The Chemical Bond I

1
The Chemical Bond I

• Bonds as Orbital Overlap
• Molecular Orbital Diagrams
• Hybridization
• Additional Bonding Schemes

2
Atomic Orbitals and Orientation

• Weve solved hydrogen-like atoms and found the
  orbital shapes
• Lets get the orientation of each down
• Our orbitals had no specific orientation, except
  with respect to each other
• Well use some alternate pictures that have a
  specific orientation
• For example

z
z
y
y
x
3
Orbitals Pictures

• Well picture the orbitals in this way

Two different phases

• In terms of energy, we write these as an energy
  level diagram

E
4
The Energetics of Bonding I

• Can imagine the bonding process in terms of
  bringing two hydrogen atoms together from far
  away
• As they approach, the E lowers as the atomic
  orbitals begin to interact
• The interaction is composed of (1)
  nuclear-nuclear repulsion, (2) electron-electron
  repulsion, and (3) electron-nuclear attraction
• The most stable distance (minimum energy on this
  potential energy curve) is where the attractions
  outweigh the repulsions

Increased electron density between the nuclei
stabilizes the molecule!
5
The Energetics of Bonding II

• But, need to know why an atom would bond?
• All bonds result in the lowering of energy of the
  electrons in the system
• Not all electrons are lowered in energy, but the
  net result is a more stable arrangement of the
  electrons
• Consider the H2 molecule
• Each has one occupied orbital 1s
• Lets watch the energy change
• But what about He2?

Region of energy where two electrons can reside
Atomic orbital
Result of bonding
There is no net E-loss in this alteration of
electron energies. That is, the energy released
in lowering 2 e- is used to promote the other 2.
Thus, this bond doesnt happen nonbonding!
Called molecular orbitals. Formed from the two
atomic orbitals interacting. Note that the net
effect is two lower energy e-s.
6
Molecular Orbitals I

• To picture the MOs, consider them as the
  overlap of the AOs.
• Phase of overlap matters
• Since made from s-orbitals, well denote this MO
  in similar terms
• But, well use Greek letters for bonds
• Call the overlap a s molecular orbital
• If overlap is out of phase, then well denote it
  as an antibonding orbital (s)
• Other orbital can overlap similarly
• Look at p and s

Overlap of s-orbitals
Internuclear axis
If overlap is along this axis, then the MO formed
is s.
s
s
7
Molecular Orbitals II
In terms of probability, we can see that bonding
regions show an enhanced electron density between
the two nuclei. The probability is high that the
electron-nucleus attraction will keep nuclei
together. Antibonding regions show a reduced
electron density between the nuclei, and thus the
electron-nucleus attraction is away from the
stable bond length.
8
Molecular Orbitals III

• Any set of orbitals that overlap along the
  internuclear axis are considered to be s bonds.
• And the antibonding MO is a s bond
• Here are a few other examples
• Can also make a s-bond with d-orbitals

s
py ? py

s
y
x
9
Molecular Orbitals IV

• Any set of orbitals that overlap perpendicular to
  the internuclear axis are said to p-bond
• The antibonding orbital is p

• Any set of orbitals that overlap at any other
  angle to the internuclear axis are said to d-bond
• The antibonding orbital is d
• Best example is two dyz orbitals

10
Putting It All Together

• Carbon Monoxide
• First draw Lewis Dot Structure
• This shows 3 bonding pairs (between nuclei) and 2
  nonbonding pairs
• Expect a s, a p and another p bond
• Now consider orientation and orbitals involved
  (well draw 2 of 3 dimensions)
• This should match Lewis Structure
• We see py-py overlap forming s bond
• We see p bonds in px-px and pz-pz overlap

p-bond
pz
s-bond
In the other p
px
In the other p
11
More Diatomic MO-Diagrams

• Homonuclear diatomics show a slight change as Z
  increases
• p mos appear before s mos until Z 7 (Nitrogen)

12
Polyatomic Molecules

• MOs are easy to create for diatomics
• Things get tougher if we add atoms
• Take AlCl3 as an example
• Doesnt obey octet rule
• Lewis dot structure shows three single bonds
• Thus, three s bonds
• Structure looks like this
• How do p-orbitals arrange themselves this way and
  stay orthogonal?
• Dont appear to be perpendicular
• Make a basis set of the H-like atomic orbitals
  make new orbitals
• Requires us to make linear combinations of atomic
  orbitals to make NEW atomic orbitals
• Call this hybridization
• But why? Can we justify this?

13
Hybridization

• Cl has its p-orbitals ready to bond to the Al,
  but Al has two types of valence orbitals
  available s and p (px, py, pz)
• This means that the lowest energy orbital
  available for overlap is the s.
• But, only one Cl can bond with this orbital
• To make three equal energy orbitals available to
  the Cls, Al hybridizes

p
p
p
p
Energy
sp2
sp2
sp2
s

• So we use the H-like orbitals to generate three
  different but energetically equivalent atomic
  orbitals
• In math terms, the linear combinations are

14
sp2 hybrids and AlCl3

• We can picture the hybrid orbitals as spreading
  out perpendicular to the remaining p-orbital
• They are in the xy-plane
• Three lobes must get as far apart as possible
• This is a trigonal planar arrangement of hybrid
  orbitals
• Can see how the orbitals do this pictorially,
  too

15
sp hybrids

• If need two identical bonding orbitals, use an s
  and a p orbital in an sp hybrid
• For example, LiH2

• Pictorially, the linear combination goes like

16
Multiple Bonds

• In sp and sp2 hybridization, there remains a
  p-orbital (or two)
• Can this orbital involve itself in some sort of
  bonding?
• Sure, but not along the internuclear axis, so
  must be p-bonding!
• This is the basis for double and triple bonds
• For example, consider ethane

17
sp3 hybrids

• If need four identical bonding orbitals, use an s
  and all three p orbitals in an sp3 hybrid
• For example, H2O

O
H
H
18
Other Bonding Types

• So far, only showed covalent bonding
• Other bonds
• Metallic
• Ionic
• Coordinate Covalent
• Three center, two electron bonds
• Ionic Bonds
• Purely Coulombic interactions
• Electrons are not shared they are transferred
  (in a sense)
• NaCl is perfect example
• NaCl Na--Cl- or Na---Cl
• We know first ionic species is best, but both are
  probably present in any sample
• NaCl has character of both, but has mainly the
  character of Na -- Cl-

19
Coordinate Covalent

• Often the es shared in a covalent type bond
  dont come from both atoms, but instead from one
  atom, molecule, or ion
• For Example W(CO)6
• Usually occurs with a transition metal as central
  atom (d-orbitals are the key)
• Species that donates both electrons is called a
  ligand
• CO and O2 are both ligands for Hemoglobin, and
  this is why CO can suffocate you when inhaled in
  great amounts
• Not only is it a substitute ligand, it also bonds
  better because the O can pull electron density
  from the C. This makes the Carbon antibonding MO
  a better electron donar AND it makes the
  backbonding more stabilizing
• Backbonding is the donation of electron density
  of the metal back to the ligand
• In regular O2, the nonpolar nature of the
  molecule limits these effects

20
3 Center, 2 Electron Bonds

• Most bonds are between two atoms
• They are 2 center, 2 electron bonds (2c-2e bonds)
• A center is a nucleus
• 3c-2e bonds occur when two electrons hold
  together 3 nuclei
• Most common examples Al2H6 and B2H6
• The second is called diborane
• BH3 is hard to make because diborane is so stable
  in comparison
• Orbital overlap looks like

2
1




sp3 hybrid orbital of boron 2
sp3 hybrid orbital of boron 1
s-orbital of H