/√2 py
hAO’s for centers with linear double coordination
for an atom with a linear arrangement of two bonds,
2 equivalent valence sp HybridAO’s are defined
sp
sp
p
p
(1)
(2)
(3)
(4)
z
z
y
y
x
x
sp
sp
(1)
(2)

+
+

+
qualitative LMO‘s from hAO‘s, 1sH AO‘s, and residual pAO‘s
A
B
A
H
approximate
sABLMO
approximate
s*ABLMO
approximate
sAHLMO
approximate
s*AHLMO
The linear combination of two spx hAO‘s oriented along the connection axis of two
adjacent atoms results in a bonding sLMO and an antibonding s*LMO. In the case
of bonds to hydrogen atoms, the s and s*LMO are formed by linear combinations with the 1sAO of the hydrogen atom.
Although such linear combinations are only crude approximations to the LMO‘s obtained
from rigorous LCAO MO SCF calculations, followed by a chemically unbiased orbital
localization procedure, the results are in many cases remarkably close.
Positive and negative linear combinations of pAO‘s orthogonal to a given bond axis between
adjacent atoms, can create, respectively, a bonding pLMO and an antibonding p*LMO,
provided the pAO axes on the adjacent atoms are properly aligned in a common pplane.
pAO‘s twisted
p plane
reduction of pp overlapand hence pp interaction;
p and p*LMO‘s with
reduced bonding and
antibonding character, resp.
B
A
pAO‘s 90° twisted
pp overlap and interaction
vanish by symmetry;
no bonding pLMO and
no antibonding p*LMO
can be formed.
approximate
pABLMO
approximate
p*ABLMO
is available, remain as nonbonding nLMO‘s.
If electronically doubly occupied, these orbitals generally represent reasonable
approximations to nonbonding lone pair orbitals as also obtained from rigorous
LCAO MO SCF calculations followed by a chemically unbiased localization procedure.
If electronically unoccupied, they represent vacant nLMO‘s at an electrondeficient
atom center.
e.g.:
B
N
Interactions between localized MO‘s
Under which conditions do LMO‘s interact significantly?
Rule 1: The interaction between two LMO‘s situated at neighboring atoms
is related to the overlap integral between the LMO‘s.
hence:  the interaction between two LMO‘s is attenuated rapidly with increasing spatial separation of the neighboring atom centers.
Rule 2: The interactions between two LMO‘s situated at the same atom center
is generally quite significant.
hence:  for atoms in a saturated structural environment, local interactions between geminal LMO‘s are the largest interactions, followed by interactions between
vicinal LMO‘s.
Rule 3: There are no interactions between LMO‘s that are orthogonal by symmetry,
i.e., either symmetrical or antisymmetrical with respect to global or even
local symmetry elements.
hence:  there are no (or essentially no) interactions between stype and ptype LMO‘s pertaining to a local unsaturated structural unit, independently of the symmetry
of the whole molecule.
interactions between geminal LMO‘s in saturated systems
geminal
(ns*)interactions
small
geminal
(ss)interactions
large
geminal
(ns)interactions
large
geminal
(ss*)interactions
small
interactions between vicinal LMO‘s in saturated systems
vicinal synplanar
ns interactions significant;
increasing with increasing
pp components in n and sLMO
LMO axes twisted by 90°
vicinal ns interactions
small, decreasing withincreasing pp componentsin n and sLMO
vicinal antiplanar
ns interactions small;
more significant with
increasing pp components
in n and sLMO
antiplanar vicinal
ns*interaction
more significant
since phase change
in s*LMO opposite to
large lobe of nLMO;
interaction increasing
with increasing ppcharacter of s*LMO
vicinal synplanar
ns*interactions
comparatively small
due to phase change in s*
geminal interactions
between pp nLMO and sLMO
vanish for symmetry reasons
geminal interactions
between pLMO and sLMO
vanish for symmetry reasons
geminal interactions
between p*LMO and sLMO
vanish for symmetry reasons
dominant interaction
dominant interaction
nLMO
nLMO
nLMO
pLMO
pLMO
pLMO
vicinal interaction
between pp nLMO and pLMO
significant if pporbitals
properly aligned
vicinal interaction
between spx nLMO and pLMO
reduced, but significant
if ppcomponents properly aligned;
increasing with increasing
ppcomponent in nLMO
orbital axes of
pp nLMO and pLMO
twisted by 90°;
(np)orbital interaction vanishes
for symmetry reasons
similar arguments for vicinal interaction between nLMO and p*LMO
dominant interaction
dominant interaction
vanishing interaction
for symmetry reasons
nLMO
nLMO
nLMO
p*LMO
p*LMO
p*LMO
An interaction between two LMO’s results in characteristic energy shifts (‘splitting’)
and mixing effects as illustrated below for the degenerate and nondegenerate case:
antibonding
linear combination
‘orbital splitting due to orbital interaction’
DE = 0
bonding
linear combination
nLMO
nLMO
weakly antibonding
linear combination
‘orbital splitting and mixing effects due to
interaction between nLMO and p*LMO
p*LMO
DE >0
weakly bonding
linear combination
nLMO
The orbital splitting and mixing effects
 increase with increasing magnitude of the orbital interaction
The orbital splitting and mixing effects
 are maximal if the interacting orbitals are degenerate;
 and decrease with increasing energy gap between
the interacting orbitals
unoccupied
energetically
higherlying
orbital
f2
doubly occupied
energetically
lowerlying
orbital
electron pair is stabilized by deb
due to orbital interaction between
LMO’s f1 and f2
f1
deb
examples for conjugatively stabilized 2electron 2orbital systems:
carbenium ion
in aposition to
ether oxygen
carboxamide
1,3butadiene
N
O
O
pLMO
doubly
occupied
p*LMO
unoccupied
nLMO (pAO)
unoccupied
in valence
sextett
nLMO (pAO)
doubly
occupied
nLMO
(pNAO)
doubly
occupied
p*COLMO
unoccupied
p*LMO
unoccupied
pLMO
doubly occupied
2 electrons are destabilized by deab
due to the interaction between the
LMO’s f1 and f2
deab
f2
both
LMO’s
doubly
occupied
f1
2 electrons are stabilized by deb
due to the interaction between the
LMO’s f1 and f2
deb
note that: deab ≥ deb
hence, the net effect of the orbital
interaction is a conjugative destabilization
of the 4electron 2orbital system. → “Pauli exclusion principle repulsion”
→ “overlap repulsion”
examples for conjugatively destabilized 4electron 2orbital systems:
cyclopropenyl
anion
ethane
ecliptic conformation
hydrazine
N
N
nNLMO
doubly
occupied
nNLMO
doubly
occupied
pCCLMO
doubly
occupied
sCHLMO
doubly
occupied
sCHLMO
doubly
occupied
nLMO (pCAO)
doubly
occupied
for conjugated systems.
Two structural subunits are said to be ‘conjugated’
if at least one LMO of one subunit interacts (significantly)
with at least one LMO of the other subunit.
The total ‘conjugative effect’ for two conjugated structural subunits
can be approximated by the sum of conjugative effects for all
individual twoorbital interaction systems between the two subunits.
conjugative stabilization in the
2orbital 2electron system;
DEn,p* ‘small enough’ to produce
significant pconjugative stabilization,
resulting in net conjugative stabilization
of the full system.
N
p*
O
conjugative destabilization in the
2orbital 4electron system
N
nN
O
p
N
O
conjugative effects in empty 2orbital
system are not relevant for the discussion
of conjugative effects in the electronic
ground state of the full system.
p*
p*
conjugative stabilization in both
2orbital 2electron systems,
small net conjugative stabilization
of the full system.
p
p
conjugative destabilization in the
2orbital 4electron system
s*
s*
conjugative effects in empty 2orbital
system are not relevant for the discussion
of conjugative effects in the electronic
ground state of the full system.
conjugative stabilization in both
2orbital 2electron systems,
very small conjugative stabilization
due to weak interaction and large DE gap
conjugative destabilization in the
2orbital 4electron system dominates,
resulting in small net destabilization
of the full system.
s
s
 small energy gap between these interacting orbitals
schematic illustrations
s*
s*
s*
p*
p*
p*
DE
DE
n
n
n
DE
DE
DE
DE
DE
DE
n
n
n
DE
..
p
p
p
..
s
s
s
..