8-2.5%20Molecular%20Orbital%20Theory

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8-2.5 Molecular Orbital Theory

• Molecular orbital theory describes
• covalent bonds in terms of molecular
• orbitals, which result from interaction
• of the atomic orbitals of the bonding
• atoms and are associated with the
• entire molecule.

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?. The key ideas of MO Theory
1. Every electron of molecules may spread over
the entire molecule. Just as atoms have
atomic orbitals (AOs) of a given energy and
shape that are occupied by the atom's
electrons, molecules have molecular
orbitals (MOs) of a given energy and shape
that are occupied by the molecule's
electrons.
Note that molecular orbitals are labeled by
the Greek letter s, p, d, etc., corresponding to
the Roman letters s, p, d, etc. for atomic
orbitals.
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2. Formation of molecular orbitals
In order to obtain wave function for the
molecular orbitals, we assume that these are
linear combinations of atomic orbitals .
The number of molecular orbitals that are formed
must equal the number of atomic orbitals used to
make them. The molecular orbitals are formed
by the addition and subtraction of the two
atomic wave functions.
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(1) Adding the wave functions together.
This combination forms a bonding MO, which has a
region of high electron density between the
nuclei.
(2) Subtracting the wave functions from each
other.
This combination forms an antibonding MO, which
has a node between the nuclei, a region of lower
electron density
The bonding MO is lower in energy and the
antibonding MO higher in energy than the AOs that
combined to form them. The bonding MO is denoted
by s (p), and antibonding MO is denoted with a
superscript star, s (p) .
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Bonding and Antibonding Molecular Orbitals
Bonding molecular orbital
atomic orbital

• A bonding molecular orbital is of lower
• energy and greater stability than the atomic
• orbitals from which it was formed.

Antibonding molecular orbital

• An antibonding molecular orbital is of
• higher energy and lower stability than the
• atomic orbitals from which it was formed.

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3. To interact effectively and form MOs,
three principles are accepted
(1) atomic orbitals bear the same symmetry
with respect to the molecular axis. (2)
appropriate wave functions for two atoms
can be combined only if they represent
similar energy states. (3) extensive overlap of
appropriate atomic orbitals can occur.
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4. Filling Molecular Orbitals with Electrons
Electrons fill MOs just as they fill AOs
(1) Orbitals are filled in order of increasing
energy (aufbau principle) (2)
An orbital has a maximum capacity of two
electrons with opposite spins
(exclusion principle) (3) Orbitals of equal
energy are half filled, with spins
parallel, before any is filled
(Hund's rule)
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Stability of molecule and Rules of
Molecular Electron Configuration

• In a stable molecule, the number of electrons in
  bonding molecular orbitals is always greater than
  that in antibonding molecular orbitals.

• The number of electrons in the molecular orbitals
  is equal to the sum of all the electrons on the
  bonding atoms.

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When electrons are added to molecular orbitals
having the same energy, the most stable
arrangement is that predicted by Hund's rule,
that is, electrons enter these molecular orbitals
with parallel spins.

• Like an atomic orbital, each molecular orbital
  can accommodate up to two electrons, with
  opposite spins in accordance with the Pauli
  exclusion principle.

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5. Bond Order
The bond order is the number of electrons in
bonding MOs minus the number in antibonding
MOs, divided by two Bond order 1/2 (no. of
e- in bonding MO)-
(no. of e- in antibonding MO)
A bond order greater than zero indicates that
the molecular species is stable relative to the
separate atoms, whereas a bond order of zero
implies no net stability, and, thus, no
likelihood of forming. In general, the higher the
bond order, the stronger the bond.
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?. MO energy order

• Homonuclear Diatomic Molecules

There are two different energy orderings for
diatomic molecules formed from second-period
elements
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• B2 , N2 (Z7)

• O2 , F2 (Z8)

• The distinction between the two is with the
• p2p and s2p orbitals, which are quite close
• in energy and reverse their order once oxygen
  
• is reached.

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Energy levels diagram of MO orbits for N2,O2 and
F2 .
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the electron configuration
H2 (s1s)2
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He2(s1s)2 (s1s)2
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Li2 (s1s)2 (s1s)2 (s2s)2
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Be2(s1s)2 (s1s)2 (s2s)2 (s2s)2
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B2(s1s)2(s1s)2(s2s)2(s2s)2(p2py)1(p2pz)1
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N2KK(s2s)2 (s2s)2 (p2py)2(p2pz)2(s2px)2
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KK(s2s)2 (s2s)2(s2px)2(p2py)2(p2pz)2(p2py)1(p2p
z)1
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bond order
½
1
0
½
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Heteronuclear Diatomic Molecules

• Molecular orbitals can be constructed
• from their atomic orbitals, just as in the
• homonuclear case.
• ZZ14, MO ordering is the same as N2
• ZZ gt14, MO ordering is the same as O2

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KK(s2s)2(s2s)2(s2px)2(p2py)2(p2pz)2(p2py)1
NO
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(s2s)2 (s2s)2 (p2py)2(p2pz)2 (s2px)2
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-13.6eV
-18.6eV
Nonbonding orbitals
- 40.12eV