Theoretical basis of energy and electron transfer

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Theoretical basis of energy and electron transfer
EPA summerschool, Egmond, June 2003
Gert van der Zwan (zwan_at_few.vu.nl) Department
of Analytical Chemistry and Applied
Spectroscopy Vrije Universiteit, Amsterdam
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Contents.
Day 1 Polarization properties of solvents

• Statics and dynamics of dielectrics
• Onsager, Lorentz, Debye, Lippert-Mataga
• Dynamic Stokes shift

Day 2 Reaction rates and Marcus theory

• From transition state theory to solvent
  coordinates
• Non-equilibrium free energy surfaces
• Electron transfer and Marcus theory

Day 3 Molecules in solution and energy transfer

• How molecules feel the world and each other
• Excitonic interaction, coherent transfer
• Dipole interaction and the Förster rate

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Polarization properties of solvents (1)
Properties of molecules
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Polarization properties of solvents (2)
Molecules in static fields
P.J.W. Debye (1884-1966)
1 D 3.33564x10-30 Cm
-e
e
0.2 ?
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Polarization properties of solvents (3)
The dielectric constant
J.C. Maxwell (1831-1879)
?0 permittivity of vacuum 8.85419x10-12
C2N-1m-2
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Polarization properties of solvents (4)
Gas of (non)polarizable molecules
H.A. Lorentz (1853-1928)
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Polarization properties of solvents (5)
Example dipole moment of water
Sänger, Steiger, and Gächter, Helv. Physica
Acta, 5, (1932), 200.
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Polarization properties of solvents (6)
The internal field due to Lorentz
Potential field of a point dipole
Electric field of a point dipole
WARNING The above field is known as the Lorentz
cavity field. Since in the derivation Lorentz
assumed that the dipoles in the medium are not
influenced by the presence of the cavity, it is
WRONG for anything but dilute gases. The effect
of the polarization is grossly over- estimated in
liquids. Nevertheless it is widely used.
Interaction energy of two dipoles
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Polarization properties of solvents (7)
Debyes theory of dielectrics

• methanol
• ethanol
• propanol
• isobutyl alcohol
• amyl alcohol
• ethyl ether

Debye, Physik. Zeitsch. XIII, 1912
Historical note Debye was editor of the journal
to which Onsager submitted his paper with
critique of Debyes theory, and it was rejected!
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Polarization properties of solvents (8)
Boundary value problems
There are more pitfalls in the theory of
dielectrics than there are zeroes in the Riemann
zeta function
Lars Onsager
S
Electrostatics
Boundary conditions
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Polarization properties of solvents (9)
Onsager reaction field
L. Onsager (1903-1976)
?
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Polarization properties of solvents (10)
Onsagers theory of dielectrics
Exercise derive these results.
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Polarization properties of solvents (11)
Beyond Onsager
J.G. Kirkwood (1907-1959)
Jiri Kolafa, Ivo Nezbeda Effect of short- and
long-range forces on the structure of water.II.
Orientational ordering and the dielectric
constantMol. Phys. 98, 1505-1520 (2000)
For those interested an (unfinished) .pdf
document Theories of dielectrics with more
on this and some literature references can be
obained upon request.
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Intermezzo absorption and emission spectra (1)
Fluorescence is usually redshifted with respect
to the absorption Stokes shift
77K Bacteriochlorophylla absorption and
fluorescence (Qy band).
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Intermezzo absorption and emission spectra (2)
A note about units
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Polarization properties of solvents (12)
The (external) Stark effect
J. Stark (1874-1957)
Absorption and Stark difference spectrum of
bacteriochlorophylla in toluene.
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Polarization properties of solvents (13)
The Lippert-Mataga expressions
Absorption
Emission
Note that the dependence on the dielectric
constant is actually rather weak, especially for
polar fluids. The expressions are much more
sensitive to small changes in the radius a
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Polarization properties of solvents (14)
Fluctuations and lineshapes
?
Gaussian line due to inhomogeneous broadening,
linewidth ?.
Transition dipole moment and energy as function
of electric field strength
4K absorption spectrum of BChla, fitted with
correlated disorder model.
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Polarization properties of solvents (15)
Self-consistency
Calculate molecular properties using the
Schrödinger equation.
Calculate the electric fields the molecule
generates
From this obtain the polarization in the medium.
Calculate electric fields acting on the molecule
and add the interaction term to Hamiltonian
Exercise Show that for the two-level system the
solution requires solving a fourth order equation
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Polarization properties of solvents (16)
Dynamics
e
e
e
The dynamical equation that the polarization
satisfies means that polarization can adjust
locally to changes. More sophisticated models
also allow for diffusion or inertia effects.
e
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Polarization properties of solvents (17)
Dielectric friction
Rotate central dipole
Eventually the reaction field will catch up
If we rotate the central dipole at a fixed rate,
the reaction field will just lag behind
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Polarization properties of solvents (18)
Dynamic Stokes shift (1)
G.G. Stokes (1819-1903)
In 1852 Stokes formulated the law that the
fluorescent light is of longer wavelength than
exciting light. In 1853 he coined the term
fluorescence in stead of the term
internal dispersion.
Spectra of C153, every 600ps. Cichos et al,
JPCA,101,1997,8197
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Polarization properties of solvents (19)
Dynamic Stokes shift (2)
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Polarization properties of solvents (20)
Non equilibrium free energy
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Polarization properties of solvents (21)
Modeling solvents
? polarity/polarizability. ? hydrogen bonding
acidty. ? hydrogen bonding basicity.
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Polarization properties of solvents (22)
What have we done?
SC
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