Chapter 10Bonding and Molecular Structure: Orbital

Hybridization and Molecular Orbitals

Atoms are bonded together by electrons, but what is a bond?

A bond forms when two atomic orbitals overlap to make a molecule more stable than when there was no overlap

Bonds

The atomic orbitals constructively interfere to form molecular orbitals

1s(1) 1s(2) 1

Atom 1 Atom 2

Molecule

Nucleus 1 Nucleus 2

Wavefunction of the atoms combine to form wavefunctions for the molecule

Simple Molecular Orbitals

In LCAO, each AO is combined both in-phase and out-of-phase, corresponding to constructive and destructive interference.

The simplest atomic orbitals (AO’s) are the 1s orbitals, which are the ground state of hydrogen and helium

H forms bonds: H—H

He does not form bonds

The exact wavefunction of one-electron molecules such as H2

+ and He23+

, are known.

These exact wavefunctions can be approximated using linear combinations of atomic orbitals, LCAO

Constructive interference - Bonding orbital

Destrstructive interference - Anti bonding orbital Has a node between atoms

How do we explain this?

Energy Levels of LCAO-molecular orbitals

MO’s orbitals energy increases with # of nodes

The MO that forms when two 1s orbitals constructive interference have lower energy than those that destructively interfere.

MO energy levels are depicted using a correlation diagram which relates the energies of the MO’s relative to their constituent AO’s

Adding e’s to H2 a bond is formed (BO = 1)

Adding e’s to He2 no bond is lost (filling both the bonding and the antibonding MO leaves the “molecule” in a higher energy state (BO = 0), than free atoms)

H2

He2

21MO configuration: ( )s

2 * 21 1MO configuration: ( ) ( )s s

LCAO for the 2nd Period Elements

Ignore “core” orbitals in LCAO theory

22MO configuration: ( )s

The “dilithium” molecule can exist in very low-pressure vapours, whereas the normal state of lithium is the metallic solid

Lewis theory predict Li—Li, with only two bonding electrons in its valence

The net overlap of the 1s levels cancels out

The net overlap of the 2s wave functions leads to a single bond, the BO = 1

The Li—Li distance in Li2 is 159 pm; at this distance the degree of overlap of the 1s orbitals of Li is negligibly small

The assumption of “core” orbitals is thus valid

The next molecule to consider is Be2, and like He2 it should not exist.

LCAO from atomic p orbitals: σ-MO’s

For B2, with 6 valence e-, we need additional orbitals, made from next lowest atomic orbitals 2p

Here we must distinguish the orientation of the orbitals w.r.t. each other

Bond axis: z-axis for simple molecules,

consider pz orbital

p orbitals have a node at the nucleus,

out-of-phase MO will have an additional node, between the nuclei

Both MO’s are defined as σ = cylindrical

In-phase combination between two pz orbitals will have two nodes, at the nuclei but not between them.

- antibonding

- bonding

Since antibonding orbital has more nodes it is higher in energy

LCAO from atomic p orbitals: π-MO’s

Two orbitals remain at right angles to the bond axis on each atom, the px and the py

Side-on overlap which leads to a new kind of bond, the π-bond

The diagram shows the case for p x

It is called a π-orbital because from end-on it resembles an atomic p orbital

π orbitals contain a nodal plane throughout the molecule

The out-of-phase MO also has an additional node between the atoms, making it an antibonding MO

The pz orbital were higher in energy than px and py. Therefore, 2pz orbitals are higher in energy (less stable) than the two 2p orbitals which are equal in energy

Molecular OrbitalsAtomic orbitals will combine when:

1) Geometry makes it possible

Have the right shape

2) Are close in energy.

The degree of mixing depends on energy difference

3) If they have the right phase

Same phase – constructive interference

Opposite phase – destructive interference

Bond Order = [(# bonding e’s) – (# anti-bonding e’s)]/2

Correlation Diagram for the orbitals in the second period

X

2pz

X

2pz

The energy of the MO reflect that of the AO,s when atoms are aligned along the bond axis

Pz is higher than Px and Py

Similarly 2p is higher than 2p

Bonding behavior of the second period diatomic molecules can be predicted by filling the M.O.

The electron configurations of the diatomic molecules are analogous to the atom

Electrons fill in the order of MO energies from lowest to highest

(1s)2(1s*)2(2s)2(2s*)2(2p)4(2p)2(2p*)4(2p*)2

The complete energy level diagram

All the orbitals in the ground-state 2nd period elements have been considered

Bonding between these elements can be predicted by adding electrons to this orbital correlation energy level diagram

Li2 – bond order 1

Be2 - fills the σ2s* orbital, BO = 0

B2 - partially fills π2p levels, BO = 1

-2 e’s parallel i.e. paramagneticC2 - fills π2p, - BO = 2

- diamagnetic

O2 - partially fills π2p* levels, BO = 2

- paramagneticF2 - fills π2p* levels - BO = 1

Ne2 – fills σ2p*, BO = O, does not exist

N2 - fills σ2p - BO = 3 - diamangetic

Electron Configurations of diatomic molecules

You should be able to:

1. Write the MO electron configurations of each of these molecules

2. Write their Lewis Diagrams

3. Compare the predictions of Bond Order from the Lewis and the LCAO-MO descriptions

4. Compare the predictions of diamagnetism or paramagnetism from the LCAO-MO descriptions

Method of hybrid orbitalsFor molecules with more than 2 atoms, the LCAO method is computationally complex - done on a computer

Simplified molecular orbital method that retains the notion of a “chemical bond” rather than just a “net bond order” .

The method of hybrid orbitals or sometimes valence bond theory

It is derived from molecular shape and used to define common bonding situations.

Ex) BeH2 with a central Be atom

BeH2 is linear by the VSEPR method, having two equal bonds

There are not two identical atomic orbitals on Be that allow us to define two equivalent bonds

These are obtained by combining the atomic 2s and 2p orbitals and hybridize them into two new hybrid atomic orbitals

Overlap of these new hybrid orbitals and the H 1s orbitals leads to the desired bonding orbitals

BeH2 and sp hybridization

Two hybrid atomic orbitals are made to fit the shape of the molecule, in this case linear, using atomic orbitals of an excited state Be atom!

unhybridzed2

2( )

p

sp

2

2

p

s

Be 2 H

sp hybrids

1s 1s

2 Be-H bonds

2 Be-H "antibonds"

2px 2py 2px 2py

Unused AO are left behind as unhybridized atomic orbitals

The energy of the hybrid atomic orbitals are intermediate between those of the original constituent AO’s

The hybrid orbitals combine with other orbitals, atomic or hybrid, creating both bonding and anti-bonding molecular orbitals, which are localized molecular orbitals

BH3 and sp2 hybridization unhybridzed

2

2

2( )

p

sp

2

2

p

s

B 3 H

sp2 hybrids1s 1s 1s

3 B-H bonds

3 B-H "antibonds"

2py 2py

BH3 is trigonal planar with three equal B—H bonds

To get this shape the 2s with two 2p AO’s to generate three equivalent hybrid atomic orbitals

Combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitals pointing to the corners of a triangle

CH4 and sp3 hybridizationno unhybridzed orbitals in 2nd shell

3

2( )sp

2

2

p

s

C 4 H

sp3 hybrids1s 1s 1s 1s

4 C-H bonds

4 C-H "antibonds"

CH4 is tetrahedral with 4 equal C-H bonds

To get this shape, we need to combine all the n=2 AO’s to generate four equivalent hybrid atomic orbitals

In combination with the H 1s leads to bonding and anti-bonding molecular orbitals, which are localized molecular orbitals pointing to the corners of a tetrahedron

Hybrid AO’s and VSEPRA hybridization scheme exists for each member VSEPR shape families

Hybrid AO’s can be used both for bond pairs and for lone pairs

The hybridizations are:

Shape Family Hybridization No. of equivalent bondsLinear sp 2Trigonal planar sp2 3Tetrahedral sp3 4Trigonal bipyramidal sp3d 5Octahedral sp3d2 6

The hybrid atomic orbitals for the Trigonal bipyramidal and octahedral shapes will not be discussed further

For the first three shape families, the localized hybrid atomic orbitals description and a fully delocalized molecular orbital description are essentially equivalent

This method is used throughout most organic chemistry courses

H2O and sp3 hybridizationno unhybridzed orbitals in 2nd shell

3

2( )sp 2

2

p

s

H2O is bent and belongs to the tetrahedral family with 2 BP and 2 LP

The s and p orbitals combine sp3 hybrids

The 6 e’s from O, singly occupy 2 sp3 orbitals and doubly occupy the remaining 2 as LP’s

O 2 H

sp3 hybrids1s 1s

2 C-H

2 LP’s

The 2 sp3 orbitals combine with 2 1s orbital to form 2 C-H bonds

Two central atoms: ethane

C C

H

H

H

H

H

H

= H 1s = C sp3

VSEPR theory requires both carbon atoms to be tetrahedral

The shape of the molecule, its conformation, requires that contacts be minimized between the atoms – this is known as the staggered conformation

Bonding in ethane can be explained by using sp3 hybrid orbitals on each carbon atoms

The H atoms bond using their 1s atomic orbitals

In all there are 14 electrons or 7 electron pair bonds in the molecule

1 C-C sp3-sp3 single bond and 6 C-H sp3-s single bonds are formed

Double bonds: ethene

= H 1s = C sp2

2px2px

The sigma skeleton of ethene The pi manifold of ethene

Change perspective to show the π bond!

If we treat ethane by the VSEPR theory, we find that both carbon atoms are trigonal planar

The molecule is planar. Why ?

sp2 hybrid orbitals on each carbon atom, which leaves one atomic p orbital unused on each C atom, while H atoms use their 1s atomic orbitals

There are 6 e’ pair bonds in the molecule, 5 in σ orbitals, 1 in the π orbital

sp2-sp2 C-C bond, 1 px-px C-C bond , and 4 sp2-s C-H bonds

Planarity in double bonds: ethene againplanar structure of ethene can now be explained

When the two CH2 fragments are co-planar can there sufficient overlap between the unhybridized p orbitals leading to the π bond

If ethene is rotated by 90 along the C—C bond, the atomic p orbitals have zero net overlap

Double bonds impose coplanar conformations on the joining atoms

This is true for all double-bonded molecules, and is a powerful support for the bonding theories discussed

Note that a double bond is always the sum of a sigma + a pi bond

Single bonds are always sigma bonds, so that in ethane, all the bonds are sigma

Double bonds: ethyne

= H 1s

2px & 2py

The sigma skeleton of ethyne The pi manifold of ethyne

If we treat ethane by the VSEPR theory, we find that both carbon atoms are linear planar

The molecule is linear. Why ?

sp hybrid orbitals on each carbon atom, which leaves two atomic p orbitals unused on each C atom, while H atoms use their 1s atomic orbitals

There are 5 e’ pair bonds in the molecule, 3 in σ orbitals, 2 in the π orbital

sp-sp C-C bond, 2 p-p C-C bonds , and 2 sp-s C-H bonds

= C sp

C

H

H

O

Bonding in FormaldehydeLewis structure VSEPR geometry

bonding

OCH

H

:.. sp2sp2

= H 1s

= C sp2

2py2py

LP

LP

bonding

Flat

Triangular

1 sp2-sp2 C-C bond

2 sp2-s C-H bonds

2 sp2 LP’s

1 py-py C-C bond

Bonding in OzoneLewis structure VSEPR geometry

Bent

: :

::::

: :

::

::

sp2sp2

sp3sp3

sp2 sp2 sp3-sp2 bond

sp2-sp2 bond

3 sp2 LP’s

3 sp3 LP’s

p-p bond

Resonance

..OO

O..:

..

:

:

-1

+1

O

OO

:..

..

..:

:-1

+1

O

O

O-1/2 -1/2

+1

Localized electrons !

Bonding in Ozone Revisited

sp2sp2

sp2sp2

sp2 sp2

sp2-sp2 bonds

5 sp2 LP’s

p-p bond

1 p LP

: :

: :::

:::

: :

:

All Oxygen atoms can be considered to be sp2 hybridized instead

There are 4 p electrons

All 3 p orbitals combine to form 3 MO’s, therefore the LP in a p orbital and a BP in a two centre bonding orbital is not strictly speaking correct.

MO’ s of Ozone

3p

O-O-O

bondingorbital

non-bondingorbital

anti-bondingorbital

Three centre bonding orbital

LP’s

Resonance, Delocalization & Conjugation

CCCCA chain of alternating single and double bonds resonance allows the bonds to to be interchanged.

CCCC

sp2 sp2 sp2 sp2

The real situation is an average between them

All the carbons are considered to be sp2

hybridized.

The chain does not have to contain only carbon any atom that can involve at least 3 electrons in bonding will work as long as it can be sp2 hybridized, ex) N

For a chain of N carbons that are conjugated, there are N p orbitals that form N M.O.’s, where the first N/2 are occupied. The MO will increase in energy with incresing nodes.

Ex N = 4Linear molecule

# nodes

0

1

2

3

B’ing

B’ing

A. B’ing

A. B’ing

E

P orbitals

CCCC

Bonding in trans-1,3-butadieneLewis structure VSEPR geometry

bonding

bonding

C H

H

CCCH

H HHC

H

H

C

CC

H

H

H

H

sp2

sp2

sp2

Electrons are delocalized

sp2

4 MO’s with 0, 1, 2 and 3 nodes:

+ - + - a-bonding+ - - + a-bonding+ + - - bonding+ + + + bonding

Bonding in benzeneLewis structure

VSEPR geometry

bonding

C

CC

C

CC

H

H

H

H

H

H

H

H

H

6 sp2-s C-H bonds

6 sp2-sp2 C-C bonds

3 p-p C-C bonds

Bond order for C-C bonds is 1.5

p orbitals overlap

Electrons are delocalized

H

H

H

H

H

H

MO’s of Benzene

The 6 p orbital form 6 MO with 0,1,2 and 3 nodes

The MO’s with 0 and 1 node are bonding orbitals and are occupied

These represent 6 centered bonding orbitals

6 p

anti-bondingorbitals

bondingorbitals

# nodes

0

1

2

3

Bonding in Allene

bonding

bonding

Lewis structure

C H

H

CCH

H

VSEPR geometry

C

H

H

CC

H

H

4 sp2-s C-H bonds

2 sp2-sp C-C bonds

2 p-p C-C bonds

orbitals are perpendiculardo not overlap

e’s not delocalized

C-C B.O. = 2

sp2 sp sp2

Bonding in large molecules

sp3

sp3

sp3

sp3

sp3

sp2

sp2

sp3-sp3 S-C bond

s-sp3 H -S bond

2 s-sp3 H-C bonds

sp3-sp3 C-N bond

s-sp3 H-C bonds

2 s-sp3 N-H bonds

1 sp3 LP

sp3-sp2 C-C bond sp3-sp3 C-C bond

sp2-sp2 O-C bond

p-p O-C bond

sp2-sp3 C-O bond

s-sp3 H-O bond

2 sp2 LP’s

2 sp3 LP’s

Concepts from Chapter 10

MOLECULAR ORBITALS

LCAO theory

Correlation diagrams

Bonding, nonbonding and antibonding interactions

Calculating bond order using MO theory

hybridization (sp, sp2 and sp3 orbitals)

Sigma (σ) vs. pi (π) bonds

Composition of single, double and triple bonds

Resonance according to MO theory