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OC-IV. 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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Oc iv

OC-IV

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]


Oc iv

Chapter 2

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/


Oc iv

1/2 s + √3/2 pz

√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 hybrid-AO’s are used

sp3

sp3

sp3

sp3

(1)

(2)

(3)

(4)

- sp3-hAO’s have 25% s-character and 75% p-character; hence the squared mixing coefficients for the s-AO and p-AO components are, 1/4 and 3/4, respectively, and the linear mixing coefficients are 1/2 and .

- proper vector components for the px, py, pz-AO’s ensure that the sp3-hAO’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)


Oc iv

/

√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 hybrid-AO’s are defined

sp2

sp2

sp2

p

(1)

(2)

(3)

(4)

  • since two orthogonal p-AO’s span a plane, it is convenient to choose the coordinate

  • system in such a way that two p-AO’s lie in the plane of the trigonal bond vectors;

  • this leaves a third p-AO unused, which is orthogonal to the plane,.

  • from the s-AO and two p-AO’s, three equivalent sp2-HAO’s can be formed, which

  • are mutually orthogonal and have 1/3 s-character and 2/3 p-character; hence, the squared mixing coefficients for the s-AO and p-AO components are 1/3 and 2/3, respectively, and the linear coefficients and , accordingly.

- proper vector components for the px, py-AO’s ensure that the sp2-hAO’s

are correctly oriented and remain mutually orthogonal and normalized;

this is illustrated below for the case where the three sp2-HOA’s are defined

in the (xy)-plane; the pz-AO 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


Oc iv

sp(1)

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 Hybrid-AO’s are defined

sp

sp

p

p

(1)

(2)

(3)

(4)

  • it is convenient to orient the coordinate system so that one coordinate axis coincides with the linear coordination of the center. One p-AO along the linear

  • bond axis can then combine with the s-AO to generate two orthonormal sp-hAO’s;

  • the other two p-AO’s are orthogonal to this coordination axis and remain unused.

  • both sp-hAO’s have ½ s-character and ½ p-character; the squared mixing

  • coefficients on the two orthonormal sp-hAO’s are thus both ½, and the linear coefficients are ±1/√2.

z

z

y

y

x

x

sp

sp

(1)

(2)


Oc iv

-

-

+

+

-

+

qualitative LMO‘s from hAO‘s, 1sH AO‘s, and residual p-AO‘s

A

B

A

H

approximate

sAB-LMO

approximate

s*AB-LMO

approximate

sAH-LMO

approximate

s*AH-LMO

The linear combination of two spx hAO‘s oriented along the connection axis of two

adjacent atoms results in a bonding s-LMO 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 1s-AO 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 p-AO‘s orthogonal to a given bond axis between

adjacent atoms, can create, respectively, a bonding p-LMO and an antibonding p*-LMO,

provided the p-AO axes on the adjacent atoms are properly aligned in a common p-plane.

p-AO‘s twisted

p plane

reduction of p-p overlapand hence p-p interaction;

p- and p*-LMO‘s with

reduced bonding and

antibonding character, resp.

B

A

p-AO‘s 90° twisted

p-p overlap and interaction

vanish by symmetry;

no bonding p-LMO and

no antibonding p*-LMO

can be formed.

approximate

pAB-LMO

approximate

p*AB-LMO


Oc iv

spx-hAO‘s or p-AO‘s for which no suitable partner orbital at an adjacent atom

is available, remain as nonbonding n-LMO‘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 n-LMO‘s at an electron-deficient

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 s-type and p-type LMO‘s pertaining to a local unsaturated structural unit, independently of the symmetry

of the whole molecule.


Oc iv

Qualitative considerations of geminal and vicinal orbital interactions

interactions between geminal LMO‘s in saturated systems

geminal

(n-s*)-interactions

small

geminal

(s-s)-interactions

large

geminal

(n-s)-interactions

large

geminal

(s-s*)-interactions

small

interactions between vicinal LMO‘s in saturated systems

vicinal synplanar

n-s interactions significant;

increasing with increasing

pp components in n- and s-LMO

LMO axes twisted by 90°

vicinal n-s interactions

small, decreasing withincreasing pp componentsin n- and s-LMO

vicinal antiplanar

n-s interactions small;

more significant with

increasing pp components

in n- and s-LMO

antiplanar vicinal

n-s*-interaction

more significant

since phase change

in s*-LMO opposite to

large lobe of n-LMO;

interaction increasing

with increasing pp-character of s*-LMO

vicinal synplanar

n-s*-interactions

comparatively small

due to phase change in s*


Oc iv

Qualitative considerations of geminal and vicinal orbital interactions

geminal interactions

between pp n-LMO and s-LMO

vanish for symmetry reasons

geminal interactions

between p-LMO and s-LMO

vanish for symmetry reasons

geminal interactions

between p*-LMO and s-LMO

vanish for symmetry reasons

dominant interaction

dominant interaction

n-LMO

n-LMO

n-LMO

p-LMO

p-LMO

p-LMO

vicinal interaction

between pp n-LMO and p-LMO

significant if pp-orbitals

properly aligned

vicinal interaction

between spx n-LMO and p-LMO

reduced, but significant

if pp-components properly aligned;

increasing with increasing

pp-component in n-LMO

orbital axes of

pp n-LMO and p-LMO

twisted by 90°;

(n-p)-orbital interaction vanishes

for symmetry reasons

similar arguments for vicinal interaction between n-LMO and p*-LMO

dominant interaction

dominant interaction

vanishing interaction

for symmetry reasons

n-LMO

n-LMO

n-LMO

p*-LMO

p*-LMO

p*-LMO


Oc iv

Interaction effects in the 2-LMO system

An interaction between two LMO’s results in characteristic energy shifts (‘splitting’)

and mixing effects as illustrated below for the degenerate and non-degenerate case:

antibonding

linear combination

‘orbital splitting due to orbital interaction’

DE = 0

bonding

linear combination

n-LMO

n-LMO

weakly antibonding

linear combination

‘orbital splitting and mixing effects due to

interaction between n-LMO and p*-LMO

p*-LMO

DE >0

weakly bonding

linear combination

n-LMO

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


Oc iv

Conjugative stabilization in the 2-orbital-system with 2-electrons

unoccupied

energetically

higher-lying

orbital

f2

doubly occupied

energetically

lower-lying

orbital

electron pair is stabilized by deb

due to orbital interaction between

LMO’s f1 and f2

f1

deb

examples for conjugatively stabilized 2-electron 2-orbital systems:

carbenium ion

in a-position to

ether oxygen

carboxamide

1,3-butadiene

N

O

O

p-LMO

doubly

occupied

p*-LMO

unoccupied

n-LMO (p-AO)

unoccupied

in valence

sextett

n-LMO (p-AO)

doubly

occupied

n-LMO

(pN-AO)

doubly

occupied

p*CO-LMO

unoccupied

p*-LMO

unoccupied

p-LMO

doubly occupied


Oc iv

Conjugative destabilization in the 2-orbital-system with 4-electrons

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 4-electron 2-orbital system. → “Pauli exclusion principle repulsion”

→ “overlap repulsion”

examples for conjugatively destabilized 4-electron 2-orbital systems:

cyclopropenyl

anion

ethane

ecliptic conformation

hydrazine

N

N

nN-LMO

doubly

occupied

nN-LMO

doubly

occupied

pCC-LMO

doubly

occupied

sCH-LMO

doubly

occupied

sCH-LMO

doubly

occupied

n-LMO (pC-AO)

doubly

occupied


Oc iv

Qualitative aspects of conjugative stabilization

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 two-orbital interaction systems between the two subunits.

conjugative stabilization in the

2-orbital 2-electron system;

DEn,p* ‘small enough’ to produce

significant p-conjugative stabilization,

resulting in net conjugative stabilization

of the full system.

N

p*

O

conjugative destabilization in the

2-orbital 4-electron system

N

nN

O

p

N

O

conjugative effects in empty 2-orbital

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

2-orbital 2-electron systems,

small net conjugative stabilization

of the full system.

p

p

conjugative destabilization in the

2-orbital 4-electron system

s*

s*

conjugative effects in empty 2-orbital

system are not relevant for the discussion

of conjugative effects in the electronic

ground state of the full system.

conjugative stabilization in both

2-orbital 2-electron systems,

very small conjugative stabilization

due to weak interaction and large DE gap

conjugative destabilization in the

2-orbital 4-electron system dominates,

resulting in small net destabilization

of the full system.

s

s


Oc iv

conditions for significant net conjugative stabilization effects are

  • strong orbital interaction between

  • occupied and unoccupied orbitals

- 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

..


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