Absorption of energy
Energy is conserved in the
transfer of energy from the
electromagnetic field to a
molecule
Physical Chemistry

Lecture 10
Photochemistry and photophysics
in biological systems


Absorption and emission only
indicate energy differences
between states of a system
Types of energy states in a
molecule




Light and energry





Energy absorbed by system =
energy lost by field
Energy states of a molecule are
limited to certain energies (quantum
condition)
Photon energy determined by its
frequency





Joules
Wavelength, 
Inverse wavelength (called
wavenumber), 1/ 
Frequency
 Circular frequency, 
 Radial frequency, 


Conversion between units is
easy
Unit commonly used depends
on the region of the
electromagnetic spectrum
Flow of energy per unit
area
Units of watts/m2
E photon


Absorption of energy from an
electromagnetic field causes
 h

 c


E photon

E photon
1 dE
A dt

Change of molecular state
Decrease in intensity
May react from the excited state
h
A 
A*
Macroscopic sample has repeated
absorptions over the sample that
reduce the intensity
1
 hc  


Described by the BouguerLambert-Beer law
 = molar absorptivity

l = path length


 Units: dm2 mole-1 (or cm2 mole-1)
2

I
Absorption and the BouguerLambert-Beer law
Planck’s relation

Electronic
Vibrational
Rotational
Translational
When passing through
a medium, energy may
be absorbed and some
is transmitted
Absorbed light causes
molecular state change
Vision
Photosynthesis
Vitamin D synthesis
Sunburn (!!!)
Energy of a photon related to
frequency and wavelength in
a vacuum
May express energy in several
different units
 E photon
Light is described by a
flow of energy
The strength of the field
of light is measured by
the intensity
Many biological processes involve
exchange of energy by emission or
absorption

Emolecule
Energy and intensity
Electromagnetic radiation occurs in
quanta called photons
The absorption of emission of
electromagnetic radiation results in
an exchange of energy by a
molecule with the field in space

Energy absorbed by system =
energy lost by field
Energy states of a molecule are
limited to certain energies
(quantum condition)
Emission is loss of energy as
the system goes to a state of
lower energy
 Units: cm (or dm or m)
h

2
 



I0 = initial intensity
I1 = transmitted intensity
Ia = absorbed intensity
I1
I0
Ia
 10  l C A
 I0
 I1

 I 0 1  10  lC A

1
Energetics after absorption
Steady-state effects
The absorption of energy from an
electromagnetic field may be followed
by additional processes

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Constant irradiation
leads to a steady state
concentration of the
first excited singlet
Fluorescence
Internal conversion
Vibrational relaxation
Intersystem crossing
Phosphorescence
All processes involve the redistribution
of energy



Emission
Transfer to other modes

Concentration depends
on the absorption rate
constant and the
fluorescence lifetime
Fluorescence intensity
depends on [S1]
Defines


Photochemical steps
The molecule may react
upon excitation
The rate depends on
how many molecules
absorb light


Proportional to the
absorbed intensity
For weak absorption, rate
is directly proportional to
1000 I a
l
1000

I 0 1  10 lC A
l
1000

I 0 1  e (ln10)lC A
l
 1000(ln 10)I 0C A



 Concentration
 Initial intensity

First order equation
 Loss of reactant is first
order
 “Rate constant” contains
molar absorptivity and
light intensity

 C A (0)e 1000 (ln10 )I 0t
C A (t )
Elementary photoprocesses
affecting the S1 state; quenching
Many ways for molecules to
lose energy



Radiative decay
Intersystem crossing
Internal conversion
Can also exchange energy
by interaction with a
mediator (called a quencher)
that removes energy
Think of this as changing the
“lifetime” of the excited state

Lifetime depends on the
concentration of the
quencher
S0
ka
 h 
S1
S1
f

S0
k
S `1
k isc

T1
S1
k ic

S0
S1
 Q
Q

S0
k
 h




 k f k a f [ S 0 ]ss
 k f [ S1 ]ss
  f ka [S0 ]   f  A I 0
f
 k f f

kf
k f  kic  kisc  kQ [Q]

1 
1 
I f , 0 
kQ
kf

[Q] 


Example: Stern-Volmer plots
for quenching of Zn
cytochrome-c fluorescence
by acrylamide with (a)
nothing added; (b) Apaf-1
added; and (c) Apaf-1 and
dATP added
From Purring-Koch and
McLendon, PNAS, 97, 11928
(2000).
Transient S1
concentration is created
by exposure to a short
light pulse

 Q
1
k f  kisc  kic  kQ [Q ]
1
If
Optical perturbation to determine
lifetimes

d [ S1 ]
 k a [ S 0 ]  k f  kisc  kic  kQ [Q ][ S1 ]
dt
f
If
 k a f [ S 0 ]ss
Quantum yield
Absorption cross-section
Steady-state fluorescence
intensity depends on the
lifetime
With a quencher present,
one can isolate the effects
on fluorescence by
monitoring it as a function of
the quencher concentration
A  P
dC A
dt
f
[ S1 ]ss
Stern-Volmer plots
h

d [ S1 ]
 0
dt
1
 k a [ S 0 ]ss  [ S1 ]ss
Fluorescence builds
rapidly during the pulse
Concentration dissipates
by various processes
characterized by the
lifetime
Fluorescence intensity
after the pulse is timedependent



Often exponential decay
Analysis is complex due
to finite excitation
Determines the lifetime
 t
I (t )  I (0) exp 
 
 f




2
FRET
Kinetics of electron transfer
Fluorescent quenching
occurs in many ways


Oxidation and
reduction are majors
processes in
chemistry
Transfer within molecule
Transfer outside of molecule
Fluorescent resonant energy
transfer (FRET) involves
interaction with another
molecule to form a complex
Mechanism

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h
D*

D
Excitation
Intersystem crossing
Resonant energy transfer to
another molecule, the
acceptor (A)
Acceptor fluorescence
*
 D
D*
k isc
D

D
 D*



Detected by change in
quantum yield


kf
fret
A 
D 

k

kf '
*
A
*
A
A* 



FRET

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Photosynthesis
D 
Excitation of donor (D)
Intersystem crossing
Resonant energy transfer to
another molecule, the
acceptor (A)
Acceptor fluorescence
Changes quantum yield
Förster theory shows strong
dependence of efficiency of
transfer on the donoracceptor distance in the
complex

Common process
involving electron
transfer
Kinetics of electron transfer
Mechanism

Involve transfer of
electrons
 D*




0

Can be used to measure
distances
Distances need to be
roughly of molecular
dimensions
D
h

D*
D*
f

D
D*
k isc

D
k
fret

A 
D 
k
f

k '
A*
 fret 
A*
A* 



kf
k f  kisc
kf
k f  kisc  k fret
Eff  1 
 fret
0

r06
r06  r 6
Mechanism of transfer
involves formation of a
donor-acceptor complex
Both the donor-acceptor
complex and the
charge-transfer complex
are intermediates
The rate constant for
transfer depends on all
of the possible rate
constants of the
elementary steps
kd

DA
kd '
DA 
D 
A
k et
DA 
D  A
b et
D  A k

 DA
sep
D  A 
D
k
d [ DA]
 0
dt

A
d [ D  A ]
 0
dt
v  k sep [ D  A ]
k sep ket k d
[ D ][ A]

k sep ket  k d '   kb et k d '
Marcus theory of electron
transfer
FRET
FRET allows one to see
different structures
because of contrast
provided by different
quenching rates
Separate structure form
complexes differently,
giving different FRET
emission
Example: alpha-synuclein
antibody labeled with
fluorescein forming
complexes with HSP-3
A
The rate constant for
electron transfer
depends on a number of
factors


k  e   r e  G

/ RT
Structure of the complex
(r)
Energy differences
between states
 Free energy
 Reorganization energy
 Free energy of activation
depends on both

Image by Brian J. Bacskai, Massachusetts
General Hospital
Rate goes through a
maximum
 Experimentally
demonstrated for
biphenyl and a variety of
acceptors
3
Summary
Absorption of energy in the form of photons
plays a fundamental part in biological
processes



Redistribution of energy
Change of structure
Reaction
Oxidation-reduction is a fundamental
process in biological systems


Occurs in many reactions
Kinetics of steps important
4