Transcript Molecular Orbital Theory

Molecular Orbital Theory
Atomic Orbital's
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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.
Atomic Subshells
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These are some examples of atomic orbitals:
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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 atom’s nucleus.
http://www.chm.davidson.edu/ronutt/che115/AO.htm
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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
Atomic Subshells (cont’d)
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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.
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.
Forming a Covalent Bond
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Molecules can form bonds by sharing electron
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Atoms can share one, two or three pairs of
electrons
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Two shared electrons form a single bond
forming single, double and triple bonds
Other types of bonds are formed by charged
atoms (ionic) and metal atoms (metallic).
Atomic and Molecular Orbitals (cont’d)
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Orbital Mixing
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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:
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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
Energy Diagram of Sigma Bond
Formation by Orbital Overlap
3
sp
Hybrid atomic orbitals
2
sp
Hybrid atomic orbitals
sp Hybrid atomic orbitals
Multiple bonds with VB
Multiple bonds with VB
Molecular Orbital Theory
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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
Molecular Orbital Theory
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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.)
Diatomic Molecular Orbital Theory
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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!
Atomic and Molecular Orbitals
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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/main.html
The He “dimer”
Examples of Sigma Bond Formation
Molecular Orbital Diagram (H2)
http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html
Molecular Orbitals from p A.O.s
NOTE: Symmetry is important in forming M.O. from A.O.s (LCAO)
Molecular Orbitals from p A.O.s
MO Diagram for O2
http://www.chem.uncc.edu/faculty/murphy/1251/slides/C19b/sld027.htm
M.O.s from O2
s*1s
s1s
s2p
s2s
p2p
s*2s
p*2p
Molecular Orbital Diagram (HF)
http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html
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.
2p
1s
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Valence MOs
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.
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3. H 1s and F 2p valence electrons go
into molecular orbitals with new
energies.
H
HF
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F
2s
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.
This core orbital is
almost unchanged
from the F 1s orbital.
The electrons are
bound tightly to the F
nucleus.
2p
1s
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n
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H
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F
H
HF
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n
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F
2s
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) HOMO’s are
centred on the F atom, like 2px and 2py orbitals.
s*
1s
n
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n
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s
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n
2p
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Electrons in these two orbitals are not
shared (much) by the fluorine nucleus. They
behave like the 2p orbitals and are also nonbonding (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.
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H
HF
n
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F
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/main.html
Molecular Orbital Diagram (H2O)
Molecular Orbital Theory
Diatomic molecules: The bonding in F2
The second set of combinations with p symmetry (orthogonal to the first set):
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+
2pxA
2pxB
This produces an MO over
the molecule with a node on
the bond between the F
atoms. This is thus a
bonding MO of pu symmetry.
pu =  0.5 (2pxA + 2pxB)
2pxA

-
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 pg
pg* =  0.5 (2pxA - 2pxBsymmetry.
)
2pxB
Molecular Orbital Theory
MO diagram for F2
F
You will typically see the
diagrams drawn in this way. The
diagram is only showing the
MO’s derived from the valence
electrons because the pair of
MO’s from the 1s orbitals are
much lower in energy and can
be ignored.
F
F2
3su*
1pg*
2p
Energy
2p
1pu
2su*
2s
2sg
Although the atomic 2p orbitals
are drawn like this:
they are actually all the same
energy and could be drawn like
this:
at least for two non-interacting F
atoms.
3sg
2s
(px,py)
pz
Notice that there is no mixing of
AO’s of the same symmetry
from a single F atom because
there is a sufficient difference in
energy between the 2s and 2p
orbitals in F.
Molecular Orbital Theory
MO diagram for F2
F
LUMO
F
F2
Another key feature of such
diagrams is that the p-type MO’s
formed by the combinations of
the px and py orbitals make
degenerate sets (i.e. they are
identical in energy).
3su*
1pg*
HOMO
2p
Energy
2p
1pu
3sg
2su*
2s
2s
2sg
(px,py)
pz
The highest occupied molecular
orbitals (HOMOs) are the 1pg*
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
3su* orbital - this is where F2 will
react as an electron acceptor.
Molecular Orbital Theory
MO diagram for B2
B
B
B2
3su*
1pg*
Energy
2p
2p
LUMO
3sg
1pu
HOMO
2su*
2s
2s
2sg
(px,py)
pz
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 MO’s that are
produced.
The highest occupied molecular
orbitals (HOMOs) are the 1pu
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 Hund’s rule.
Sometimes orbitals that are only
Molecular Orbital Theory
Diatomic molecules: MO diagrams for Li2 to F2
In this diagram,
the labels are
for the valence
shell only - they
ignore the 1s
shell. They
should really
start at 2sg and
2su*.
2s-2pz mixing
Molecule
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 3sg and
the 1pu MO’s 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
ofLi2each
Beatom,
B2 the
C2bond
N2 order
O2 and
F2 by Ne
2
examining
the orbitals that are filled. 2
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
Modern MO calculations
W. Kohn
(1923-)
J. A. Pople
(1925-2004)
Nobel prize in Chemistry
1998
Conclusions
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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.
References
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http://www.chemguide.co.uk/atoms/properties/atomorbs.html
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http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html
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http://en.wikipedia.org/wiki/Molecular_orbital_theory
http://library.thinkquest.org/27819/ch2_2.shtml
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