Download Molecular Orbital Theory

Molecular Orbital Theory
16 February, 2016
Dr. Emőke Bódis
The Wave Mechanical Model of the Atom
Some small history
1859: Black body radiation (a problem by Kirchoff)
1877: Boltzmann suggested that the energy states of a physical system can be discrete
1887: Problem of photoelectric effect
1900: Quanrum hypothesis by Max Planck: Planck's hypothesis that energy is radiated and
absorbed in discrete "quanta" (or energy elements) precisely matched the observed
patterns of black-body radiation.
E = hf
1905: Einstein offered a quantum-based theory to explain the photoelectric effect
Rutherford Atomic Model (Sir E. Rutherford, 1911):
Gold foil experiment: he shot a thin film of gold atoms high velocity alpha
particles (helium nuclei). As expected, most alpha particles went right
through the gold foil but to his amazement a few alpha particles
rebounded almost directly backwards.
He developed the planetary model of the atom.
Bohr Atomic Model (Nils Bohr, 1913):
1. An atom has a number of stable orbits in which an electron
can reside without the emission of radiant energy.
2. An electron may jump spontaneously from one orbit to the
other orbit, ∆E = E2-E1 = hv
3. The motion of an electron in a circular orbit is restricted in
such a manner that its angular momentum is an integral
multiple of h/2π, Thus mvr = nh/2π.
The Wave Mechanical Model of the Atom
Planck
Boltzmann
Heisenberg
Einstein
Schrödinger
de Broglie
The Wave Mechanical Model of the Atom
Heisenberg's Uncertainty Principle
One of the biggest problems with quantum experiments is the seemingly unavoidable
tendency of humans to influence the situation.
To know the velocity of a particle we must measure it, and to measure it, we are forced to
affect it. The same goes for observing an object's position.
The Wave Mechanical Model of the Atom
Wave-Particle Duality
The Wave Mechanical Model of the Atom
Matter Waves
In 1924 a French graduate student, Louis de Broglie (was impressed with Einstein's 1905
discovery and the dual nature of light) he suggested in his graduate thesis that since
nature is often symmetric, matter which is mostly particle should also have wave
properties. These waves were not electromagnetic but a new kind of wave, matter
waves.
In 1927, the American physicists Clinton J. Davisson and Lester H. Germer verified de
Broglie's hypothesis experimentally. They were able to diffract a beam of electrons in a
crystal of nickel and only waves can be diffracted. Therefore, if an electron that is particle
can be diffracted, it must have wave properties. De Broglie was right matter has wave
properties.
The Wave Mechanical Model of the Atom
Standing Waves
In 1926 Erwin Schrödinger proposed the electron was
a 3-D waveform waveform circling the nucleus in a
whole number of wavelengths allowing the waveform
to repeat itself as a stable standing wave representing
the energy levels of the Bohr model.
• a whole number of waves
• does not transfer energy
• it can absorb energy from a nearby source which is oscillating at a proper frequency
• the energy needed to change from one standing wave to another must be quantized
in order to maintain a whole number of wavelengths and avoid collapsing
The Wave Mechanical Model of the Atom
Newtonian world: Everything appears to have a definite position, a definite momentum, a
definite energy, and a definite time of occurrence.
Quantum world: The state of a system at a given time is described by a complex wave
function (also referred to as state vector in a complex vector space)
Quantum mechanics does not assign definite values, instead an abstract mathematical
object allows for the calculation of probabilities of outcomes)
Probability clouds
The Schrödinger equation describes how wave functions change in time, playing a role
similar to Newton’s II. law.
(The Schrödinger equation predicts that the center of a wave packet will move through space at a constant velocity (like a classical
particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position
becomes more uncertain with time. )
„Itt láthatják a táblán a nevezetes Schrödinger-féle hullámegyenletet. Ezt az
egyenletet Önök persze nem értik. Én sem értem. Schrödinger úr sem értette, de ez
ne zavarja Önöket. Én ezt majd minden óra elején felírom a táblára, és
elmagyarázom, mire lehet használni. Önök pedig majd lassan hozzászoknak.”
Marx György, egyetemi tanár egyik előadásának kezdete
Firefly Experiment
• Suppose a male firefly is in a dark room with an open vial of female sex-attractant
hormones. If we set up a camera to take pictures every time the firefly flashes and records
the firefly’s location in the room we will find that most of it’s time is around the female,
however, sometimes he flies farther away and around the room.
• If we plot the firefly’s location we would see a picture like the one here
• The area most often occupied is darkest in the picture and is the center where the
hormones are found.
• Now suppose you see the firefly flash in the
center of the room, where will you see it flash
next? Is there any way to know? Is the path of the
firefly predictable?
• NO, we cannot predict the location, but we can
find the probability of its location. Thus the picture
on the right is a sort of probability map.
Atomic orbital
An atomic orbital is a mathematical function (wave function) that describes the wave-like
behavior of e.g. an electron in an atom. This wave function can be used to calculate the
probability of finding any electron of an atom in any specific region around the atom's
nucleus.
Orbitals and orbits
When a planet moves around the sun, its definite path, called
an orbit, can be plotted. A drastically simplified view of the
atom looks similar, in which the electrons orbit around the
nucleus. The truth is different; electrons, in fact, inhabit
regions of space known as orbitals. Orbits and orbitals sound
similar, but they have quite different meanings. It is essential
to understand the difference between them.
Molecular Orbital Theory
LCAO: Lineare Combination of Atomic Orbitals
( F. Hund, R. Mulliken, E. Hückel, 1927-29)
• Atomic and Molecular Orbitals are wave functions.
• Molecular orbitals are the lineare combination of atomic orbitals
• Atomic orbitals approach each other and form new orbitals, the molecular orbitals.
Remember
The Valence Bond Theory
- that considers the overlapping of orbitals to create bonds.
- is only limited in its use because it does not explain the molecular geometry of molecules
very well.
The atomic orbitals
Interaction of the waves (Interference)
Additive
Remember:
Subtractive
How do the wave functions behave during the interaction?
in Atom: s,p, d, f  in Moleculs: σ, π, δ, φ
Example: H2
s
s
σ (1sσ)

constructive Interference, bonding effect
s
σ★
s

destructive Interference,
antibonding effect
„node” where there is
zero chanche of
finding electrons
The wave function
in Atom: s,p, d, f  in Molecule: σ, π, δ, φ
Example: H2
s
s
σ (1sσ)

constructive Interference, bonding effect
s
σ★
s

destructive Interference,
antibonding effect
Node
ΣAO = ΣMO
Energy of Hydrogen
σ★ (1sσ★)
E
1s
1s
A
B
σ (1sσ)
Energy of Hydrogen
Energy taker
σ★ (1sσ★)
E
1s
1s
A
B
σ (1sσ)
Energy giver:
stabiler, bevorzugter
Zustand
Energy of Hydrogen
Energy taker
σ★ (1sσ★)
E
Jump between bondings: energy is
needed, eg light
Energie
1s
1s
A
B
σ (1sσ)
Energy giver:
stabiler, bevorzugte Zustand
Energy of Hydrogen
antibonding MO
σ★
E
1s
1s
A
B
σ
bonding MO
Bond Order
Bond order is the number of chemical bonds between a pair of atoms and indicates the
stability of a bond:
1: Single bond
2: double bond
3: triple bond
Example 1: H2
BO = (2-0) / 2 = 1
σ★
E
Singel bond
1s
A
B
1s
H-H
σ
Bindungselektronpaare
Example 2: He2
σ★
E
1s
A
B
1s
σ
BO = (2-2) / 2 = 0
Unknown molecule
Example 2: N2
N2
E
BO = (10 – 4) / 2 = 3
Dreifachebindung
Example 2: N2
N2
BO = (10 – 4) / 2 = 3
Tripple bond
verantwortlich
für Bindung
HOMO (Highest Occupied Molecular Orbital,)
LUMO (Lowest Unoccupied Molecular Orbital)
Formaldehyd
As the electronegativity differences
increases
the interacting orbitals will be at
different energies.
The „Aufbau” Principle: the order of filling orbitals
(Aufbau is a German word meaning building up or construction.)
Notice that the s orbital always has a slightly lower energy
than the p orbitals at the same energy level, so the s orbital
always fills with electrons before the corresponding p orbitals
do. The oddity is the position of the 3d orbitals. They are at a
slightly higher level than the 4s, so the 4s orbital fills first,
followed by all the 3d orbitals and then the 4p orbitals.
Types of bonding
1s
2s
3 x 2p
σ+σ★
σ+σ★
π + π★

Atoms from the 2. Periode
Rotational symmetry
- σ- Symmetry
- σ- MO
- σ - Bond

p Orbitals
- the electron density is not distributed in a spherically symmetric fashion as in
an sorbital
- electron density is concentrated on two sides of the nucleus, separated by a
node at the nucleus
- this orbital has two lobes
- there are three 2p orbitals: px, py,and pz orbitals
3*2p
1. Overlap of p-AO’s : 2*px
same phase
opposite phase
Node
3*2p
1. Overlap of p-AO’s : 2*px
σ-rotational symmetry
σ – Bond
σ(2pσ)
σ★(2pσ★)
3*2p
2. Parallel p-AO’s: 2*py
Same Phase
Opposite Phase
3*2p
2. Parallel ausgerichtete p-AO’s
π
NO rotational symmerty
π★
- π- Symmetrie
- π- MO
- π - Bindung
2 x 2s  σ + σ★
2 x 2px  σ + σ★
2 x 2py  π + π★
2 x 2pz  π + π★
Thank you!