chem 104a, uc, berkeley orbital interaction diagram 1...

1

Chem 104A, UC, BerkeleyOrbital Interaction Diagram

1. Plot atomic valence orbital energies (or fragment orbitals forMore complex molecules).

2. Determine which orbitals can interact (those with S0).

3. Determine magnitude of each interaction: scales directly with magnitude of overlapscales inversely with orbital energy difference

4. Plot MO energies and draw orbitalsInteraction bonding + antibondingNone no change

5. Use Aufbau principle to fill in electrons

Chem 104A, UC, Berkeley

2



x

-40 eV

-18.7 eV

-13.6 eV

3



-19.5 eV

-10.7 eV

-32.4 eV

-15.9 eV

4

Chem 104A, UC, Berkeley+ -- +

g1

u2Antibonding

+ +- -

- -+ +

- ++ -

u1

u1

g1

g2 Relative non-bondingOr Slightly bonding

Relative non-bondingOr Slightly antibonding

bonding


5


LUMO

HOMO

Frontier Orbitals

More carbon s character

More carbon p character

Chem 104A, UC, BerkeleyCO,

without C2s-O2pz interactionCO,

with C2s-O2pz interaction

C O

+

-Extra C2s character

Extra O2p character

6


- -+ +

g1

g2 Relative non-bondingSlightly bonding

CO

N2LUMO

HOMO

+

_

+

+

+_

_C O

2

C O


7



8


Chem 104A, UC, BerkeleyOrbital Interaction Diagram

1. Plot atomic valence orbital energies (or fragment orbitals forMore complex molecules).

2. Determine which orbitals can interact (those with S0).

3. Determine magnitude of each interaction: scales directly with magnitude of overlapscales inversely with orbital energy difference

4. Plot MO energies and draw orbitalsInteraction bonding + antibondingNone no change

5. Use Aufbau principle to fill in electrons

9


Ligand Group OrbitalsLGOs

bu1

bg1

u1

*2 g

*2 u


10


90° 180°HAH

1g

1u

1u

Walsh Diagram for AH2

+ +++ ++

+ +

+ -+ -+++

-

+ -+- Walsh’s correlation diagram:

Plot course of MO energies with change in geometry


Walsh’s Rules:

An AH2 molecule will be

Linear if it contains 3 or 4 valence elecronse.g. BeH2, BH2

+

Bent if it contains 1,2, or 5-8 valence electronse.g. BH2, CH2, NH2, H2O, H2S

11



H H

LGO

2pz

2px

2py

2s

O

1s

OH H

x

z

y

O

-15.9 eV

-32.4 eV

12



Ligand Group OrbitalsLGOs

bu1

bg1

u1

*2 g

*2 u

13


)22(2

1xa ps

)22(2

1xb ps

p

character

s

character

Bonding

orbital

50% 50%


H H

LGO

2pz

2px

2py

2s

O

1s

OH H

x

z

y

O

-15.9 eV

-32.4 eV

14


)2(2

1

)2(2

1

1

1

lpxlp

lpxlp

p

p

p

character

s

character

Bonding

orbital

80% 20%

lp

orbital

70% 30%


AH3 Molecule

BH3 vs NH3

15


(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

Chem 104A, UC, BerkeleyProjection Operator Method

1. Construct a reducible rep. using ligand orbitals as a basis.(any basis function that moves contribute nothing).

2. Apply reduction formula:

3. Apply projection operator:

to the basis orbitals to generate LGOs

)(1

# rirNh

RRh

lcP ii

i

)(

il Dimension of i

iR )( Character for operator R in i

Cotton, Chemical Applications of Group Theory, Wiley, 1990, chapt 6, 8

16


Construct a reducible rep. Using ligand orbitals as a basis.(any basis function that moves contribute nothing).

Sa

Sb

Sc3h 3 0 1 3 0 1

Apply reduction formula:

''13 EAh

(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

Chem 104A, UC, BerkeleyApply projection operator:

RRh

lcP ii

i

)(to the basis orbitals to generate LGOs

Sa

Sb

Sc

(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

)(3

1

)(412

.............

)](1)(11.................

)(1)(11[12

)(

'1

'1

cbaa

cba

cbacba

cbacbaa

A

SSS

SSSc

SSSSSS

SSSSSSc

SP

LGO1

H

H H

'1a

?ˆ aSR

17

Chem 104A, UC, BerkeleyApply projection operator:

RRh

lcP ii

i

)(to the basis orbitals to generate LGOs

(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

Sa

Sb

Sc

)2(6

1

)224(12

2.............

)](0)()1(2.................

)(0)()1(2[12

2)(

'

'

cbae

cba

cbacba

cbacbaa

E

SSS

SSSc

SSSSSS

SSSSSSc

SP

LGO2

H

H H

'xe

LGO3

H

H H

'ye

)224()(

)224()('

'

bacc

E

cabb

E

SSScSP

SSScSP

)(2

1' cbe SS

subtraction

addition


BH H

H

y

X

LGOs

Orbitals from Boron: 2s, 2px, 2py, 2pz

H

H H

H

H H

H

H H

2s 2px 2py

LGO1

H

H H

'1a

LGO2

H

H H

'xe

LGO3

H

H H

'ye

'.........'1 EA

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(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

S orbital


LGO1

LGO2

LGO3

2s

2px 2py 2pz

B 3 H

bs

bx b

y

nbz

*s

*x *

y

'11a

'11e

''21a

'1

'1

2

2

a

e

BH3

-14eV

-8.3 eV

~-13.6 eV

19


90° 120°HAH

Walsh Diagram for AH3


Walsh’s Rules:

An AH3 molecule will be

pyramidal if it contains 1,2 or 8 valence electronse.g. NH3

planar if it contains 3-6 or 7 valence electronse.g. BH3, NH3

+

20

Chem 104A, UC, BerkeleyWalsh Diagrams

from Gimarc, B. J. Acc. Chem. Research 1974, 7, 384.

AH2

AH3

AH4


Isolobal analogy

Two molecular fragments are isolobal if their frontierorbitals have the same symmetry, similar energies and bring in same No. of electron

..

..3 : XCHH

Pyramidal: NX3, PX3, AsX3, SbX3, NR3…..8ePlanar: BX3, GaI3, InMe3….6e

ClF3 ??

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LGO1

LGO2

LGO3

2s

2px

2py

2pz

B 3 H

bs

bx b

y

nbz

*s

*x *

y

'11a

'11e

''21a

'1

'1

2

2

a

e

BH3


LGO1

LGO2

LGO3

3s

3px

3py

3pz

Cl 3 H

bs

bx b

y

nbz

*s

*x *

y

ClF3 ClH3 10 e

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3s 3p

Cl

Cl*

3d

Valence bond theory treatment of bonding: a hypervalent molecule, ClF3

F Cl

F

F

3dCl* (sp3d)

F F F

The overlap of the sp3d hybrid orbitals on Cl with the 2p orbitals on the F atoms gives three P-F (sp3d)-2p bonds in two sets: the two axial bonds along the z-axis (less than 180° from each other because of the repulsion from the lone pairs) and the one equatorial bond halfway between the other Cl bonds. Again, the bond lengths will not be the same because there is more d contribution to the axial hybrid orbitals.

There are five “objects” around Cl so the geometry is trigonal bipyramidal and the shape is given by AX3E2 (T-shaped).


23


VSEPRValence Shell Electron Pair Repulsion

DG Chapt 2

Allows the prediction of molecular geometry

Sidgwick + Powell 1940

Gillespie + Nyholm 1957

Count up the number of steric contribution around the central atom. Steric number (SN) =# of attached atom + # of lone pairs

Rule 1: Assume that electron pairs around central atom repel each other, the most stable geometry corresponds to that obtained by maximizing the distance between SN points on the surface of a sphere, minimizing electron pair repulsion.


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VSEPRValence Shell Electron Pair Repulsion

Rule 2: Lone pair electrons are held in closer to the nucleus. Most prohibitive repulsion is lp-lp, followed by lp-bp, then bp-bp…lps will spread out as much as possible.

Rule 3: lps occupy more space than bond pairs, ….large angle between lps than bps.


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ClF3 ??

SN=5

Rule 1: Structure based on trigonal bypyramid.

Rule 2: LPs are on equatorial positions.

Rule 3. axial F atoms bend away from LPs.

87.5°

87.5°

ClF3

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LGO1

LGO2

LGO3

2s

2px

2py

2pz

B 3 H

bs

bx b

y

nbz

*s

*x *

y

'11a

'11e

''21a

'1

'1

2

2

a

e


87.5°

87.5°

ClF3

Note different energies for two LPs

27


(xz, yz)(Rx, Ry)01-20-12E’’

z1-1-1-111A’’ 2

-1

-1

1

1

2 S3

1

0

-1

1

3 C2

-1-111A’’ 1

(x2 - y2, xy)

x2 + y2, z2

(x,y)

Rz

02-12E’

-1111A’2

1111A’1

3 vh2 C3ED3h

S orbital


E C2 v v’

1 1 1 1 z

1 1 -1 -1 Rz xy

1 -1 1 -1 x, Ry xz

1 -1 -1 1 y,Rx yz

C2v

A1

A2

B1

B2

222 ;; zyx

S Pz both become a1, mixing

28


p

character

s

character

Bonding

orbital

75% 25%


29


214 TAH

E 8C3 3C2 6S4 6σdlinear,

rotationsquadratic

A1 1 1 1 1 1 x2+y2+z2

A2 1 1 1 -1 -1

E 2 -1 2 0 0 (2z2-x2-y2, x2-y2)

T1 3 0 -1 1 -1 (Rx, Ry, Rz)

T2 3 0 -1 -1 1 (x, y, z) (xy, xz, yz)

4 1 0 0 2H4


214 TAH

30


“phase match”


31


8e Td molecules: 444 ,),,,,( BFARPbSnGeSiAAX


103°

Fax-S-Fax 179°

SF4

222244 ,,, TeClRSeClRSeClSCl

10e AH4

32


XeFFF

Fsquareplanar

XeF4

44 , BrFICl

12e AH4

chem 104a, uc, berkeley orbital interaction diagram 1...

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