Molecular Orbitals in Chemical Bonding

Chapter 9

Valence Bond Theory

• Explains the structures of covalently bonded molecules– ‘how’ bonding occurs

• VSEPR is part of VB theory• Principles of VB Theory

– Bonds form from overlapping atomic orbitals and electron pairs are shared between two atoms

• A new set of hybridized orbitals can form

– Lone pairs of electrons are localized on one atom

Molecular Orbital(MO) Theory• Explains the distributions and energy of electrons in

molecules• Useful for describing properties of compounds

– Bond energies, electron cloud distribution, and magnetic properties

• Basic principles of MO Theory– Atomic orbitals combine to form molecular orbitals– Molecular orbitals have different energies depending on type of

overlap• Bonding orbitals (lower energy than corresponding AO)• Nonbonding orbitals (same energy as corresponding AO)• Antibonding orbitals (higher energy than corresponding AO)

Formation of Molecular Orbitals

• Recall than an electron in an atomic orbital can be described as a wave function utilizing the Schröndinger equation. The ‘waves’ have positive and negative phases. To form molecular orbitals, the wave functions of the atomic orbitals combine. How the phases or signs combine determine the energy and type of molecular orbital.

• Look at Figure 9-1 to see how the phases combine.

Formation of Molecular Orbitals• Bonding orbital – the wavefuntions are in-

phase and overlap constructively (they add).– Bonding orbitals are lower in energy than AOs

• Antibonding orbital – the wavefunctions are out-of-phase and overlap destructively (they subtract)– Antibonding orbitals are higher in energy than

the AO’sWhen two atomic orbitals combine, one bonding

and one antibonding MO is formed.

Overlap of Two 1s Atomic Orbitals

• Two MO’s are formed when the two 1s atomic orbitals overlap– The in-phase combination produces a 1s

molecular bonding orbital.• Has lower energy than corresponding AO’s

– The out-of-phase contribution produces a molecular antibonding orbital

• Has higher energy than corresponding AO’s

*s1

Overlap of Two 1s Atomic Orbitals

2 1s orbitals that are far apart

Constructive interference from the 1s orbitals (1s)

Destructive inteference form the 1s orbitals ( )

The molecular orbital has a nodal plane bisecting the internuclear axis. A node or nodal plan is a region in which the probability of finding an electron is zero.

*s1

*s1

Overlap of 2px Orbitals

• Head-on overalp produces a p (actually ) and a (actually ). These are also termed as sigma orbitals since they are cylindrically symmetric about the internuclear axis.

• Constructive interference from the 2px orbitals

• Destructive interference for the 2px orbitals

xp2*p *

p2 x

Overlap of 2px Orbitals

Page 356

Overlap of 2py Orbitals

• These atomic orbitals overlap ‘side-on’ forming molecular orbitals – The bonding combination is – The antibonding combination is

• Termed as molecular orbitals because they have a nodal plane along the internuclear axis – The antibonding combination also has a nodal

plane bisecting the internuclear axis

yp2*p2 y

Overlap of 2py Orbitals

Constructive interference from the 2py orbitals

Destructive interference from the 2py orbitals

Overlap of 2pz Orbitals

• The 2pz atomic orbitals can overlap in the same fashion except that the orientation in space is different – The 2pz atomic orbitals overlap ‘side-on’ to

produce a bonding and an antibonding orbital

Together, the 2pz and the 2py atomic orbitals produce two bonding orbitals and two antibonding orbitals. MO theory commonly illustrates these orbitals as the same.

Molecular Orbital Filling-Energy Diagram

• Order of filling of MO’s obeys same rules as for atomic orbitals.

• Including– Aufbau principle– Hund’s RuleRecall that bonding orbitals have lower energies

than the corresponding atomic orbitals and antibonding orbitals have higher energies than corresponding atomic orbitals

Molecular Orbital Filling-Energy Diagram for Homonuclear Molecules

Page 357

Using Energy Diagrams in MO Theory

• Draw (or select) the appropriate molecular orbital energy level diagram

• Determine the total number of electrons in the molecule.– In MO theory, this includes all the electrons

• Add these electrons to the energy level diagram, putting each electron into the lowest energy level available– Only two electron can be in a given orbital– Electrons must occupy all the orbitals of the same energy

singly before pairing

Bond Order and Bond Stability

2electronsgantibondinof#electronsbondingof#

orderbond

Usually, the bond order corresponds to the number of bonds described by the VB theory

A bond order equal to zero indicates that there are the same number of electron in bonding and antibonding orbitals

The greater the bond order, the more stable the molecule or ion. Also, the greater the bond order, the shorter the bond length and the greater the bond energy. Bond energy is the amount of energy necessary to break a mole of bonds.

Homonuclear Diatomic Molecules

• Draw the energy level diagrams and write the MO electron configurations– H2

– He2

– B2

– N2

– O2 and O2-

Notice the differences in the energy diagrams (it switches)

Homonuclear Diatomics

• Look at Table 9-1• Trends in bond order versus bond length and bond

energy• A few diatomics have unpaired electrons in the

MO’s. These diatomics would be classified as being paramagnetic. Diamagnetic species have no unpaired electrons.

What molecules (or ions) form the previous slide are paramagetic?

Heavier Homonuclear Diatomic Molecules

• Many heavy atoms such as S2 are instable due to inability to form strong bonds– Bond length is too great for effective ‘side-on’

overlap of p orbitals.• N2 is much more stable than P2

• The effectiveness of the ‘side-on’ overlap decreases much quicker than the ‘head-on’ overlap

Heteronuclear Diatomic Molecules

• Molecular orbital diagrams for heteronuclear molecules have skewed energies for the combining atomic orbitals to take into account the differing electronegativities.

• The more electronegative elements are lower in energy than those of the less electronegative element.

Heteronuclear Diatomic Molecules

• Let’s examine the energy level diagram for NO (in your books on page 363)

• The closer the energy of a MO is to the one of the AO from which it is formed, the more of the character of that atomic orbital it shows– Illustrate with NO

Energy Level Diagram for NO

Heteronuclear Diatomic Molecules

• The energy differences between bonding orbitals depend on the electronegativity differences between the two atoms– The larger the difference the more polar the

bond that is formed (ionic character increases)– The difference reflects the amount of overlap

between the bonding orbitals. If the difference is too great the orbitals cannot overlap effectively and nonbonding orbitals will be formed.

Formation of MO’s in HF• The bond in HF involves the 1s electron of

H and the 2p orbital of F– A bonding and antibonding MO are produced

sp and MO’s

– The remaining 2p orbitals on F have no overlap with H orbitals. They are termed as ‘nonbonding’ orbitals. These orbitals retain the characteristics of the F 2p atomic orbitals.

Lack of overlap to produce nonbonding orbitals is much more pronounced for side-on bonding

*sp

The Energy Level Diagram for HF

Delocalization and Shapes of MO’s

• Molecular orbital theory describes shapes in terms of delocalization of electrons.– All the contributing AO’s will be combined

• Let’s look at the structure of benzene– VB theory indicates sp2 hybridization

– There are sigma bonds from each C atom to the two adjacent C atoms and to one H atom. There is one unhybridized 2pz orbital on each C atom remaining

Benzene

Resonance structures with VB theory. MO theory, however, indicates that the electrons are delocalized. Experiemental data shows that all the C-C bond are equal.

Benzene

Overlap according to VB theory. This theory does not describe the molecule accurately.

Benzene

Structure according to MO theory. The electrons are delocalized over the 6 C-C bonds. The electrons contribute to bonding throughout the molecule as a whole.

Molecular Orbital Diagram for H2O

Molecular Orbital Diagram for Cr(Cl)63+