AP Chemistry - Molecular Orbital Theory

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Molecular Orbital Theory
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Atomic Orbitals

• Heisenberg Uncertainty Principle states that it
  is impossible to define what time and where an
  electron is and where is it going next. This
  makes it impossible to know exactly where an
  electron is traveling in an atom.
• Since it is impossible to know where an electron
  is at a certain time, a series of calculations
  are used to approximate the volume and time in
  which the electron can be located. These regions
  are called Atomic Orbitals. These are also known
  as the quantum states of the electrons.
• Only two electrons can occupy one orbital and
  they must have different spin states, ½ spin and
  ½ spin (easily visualized as opposite spin
  states).
• Orbitals are grouped into subshells.
• This field of study is called quantum mechanics.

3
Atomic Subshells

• These are some examples of atomic orbitals
• S subshell (Spherical shape) There is one S
  orbital in an s subshell. The electrons can be
  located anywhere within the sphere centered at
  the atoms nucleus.

http//www.chm.davidson.edu/ronutt/che115/AO.htm

• P Orbitals (Shaped like two balloons tied
  together) There are 3 orbitals in a p subshell
  that are denoted as px, py, and pz orbitals.
  These are higher in energy than the corresponding
  s orbitals.

http//www.chm.davidson.edu/ronutt/che115/AO.htm
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Atomic Subshells (contd)

• D Orbitals The d subshell is divided into 5
  orbitals (dxy, dxz, dyz, dz2 and dx2-y2). These
  orbitals have a very complex shape and are higher
  in energy than the s and p orbitals.

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Molecular Orbital Theory

• The goal of molecular orbital theory is to
  describe molecules in a similar way to how we
  describe atoms, that is, in terms of orbitals,
  orbital diagrams, and electron configurations.

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Forming a Covalent Bond

• Molecules can form bonds by sharing electron
• Two shared electrons form a single bond
• Atoms can share one, two or three pairs of
  electrons
• forming single, double and triple bonds
• Other types of bonds are formed by charged atoms
  (ionic) and metal atoms (metallic).

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Atomic and Molecular Orbitals (contd)

• Orbital Mixing
• When atoms share electrons to form a bond, their
  atomic orbitals mix to form molecular bonds. In
  order for these orbitals to mix they must
• Have similar energy levels.
• Overlap well.
• Be close together.

This is and example of orbital mixing. The two
atoms share one electron each from there outer
shell. In this case both 1s orbitals overlap and
share their valence electrons.
http//library.thinkquest.org/27819/ch2_2.shtml
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Energy Diagram of Sigma Bond Formation by Orbital
Overlap
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sp3 Hybrid atomic orbitals
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sp2 Hybrid atomic orbitals
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sp Hybrid atomic orbitals
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Multiple bonds with VB
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Multiple bonds with VB
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Molecular Orbital Theory

• Each line in the diagram represents an orbital.
• The molecular orbital volume encompasses the
  whole molecule.
• The electrons fill the molecular orbitals of
  molecules like electrons fill atomic orbitals in
  atoms

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Molecular Orbital Theory

• Electrons go into the lowest energy orbital
  available to form lowest potential energy for the
  molecule.
• The maximum number of electrons in each molecular
  orbital is two. (Pauli exclusion principle)
• One electron goes into orbitals of equal energy,
  with parallel spin, before they begin to pair up.
  (Hund's Rule.)

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Diatomic Molecular Orbital Theory

• In the case of diatomic molecules, the
  interactions are easy to see and may be thought
  of as arising from the constructive interference
  of the electron waves (orbitals) on two different
  atoms, producing a bonding molecular orbital, and
  the destructive interference of the electron
  waves, producing an antibonding molecular orbital

• This Approach is called LCAO-MO
• (Linear Combination of Atomic Orbitals to Produce
  Molecular Orbitals)

A Little Math is need to understand
Only a Little I promise!
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Atomic and Molecular Orbitals

• In atoms, electrons occupy atomic orbitals, but
  in molecules they occupy similar molecular
  orbitals which surround the molecule.
• The two 1s atomic orbitals combine to form two
  molecular orbitals, one bonding (s) and one
  antibonding (s).

• This is an illustration of molecular orbital
  diagram of H2.

• Notice that one electron from each atom is being
  shared to form a covalent bond. This is an
  example of orbital mixing.

http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/m
ain.html
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The He dimer
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Examples of Sigma Bond Formation
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Molecular Orbital Diagram (H2)
http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/m
ain.html
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Molecular Orbitals from p A.O.s
NOTE Symmetry is important in forming M.O. from
A.O.s (LCAO)
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Molecular Orbitals from p A.O.s
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MO Diagram for O2
http//www.chem.uncc.edu/faculty/murphy/1251/slide
s/C19b/sld027.htm
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M.O.s from O2
s1s
s1s
s2s
s2s
p2p
s2p
p2p
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Electron configurations for diatoms
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Molecular Orbital Diagram (HF)
http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/m
ain.html
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Valence MOs
Energy Levels in HF
This diagram shows the allowed energy levels of
Isolated H (1s1) and F (1s22s22p5) atoms and,
between them, the HF molecule. Note 1. F 1s is
at much lower energy than H 1s (because of the
higher nuclear charge) 2. F 1s2 electrons are
core electrons. Their energy does not change
when HF is formed. 3. H 1s and F 2p valence
electrons go into molecular orbitals with new
energies.
2p
1s









2s


F
H
HF
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Molecular Orbitals in HF
This non-bonding molecular orbital (n) has an
almost spherical lobe showing only slight
delocalisation between the two nuclei. Non-bonding
orbitals look only slightly different to atomic
orbitals, and have almost the same energy.
2p
1s







n


2s
This core orbital is almost unchanged from the F
1s orbital. The electrons are bound tightly to
the F nucleus.
n


H F
F
H
HF
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Molecular Orbitals in HF
This (empty) LUMO is an antibonding orbital with
a node on the interatomic axis between H and F.
These two degenerate (filled) HOMOs are centred
on the F atom, like 2px and 2py orbitals.
s
2p
1s

n
n





s

n


Electrons in these two orbitals are not shared
(much) by the fluorine nucleus. They behave like
the 2p orbitals and are also non-bonding (n).
This MO, which is is like a 2pz orbital, is
lower in energy in the molecule (a bonding
orbital), and one lobe is delocalised around the
H atom.
n


F
H
HF
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Molecular Orbital Diagram (CH4)

• So far, we have only look at molecules with two
  atoms. MO diagrams can also be used for larger
  molecules.

http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/m
ain.html
31
Molecular Orbital Diagram (H2O)
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Molecular Orbital Theory
Diatomic molecules The bonding in F2
The second set of combinations with ? symmetry
(orthogonal to the first set)
This produces an MO over the molecule with a node
on the bond between the F atoms. This is thus a
bonding MO of ?u symmetry.

?
2pxA
2pxB
?u ? 0.5 (2pxA 2pxB)
This produces an MO around both F atoms that has
two nodes one on the bond axis and one
perpendicular to the bond. This is thus an
antibonding MO of ?g symmetry.
-
?
2pxA
2pxB
?g ? 0.5 (2pxA - 2pxB)
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Molecular Orbital Theory
MO diagram for F2
F
F
F2
3?u
1?g
2p
(px,py)
pz
2p
1?u
Energy
3?g
2?u
2s
2s
2?g
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Molecular Orbital Theory
MO diagram for F2
F
F
F2
Another key feature of such diagrams is that the
?-type MOs formed by the combinations of the px
and py orbitals make degenerate sets (i.e. they
are identical in energy). The highest occupied
molecular orbitals (HOMOs) are the 1?g pair -
these correspond to some of the lone pair
orbitals in the molecule and this is where F2
will react as an electron donor. The lowest
unoccupied molecular orbital (LUMO) is the 3?u
orbital - this is where F2 will react as an
electron acceptor.
3?u
LUMO
1?g
HOMO
2p
(px,py)
pz
2p
1?u
Energy
3?g
2?u
2s
2s
2?g
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Molecular Orbital Theory
MO diagram for B2
In the MO diagram for B2, there several
differences from that of F2. Most importantly,
the ordering of the orbitals is changed because
of mixing between the 2s and 2pz orbitals. From
Quantum mechanics the closer in energy a given
set of orbitals of the same symmetry, the larger
the amount of mixing that will happen between
them. This mixing changes the energies of the
MOs that are produced. The highest occupied
molecular orbitals (HOMOs) are the 1?u pair.
Because the pair of orbitals is degenerate and
there are only two electrons to fill, them, each
MO is filled by only one electron - remember
Hunds rule. Sometimes orbitals that are only
half-filled are called singly-occupied molecular
orbtials (SOMOs). Since there are two unpaired
electrons, B2 is a paramagnetic (triplet)
molecule.
B
B
B2
3?u
1?g
2p
(px,py)
pz
2p
3?g
LUMO
Energy
1?u
HOMO
2?u
2s
2s
2?g
36
Molecular Orbital Theory
Diatomic molecules MO diagrams for Li2 to F2
Remember that the separation between the ns
and np orbitals increases with increasing atomic
number. This means that as we go across the 2nd
row of the periodic table, the amount of mixing
decreases until there is no longer enough mixing
to affect the ordering this happens at O2. At
O2 the ordering of the 3?g and the 1?u MOs
changes. As we go to increasing atomic
number, the effective nuclear charge (and
electronegativity) of the atoms increases. This
is why the energies of the analogous orbitals
decrease from Li2 to F2. The trends in bond
lengths and energies can be understood from the
size of each atom, the bond order and by
examining the orbitals that are filled.
In this diagram, the labels are for the valence
shell only - they ignore the 1s shell. They
should really start at 2?g and 2?u.
Molecule Li2 Be2 B2 C2 N2 O2 F2 Ne2
Bond Order 1 0 1 2 3 2 1 0
Bond Length (Å) 2.67 n/a 1.59 1.24 1.01 1.21 1.42 n/a
Bond Energy (kJ/mol) 105 n/a 289 609 941 494 155 n/a
Diamagnetic (d)/ Paramagnetic (p) d n/a p d d p d n/a
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More complicated molecules
38
Modern MO calculations
W. Kohn (1923-)
J. A. Pople (1925-2004)
Nobel prize in Chemistry 1998
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Conclusions

• Bonding electrons are localized between atoms (or
  are lone pairs).
• Atomic orbitals overlap to form bonds.
• Two electrons of opposite spin can occupy the
  overlapping orbitals.
• Bonding increases the probability of finding
  electrons in between atoms.
• It is also possible for atoms to form ionic and
  metallic bonds.

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References

• http//www.chemguide.co.uk/atoms/properties/atomor
  bs.html
• http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/m
  ain.html
• http//en.wikipedia.org/wiki/Molecular_orbital_the
  ory
• http//library.thinkquest.org/27819/ch2_2.shtml