Lecture 16 C1403 October 31, 2005

18.1 Molecular orbital theory: molecular orbitals and diatomic molecules

18.2 Valence bond theory: hybridized orbitals and polyatomic molecules. From steric number to hybridization of atoms

Concepts: Bond order, bond lengths, connections of MO theory and VB theory with Lewis structures

1 + _ + + _ +

+ + + _ _ _

+ + _

2 Potential energy curves for the ! and !* orbitals of a diatomic molecule

Distance dependence of the energy of a ! and !* orbital

3 Making of a !z and !z* orbital from overlap of

two 2pz orbitals

Making of a "x and "x* orbital from overlap of two

2px orbitals

Making of a "y and "y* orbital from overlap of two

2py orbitals

4 The reason for the “switch” in the s and p MOs

Larger gap between

!2s and !2p with increasing Z

Switch

5 Bond order: connection to bond energy and bond length

Bond enthalpy = bond energy = energy required to break the bonds between two atoms

Bond length = distance between two nuclei in a bond

6 Some examples of configurations, bond lengths, bond strength and bond order

2 2 2 4 2 O2 = (!2s) (!2s*) (!2p) ("2p) ("2p*)

+ 2 2 2 4 1 O2 = (!2s) (!2s*) (!2p) ("2p) ("2p*)

1- 2 2 2 4 3 O2 = (!2s) (!2s*) (!2p) ("2p) ("2p*)

2- 2 2 2 4 4 O2 = (!2s) (!2s*) (!2p) ("2p) ("2p*)

O2 Bond length = 1.21Å Bond order = 2

+ O2 Bond length = 1.12 Å Bond order = 5/2

- O2 Bond length = 1.26 Å Bond order = 3/2

2- O2 Bond length = 1.49 Å Bond order = 1 7 Compare the Lewis and MO structures of diatomic molecules

2 2 4 0 0 0 C2 (!2s) (!2s*) ("2p) (!2p) ("2p*) (!2p*) C C

2 2 4 2 0 0 N2 (!2s) (!2s*) ("2p) (!2p) ("2p*) (!2p*) N N

2 2 2 4 2 0 O O O2 (!2s) (!2s*) (!2p) ("2p) ("2p*) (!2p*)

2 2 2 4 4 0 F2 (!2s) (!2s*) (!2p) ("2p) ("2p*) (!2p*) F F

8 What is the bond order of NO in Lewis terms and MO theory?

Valence electrons = 11

2 2 2 4 1 0 NO: (!2s) (!2s*) (!2p) ("2p) ("2p*) (!2p*)

BO = 1/2(8 - 3) = 5/2

Lewis structure: BO = 2? N O

Odd electron is in an antibonding orbital

9 18.2 Polyatomic molecules

Valence bond versus molecular orbital theory

Hybridization of atomic orbitals to form molecular orbitals

From steric numbers to sp, sp2 and sp3 hybridized orbitals

Hybridized orbitals and Lewis structures and molecular geometries

Double bonds and triple bonds

10 Hybridization is a theory that starts with geometry of molecules and then decides on the hybridization of the atoms based on steric number of the atoms

Steric number happens to be the same as the number of hybrid orbitals

11 Hybridization If more than two atoms are involved in a molecule, the shapes of the orbitals must match the shape of the bonds that are needed (trigonal, tetrahedral, etc.). The atomic orbitals do not have these shapes, and must be mixed (hybridized) to achieve the needed shapes

Three exemplar organic molecules

12 The hybridization of a s orbital and two p orbitals to produce three sp2 orbitals

Three Three hybrid Atomic Orbitals orbitals HAOs Aos sp2 2s + two 2p

13 1188..22 BBoonnddiinngg iinn MMeetthhaannee aanndd OOrrbbiittaall HHyybbrriiddiizzaattiioonn Structure of Methane

tetrahedral bond angles = 109.5° bond distances = 110 pm but structure seems inconsistent with electron configuration of carbon Electron configuration of carbon

only two unpaired 2p electrons should form ! bonds to only two hydrogen atoms bonds should be 2s at right angles to one another sp3 Orbital Hybridization

2p

Promote an electron from the 2s to the 2p orbital

2s sp3 Orbital Hybridization

2p 2p

2s 2s sp3 Orbital Hybridization

2p

Mix together (hybridize) the 2s orbital and the three 2p orbitals

2s sp3 Orbital Hybridization

2p

2 sp3

4 equivalent half-filled orbitals are consistent with four bonds and tetrahedral geometry 2s The C—H ! Bond in Methane

In-phase overlap of a half-filled 1s orbital of hydrogen with a half-filled sp3 hybrid orbital of carbon: + s H + C – sp3 gives a ! bond. + H—C ! H C – Justification for Orbital Hybridization

consistent with structure of methane allows for formation of 4 bonds rather than 2 bonds involving sp3 hybrid orbitals are stronger than those involving s-s overlap or p-p overlap 1188..22 sspp3 HHyybbrriiddiizzaattiioonn aanndd BBoonnddiinngg iinn EEtthhaannee Structure of Ethane

C2H6

CH3CH3

tetrahedral geometry at each carbon C—H bond distance = 110 pm C—C bond distance = 153 pm The C—C ! Bond in Ethane

In-phase overlap of half-filled sp3 hybrid orbital of one carbon with half-filled sp3 hybrid orbital of another. Overlap is along internuclear axis to give a ! bond. The C—C ! Bond in Ethane

In-phase overlap of half-filled sp3 hybrid orbital of one carbon with half-filled sp3 hybrid orbital of another. Overlap is along internuclear axis to give a ! bond. 1188..22 sspp2 HHyybbrriiddiizzaattiioonn aanndd BBoonnddiinngg iinn EEtthhyylleennee Structure of Ethylene

C2H4

H2C=CH2

planar

bond angles: close to 120°

bond distances: C—H = 110 pm C=C = 134 pm sp2 Orbital Hybridization

2p

Promote an electron from the 2s to the 2p orbital

2s sp2 Orbital Hybridization

2p 2p

2s 2s sp2 Orbital Hybridization

2p

Mix together (hybridize) the 2s orbital and two of the three 2p orbitals

2s sp2 Orbital Hybridization

2p

2 sp2

3 equivalent half-filled sp2 hybrid orbitals plus 1 p orbital left unhybridized 2s sp2 Orbital Hybridization

p 2 of the 3 sp2 orbitals 2 sp2 are involved in ! bonds to hydrogens; the other is involved in a ! bond to carbon 11..1188 sspp HHyybbrriiddiizzaattiioonn aanndd BBoonnddiinngg iinn AAcceettyylleennee Structure of Acetylene

C2H2 HC CH

linear

bond angles: 180°

bond distances: C—H = 106 pm CC = 120 pm sp Orbital Hybridization

2p

Promote an electron from the 2s to the 2p orbital

2s sp Orbital Hybridization

2p 2p

2s 2s sp Orbital Hybridization

2p

Mix together (hybridize) the 2s orbital and one of the three 2p orbitals

2s sp Orbital Hybridization

2 p 2p

2 sp

2 equivalent half-filled sp hybrid orbitals plus 2 p orbitals left unhybridized 2s sp Orbital Hybridization

2 p

1 of the 2 sp orbitals 2 sp is involved in a ! bond to hydrogen; the other is involved in a ! bond to carbon sp Orbital Hybridization

2 p !

! 2 sp ! " Bonding in Acetylene

the unhybridized p orbitals of 2 p carbon are involved in separate " bonds to the other carbon

2 sp " Bonding in Acetylene

2 p

2 sp

one " bond involves one of the p orbitals on each carbon there is a second " bond perpendicular to this one " Bonding in Acetylene

2 p

2 sp " Bonding in Acetylene

2 p

2 sp How to determine the hybridization of an atom in a polyatomic molecule

Draw a Lewis structure of the molecule

Determine the steric number of the atoms of the molecule

From the steric number assign hybridization as follows:

Steric number Hybridization Example 2 sp HC CH 2 3 sp H2C=CH2 3 4 sp H3C-CH3

46 sp hybridization and acetylene: H C C H one s orbital and one p orbital = two sp orbitals

An isoelectroic molecule

H C N

47 Other examples of sp2 and sp hybridized carbon

Formaldehyde: H2C=O Carbon dioxide: O=C=O

Typo: CH bond in figure below should be labeled sp2

48 2 sp hybridization and ethylene: H2C=CH2

49 Hybridization and methane: CH4

50 Hybrid orbitals are constructed on an SN = 2 atom to reproduce the electronic arrangement SN = 3 characteristics that will yield the

SN = 4 experimental shape of a molecule

SN = 5

SN = 6

51 Examples

BeF2: SN = 2 = sp

2 BF3: SN = 3 = sp

3 CH4: SN = 4 = sp

3 PF5: SN = 5 = sp d

3 2 SF6: SN = 6 = sp d

52 Extension to mixing of d orbitals

d2sp3 hybridization six orbitals mixed = octahedral

dsp3 hybridization Five orbitals mixed = trigonal bipyramidal

53 54 55