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Molecular Orbital Theory
1. MO theory suggests that atomic orbitals of different
atoms combine to create MOLECULAR ORBITALS
2. Electrons in these MOLECULAR ORBITALS belong to the
molecule as whole
3. This contrasts to VB theory which suggests that electrons are
shared by simple overlap atomic orbitals or hybridized atomic
orbitals
Molecular orbital can be constructed from linear combination of
atomic orbitals
MO = LCAO
In terms of approximate solutions to the Scrödinger equation
Molecular Orbitals are linear combinations of atomic orbitals (LCAO)
Y = caya + cbyb (for diatomic molecules)
As the distance between atoms decreases
Atomic orbitals overlap
Bonding takes place if:
the orbital symmetry must be such that regions of the same sign overlap
the energy of the orbitals must be similar
the interatomic distance must be short enough but not too short
Bonding and Antibonding Orbitals
When two atomic orbitals are added together
1. A set of lower energy BONDING orbitals are created
Bonding orbitals have most of the electron (negative) density
between the 2 positive nuclei
2. A set of higher energy ANTI-BONDING orbitals are created
Antibonding orbitals have most of the electron density on the
opposite side from the region where the bond must be formed
Nonbonding Orbital: the energy of which is essentially that of an
atomic orbital
No interaction –
different symmetry
magnetism
The orbital motion of electrons creates tiny atomic current loops,
which produce magnetic fields. When an external magnetic field
is applied to a material, these current loops will tend to align in
such a way as to oppose the applied field: induced magnetic fields
tend to oppose the change which created them. Materials in which
this effect is the only magnetic response are called diamagnetic.
All materials are inherently diamagnetic, but if the atoms have
some net magnetic moment as in paramagnetic materials, or if
there is long-range ordering of atomic magnetic moments as in
ferromagnetic materials, these stronger effects are always
dominant. Diamagnetism is the residual magnetic behavior when
materials are neither paramagnetic nor ferromagnetic.
Chapter 5 p126
Covalent radius N > O> F, bond distance N2 < O2< F2,
because of the increasing population of antibonding
electrons
Chapter 5 p129
The covalent radius of the atoms decrease as the number of
valence electrons increase because the increasing nuclear
charge pulls the electrons closer to the nucleus
Chapter 5 p130
Photoelectron Spectroscopy
Photoelectron spectroscopy utilizes photo-ionization and energy-dispersive analysis of the
emitted photoelectrons to study the composition and electronic state of the surface region of a
sample. Traditionally, when the technique has been used for surface studies it has been
subdivided according to the source of exciting radiation into :
X-ray Photoelectron
Spectroscopy
(XPS)
- using soft (200-2000 eV) x-ray
excitation to examine core-levels.
Ultraviolet Photoelectron
Spectroscopy
(UPS)
- using vacuum UV (10-45 eV)
radiation from discharge lamps to
examine valence levels.
In this technique, UV light or X-rays dislodge electrons from
molecules:
O2 + hv (photons)  O2+ + eThe kinetic energy of the expelled electrons can be measured:
the difference between the energy of the incident photons and
this kinetic energy equal the ionization energy (bonding energy)
of the electrons:
Ionization energy = hv photons – kinetic energy of the expelled
electrons
UV removes outer electrons, usually from gases; X-rays are
more energetic and remove inner electrons as well, from any
physical state
O2
N2
sg (2p)
pu (2p)
s*u (2s)
p*u (2p)
sg (2p)
s*u (2s)
pu (2p)
Very involved in bonding
(vibrational fine structure)
(Energy required to remove electron, lower energy for higher orbitals)
Note subscripts g and u
symmetric/antisymmetric upon i
Place labels g or u in this diagram
s*u
p*g
pu
sg
A correlation diagram shows
the calculated effect of
moving two atoms together,
from a large interatomic
distance on the right, with no
interatomic interaction, to
zero interatomic distance on
the right, where the two
nuclei become, in effect, a
single nucleus. The simplest
example has two H atoms on
the right and a He atom on
the left.
Symmetry is used to connect the molecular orbitals with the
atomic orbital of the united atom.
1su*  2pz on the left
1pu  2px or 2py
1pg*  3d (dxz or dyz)
Another consequence of this phenomenon is called the
noncrossing rule, which states that orbitals of the same
symmetry interact so that their energy never cross
Heteronuclear diatomic molecules
Heteronuclear diatomic
molecules follow the same
general bonding pattern as the
homonuclear molecules, but a
greater nuclear charge on one
of the atoms lowers its atomic
energy levels and shifts the
resulting MO levels.
The potential energies are
negative because they
represent attraction between
the valences and the nuclei
Chapter 5 p134
The atomic orbitals of
homonuclear diatomic
molecules have identical
energies and both atoms
contributes equally to a given
MO. Therefore, in the equation
for the MO, the coefficients for
the two atomic orbitals are
identical. In heteronuclear
diatomic molecules, the
coefficients are different. The
atomic orbital closer in energy
to an MO contributes more to
the MO and its coefficient is
larger in the wave functions.
Using C2V point group,
the s and pz orbital have
A1 symmetry, and form
MO with σsymmetry,
while px and py orbitals
have B1 and B2
symmetry and for p MO.
M-C-O: The HOMO of
CO is 3σ, with a higher
electron density and a
larger lobe on carbon.
The LUMo are the 2 p*
and concentrated on
carbon
LiF
Ionic compounds can be considered the
limiting form of polarity in heteronuclear
molecules.
Molecular Orbitals for Larger molecules:
1.
Determine the point group for the molecule. Substitute D2h for Dh and
C2v for Cv
2.
Assign x, y and z coordinate to the atoms. Highest order rotation axis of
the molecule is chosen as the z axis of the central atom
3.
Find the characters of the representation for the combination of 2s and 2p
orbitals: change position 0, same position and same sign 1, same position
but reversed sign -1.
4.
Reduce the representation from step 3 to irreducible representations. This
is equivalent to finding the symmetry of the group orbitals or the
symmetry-adapted linear combinations (SALCs)
5.
Find the atomic orbitals of the central atom with the same symmetries
6. Combine the atomic orbitals of the central atom and those of the group
orbitals with the same symmetry and similar energy to form molecular
orbitals.
Group orbitals
for F----F of
F-H-F-
Atomic orbitals and group
orbitals of the same
symmetry can combine to
form molecular orbitals, just
as atomic orbitals of the
same symmetry can
combine to form group
orbitals.
The energy match of the 1s
orbital of H atom (-13.16ev)
is much better with the 2pz
of F (-18.7ev) than with 2s
of F (-40.2 ev)
Chapter 5 p148
Chapter 5 p148
Symmetry-adapted linear combinations
--- SALCs
Projection operator
--- The fundamental, universally applicable tool for constructing SALCs
Chapter 5 p149
Chapter 5 p149
NH3
Chapter 5 p152
Chapter 5 p152
Chapter 5 p152
Chapter 5 p154
Chapter 5 p159
Chapter 5 p159
Group theory approach
Sp3 or sd3
Chapter 5 p161