XV–74
Fluorescence - 2014 (Notes 16)
Jablonski diagram – Where does the energy go?
Can be viewed like multistep kinetic pathway
1) Excite system through A – Absorbance
S0  Sn Excite from ground  excited “singlet”
 S = 0 – could be any of them (FC overlap  Pij)
– must change dipole (very fast process, fsec)
2) If Sn > S1  often rapid decay/relax down (use VR, NR)
Sn  S1 called: IC – internal conversion
(E ~ 0 fastest steps, goes to excited vibration level)
VR within state fast in condensed phase – heat, vibra. media
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3) Options to release energy from S1,  = 0 next step (big gap):
a) NR - non-radiative decay to S0 – less probable -implies
1. - IC to another singlet, S0, but big separation, slow
2. - VR - Vibrational relaxation – through collision
– vibrational energy taken to solvent (surround)
– relax to lowest vibrational state S0, ” = 0
(relatively fast process < ns)
b) Fluorescence  emit photon to S0
– most probable for S1 – trap there (unlikely from S2)
Fluorescence lifetime / quantum yield reflects
probability of this process - ns  s typical
 competitive process with IC/VR to S0
c) ISC – cross to triplet -- “intersystem crossing” – slow S≠0
In triplet VR relax to  = 0 again – trap energy, long time
Phosphorescence – much slower (S  0) & weaker
– aided by heavy atoms (spin-orbit coupling)
Fluorescence intensity –
depends on how molecules
are excited and on the
probablity of transition to
ground state.
kinetic process—compete
between pathways in
Jablonski diagram, typically
excite by absorbance
Multistep kinetic process:
Competition between
fluorescence, non-radiative
decay, and intersystem
crossing.
XV–76
First order kinetics: -d[M*]/dt = kd[M*] (linear in conc.)
Lifetime decay:  = 1/kd - if only fluorescence:  = 1/kf
Other processes – take away excitation,
--lead to shorter observed lifetimes
-d[M*]/dt = kf[M*] + knr[M*] + kQ[M*][Q] = kd[M*]
where knr [non-radiative decay], kQ [quenching]
observed lifetime:  = 1/(kf + knr + kQ [Q]) = 1/kd
Quantum yield – ratio: photons fluoresce / photon absorb ≠ A!

f = #photon(F)/#photon(A) = kf[M*]/ kd[M*] =
Quantum Mechanics role
1) Quantum mechanics used to describe excited states
– much less accurate than for vibrations (excited state)
– requires a surface not just single geometry
– calculations need “configuration interaction”
states become mix of configurations: ()n ()m …
idea –change occupied orbitals of electron to change states
– states mix different orbital configurations (e.g. *)
impact – calculations large and less accurate
2) Quantum mechanics and symmetry used to describe which
vibronic excitation are allowed with electronic state change
S = 0– Electric field cannot change spin
Except– (Phosphoresce – mix spins - spin-orbit coupling)
Dipole must change: A ~   ex* el g d2
integral zero if ex and g same dipole
 = 0, 1, 2 … no restriction on  - sym. modes
” = 1, for asymmetric modes (distort molec. to get dipole)
A: Absorb: most transition start g = 0 (most populated)
F: Fluorescence is same but ex = 0 by relaxation (VR)
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Absorption and Fluorescence sample the same states,
but processes give fluorescence added dimension
Intensity – dipole strength Dij = |ij|2 = 0.92x10-38∫(d(esu-cm)2
[or x10-2 in units of Debye2, 1 D = 10-18 esu•cm = 3.34x10-30 C•m]
Absorption—detect same photons as excite, A = -log I/I0
To go beyond spatial average, need to orient molecule
use polarization (next section), lifetime no meaning
Sensitivity limited – difference of big #s: [log I – log I0]
Fluorescence – excite different photon (abs.) than detect (emit)
Transfer of energy between states – kinetic process
Polarization can detect change in orientation while excited
Can go outside of chromophore – intramolecular processes
Excitation–fluorescence intensity vs. excitation wavelength
-detect states that absorb - transfer energy to emitting
state. Sensitive - selective absorbance method
FRET – fluorescence resonant energy transfer (Engel 19.13)
Efficiency of transfer from Donor (D) and Acceptor (A)
T = kT/(kT + kf) compare rates: fluoresce. (kf) & transfer (kT)
In terms of quantum efficiency: T = 1- (f/f0)
Rate/efficiency depend on distance and spectral overlap
T = R06/(R06+r6) - transfer rate: kFRET = (1/D)(R0/r)6
where: D = Donor lifetime, r = distance DA
R0 = experimental param., rate transfer  rate decay
Result: FRET can provide a spectroscopic “ruler”
For molecules in 10-100 nm(Å?) range – note 6th power!
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Resonance- overlap donor fluorescence - acceptor absorbance
Pron end-to-end vary efficiency vs. length (Engel book)
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Bio-applications—see Engel Ch. 19.13 (range overestimated?)
tag part of protein or DNA with fluorophores (D and A)
observe relative intensity of fluorescence from A or D
or better change in its lifetime,  = 1/kFRET
Calibrate with known lengths—eg dsDNA, poly-Pro
Can use dyes, or – proteins – Tryptophan to dye
XV–80
BPTI was labeled with just D, see 6.8 ns decay, but with D and A
get much faster decay (reduced, unfolded)
Folded and unfolded change lengths, more D and less A
emission for unfolded. Length distribution changes
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Quenching – process deactivates excited state/reduce F
Collision can take away energy or cause
molecule to change states to non-fluorescent one
e.g. O2 : M*(sing) + O2(trip)  M*(trip) + O2(sing)
Process, multistage kinetic path
M + h  M*
(excitation)
M*  M + h’
(fluorescence)
M* + Q  M’ + Q’ (quenching)
Rates: no quenching:
f0 = kf/(kf+knr+kISC)
With quenching: f = kf/(kf+knr+kISC +kQ[Q])
Stern-Volmer relation:
f0/f = 1 + kQ[Q]/ (kf+knr+kISC) = 1 + K[Q]
lifetime as well:f0/f - 1 = kQ’[Q] with ’ = 1/(kf+knr+kISC)
plot: F0/F vs. [Q] and slope is kQ’
Can use this to sense exposure of fluorphores to surface
Reflects change in environment—e.g. unfold tertiary
Polarization-Useful if chromophore – fluorescing species
– has different absorbance with one polarization
– called dichroism (linear)
– can use for analysis of orientation
in fluorescence – excite with one polarization (1st photon)
observe emission in   and  orientation (2nd photon)
fluorescence anisotropy  degree of motion / flexibility
ideal - measure change in polarization with time
r = (I‫ ׀׀‬- I┴)/(I‫ ׀׀‬+ 2I┴)
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XV–83
Fluorescence anisotropy
Changes in fluorescence anisotropy
0.08
A pH6.8
DPH
TMA-DPH
0.06
0.04
0.02
0.00
DMPG
0.12
DOPG
DSPG
B pH4.6
0.10
0.08
0.06
0.04
0.02
0.00
DMPG
DOPG
DSPG
(left) DPH A and F polarized long axis, used to sense lipid
organization. DPH deep, TMA-DPH near surface. Measure
change in polarization on lipid vesicle binding protein, see BLG
cause more disorder in DMPG vesicle pH 6.8, more in all at 4.6.
Aside:
3) Transitions seen are determined by symmetry “group theory”
– tool for organizing symmetry
– useful in small molecules (Chem 444)
Biomolecules – less use – no symmetry
– use correlation to small molecule components
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Phosphorescence