Part 2.7: Orbital Diagrams 1. Orbital Diagrams Orbital Interactions Molecular Orbital Theory Orbital Energies MO Diagrams – HF, H 2 O, CO 2, C 2 H 4,

1

Part 2.7: Orbital Diagrams

2

Orbital Diagrams• Orbital Interactions• Molecular Orbital Theory• Orbital Energies• MO Diagrams

– HF, H2O, CO2, C2H4, NH3, Benzene

• SALC• Hybridization• Symmetry and Reactivity

3

Atomic Orbital- is a mathematical function (Y) that describes the wave-like behavior of electrons in an atom.Used to calculate the probability (Y2 ) of finding any electron of an atom in any specific region around the atom's nucleus.

Atomic Orbitals

1s orbital

2p orbital

4


Atomic Orbitals

1s orbital

2p orbital

5

Atomic Orbitals

constructively = bonding destructively = antibonding

not at all = non-bonding

Waves can interact-


6

1. ATOMIC ORBITALS of different atoms combine to create MOLECULAR ORBITALS 2. The number of ATOMIC ORBITALS = the number of MOLECULAR ORBITALS

3. Electrons in these MOLECULAR ORBITALS are shared by the molecule as whole

4. MOLECULAR ORBITALS can be constructed from Linear Combination of Atomic Orbitals (LCAO)

Molecular Orbital Theory

Y = caya + cbyb (for diatomic molecules)LCAO

BONDING Orbitals have most of the electron density between the two nuclei

ANTI-BONDING Orbitals have a node between the two nuclei

NONBONDING Orbitals are essentially the same as if it was only one nuclei

7

Combining Atomic Orbitals

Bonding:Ψ(σ) or Ψ+ = (1/√2 ) [φ(1sa) + φ(1sb) ]

Antibonding:

Ψ(σ*) or Ψ- = (1/√2 ) [φ(1sa) - φ(1sb) ]

8

Combining Atomic Orbitals (H2)Antibonding

Bonding

9

Combining Atomic OrbitalsH2 Fe(C5H5)2

•2 atoms•Only s orbitals•Linear interaction•Same energy•Uniform symmetry

•11 relevant atoms•s, p, and d orbitals•various interactions•different energies

10

Degree of orbital overlap/mixing depends on: 1) Energy of the orbitals

The closer the energy, the more mixing.

2) Spatial proximityThe atoms must be close enough that there is

reasonable orbital overlap.

3) SymmetryAtomic orbitals mix if they have similar symmetries.


Strength of the bond depends upon the degree of orbital overlap.

Y = caya + cbyb … cnyn

11

For heteronuclear molecules:

1. The bonding orbital(s) will reside predominantly on the atom of lower orbital energy (the more electronegative atom).

2. The anti-bonding orbital(s) will reside predominantly on the atom with greater orbital energy (the less electronegative atom).

Energy of the Orbitals

How do we determine orbital energies?

12

Energy of Orbitals1) Theoretical calculations

2) Photoelectron spectroscopy

3) Tabulated dataOther peoples UPS/XPS data

13

Photoelectron Spectroscopy

Ionization occurs when matter interacts with light of sufficient energy (Heinrich Hertz, 1886) (Einstein, A. Ann. Phys. Leipzig 1905, 17, 132-148.)

14

Photo-ionization and energy-dispersive analysis of the emitted photoelectrons to study the composition and electronic state of the sample.

X-ray Photoelectron Spectroscopy(XPS)

- using soft (200-2000 eV) x-ray excitation to examine core-levels.

Ultraviolet Photoelectron Spectroscopy(UPS)

- using vacuum UV (10-45 eV) radiation from discharge lamps to examine valence levels.


hνo = I(BE) + Ekinetic

15

X-Ray source

Ion source

Axial Electron Gun

Detector

CMAsample

SIMS Analyzer

Sample introduction Chamber

Sample Holder

Ion PumpRoughing Pump Slits

Photoelectron Spectrometer

16

Photoelectron Spectrometer

17


Counts

18


Counts

19

20

Miessler and Tarr, Inorganic Chemistry

Tabulated Data

Diagram for methane

(CH4)?

21http://en.wikipedia.org/wiki/Ionization_energy

Tabulated Data

22

Degree of orbital overlap/mixing depends on: 1) Energy of the orbitals

The closer the energy, the more mixing.

2) Spatial proximityThe atoms must be close enough that there is

reasonable orbital overlap.

3) SymmetryAtomic orbitals mix if they have similar symmetries.


Strength of the bond depends upon the degree of orbital overlap.

Y = caya + cbyb … cnyn

23

Symmetry and Orbital Diagrams

J. Chem. Edu. 2004, 81, 997.

1. Number of MOs = number of incipient orbitals. This rule could be

referred to as “the conservation of orbitals.” 2. Orbitals of the same symmetry mix.

3. Orbital interactions can be bonding, nonbonding or antibonding.

4. There are three basic types of orbital overlap: s (end on interaction), p (side by side approach) and d (off-axis approach).

5. Orbitals with the correct symmetry and most similar energy mix to the greatest extent.

24

Constructing MOs

• From inspection

• From Group Theory

25

Constructing MOss bond (s, p and d)

d d

p bond (p and d)

p p p d

d bond (d)

26

Constructing MOs (s-s)

27

Constructing MOs (p-p)

28

Constructing MOs (d-d)

29

Simple Diatomics

30

MO Diagrams from Group Theory1. Assign a point group2. Choose basis function (orbitals)3. Apply operations

-if the basis stays the same = +1-if the basis is reversed = -1-if it is a more complicated change = 0

4. Generate a reducible representation5. Reduce to Irreducible Representation6. Combine central and peripheral orbitals by their symmetry7. Fill MOs with e-

8. Generate SALCs of peripheral atoms9. Draw peripheral atoms SALC with central atom orbital to

generate bonding/antibonding MOs.

31

MO Diagrams from Group Theory• H-F

– diatomic, H = 1s; F = 2s, 3 x 2p

• H2O– triatomic, H = 2 x 1s; O = 2s, 3 x 2p

• CO2

– p bonding, O = 2s, 3 x 2p; C = 2s, 3 x 2p

• C2H4

– Fragmentation method• Benzene

– Real + Imaginary SALC

32

HF Orbital Diagram1. Assign a point group

C2vC∞v

H-FC2v

33

HF Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


F

H

z

xy

GH 1 1 1 1

H s orbitalF s, px, py and pz orbitals

H-FC2v

A1

34

HF Orbital DiagramH-F1. Assign a point group

2. Choose basis function (orbitals)3. Apply operations


C2v

F

H

z

xy

GFs 1 1 1 1


A1

A1

35





C2v

F

H

z

xy

GFpz 1 1 1 1

A1

A1 A1

36





C2v

F

H

z

xy

GFpx 1 -1 1 -1

A1

A1 A1B1

37





C2v

F

H

z

xy

GFp

y

1 -1 -1 1

A1

A1 A1B1 B2

38

HF Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


4. Generate a reducible representation5. Reduce to irreducible representation6. Combine orbitals by their symmetry


H-FC2v

A1

A1 A1B1 B2

39

HF Orbital Diagram6. Combine orbitals by their symmetry


40


H F

2s (A1)


A1

A1 A1B1 B2

pz (A1)py (B2)

px (B1)1s (A1)

H-F

41


H F

2s (A1)

pz (A1)py (B2)

px (B1)1s (A1)

A1

A1

A1

py (B2) px (B1)

H-F

42

HF Orbital Diagram7. Fill MOs with e-

H F

2s (A1)

pz (A1)py (B2)

px (B1)1s (A1)

A1

A1

py (B2) px (B1)

1 e- 7 e-

A1

H-F

43

e- in MOs1. Electrons preferentially occupy molecular

orbitals that are lower in energy. (Aufbau Principle)

2. If two electrons occupy the same molecular orbital, they must be spin paired. (Pauli Exclusion Principle)

3. When occupying degenerate molecular orbitals, electrons occupy separate orbitals with parallel spins before pairing. (Hund’s Rule)

44

HF Orbital Diagram7. Fill MOs with e-

H F

2s (A1)

pz (A1)py (B2)

px (B1)1s (A1)

A1

A1

py (B2) px (B1)

H-F

A1

45

1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


4. Generate a reducible representation5. Reduce to irreducible representation6. Combine orbitals by their symmetry7. Fill MOs with e-



2s (A1)

HF Orbital Diagram

H F

pz (A1)

py (B2)

px (B1)1s (A1)

A1

A1

A1

py (B2) px (B1)

H-F

46

HF Orbital Diagram8. Draw orbitals

2s (A1)

pz py px

1s (A1)

A1

A1

B2 B1

F

H

z

xy

F

F

H

F

F

FF

H F

F

F

H

A1

H-F

47

• H-F– diatomic, H = 1s; F = 2s, 3 x 2p


• CO2


• C2H4

– Fragmentation method

• NH3/Benzene– Real + Imaginary SALC

MO Diagrams from Group Theory

48

H2O Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


OH

z

xy

GH 2 0 2 0

H s orbitalsO s, px, py and pz orbitals

H2OC2v

H

A1 + B1GH

A1 + B1

49



OH

z

xy


H2OC2v

H

A1 + B1

A1 A1B1 B2

50





H2OC2v

A1 + B1

51


H s orbitalO s, px, py and pz orbitals

52

H2O Orbital Diagram6. Combine orbitals by their symmetry

2 x H O

2s (A1) H s orbitalO s, px, py and pz orbitals

A1 + B1

A1 A1B1 B2

pz (A1)py (B2)

px (B1)A1 B1

53

H2O Orbital Diagram6. Combine orbitals by their symmetry

2 x H O

2s (A1)

pz (A1)py (B2)

px (B1)A1 B1

H2OA1

A1

A1

B1

B1

py (B2)

H2O Orbital Diagram7. Fill MOs with e-

2 x H O

2s (A1)

pz (A1)py (B2)

px (B1)A1 B1

H2OA1

A1

A1

B1

B1

py (B2)

2 e- 6 e- 54

55






2s (A1)

pz (A1)

py (B2)

px (B1)A1 B1

A1

A1

B1

B1

py (B1)

A1

56

H2O Orbital Diagram8. Generate SALCs of peripheral atoms

• Use projection operator to generate SALC.

• Projection operators constitute a method of generating the symmetry allowed combinations.

• Taking one AO and projecting it out using symmetry.

Symmetry adapted linear combination of atomic orbitals (SALC)

Pi is the projection operatorli is the dimension of Gi

h is the order of the groupi is an irreducible representation of the groupR is an operation of the groupχi (R) is the character of R in the ith irreducible representation(R) non-symmetry-adapted basis

57


To generate SALCs, the steps are:

1) group the atomic orbitals in the molecule into sets which are equivalent by symmetry

2) generate the rep. then irr. rep. for each set

3) Use projection operator for one basis

58



1) group the similar AOs



OH

z

xy

Hf1 f2

A1 + B1GH =

PA1 = 1/4 [((1) E f1 ) + ((1) C2 f1 ) + ((1) sxz f1 ) + ((1) syz f1 )]

59






OH

z

xy

Hf1 f2

A1 + B1GH =

PA1 = 1/4 [((1) E f1 ) + ((1) C2 f1 ) + ((1) sxz f1 ) + ((1) syz f1 )]

60

PA1 = 1/4 [((1) E f1 ) + ((1) C2 f1 ) + ((1) sxz f1 ) + ((1) syz f1 )]






OH

z

xy

Hf1 f2

A1 + B1GH =

61






OH

z

xy

Hf1 f2

A1 + B1GH =

PA1 = 1/4 [((1) E f1 ) + ((1) C2 f1 ) + ((1) sxz f1 ) + ((1) syz f1 )]

f1 f2 f1 f2

PA1 = 1/4 [f1 + f2 + f1 + f2]

PA1 = 1/4 [2f1 + 2f2]

PA1 = 1/2 [f1 + f2]

HO

H

A1 H1s orbitals

62






OH

z

xy

Hf1 f2

A1 + B1GH =

PB1 = 1/4 [((1) E f1 ) + ((-1) C2 f1 ) + ((1) sxz f1 ) + ((-1) syz f1 )]

63






OH

z

xy

Hf1 f2

A1 + B1GH =

PB1 = 1/4 [((1) E f1 ) + ((-1) C2 f1 ) + ((1) sxz f1 ) + ((-1) syz f1 )]

64






OH

z

xy

Hf1 f2

A1 + B1GH =

PB1 = 1/4 [((1) E f1 ) + ((-1) C2 f1 ) + ((1) sxz f1 ) + ((-1) syz f1 )]

65






OH

z

xy

Hf1 f2

A1 + B1GH =

f1 f2 f1 f2

PB1 = 1/4 [f1 - f2 + f1 - f2]

PB1 = 1/4 [2f1 - 2f2]

PB1 = 1/2 [f1 - f2]

HO

H

B1 H1s orbitals

PB1 = 1/4 [((1) E f1 ) + ((-1) C2 f1 ) + ((1) sxz f1 ) + ((-1) syz f1 )]

66

H2O Orbital Diagram9. Draw SALC with central atom.

2s (A1)

pz (A1)py (B2)

px (B1)A1 B1

H2OA1

A1

A1

B1

B1

py (B2)

OH

z

y

H

x

67






2s (A1)

pz (A1)

py (B2)px (B1)

A1 B1

A1

A1

A1

B1

B1

py (B2)

68

Sidenote: Many Electron States

H2OA1

A1

A1

B1

B1

B2

• Determining the symmetry of many electron states from the symmetry of the individual one electron wavefunctions.

• Important for formulating spectroscopic selection rules between orbitals or electronic states.

• State symmetry found from the direct product of all electron symmetries.

69H2OA1

A1

A1

B1

B1

B2

• Determining the symmetry of many electron states from the symmetry of the individual one electron wavefunctions.

• Important for formulating spectroscopic selection rules between orbitals or electronic states.

• State symmetry found from the direct product of all electron symmetries.


70H2OA1

A1

A1

B1

B1

B2

H2O: A1 A1 B2 B2 A1 A1 =

A1 B2 B2 A1 A1

B2 …etc.

or closed shell configurations cancel!

A1 A1 A1

A1 B2 B2

= A1 B2 B2

H2O: A1 A1 B2 B2 A1 A1 = A1 B2 B2

A1


71H2OA1

A1

A1

B1

B1

B2

H2O: A1 A1 B2 B2 A1 A1 = A1 B2 B2


72H2O+

A1

A1

A1

B1

B1

B2

H2O: A1 A1 B2 B2 A1 A1 = A1 B2 B2

H2O+: A1 A1 B2 B2 A1 A1 =B2 B2


73H2O-

A1

A1

A1

B1

B1

B2

H2O: A1 A1 B2 B2 A1 A1 = A1 B2 B2

H2O+: A1 A1 B2 B2 A1 A1 =B2 B2

H2O- = A1


74H2O*

A1

A1

A1

B1

B1

B2

H2O: A1 A1 B2 B2 A1 A1 = A1 B2 B2

H2O+: A1 A1 B2 B2 A1 A1 =B2 B2

H2O- = A1


H2O* = B2

75

(2s+1)G1 or 2

A1

A1

B2

H2O

A1

H2O+

B2

H2O-

A1

Sidenote: Spin MultiplicityH2O*

B2

A1

A1

B2

A1

A1

B2

A1

A1

B2

Spin Multiplicity:

s = 0

1A1

s = 1/2

2B2

s = 1/2

2A1

s = 0

1B2

A1

A1

B2

or

s = 1

3B2

76






2s (A1)

pz (A1)

py (B2)px (B1)

A1 B1

A1

A1

A1

B1

B1

py (B2)

Ground State Symmetry of H2O is 1A1

77

MO Diagrams from Group Theory• H-F

– diatomic, H = 1s; F = 2s, 3 x 2p


• CO2


• C2H4



78

CO2 Orbital Diagram1. Assign a point group

D2hD∞h

CO2D2h

79

CO2 Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)

C s, px, py and pz orbitalsO px, py and pz orbitals

CO2D2h

80

CO2 Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


z


CO2D2h

81



Ag

z


CO2D2h

B3u B2u B1u

82



Ag

z


CO2D2h

B3u B2u B1u

GOpz 2 2 0 00 0 2 2

GOpz Ag + B1u

83



Ag

z


CO2D2h

B3u B2u B1u

GOpx 2 -2 0 00 0 2 -2

GOpx B3u + B2g

84



Ag

z


CO2D2h

B3u B2u B1u

GOpy 2 -2 0 00 0 -2 2

GOpy B2u + B3g

85




Ag

C s, px, py and pz orbitals

CO2D2h

B3u B2u B1u

O px

py pz

B2u + B3g

B3u + B2g

Ag + B1u

86

CO2 Orbital Diagram6. Combine orbitals by their symmetry


87

Ag

CO2 Orbital Diagram6. Combine orbitals by their symmetry

C 2 x O

Ag

B3u B2u B1u

2s

2p

2pB2g

B3u

px py pz

B2u

B3g

Ag

B1u

px py pz

B2g B3g

OCO

Ag

B1u

B1u

B3u B2u

B3u B2u

88




C 2 x O

Ag

B3u B2u B1u

2s

2p

2pB2g

B3u

px py pz

B2u

B3g

Ag

B1u

px py pz

B2g B3g

OCO

Ag

Ag

B1u

B1u

B3u B2u

B3u B2u

89

CO2 Orbital Diagram7. Fill MOs with e-

C 2 x O

Ag

B3u B2u B1u

2s

2p

2pB2g

B3u

px py pz

B2u

B3g

Ag

B1u

px py pz

B2g B3g

OCO

Ag

Ag

B1u

B1u

B3u B2u

B3u B2u

4 e- 8 e-

90






C 2 x O

Ag

B3u B2u B1u

2s

2p

2pB2g

B3u

px py pz

B2u

B3g

Ag

B1u

px py pz

B2g B3g

OCO

Ag

Ag

B1u

B1u

B3u B2u

B3u B2u

91

CO2 Orbital Diagram8. Generate SALCs of peripheral atoms

z

GOpz Ag + B1u

f1f2

PAg = 1/8 [((1) E f1 ) + ((1) C2 f1 ) + ((1) C2 f1 ) … etc.]

PAg = 1/8 [4f1 + 4f2]

92

CO2 Orbital Diagram8. Generate SALCs of peripheral atoms

z

93

CO2 Orbital Diagram9. Draw SALC with central atom.

C 2 x OOCO

94






95



• CO2


• C2H4




96

Two different approaches (D2h)

Ethene Orbital Diagram

C1 + C2

H1-4

then combine

CH2

then combine

C CH

HH

H

z

y

x

C CH

HH

HC C

H

HH

H

J. Chem. Edu. 2004, 81, 997

97

C CH

HH

H


98


C CH

HH

H

99

C CH

HH

H


100



• CO2


• C2H4




101

N

HH

H

NH3 Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)3. Apply operations


z

x

y

GH 3 0 1

H s orbitalsN s, px, py and pz orbitals

NH2C3v

A1 + EGH

A1 + E

102

N

HH

H



z

x

y

H s orbitalsN s, px, py and pz orbitals

NH2C3v

A1 + E

A1 E A1

103

NH3 Orbital Diagram6. Combine orbitals by their symmetry

H s orbitalN s, px, py and pz orbitals

104

E

A1

NH3 Orbital Diagram6. Combine orbitals by their symmetry

3 x H N

s (A1)

pz (A1) py, px (E)EA1

NH3

A1

A1

E

105

E

A1

NH3 Orbital Diagram

3 x H N

s (A1)


NH3

A1

A1

E

7. Fill MOs with e-

3 e- 5 e-

106






E

A1

s (A1)

pz (A1)

py, px (E)EA1

A1

A1

E

107

NH3 Orbital Diagram8. Generate SALCs of peripheral atoms


1) group the atomic orbitals in the molecule into sets which are equivalent by symmetry



f1f2

A1 + EGH =

N

HH

H

z

x

y

f3

108

8. Generate SALCs of peripheral atoms

NH3 Orbital Diagram

Separate classes

109


NH3 Orbital Diagram

f1f2

N

HH

H

z

x

y

f3

110


NH3 Orbital Diagram

PA1 ≈ ((1) E f1 ) + ((1) C3+f1 ) + ((1) C3

-f1 ) + ((1) s1 f1 ) + ((1) s2 f1 ) + ((1) s2 f1 )

f1 f2 f3

PA1 ≈ [f1 + f2 + f3 + f1 + f3 + f2 ]

PA1 ≈ [ 2f1 + 2f2 + 2f3]A1 H1s orbitals

f1 f3 f2

PA1 ≈ [ f1 + f2 + f3] f1f2

HH

Hf3

111


NH3 Orbital Diagram

PE ≈ ((2) E f1 ) + ((-1) C3+f1 ) + ((-1) C3

-f1 ) + ((0) s1 f1 ) + ((0) s2 f1 ) + ((0) s2 f1 )

f1 f2 f3

PA1 ≈ [2f1 - f2 - f3] One of the E orbitals

0 0 0

f1f2

HH

Hf3

What about the other E orbital?

112


NH3 Orbital Diagram

113


NH3 Orbital Diagram

f1f2

HH

Hf3

3 different E SALCS have been generated but they are all similar.

Use subtraction or addition to generate new SALC.

f1f2

HH

Hf3

114

E

A1

NH3 Orbital Diagram

3 x H N

s (A1)


NH3

A1

A1

E

9. Draw SALC with central atom.

HH

HH

HH

HH

H

115

NH3 Orbital Diagram9. Draw SALC with central atom.

3 x HN

HH

HH

HH

HH

H

116






117



• CO2


• C2H4




118

Benzene MOs and SALC

0 nodes

1 node

2 nodes

3 nodes

119

C6H6 Orbital Diagram1. Assign a point group2. Choose basis function (orbitals)

C6H6D6h

only p bondingC pz orbitals

120

C6H6 Orbital DiagramC6H6D6h




D6h E 2C6 2C3 C2 3C′2 3C″2 i 2S3 2S6 σh 3 σd 3 σv

Гπ

z axis

C′2C″2

C6

6 0 0 0 -2 0 0 0 0 -6 0 2

121




Гπ

z axis

Gp: B2g + E1g + A2u + E2u

C′2C″2

C6



4. Generate a reducible representation5. Reduce to irreducible representation

6 0 0 0 -2 0 0 0 0 -6 0 2

122




Гπ 6 0 0 0 -2 0 0 0 0 -6 0 2

C′2C″2

C6





123

C6H6 Orbital Diagram6. Combine orbitals by their symmetry

E1g

B2g

A2u

E2u

124

C6H6 Orbital Diagram

E1g

B2g

A2u

E2u

7. Fill MOs with e-

6 pz orbitals = 6 e-

125









126

Simplify usingC6!

C6H6 Orbital Diagram8. Generate SALCs of peripheral atoms

C6D6h

127

Simplify usingC6!

C6

D6h


128






A orbital

129






130






B orbital

131


E1

B

A

E2


B ≈ B2g

A ≈ A2u

132






ok

ok

What?

Contain imaginary components; the real component of the linear combination may be realized by taking ± linear combinations:


133

134


For C6 point group:

or from Euler’s formula


135


divide out and remove prefactor constant (-i√3)


136

What are the pictorial representation of the SALC’s?


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What are the pictorial representation of the SALC’s?


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Projection Operator: BenzeneWhat are the pictorial representation of the SALC’s?

0 nodes

1 node

2 nodes

3 nodes

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• CO2


• C2H4




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Side Note: Orbital HybridizationIn chemistry, hybridization is the concept of mixing atomic orbitals into new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds.

CH

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Miessler and Tarr, Inorganic Chemistry

s + p Hybrid Orbitals

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s + p + d Hybrid Orbitals

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1. Assign a point group2. Choose basis function (s bonds)3. Apply operations


BF3 HybridizationSteps to determine the hybridization of a bond.

BF3D3h

s bonds

D3h

Гs 3 0 1 3 0 1

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4. Reduce to irreducible representation


BF3D3h

s bonds

Гs 3 0 1 3 0 1

Gs: A1’ + E’

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6. Compare symmetry of irr. rep. to central atom MOs


BF3D3h

Gs: A1’ + E’

B (s) = A1’

B (px)= E’

B (py)= E’

B (pz)= A2”

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6. Compare symmetry of irr. rep. to central atom MOs


Gs: A1’ + E’ s = A1

’

z

y

x

z

y

x

z

y

x

px = E’ py = E’

z

y

x

y

z

y

x

pz = A2”

sp2 hybridization (s, px, py)

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Hybridization

1. Assign a point group2. Choose basis function (s bonds)3. Apply operations


4. Generate a reducible representation5. Reduce to irreducible representation6. Compare symmetry of irr. rep. to central atom MOs

Steps to determine the hybridization of a bond.

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(2 + 2) cycloaddition

Symmetry and Reactivity

p orbitals2 x ethylene cyclobutane

s bonds

Orbital symmetry is retained during the reaction!

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(2 + 2) cycloaddition



2 bonding + 2 antibonding e-

Thermally Forbidden(~115 kcal/mol)

3 bonding + 1 antibonding e-

Photochemically Allowed

Thermal Reaction

Photo Reaction

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Documents

Part 2.7: Orbital Diagrams 1. Orbital Diagrams Orbital Interactions Molecular Orbital Theory Orbital Energies MO Diagrams – HF, H 2 O, CO 2, C 2 H 4,