Molecular Orbitals The overlap of atomic orbitals from separate atoms
makes molecular orbitals Each molecular orbital has room for two electrons Two types of MO Sigma ( σ ) between atoms Pi ( π ) above and below atoms
Sigma bonding orbitals From s orbitals on separate atoms +
+
s orbital s orbital
+ +
+ +
Sigma bonding molecular orbital
Sigma bonding orbitals From p orbitals on separate atoms ⊕
⊕
p orbital
p orbital
⊕
⊕
⊕
⊕
Sigma bonding molecular orbital
Pi bonding orbitals ⊕ ⊕
⊕
⊕
⊕ ⊕
p orbitals on separate atoms
Pi bonding molecular orbital
Sigma and pi bonds All single bonds are sigma bonds A double bond is one sigma and one pi bond A triple bond is one sigma and two pi bonds.
Atomic Orbitals Don’t Work to explain molecular geometry. In methane, CH4 , the shape s tetrahedral. The valence electrons of carbon should be two in s,
and two in p. the p orbitals would have to be at right angles. The atomic orbitals change when making a molecule
Hybridization We blend the s and p orbitals of the valence electrons
and end up with the tetrahedral geometry. We combine one s orbital and 3 p orbitals.
sp3 hybridization has tetrahedral geometry.
In terms of energy 2p Energy
Hybridization
2s
sp3
How we get to hybridization We know the geometry from experiment. We know the orbitals of the atom hybridizing atomic orbitals can explain the
geometry. So if the geometry requires a tetrahedral shape, it is sp3 hybridized This includes bent and trigonal pyramidal molecules because one of the sp3 lobes holds the lone pair.
2 sp
hybridization
C2H4
Double bond acts as one pair. trigonal planar Have to end up with three blended orbitals.
Use one s and two p orbitals to make sp2 orbitals. Leaves one p orbital perpendicular.
In terms of energy 2p Energy
Hybridization
2s
2p sp2
Where is the P orbital? Perpendicular The overlap of orbitals
makes a sigma bond (σ bond)
Two types of Bonds Sigma bonds from overlap of orbitals. Between the atoms. Pi bond (π bond) above and below atoms Between adjacent p orbitals. The two bonds of a
double bond.
H
H C
H
C H
2 sp
hybridization
When three things come off atom. trigonal planar 120º One π bond, σ + lp =3
What about two When two things come off. One s and one p hybridize. linear
sp hybridization End up with two lobes 180º apart. p orbitals are at right angles Makes room for two π bonds and
two sigma bonds. A triple bond or two double bonds.
In terms of energy 2p Energy
Hybridization
2s
2p sp
CO2
C can make two σ and two π O can make one σ and one π
O
C O
N2
N2
Breaking the octet PCl5
The model predicts that we must use the d orbitals. dsp3 hybridization
There is some controversy about how involved the d
orbitals are.
3 dsp Trigonal bipyrimidal can only σ bond. can’t π bond. basic shape for five
things.
PCl5 Can’t tell the hybridization of Cl Assume sp3 to minimize repulsion of electron pairs.
2 3 d sp gets us to six things around Octahedral Only σ bond
Molecular Orbital Model Localized Model we have learned explains much about
bonding. It doesn’t deal well with the ideal of resonance, unpaired electrons, and bond energy. The MO model is a parallel of the atomic orbital, using quantum mechanics. Each MO can hold two electrons with opposite spins Square of wave function tells probability
What do you get? Solve the equations for H2 HA HB
get two orbitals MO2 = 1sA - 1sB MO1 = 1sA + 1sB
The Molecular Orbital Model • The molecular orbitals are centered on a line through the nuclei
MO1 the greatest probability is between the nuclei MO2 it is on either side of the nuclei
this shape is called a sigma molecular orbital
The Molecular Orbital Model • In the molecule only the molecular orbitals exist, the
atomic orbitals are gone • MO1 is lower in energy than the 1s orbitals they came from. This favors molecule formation Called an bonding orbital
• MO2 is higher in energy
This goes against bonding antibonding orbital
The Molecular Orbital Model Energy
MO2 1s
H2
1s
MO1
The Molecular Orbital Model • We use labels to indicate shapes, and whether the MO’s are bonding or antibonding. MO1 = σ1s
MO2 = σ1s* (* indicates antibonding)
• Can write them the same way as atomic orbitals 2
H2 = σ1s
The Molecular Orbital Model • Each MO can hold two electrons, but they must have opposite spins • Orbitals are conserved.
• The number of molecular orbitals must equal the
number atomic orbitals that are used to make them.
+
Energy
H2
σ1s* 1s
1s
σ1s
Bond Order The difference between the number of bonding
electrons and the number of antibonding electrons divided by two
# bonding-#antibonding Bond Order = 2
Only outer orbitals bond The 1s orbital is much smaller than the 2s orbital When only the 2s orbitals
involved in bonding Don’t use the σ1s or σ1s* Li2 = (σ2s)2
are for Li2
In order to participate in bonds the orbitals must
overlap in space.
Bonding in Homonuclear Diatomic Molecules
Need to use Homonuclear so that we know the relative energies. Li2-
(σ2s)2 (σ2s*)1 Be2
(σ2s)2 (σ2s*)2
What about the p orbitals? How do they form orbitals? Remember that orbitals must be conserved.
B2
B2 σ2p* σ2p π2p* π2p
Expected Energy Diagram 2p
σ2p* π2p* π2p* π2p π2p
2p
σ2p σ2s* 2s
σ2s
2s
B2 2p
2p
2s
2s
B2 (σ2s)2(σ2s*)2 (σ2p)2 Bond order = (4-2) / 2 Should be stable. This assumes there is no interaction between the s and
p orbitals. Hard to believe since they overlap proof comes from magnetism.
Magnetism Magnetism has to do with electrons. Paramagnetism attracted by a magnet. associated with unpaired electrons. Diamagnetism attracted by a magnet. associated with paired electrons. B2 is paramagnetic.
Magnetism The energies of of the π2p and the σ2p are reversed by
p and s interacting The σ2s and the σ2s* are no longer equally spaced. Here’s what it looks like.
Correct energy diagram σ2p* π2p* π2p*
2p
π2p
σ2p
π2p
2p
σ2s* 2s
2s σ2s
B2
σ2p* π2p* 2p
2p
σ2p π2p σ2s*
2s
2s σ2s
Patterns As bond order increases, bond energy increases. As bond order increases, bond length decreases. Supports basis of MO model. There is not a direct correlation of bond order to bond energy. O2 is known to be paramagnetic.
Heteronuclear Diatomic Species Simple type has them in the same energy level, so can
use the orbitals we already know. Slight energy differences. NO
NO
2p
2p
2s 2s
You try NO+ CN What if they come from completely different orbitals
and energy? HF Simplify first by assuming that F only uses one if its 2p orbitals. F holds onto its electrons, so they have low energy
σ∗ 1s
2p σ
Consequences Paramagnetic Since 2p is lower in energy, favored by electrons. Electrons spend time closer to fluorine. Compatible with polarity and electronegativity.
Names sp orbitals are called the Localized electron model σ and π Μolecular orbital model Localized is good for geometry, doesn’t deal well with
resonance. seeing σ bonds as localized works well It is the π bonds in the resonance structures that can move.
