1. Relaxation Dynamics of Electronic Excite States in Organic molecules
M. H. Lee

2. Contents I Excitation & Emission processes in dye molecule
II Quantum yield, Rate constant and Decay lifetime
III Solvatochromism of molecules in polar solvents

3. Absorption and emission

4. What happens to an excited molecule ?
relaxation
excitation
Non- radiative decay
Radiative decay
re-emission

5. What happens to an excited molecule ?
Ex) hemicyanine dye
CH3
CnH2n+1 N N+

6. An example of the fluorescence lifetimes in different environments
in a polar solvent
in zeolite pore

7. Intrinsic & measured lifetime and Quantum yield,
Rate constant, k and population number, N Na Nb
kba t
ln(Nb)
Total fluorescence intensity is related to Quantum Yield
measured lifetime
intrinsic lifetime

8. Decay Lifetime

9. Relationship between absorption intensity and fluorescence lifetime
Strickler-Berg relation
The relation of the radiative lifetime of the molecule and the absorption
coefficient over the spectrum [ref. 5]
Derivation
Next
n: refractive index of medium
: position of the absorption maxima in wavenumbers [cm-1]
: absorption coefficient

10. Relationship between Einstein A and B coefficients
Suppose a large number of molecules, immersed in a nonabsorbing medium with
refractive index n, to be within a cavity in some material at temperature T,
The radiation density within the medium is given by Planck’s blackbody radiation law,
-(1)
By the definition of the Einstein transition probability coefficients,
the rate of molecules going from lower state 1 to upper state 2 by absorption of radiation,
-(2)
N1a : number of molecules in state 1a
v 1a 2b : frequency of the transition
The rate at which molecules undergo this downward transition is given by
-(3)
spontaneous emission probability
induced emission probability
At equilibrium the two rates must be equal, so by equating (2) and (3),

11. Relationship between Einstein A and B coefficients
-(4)
According to the Boltzmann distribution law, the numbers of molecules in the two
states at equilibrium are related by
-(5)
Substitution of Eqs. (1) and (5) into (4) results in Einstein’s relation,
-(6)

12. Relationship B coefficient to Absorption coefficient
The radiation density in the light beam after it has passed a distance x cm through
the sample, the molar extinction coefficient can be defined by
C: concentration in moles per liter
If a short distance dx is considered, the change in radiation density may be
-(7)
For simplicity, all the molecules will be assumed to be in the ground vibronic state,
-(8)
The number of molecules excited per second with energy hv is given by
-(9)

13. Relationship B coefficient to Absorption coefficient
Combining Eqs. (7), (8), and (9), it is found
-(10)
the probability that a molecule in state 10 will absorb of energy hv and go to some excited state
To obtain the probability of going to the state 2b, it must be realized that this can occur
with a finite range of frequencies, and Eq. (10) must be integrated over this range. Then
-(11)
If the molecules are randomly oriented, the average probability of absorption for
a large number of molecules, Eq (2) give a similar relation to (11)
-(2)
-(12)
The probability coefficient for all transitions to the electronic state 2
-(13)

14. Lifetime relationship for molecules
The wavefunctions of vibronic states are functions of both the electronic coordinates x
and the nuclear coordinates Q,
-(14)
If M(x) is the electric dipole operator for the electrons, the probability for induced
Absorption or emission between two states is proportional to the square of the
Matrix element of M(x) between two states
-(15)
Using (14), the integral in this expression can be
where
Electronic transition moment integral for the transition
Assuming the nuclei to be fixed in a position Q

15. Lifetime relationship for molecules
It can be expand in a power series in the normal coordinates of the molecule
-(16)
For strongly allowed transitions in a molecule, the zeroth-order term is dominant
Then (15) reduces to
-(17)
Taking the appropriate sums, we find
-(18)
Since the comprise a complete orthonormal set in Q space

16. Lifetime relationship for molecules
The rate constant for emission from the lowest vibrational level of electronic state 2
to all vibrational levels of state 1, , can be written by using Eqs. (6) and (17)
-(19)
It is desirable to be able to evaluate the term experimentally .
If the fluorescence band is narrow, v3 can be considered a constant and removed from
the summation, the remaining sum being equal to unity
By dividing by

17. Lifetime relationship for molecules
The sums over all vibronic bands can be replaced by integrals over the fluorescence
spectrum, so the expression reduces to
Now, by combining Eqs. (13), (18), and (19), we obtain
-(20)
It is convenient to write this equation in terms of the more common units
-(21)
Back
g1 and g2 : degeneracies of the 1, 2 states

18. Mono- and multiexponential decays of the fluorescent lifetime
Decay of a fluorescent molecule in uniform solvent,
: monoexponential function t
Log intensity t
intensity
Decay of a fluorescent molecule in multiple environment,
: multiexponential function t
Log intensity

19. Electronic relaxation processes in molecular fluorescence
Radiative deactivation
-fluorescence : spin allowed transition
-phosphorescence : spin forbidden transition
Unimolecular nonradiative deactivarion
-vibrational deactivation
-internal conversion : direct vibrational coupling between the ground and
excited electronic states
quantum mechanical tunneling (small energy gap)
-intersystem crossing
Bimolecular nonradiative deactivation
-quenching
-excimer & exiplex formation
-energy transfer

20. An example of the fluorescence lifetimes in different environments
in a polar solvent
in zeolite pore

21. Photo-excitation and PL relaxation in LE and TICT state
Absorption process (S0 ) (S1)
Emission relaxation
: LE (locally excited) state
: TICT state
Fluorescence decay lifetime
(Nonradiative relaxation)
TICT LE
(Normal Fluorescence) S0 S1
: Fluorescence lifetime
: Radiative, nonradiative rate constants

22. Constrained conformational motion of hemicyanine dye
Hemicyanine dyes in zeolite pores & PL decay curve
Showing slower decay lifetime than for the case in polar solvent

23. Environmental factors related to the excited state
Quenching : non-radiative relaxation of electronic excited state
- collisional(dynamic) quenching : energy transfer by internal conversion
- complex(static) quenching : depleting the population of chromophores that can be excited
solvent relaxation (10-11 sec) sn so
relaxation to S1(10-12 sec)
fluorescence (10-9 sec)
Fluorophore-solvent interactions
- Polarity of solvent
- Temperature
- pH
- Viscosity

24. Solvatochromism

25. Solvatochromism in absorption and emission spectra
An example of red-shifted behavior of
absorbance spectra in various solvents
(Coumarin153)
- Mark Maroncelli and Graham R. Fleming,
J. Chem. Phys. 86(11), 6221, 1987
polarity
Negative and positive Solvatochromism
In dipole-dipole interaction bet. chromophore and solvent
When dipole moment is reduced after excitation
negative solvatochromism (blue-shift)

26. Solvatochromism in absorption and emission spectra
Assuming 1. a spherical cavity dipole solute
2. solvent interacts with the electronic transition by virtue of the change
of the solute’s dipole moment
Ref.) Koutek, B. Collect. Czech.
Chem. Commun. 1978,43,2368
Transition frequency is expected to vary with solvent dielectric properties (Lippert equation)
Reaction filed factor obtained from dielectric continuum theories of solvatochromic shift
: Static dielectric constant and refractive index
of the solvent
where solute-dependent factors are given by
a : solute radius
AU – due to polarizability of solvent nuclear coordinates
BU – due to the electronic polarizability of the solvent
Next

27. Solute-Solvent interaction
Two categories of solute-solvent interaction
Short-range microscopic interaction
Long-range interaction – electrostatic interaction in dielectric continuum
Reaction field
the electric field which acts upon the dipole as a result of electric displacements
induced by its on presence ε
A cavity of radius a in an unpolarized medium
of dielectric constant ε
Back

28. Hemicyanine dye with negative solvatochromism

29. Charge distribution calculation results of hemicyanine
Ground state
A : 0.817
B : 0.183
Excited state
A : 0.410
B : 0.590
A : 0.116
B : 0.884
[Ref.3]

30. References
1. M. L. Horng, J. A. Gardecki, A. Papazyan, and M. Maroncelli, J. Phys. Chem. 1995, 99,
17311.
2. B. Herman, Fluorescence Microscopy, second ed. , BIOS Scientific Publishers, 1998.
3. Yanyi Huang, Tianrong Cheng, Fuyou Li, and Chun-Hui Huang, J. Phys. Chem. 2002,
106,
4. E. G. McRae, J. Phys. Chem. 1956, 61, 562.
5. S. J. Strickler and Robert A. Berg, J. Chem. Phys. 1962, 37(4), 814.
6. Mark Maroncelli and Graham R. Fleming, J. Chem. Phys. 86(11), 6221, 1987

31. Properties of fluorescent molecules
All fluorescent organic molecules are conjugated
i.e. they possess delocalized electronic π wavefunctions
π wavefunctions are built on H-atom p-orbitals,
and have a node in the plane of the bond.
Benzene
"moving" in a torus following the conjugation path
An example of strong electron donor-acceptor dye

32. Factors affecting spectral & temporal fluorescence
- Aromaticity : size of polycyclic system
- Electron donating functional groups
- Rigid plane of symmetry
- pi to pi* transitions
- Solvent : polarity and viscosity
- pH
- Heavy atoms make spin change more favorable