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Photochemistry
Lecture 2
Fates of excited states of
polyatomic molecules
Polyatomic molecule electronic states

Use of group theory to
define irreducible
representations for
MOs

e.g., benzene
Benzene electronic excited states

Ground state ….(1a2u)2(1e1g)4

First excited configuration
…..….(1a2u)2(1e1g)3(1e2u)1

Use direct product tables to generate the term
symbols
e1g x e2u = B1u + B2u + E1u
Resultant spin 1 or 0 (triplet/singlet)
Lowest excited state is 3B1u
Lowest singlet excited state 1B2u




1A
1g
Selection rules for allowed electronic
transitions

() x ()  (Tx) and/or (Ty) and/or
(Tz)

For benzene (D6h) (Tx),(Ty) E1u , (Tz) 
A2u

Transition to lowest excited state formally
forbidden because
A1g x B2u = B2u
Chromophores
Larger molecules may have very few
symmetry elements
 Excitation can often be traced to electrons
belonging to a small group of atoms
known as a chromophore
 Typically label excitation as e.g.,




*  n (e.g., carbonyl group)
*   (e.g., alkene or carbonyl)
* 
n indicates a non-bonding electron usually
localised (e.g, lone pair on oxygen for carbonyl)
Chromophores (cont)
Likewise, excited states may be labelled
e.g., 1(*,) or 3(*,n) indicating which
electrons are unpaired.
 *   transitions may lie deep into the
ultraviolet (7 eV or  = 180 nm) for
unconjugated double bonds, but shift
towards visible as conjugation increases
(cf particle in 1D box)
 *  n transitions in carbonyl group also
in UV at around 290 nm (4 eV)

Photochemical mechanism of vision:
*   of 11-cis retinal
Isomerization in 200 fs
* n transition is forbidden to first-order
approximation on grounds of symmetry (px  py
on oxygen – transition moments zero)
Simplified nomenclature for polyatomic
molecules
S0
 S1
 T1

ground state
lowest excited singlet state (S=0)
lowest triplet state (S=1)
S2
T2
S1
T1
S0
Vibrational modes of polyatomic
molecules


3N-6 degrees of vibrational freedom (or
3N-5 for a linear molecule)
Normal modes from group theory analysis
e.g., for ammonia -
Vibronically allowed transitions
In benzene, transition to lowest excited state 1B2u
formally forbidden because it has
A1g x B2u = B2u
whereas (Tx),(Ty) E1u , (Tz)  A2u

However, if an E2g vibration is simultaneously
excited then overall symmetry of excited state is
B2u x E2g = E1u
Hence excitation is weakly allowed, provided there
is simultaneous excitation of vibration of
appropriate symmetry mode.
(distortion of symmetry causes mixing of excited
electronic states)
Potential energy surface


Potential energy of
molecule varies as a
function of 3N-6 coordinates for polyatomic.
PE surface, not just simple
curve.
Can represent a “cut”
through this multidimensional surface by
freezing all co-ordinates
except one of interest e.g.,
for umbrella bending mode
of ammonia
PE surface for triatomic –
bending angle fixed (linear)
Franck Condon principle as applied to
polyatomic molecules

For those vibrational modes that are allowed by
symmetry, whether a long or short progression is
observed is determined by Franck Condon
principle

Need to consider whether there is a large change
in geometry on excitation along the direction of
the normal co-ordinate for the mode in question

e.g., for NH3 molecule becomes more planar in
excited states, hence a long progression in the
umbrella bending mode is excited. For benzene
the ring bond length increases, hence ring
breathing mode is excited.
Ring breathing mode vibrational
progression of Benzene
Vibrational states of polyatomic
molecules

3N-6 Normal modes of
e.g., H2O

Represent number of
quanta in each mode as
(v1,v2…..)  v1 quanta in
mode 1 etc.
(0,0,0..) is the ground
vibrational state.
Energy, E is  the sum of
vibrational energies in
each mode (harmonic
approx).
E= (v1 + ½) h1 +
(v2+½)h2 + ….



Density of vibrational states for
hexafluorides

Density of vibrational
states defined as
number of vibrational
states per
wavenumber

Estimate from number
of ways of distributing
j quanta in s
equivalent oscillators
( j  s  1)!
n
j!( s  1)!
106
101
Jablonski diagram
Vibrational levels at high energy are pseudocontinuous
Levels of S1 are degenerate with pseudo-continuum
of high vibrational levels of S0 and T1
Fates of excited states III: Polyatomic
molecules
Vibrational relaxation in solution
Molecules excited to excited vibrational
levels of S1 undergo rapid degradation to
lowest vibrational level of S1.
 Energy is transferred to the solvent
molecules (translation primarily) by
collision i.e., V-T
 Subsequent processes begin from this
lowest level and are thus independent of
the vibrational level that is originally
excited.

Absorption spectrum
determined by (a) vibronic
selection rules and (b)
Franck-Condon overlap
Energy
transfer etc
Emission (fluorescence) or
other processes follow
relaxation to lowest
vibrational level of S1
Intramolecular energy transfer
Collision free radiationless process;
molecule evolves into different electronic
state without loss or gain of energy
 Excess electronic energy transferred to
vibrations, followed by fast relaxation.
 Represented by horizontal line on
Jablonski Diagram

Different intramolecular processes

Internal Conversion (IC)


Intersystem Crossing (ISC)


No change of spin state e.g., S0  S1
Change of spin state e.g., T1S0 or S1T1
Intramolecular Vibrational Redistribution (IVR)

No change of electronic state but change of vibrational
state (more important in gas phase)
S1(v1,v2,v3….)  S1(v1’,v2’,v3’)