Theodor Förster, 15.5.1910 – 20.5.1974
• 1933: PhD thesis: „Zur Polarisation von Elektronen durch
Reflexion“ University of Frankfurt (Prof. E. Madelung)
• 1934: Assistant of Prof. K.-F. Bonhoeffer, Leipzig
(Debye, Heisenberg, Kautzky)
• 1942: o. Prof. in Posen (Poznań)
• 1945: Department head MPI for Phys. Chem., Göttingen
• 1951: University of Stuttgart
• ~80 Publications
• Förster Cycle
• FRET (Dipole-Dipole)
• Excimers (Pyrene)
• Diabatic and adiabatic reactions, kf, knr
Citation Index Theodor Förster

Albert Weller’s obituary (1974)
Albert Weller, referring to Die Fluoreszenz organischer
Verbindungen: “the Hausbibel – a very appropriate name
because in the first place this book could open new
pathways to knowledge and secondly its concise
formulations, in which every word was important, required
two or more readings or still better the interpretation of an
enlightened mediator before one could comprehend its
precious contents. For the non-German speaking people it
must have remained a book with seven seals; and since it
has not been translated into English it has secured, as many
American colleagues more or less have asserted, the
German lead in fluorescence spectroscopy for years.”
George Porter at the 1st “TheodorFörster
Gedächtnisvorlesung” 1975
„Photochemistry, which previously was concerned
mainly with the final products or the dark reactions of
intermediates such as free radicals, has become a new
science of the excited state. No single person
contributed more to this progress than Theodor
Förster.“
Three classes of photoreactions (1970)
3rd IUPAC Symposium on Photochemistry 1970
Pure and Applied Chemistry, 34, 1973, 225.
Noncrossing rule for diatomic molecules
(von Neumann, Wigner)
If there is only one degree of freedom (rX–Y): Two conditions
(E1 = E2 and V12 = 0) cannot be met at the same time
What about polyatomic molecules?
In a polyatomic molecule, two potential−energy surfaces are allowed
to cross along a (3N −8)-dimensional subspace of the (3N − 6)dimensional
nuclear coordinate space even if they have the same
spatial/spin symmetry (N is the number of nuclei).
NH2
–
O3S
SO3
––
O3S
pH < 2
pKa*(NH) = 12.7!
green fluo
yellow fluo
The Förster Cycle
~
 hc∆ Gº = –RT ln(K) = 2.3RTpK
pKa
* = pKa + 21.0(∆/m–1) for T = 298 K
~
p-Hydroxyacetophenone: Ground state protonation equilibria
Triplet state equilibria: A proton shuttle
Titration of the enol-triplet
JACS 2000, 122, 9346
O
–
O
OH
O
pKa(T1) = 4.6
+ H
+
350 400 450 500
0.0
0.4
0.8
nm
pH 7.05
pH 5.32
pH 5.05
pH 4.66
pH 4.38
pH 4.04
pH 2
² A
Förster cycle
pKa = 7.9
pKE = 16.4 (calc)
ET/2.3RT = 51.8
phospho
ET/2.3RT = 47.5
phospho
pKa = –8.5
pK*a = 2.5
pK*E = –2.1
pK*a = 4.6
h
1.52.02.53.03.5
0.0
0.5
1.0
1.5
300 350 400 500 600
/ nm
A
 / m–1~
F = 0.04
ad ≈ 1
F = 16 ns
An adiabatic electrocyclic reaction
Helv. Chim. Acta 1984, 67, 305.
h-allowed!
Th. Förster, Chem. Phys. Lett. 1972, 17, 309.
NH2
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
1.0
0.0
0.2
0.4
0.6
0.8
1.0
f
pKa*
f(ArNH2)
f(ArNH3
+
)
NH2
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
1.0
0.0
0.2
0.4
0.6
0.8
1.0
f
pKa*
f(ArNH2)
f(ArNH3
+
)
Förster’s paradox
0 5 10
0
10
20
30
pH
dedeut'n/%
OH
D
OH
h
H2O
O–
+ H+
OH
+ H+
O
H H
The competing process: C-protonation
S1
pH-Dependence of the triplet-lifetime of benzophenone
0 14

/ s
pH
?
+
OH O
PorterWyatt
Benzophenone in aqueous acid
1.52.02.53.03.54.04.55.0
300 400 500 600
0.0
5.0
1.0
1.5
2.0
2.5
0
2
4
6
8
/m–1
~
/nm
12 M HClO4
H2O
220
Kinetic analysis
J. Phys. Chem. A 2003, 107, 3305.
Photohydration of benzophenone in aquous acid
OO
O
1 3
h
kISC
k'ISC
*
6 ps
OH OH
OH
OH
k0 = 1.5 · 109
s–1
3
+ H2O
minor
– H+
50 ns
major
3
•
•
–H2O
OH OH
k + k'H+[H+
]
6 s
OH
k–H +
kH +[H+
]
3
kH+ = 6.8 · 108 M–1 s–1
pKa = –0.4
J. Phys. Chem. A 2003, 107, 3305
Photosubstitution of aromatic ketones in aqueous acid
h
H+
/H2 O
F
O
OH
O
+ HF
F F
3-Fluoroacetophenon:
3,4-Difluoroacetophenon:
3,3‘-Difluorobenzophenon:
Quantum yields
0.5
0.6
0.7
Intramolecular photoredox reactions
P. Wan, Org. Lett., 7, 2005, 3387. Photochem. Photobiol. Sci., 2008, 7, 588.
Pyrene excimer
Kasper, Förster, Z. physik. Chem. N. F., 1954, 275
Energy transfer processes are isoenergetic
Dark area: Spectral overlap integral J
Radiative energy transfer
• Donor D* fluoresces, acceptor A absorbs
• Like a radio transmission
• The concentration of A does not affect the lifetime of the donor D*, τ(D*)
• The probability p for absorption by A of a photon emitted from D* for low
absorbance of the acceptor A is:
cA is the concentration of acceptor A, is the average path-length of the
emitted photons.
• Note: This is the correct form of Eq. 2.33 in the book (which is wrong)
Resonance energy transfer
• In practice, the lifetime of the donor, τ(D*), and its quantum yield of
emission usually decrease upon addition of an acceptor A (concentration
quenching).
• Some interaction between D* and A, not like a radio transmission.
• The deactivation of D* is stimulated by the acceptor A.
• Quantum description: an interaction term Vif = <Ψi|hop|Ψf> couples the
initial wavefunction Ψi = ΨD*ΨA to the final wavefunction Ψf = ΨDΨA*.
• Multipole expansion of the Coulombic interaction Vif and retain only the
dipole–dipole term (for distances >> molecular sizes).
Förster resonance energy transfer (FRET) (1946, 1948)
• FRET was first used as an acronym in biological sciences for “fluorescence
resonance energy transfer”, a misnomer; hence “F” for Förster.
• The rate constant kFRET is proportional to Vif
2, and the dipole–dipole
interaction falls off with the third power of the distance R, hence kFRET ~1/R6.
• The distance R at which kFRET = 1/τD
0 is called the critical distance R0.
• At R = R0, the efficiency of energy transfer is 0.5:
ηFRET = kFRET/(kFRET+1/τD
0) = R0
6/(R0
6 + R6) = 0.5
“Molecular ruler”
Search for “FRET”
gives 77’000 refs
Can we predict R0 for a given pair D* … A?
• Yes! The Förster equation gives R0 as a function of experimentally
accessible quantities:
• ΦD
0 is the fluorescence quantum yield of D in the absence of A
• J is the spectral overlap integral
• NA is the Avogadro constant
• n is the refractive index of the medium
• κ is the orientation factor depending on the relative orientation of the
transition moments of D* and A, 0 [perp.] ≤ κ2 ≤ 4 [parallel]; <κ2> = 2/3
The orientation factor κ2
The spectral overlap integral
It can be expressed in wavelengths or wavenumbers:
• Quantity calculus, the manipulation of numerical values, physical
quantities and units, obeys the ordinary rules of algebra!
• Use scaled quantities Q/[Q]: Q = number * unit; [Q] = unit
• With [ε] = mol–1 dm3 cm–1, [λ] = nm, [NA] = mol–1 one obtains the practical
equation:
Conversion to a practical equation: Quantity calculus
The first number in the numerator is 9, not 9000!
10001/6 = 3.16; the correct factor for R0 is 0.02108
In most papers and textbooks the Förster equation is given as:
This would give:
A take-home lesson for calculations with physical quantities:
Photochem. Photobiol. Sci., 7, 2008, 1444
Yes: Ermolaev 1963, Kellogg, 1964
Is triplet to singlet FRET possible?
Adam, JOC, 43, 1978, 4495
Protein folding
The speed limit for protein folding measured by
triplet–triplet energy transfer (requires contact)
PNAS, 96, 1999, 9597
Wagner, Klan, JACS,
121, 1999, 9626
ket/s–1
M
PNAS, 96, 1999, 9597
Single molecule FRET: A tool to study protein folding
Single molecule detection
avoids ensemble averaging
W.E. Moerner, Stefan Hell, Eric Betzig,
Nobel prize in Chemistry, 2014
Single molecule fluorescence spectroscopy at sub-diffraction resolution
Mathematical analyses allow localization of single, luminescent
molecules to within a few nm
C. Seidel, Methods
Enzymol., Vol. 475
(2010)
pulses define the macrotime (D)
photon arrival times microtime (C)
D: Alexa 488
R0 = 52 Å for <κ2> = 2/3
A: Cy5
C. Seidel, Nature Methods,
9, 2012, 1218
2–19 base pairs
A toolkit for high precision structural modeling
Structure of HIV-1 reverse transcriptase
Folding/unfolding kinetics of protein GB1, an
immunoglobulin-binding protein in Streptococcus
W. A. Eaton, PNAS,
106, 2009, 11837
Xanthenyl dyes for FRET
6M Urea FRET efficiency
Transition path time < 200 μs; >10’000 times shorter than
the folding/unfolding rate coefficient.
Photosynthesis antenna systems
• Think! A few high-impact papers vs. publish or
perish.
• FRET as a molecular ruler has a huge impact
on biophysics. Be pedantic in quantity calculus.
• Scrutinizing Förster’s paradoxes has revealed
important chemical quenching processes.
• Proton-Transfer to C-atoms of electronically
excited states can be very fast.
• The Förster-cycle provides surprising, yet
reliable predictions.
Conclusions