What is the difference between
thermochemistry and photochemistry?
• Mode of activation
• Activated by collisions (thermo)
• Activated by light (photo)
• Selectivity in activation
• Entire molecule gets activated
• Only the chromophore that absorbs the light gets activated
• Energy distribution
• Energy used for vibrational/rotational transition
• Energy used for electronic transition mainly
• Transition state connects a single reactant to a single product (intermediate)
and it is a saddle point along the reaction course.
• Collisions are a reservoir of continuous energy (~ 0.6 kcal/mol per impact).
• Collisions can add or remove energy from a system.
• Concerned with a single surface.
Visualization of Thermal Reactions
We need to deal with two surfaces (ground and excited state.
Adiabatic Diabatic
Visualization of Photochemical Reactions
The Basic Laws of Photochemistry
The First Law of Photochemistry: light
must be absorbed for photochemistry
to occur.
Grotthuss-Draper law
Grotthus Drapper
The Second Law of Photochemistry:
for each photon of light absorbed by
a chemical system, only one molecule
is activated for a photochemical
reaction.
Stark-Einstein law
Stark Einstein
Probability of light absorption is related to the energy gap
and wavelength of light
Third law of photochemistry
DE (kcal mol-1) = [2.86 x 104 kcal mol-1 nm]/l nm
S0
S1
S0
S1
S0
S1
ΔE
ΔE
ΔE
X-RAY ULTRAVIOLET INFRARED MICRO-
WAVE
RADIO waves
X-ray
UV/Visible
Infrared
Microwave
Radio Frequency
Ionization
Electronic
Vibrational
Rotational
Nuclear and Electronic Spin
REGION ENERGY TRANSITIONS
(NMR)
The Range of Electromagnetic Radiation (Light)
400 nm 700 nm500 nm
71.5 kcal/mol 57.2 kcal/mol 40.8 kcal/mol
Ultraviolet Region
Chemical Bonds of
DNA and Proteins
Damaged
Infrared Region
Chemical Bonds Energy
too low to make or break
chemical bonds.
X-Rays
0.1 nm
300,000 kcal/mol
Microwaves
1,000,000 nm
0.03 kcal/mol
Huge energies
per photon.
Tiny energies
per photon.
Themal energies
at room temperature
ca 1 kcal/mole
Light and Energy Scales
E (kcal mol-1) = [2.86 x 104 kcal mol-1 nm]/l nm
E (kcal mol-1 nm) = 2.86 x104/700 nm = 40.8 kcal mol-1
E (kcal mol-1 nm) = 2.86 x 104/200 nm = 143 kcal mol-1
Light is emitted when an electron jumps from a higher orbit to a
lower orbit and is absorbed when it jumps from a lower to higher
orbit.
The energy and frequency of light emitted or absorbed is given
by the difference between the two orbit energies,
e.g., E(photon) = E2 - E1 (Energy difference)
Niels Bohr
Nobel Prize 1922
The basis of all
photochemistry
and spectroscopy!
Orbitals, Absorption, Emission
Electronic transitions are quantized
Atomic orbitals replace oscillators
Bohr Model of H Atoms
• Principal quantum number (n) - describes the SIZE of the
orbital or ENERGY LEVEL of the atom.
• Angular quantum number (l) or sublevels - describes the
SHAPE of the orbital.
• Magnetic quantum number (m) - describes an orbital's
ORIENTATION in space.
• Spin quantum number (s) - describes the SPIN or direction
(clockwise or counter-clockwise) in which an electron spins.
The Four Quantum Numbers Define
an Electron in an Atom
Energy level
Size of the orbital
The energy levels corresponding to n =
1, 2, 3, … are called shells and each can
hold 2n2 electrons.
The shells are labeled K, L, M, … for n
= 1, 2, 3, ….
1. Principal Quantum Number ( n )
Energy sublevel
Shape of the orbital
s
p
d
• determines the shape of the orbital
• they are numbered but are also given
letters referring to the orbital type
• l=0 refers to the s-orbitals
• l=1 refers to the p-orbitals
• l=2 refers to the d-orbitals
• l=3 refers to the f-orbitals
2. Angular Momentum Quantum # ( l )
Orientation of orbital
Specifies the number and shape of orbitals within each
sublevel
3. Magnetic Quantum Number (ml )
Electron spin Þ +½ or -½
An orbital can hold 2 electrons that spin in
opposite directions.
4. Spin Quantum Number ( ms )
• Quantum mechanics requires mathematics for a
quantitative treatment
• Much of the mathematics of quantum mechanics can be
visualized in terms of pictures that capture the qualitative
aspects of the phenomena under consideration
• Visualizations are incomplete, but it is important to note
“correct” mathematical representations fail for complex
systems as molecules
Visualization of Spin Chemistry
h
z axis
+1/2 h
3
2
55o
α
Sz
Spin angular momentum
If the electron spin were a classical quantity, the magnitude and
direction of the vector representing the spin could assume any length
and any orientation.
• Electron possesses a fixed and
characteristic spin angular momentum
of ½ 
 : Planck’s constant/2p
ℏ = h/2π = 1.0545717×10−34 J·s eV·s
This value ½ is independent of whether it is free or associated
with a nucleus, regardless the orbital that it occupies, e.g., s, p, d,
np*, pp*; always the same.

Angular momenta and vectors
• Angular momenta are vector quantities since
they are determined by their magnitude and
direction.
• A vector quantity is graphically represented by
an arrow.
• For angular momenta:
- the magnitude of the momentum is
represented by the length of the arrow
- The direction of the momentum is
represented by the direction of the arrow
(tip)
- A vector can always be thought as the sum
of three vectors oriented along each of the
three cartesian axes x, y and z.
q
• S, the spin quantum number,
related to the length of the spin
vector for an electron can assume
only value ½
• Ms (spin multiplicity) related to
the orientation of the spin vector
Quantum rules of electron spin angular
momentum
Spin multiplicity= 2S+1
1
2
3
singlet
doublet
triplet
examples
S=0
S=1/2
S=1
q=55o for Ms= 1/2
Sz
a
|S|=(31/2)/2
In particular for
S=1/2 ®|S|=(31/2)/2
q
Spin multiplicity= 2S+1 = 2s=1/2
Sz
b
|S|=(31/2)/2
q=125o for Ms=-1/2
q
Two spins of ½: S = 1
Spin multiplicity= 2S+1 = 3
a
b
MS=0
αβ−βα
a
a
b
b a
b
MS=1 MS=-1 MS=0
Ms1
Ms1
Ms1
Ms2
Ms2
Ms2
αα ββ αβ+βα
Two spins of ½: S = 0
Spin multiplicity = 2S+1 = 1
2D Vector representations for two interacting electrons
Examples of Common Organic Chromophores
Carbonyls
Olefins
Enones
Aromatics
Viewing electrons in atoms and molecules
Atoms: Electrons are present in atomic orbitals (Bohr)
Molecules: Electrons are present in molecular orbitals (Mulliken)
H
C
H
O
(no)2
Inner orbitals
Bonding orbitals
Frontier orbitals
π
n
π*
Ground state
n,π* π,π*
standard abbreviations
Types of transitions in formaldehyde
H
C
H
O
Orbital diagram
Excited states
Common Chromophores
Carbonyl Compounds
p
p*
n
p p*
170 nm
e = 100
allowed
n p*
290 nm
e = 10
forbidden E
O
H
H
p
p*
p p* p p**
Common Chromophores: Olefins
Ethylene
H
HH
H
p p* p p** p p*
Common Chromophores: Olefins
1,3-Butadiene
H
H
H
H
H
H
Light absorption and electron movement
State diagram
Electronic and Spin Configuration of States
Ground state
reactants
Excited state
reactants
Reaction
Intermediates
Ground state
products
T
1
S
1
S
0
T
1
S
1
S
0
small big
n,π* π,π*
S1-T1 energy gap
Singlet-Triplet separation in molecules and
diradical intermediates and Intersystem crossing
Role of exchange integral (J)
ΔEST = ES - ET = E0(n,π*) + K(n,π*) + J(n,π*) – [E0(n,π*) + K(n,π*) - J(n,π*)]
ΔEST = ES – ET = 2J(n,π*)
What controls the singlet-triplet energy gap?
Why triplets are lower in energy than singlets?
ES = E0(n,π*)
ET = E0(n,π*)
ES = E0(n,π*) + K(n,π*)
ET = E0(n,π*) + K(n,π*)
J(n,π*) ~ e2/r12< n(1)π*(2)|n(2)π*(1)
overlap integral controls the gap
ES = E0(n,π*) + K(n,π*) + J(n,π*)
ET = E0(n,π*) + K(n,π*) - J(n,π*)
n
p*
S1
Energies of singlet and triplet states
T1
4-fold degeneracy
2J
S1
T1
4-fold degeneracy
2J
S1
Splitting for
n,p* states
Splitting for
p,p* states
S1-T1 energy gap: Examples
Excitation energy, bond energy and radiation wavelength
Time scales
Nobels in Photochemistry
Development of Flash Photolysis and
Femtosecond Chemistry
Zewail
The Nobel Prize in Chemistry 1999
Norrish Porter
The Nobel Prize in Chemistry 1967
Perrin-Jablonski Diagram
J. Perrin 1870-1942
Nobel Prize, 1926
F. Perrin
(1901-1992)
A. Jablonski
(1898-1980)
Molecule, a collection of atoms is
defined by Y
HY = EY
Operator Eigenvalue
Schrödinger equation
Nobel Prize in Physics (1933)
What is Y ?
Y defines a molecule in terms of nuclei and
electrons
Y is made of three parts
Y = Yo c S
Electronic Nuclear Spin
The three parts are interconnected. So, it is hard to
define a molecule precisely in terms of Y
• Electronic motion faster than nuclear motion
(vibration).
• Weak magnetic-electronic interactions separate spin
motion from electronic and nuclear motion.
Born – Oppenheimer Approximation
Y = Yo c S
Electronic Nuclear Spin
J. R. Oppenheimer
1904-1967
Director, Manhattan Project
Time scale matter
Max Born
(1882-1970)
Nobel Prize, 1954
• Electronic motion and nuclear motion can be
separated (Born-Oppenheimer approximation)
• To understand molecules, first focus on the location
and energies of electrons
• Understand: Yo(electronic) independent of c and S
Born – Oppenheimer Approximation
A Model for Vibrational Wavefunctions
The Classical Harmonic Oscillator
Quantized
Harmonic OscillatorEn = PE + KE
PEv = hn(v + 1/2)
A Model for Vibrational Wavefunctions
The Classical Harmonic Oscillator
The Anharmonic Quantum Mechanical Oscillator
Potential energy increases
gradually
No restoring forceRapidincreaseinPot.energy
Non-equal separation
of vib. levels
Anharmonic Oscillator-Probablity Density
• Anharmonic
• Quantized energy level
• Probability of location of the
nuclei
To represent molecules with
more than three atoms one
needs 3N–6 space
Ammonia
To represent molecules with more than three atoms one needs 3N–6 space
Polyatomic molecules are represented in two or three dimensional space.
What may appear to be a minimum, barrier or saddle point in one subspace
may turn out to be nothing of the kind when viewed in another cross section
Representation of Polyatomic Molecules
Water
3
2
1
0
S0
0
1
2
3
S1
0
1
2
3
S2
0
1
2
3
T2
0
1
2
3
T1
Energy level diagram of molecules
S0
S1
S2
T0
T1
S0
S1
S2
T0
T1