MODULE 19(701)

The Deactivation of Excited Singlet States

The (stimulated) absorption (annihilation) of a photon by a ground state causes an electric dipole transition to

occur to form an excited electronic state.

Quantum mechanical laws govern the photon-molecule interaction.

In the Photosciences we focus on the physical and chemical properties of the excited electronic state

formed during the absorption process.

Excited electronic states have different electronic configurations from their ground states and are

therefore different chemical species, even though their nuclear framework may be identical or very similar to

that of their ground state parent.

MODULE 19(701)

Excited electronic states are intrinsically unstable.

Their excess energy can be dissipated in a variety of ways, physical and chemical.

The various decay routes can be categorized as “radiative” or “non-radiative” (radiationless).

1 0 FS S hv 1 0 PT S hv

RADIATIVE TRANSITION BETWEEN STATES OF LIKE

MULTIPLICITY

RADIATIVE TRANSITION BETWEEN STATES OF UNLIKE MULTIPLICITY

S1 S0 + hF

FluorescenceSpin-allowed and

strong

T1 S0 + hP

PhosphorescenceSpin-forbidden and

weak

MODULE 19(701)

Energy relationships and rate processes connecting electronic states are often depicted on a Jablonski

diagram

RADIATIONLESS TRANSITIONS BETWEEN STATES OF LIKE

MULTIPLICITY

RADIATIONLESS TRANSITIONS BETWEEN STATES OF UNLIKE

MULTIPLICITY

S2 S1 + heat

Internal conversionVery rapid

S1 T1 + heat

Intersystem crossingSpin forbidden and often slow

MODULE 19(701)

T1

T2

T3

Intersystem

crossing

S2

S1

S0

absorption

fluor phosph

internal conversio

n

internal conversio

n

Intersystemcrossing

T3

T2

T1

Intersystem crossing

MODULE 19(701)

S1 radiative lifetimes are in the range 1 ns to 100 ns, (some notable exceptions).

T1 radiative lifetimes are milliseconds and longer.

Recall that the radiative lifetime is the reciprocal of the radiative rate constant

Since kFM is equal to the Einstein A coefficient, which is related to the Einstein B coefficient and then to fi , and then to the integrated extinction coefficient (J), it should come as no surprise that there is a relationship between

kFM and J.

1/FM FMk 1/TM TMk

MODULE 19(701)

where nf and na are the mean refractive indices of the solvent over the fluorescence and absorption bands,

respectively

The above is the Strickler-Berg equation.

It allows a calculation of the radiative lifetime of fluorescence from a measurement of the absorption

spectrum of the fluor.

319 31/ 2.88x10 f

FM f ava

n d

n

13f av

MODULE 19(701)

The Jablonski diagram is useful but it is confined to showing energy relationships between states.

An alternative approach, useful for considerations of rates, is to use potential energy curves.

internuclear distance

60 80 100 120 140 160 180 200

ener

gy

6

8

10

12

14

16

18

20 For a diatomic molecule we can

construct a potential energy curve as

shown.

Quantized nuclear motions along the inter-nuclear axis provide a set of

vibrational energy levels.

MODULE 19(701)

For diatomics, every bound electronic state has a PE curve as shown.

The curves are separated from each other on the energy axis.

Different PE curves can intersect each other depending on the curvature of the function (force constant) and the

value of Req.

polyatomic molecules cannot be represented in the same manner as for diatomics since they have more than one

degree of vibrational freedom. A multi-dimensional surface would be required for an

equivalent characterization. However, an inaccurate, but useful picture can be gained for polyatomics, if we imagine that all individual nuclear

oscillators in the molecule are reduced to a single dimension, viz., a generalized nuclear coordinate.

MODULE 19(701)

On this model we represent a polyatomic in a Morse-type plot in an analogous way to what we do for diatomics

where now the abscissa label becomes “general nuclear coordinate”.

Also we can regard the molecule as having a particular bond as the

relevant entity, e.g. alkyl carbonyls.

Then we can confine our attention to a “local mode”

on that bond.

This approach allows for energy level juxtapositions and curve crossings to be visualized see Figure.

MODULE 19(701)

Absorption and fluorescence are inverse processes.

In solution phase at room temperature, most molecules are in lowest vibrational state (v = 0), and upward transitions originate in v = 0 and terminate at v’ =

0,1,2,3…in S1.

The transition moment dipoles for the v = 0 to v’ = n set of transitions vary (via the Franck-Condon factors)

throughout the series.

Thus the efficiency of an individual absorption vibronic transition varies along the series and the observed

spectrum is a convolution of the set.

MODULE 19(701)

At the instant of absorption, the ensemble of molecules in S1 will contain some in several of the vibrational states (Fig.).

A radiative transition from S1 can therefore originate from any of the set of vibrational

states populated in the absorption process.

However, all states above v’ = 0 are capable of undergoing internal conversion (vibrational

cascade) to v’ = 0.

MODULE 19(701)

So a molecule formed in a higher vibrational level of S1 is confronted by a choice of undergoing fluorescence or

internal conversion (vibrational cascade).

In most molecules the non-radiative process is much more rapid than the radiative one (knr ~ 1011 s-1;krad ~ 108

s-1 ).

As a general rule, fluorescence originates from S1(v’ = 0).

This effect is called Kasha’s rule.

MODULE 19(701)

One effect of this is to generate mirror

symmetry between the absorption and

fluorescence spectra of many chromophores.

Figure gives an example of this for a silicon phthalocyanine in toluene solution.

This symmetry is only found for molecules that

undergo minimal nuclear geometry

change on excitation.

550 600 650 700 750 8000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

fluor

esce

nce

(nor

m)

abso

rban

ce (n

orm

)

wavelength / nm

MODULE 19(701)

FLUORESCENCE

Electronically excited states of molecule M can deactivate in several ways, both unimolecular and bimolecular, as

indicated. M + hA M(S1)

M + hF

M(T1) +

M(S0) + N +

Bimolecularprocesses

N is formed from M(S1) in some unimolecular chemical change, e.g., cis-trans isomerization.

MODULE 19(701)

All the above processes (and more) may be competing in the de-activation of M(S1), and all are characterized by a

rate constant.

Only one of the processes is radiative (fluorescence).

Monitoring the fluorescence, either its intensity or lifetime, affords a useful and convenient way of measuring the rate of decay of 1M*, and thence

information about its reactivity.

There are two types of instruments:

Steady-state (cw): measures the fluorescence intensity as a function of wavelength.

Time-resolved: measures the fluorescence intensity as a function of time.

MODULE 19(701)

Steady-state instruments (spectrofluorimeters) are used to obtain excitation and emission spectra.

Excitation spectrum: fluorescence intensity at fixed EM and variable X

(comparison to absorption spectrum.)

Fluorescence Spectrum: fluorescence intensity at

fixed X and variable EM

MODULE 19(701)

An excitation spectrum provides information about the absorption spectrum of the molecules present that

fluoresce.

For a one-component fluor solution, sample, the

excitation spectrum closely resembles the absorption

spectrum. In a mixture where only one component is fluorescent, the excitation spectrum will be that of the fluorescent

compound only, but the absorption spectrum will contain additional bands.

The excitation and absorption spectra will be dissimilar.

excitation

MODULE 19(701)

Quantitative spectrofluorimetryThe area under the IF vs. spectrum, (GF), is proportional

to the number of photons emitted and thence to the concentration of emitting states.

qFM is the molecular quantum efficiency of fluorescence.

In many cases

and in such cases a measurement of the peak intensity can be used to follow changes in GF

Under carefully controlled conditions, GF tracks the concentration of fluorescent states.

1[ ]F FMG M q

maxFG I

MODULE 19(701)

For example, consider an experiment in which a

dilute solution of tetraphenylporphine (TPP) in benzene is examined at

three oxygen concentrations under the

same conditions of excitation.

Oxygen causes attenuation of the fluorescence signal.

IF

/ nm

0 mM

2 mM

10 mM

A plot of Imax vs. [O2] has the form shown in the next Figure.

Oxygen is said to be a quencher of the fluorescence.

MODULE 19(701)

These data can be employed to extract quantitative information about the kinetic properties of the fluorescent

species.

IF

[O2]

N2 saturated

Air-saturated

O2 saturated

MODULE 19(701)

A KINETIC SCHEME FOR FLUORESCENCE QUENCHINGAssume we have a solution of a fluor(ophore) (such as TPP) in some solvent and there are no complications.

Singlet states are populated in a continuous way by absorption of photons from cw excitation light at the

appropriate wavelength.

1M* states are depopulated via a variety of competing pathways:1 *

1 *

1 * 3 *

1 *

1 * '

Ahv

EX

F FM

TM

GM

QM

M M R

M M hv k

M M k

M M k

M Q M Q k

MODULE 19(701)

Q represents a quencher of S1 (such as oxygen).

Q’ represents the effects of the quenching act (non-specific).

Note that quenching is a bimolecular process.

The excitation parameter, Rex, is a measure of the rate at which photons are absorbed into the sample.

Since each photon absorbed generates one 1M* state, it also gives the rate of production of excited states (in mol

s-1).

For a fixed Rex (important) the amplitude of the fluorescence signal will depend on the competition

between the fluorescence process (via kFM) and all the other deactivation routes.

MODULE 19(701)

In the absence of quenchers ([Q] = 0)

Under cw, low-intensity irradiation [1M*] rapidly builds up to a

low constant level and the steady-state approximation can be used, i.e.,

1 * 1 *[ ] ( ) [ ]EX FM TM GM

dM R k k k M

dt

1 *[ ]EX i iR k M

1 *[ ] 0d

Mdt

1 *[ ] /ss EX i iM R k

MODULE 19(701)

Since

The superscript '0' indicates that [Q] = 0.

b is a proportionality (instrument) constant

When [Q] > 0, another deactivation channel is added

1 * 1 *[ ] [ ]FG M b M

0 /F EX i iG b R k

1 * 1 *[ ] ( [ ])[ ]Ex i i QM

dM R k k Q M

dt

/ ( [ ])F EX i i QMG b R k k Q

0 [ ]1 [ ]QMi i QMF

F i i i M

kk k QGQ

G k k

MODULE 19(701)

Defining M as and1M i ik SV QM MK k

0

1 [ ]Fsv

F

GK Q

G

This analysis is named the Stern-Volmer kinetic

analysis, after its originators, and KSV is the Stern-Volmer constant.

GF0/GF is measurable, and

is a linear function of [Q].

Note that the intercept is unity as required by the S-

V equation.

G0/G

[O2]

1.0

MODULE 19(701)

Whenever you make a S-V plot and it is not linear or does not have an intercept of unity you must suspect that the

kinetic scheme you are using is not correct.

Recall that

this competition kinetics approach evaluates a ratio of rate constants (bimolecular/unimolecular).

Even though kQM and Σki can be very large (approaching the theoretical limit), their relative magnitudes are

available through the competition kinetics method.

There is no requirement for time-resolved equipment.

The Stern-Volmer constant informs us how effectively the quencher can compete with the total unimolecular

deactivation.

/sv QM M QM i iK k k k

MODULE 19(701)

Relative quenching efficiency

In a series of quenchers, their individual kQM values express the different quenching efficiencies.

For the quenchers Q1, Q2, Q3, … we can write:

(since M is an intrinsic property of the fluorescent state and is independent of the quencher)

Thus we can evaluate the SV coefficient ratios.

And if we can obtain an absolute value for one kQM value, we can obtain the absolute values of the others.

1 2 3 (1) (2) (3): : ... : : ...Q M Q M Q M sv sv svk k k K K K

MODULE 19(701)

M

We defined Σiki as the sum of the rate constants that relate to intrinsic decay processes of 1M*.

Furthermore we defined its inverse as being equal to a quantity we labeled M.

The dimensions of Σiki are s-1, thus those of M are s.Suppose an ensemble of 1M* states is produced by a

brief flash of light incident upon a solution of M. A the end of the flash Rex = 0, thus when [Q] = 0

1 * 1 * 1 *[ ] [ ] [ ]i i M

dM k M k M

dt 1( )M i i Mk k

1 * 1 *0[ ] [ ] Mk tM M e /1 * 1 *

0[ ] [ ] MtM M e

MODULE 19(701)

After the flash, the population of excited states decays exponentially with time.

At time t = M

Thus M corresponds to that time at which the concentration of excited states has fallen to 1/e of the

initial value.

1 * 1 * 10[ ] [ ]

MM M e

1/ 1/M i i Mk k

M is the FLUORESCENCE LIFETIME of M

(no bimolecular processes).

We have defined via excited state concentrations.

We could equally well have used fluorescence intensity time profiles, hence the name fluorescence lifetime.

MODULE 19(701)

In general, the reciprocal of any unimolecular rate constant (s-1) has the dimensions of time and can be

called a lifetime.

For example, we saw above the RADIATIVE LIFETIME1/FM FMk

We can derive the SV equation in terms of lifetimes,

Thus when [Q] = 0

And when [Q] > 0

1/ ( [ ])M QMk k Q

1/ 1/M M i ik k

1 [ ] 1 [ ] 1 [ ]QMMQM M sv

M

kQ k Q K Q

k

MODULE 19(701)

M values fall in the range 10-11 s to 10-7 s, with most in the 1 to 10 ns range.

COMPOUND LIFETIME/NS

ROSE BENGAL/WATER 0.08

ROSE BENGAL/ACN 2.0

ANTHRACENE/c-HEX 4.0

NAPHTHALENE/c-HEX 95

PYRENE/c-HEX 450

MODULE 19(701)

Some practicalities of quenching kinetics

Fluorescence lifetimes are short and so any technique that intends to measure them must have a high time

resolution.

When quenchers are present then the lifetimes are even shorter.

A bimolecular reaxn that is to effectively quench the fluorescence process must possess a high bimolecular

rate constant, e.g.

' [ ]M M QMk k k Q

' [ ]M M M QMk k k k Q

MODULE 19(701)

kM is the rate constant difference caused by the presence of Q.

Effective quenching occurs when kM’/kM = 5, or more.

If kM is 108 s-1 (10 ns lifetime), then kM ~ 4x108 s-1, or kQM[Q] = 4x108 s-1.

The product kQM[Q] can be varied by changing [Q] within the limits of solubility.

Thus, when [Q]= 10-2 M, the above [Q] product requires kQM= 4x1010

It turns out that such a value for a bimolecular rate constant between normal-sized molecules in a mobile solvent represents the "diffusion-limited" value. (more

later)

MODULE 19(701)

QUANTUM EFFICIENCIES AND QUANTUM YIELDS

The molecular quantum efficiency of fluorescence (qFM) is the ratio of the number of photons emitted by a

population of fluorophores to the number of molecules excited into the fluorescent (S1) state (i.e. the number of

photons absorbed).

Under conditions when some of the fluorescent states are quenched (by Q) the fluorescence yield is less than qFM and we use the term molecular fluorescence quantum

yield (FM) to express this.

1 *[ ] /

/FM FM a

FM ii

FM M

q k M I

k k

k

MODULE 19(701)

X= Number of molecules of X converted per photon absorbed

=

=

Rateof X conversion

Rateof light absorption

Rateof X conversion

Rateof all processes involved

1 * 1 *[ ] /{ [ ]}[ ]FM FM FM NR QMk M k k k Q M

/ ( [ ])FM FM NR QM FMk k k k Q k

/ ( )TM TM FM NR TM Mq k k k k No quencher

The combination of quantum yield and lifetime measurements allows evaluation of the individual rate

constants.

MODULE 19(701)

SIGNIFICANCE OF FLUORESCENCE STUDIES

Fluorescence results from an electric dipole transition.

It is a property of an electronically excited state of a molecule.

It informs about how the state deactivates and how it reacts with other molecules.

Fluorescence spectra give information on:

Vibrational spacing in S0

Efficiency of v’ = 0 to v = 0, 1, 2, …transitions (via FM).

MODULE 19(701)

Fluorescence lifetimes give information on:

Effectiveness of the radiative process.

Bimolecular rate constants and the reactivity of S1 (towards energy transfer, electron transfer, proton

transfer, atom transfer, and other physical quenching processes).

In the section “SPECTROFLUORIMETRY: practical considerations” you will find a development of how the

light collected is converted into a voltage signal and how this can be employed to generate the SV relationship.

Following that is a section on errors.

MODULE 19(701)

The Module ends with an adaptation from a recent review written by Kevin Henbest and myself. There is a lot of

detail about fluorescence lifetime measurements.

Basically there are four kinds of experiments that can be used for a determination of

1 photoelectric DC recording

2 Time-correlated single photon counting

3 Fluorescence up-conversion

4 Phase shift determination

To a large extent the one you choose depends on the lifetime of the excited state you are interested in.