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13…Deactivation of Excited States

13…Deactivation of Excited States

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1 Foundations of Photochemistry



69



Fig. 1.23 Influence of changes in equilibrium nuclear geometry on absorption and emission. In

this extreme example the excited state has a significantly longer bond length than the ground

state. Absorption occurs from the first vibration level of the ground state, across the range of

nuclear coordinates represented by the vertical transitions in the grey band. In the excited-state

these nuclear coordinates correspond to a compressed bond, so absorption is into highly

vibrationally excited levels of the excited state. These quickly relax to the lowest vibrational level

of the excited state. Emission occurs from the first vibration level of the ground state, across the

range of nuclear coordinates represented by the vertical transitions in the grey band. In the ground

state these nuclear coordinated correspond to a stretched bond, so emission is into vibrationally

excited levels of the ground state. As a consequence, the emission spectrum is at lower energy,

longer wavelength, than the absorption spectrum. This difference in energy is called the Stokes

shift. The closer the ground and excited state geometries, the smaller the Stokes shift. The

vibrational spacing in the absorption spectrum corresponds to excited-state vibrations; that in

emission corresponds to ground state vibrations. The 0,0 band corresponds to the electronic

transition when both states are in their lowest vibrational energy



physicist Aleksander Jabłon´ski. The Jablonski diagram shows the electronic states

and their relative energies, which are typically singlet (S0, S1, …, Sn) and triplet

(T1, T2, …) electronic states of increasing energy for most organic molecules. The

vibrational levels associated with each electronic state are also shown and are

denoted as v = 1, 2 etc. For simplicity, only the excited-state primary relaxation

pathways are illustrated here—a more detailed Jablonski diagram may be found in

Fig. (15.1). An important distinction is made between processes involving radiative deactivation, i.e. emission, and those which are radiationless. Radiative

transitions are shown as straight vertical arrows, while non-radiative transitions are

represented by wavy horizontal, i.e. isoenergetic, arrows. Note, that neither

absorption nor radiative relaxation are restricted to transitions to the lowest

vibrational level of an electronic energy state, so that both ground and excited

states may be populated as vibrationally ‘hot’ states from radiative transitions.



70



P. Douglas et al.



Fig. 1.24 Simple Jablonski diagram illustrating the primary deactivation processes occurring

upon excitation



1.13.2 Radiative Decay Processes: Stimulated Emission,

Fluorescence and Phosphorescence

Radiative decay is the inverse of absorption and requires coupling of the two states

via either an incident photon, which results in stimulated emission, or the constantly fluctuating radiation field, which results in spontaneous emission. The

radiative lifetime is also the inverse of the Einstein A coefficient. This can be

calculated from the integrated molar absorption coefficient in the absorption

spectrum using the Strickler–Berg relationship [55].

The transition probabilities for both stimulated and spontaneous emission are

linked to the transition probability for absorption, such that a transition that is

highly allowed in absorption will be highly allowed in emission, and one forbidden

in absorption will be forbidden in emission. The transition probability for stimulated emission is exactly the same as that for absorption, and the ratio of the rates

of absorption and stimulated emission is given simply by the ratio of the ground

and excited state populations. Thus, for electronic transitions for systems in

thermal equilibrium at room temperature, absorption dominates; at a high enough

temperature to give essentially equal populations (see Boltzmann Eq. 1.16) the

rates of absorption and stimulated emission will be approximately equal, although

absorption is always slightly more probable than stimulated emission; and for

those non-equilibrium cases, where the population of the higher state exceeds that

of the lower, which is the condition of a population inversion, stimulated emission

will dominate and the system will lase (see Sect. 14.4.2.4).

The transition probability for spontaneous emission shows that the rate of

spontaneous emission depends linearly on the oscillator strength for the absorption



1 Foundations of Photochemistry



71



and the cube of the emission frequency (Eqs. 1.21 and 1.30). Thus, spontaneous

emission is a much faster process for high frequency transitions than low frequency transitions, all other things being equal. Also, because of the spin selection

rule, oscillator strengths for radiative transitions between states of the same spin

multiplicity, i.e. fluorescence, are much higher than those for radiative transitions

between states of different spin multiplicity, i.e. phosphorescence, and therefore

radiative rates are much higher for fluorescence than phosphorescence.

Fluorescence lifetimes for strongly absorbing transitions in the visible are

typically a few ns; those for symmetry-forbidden fluorescence transitions, such as

found with symmetrical polyaromatics can be hundreds of ns. Radiative lifetimes

for phosphorescence, in the absence of any heavy-atom relaxation of the spin

selection rule, can be as long as many minutes, while systems with some relaxation

of the rule typically show phosphorescence radiative lifetimes of microseconds

(ls) to milliseconds (ms).

Direct semiconductors have strongly allowed optical transitions, with relatively

short radiative rate constants and thus short-lived excited states, which can be

highly emissive following excitation. For indirect semiconductors optical transitions are forbidden, absorption coefficients are low, they have relatively long

radiative lifetimes and therefore potentially long-lived excited states, and deactivation after excitation is not usually emissive.



1.13.3 Non-Radiative Processes

All non-radiative electronic processes are isoenergetic transitions to another electronic state, which may or may not be the ground state. This other state may be

localised on the same molecule, or on molecules produced by unimolecular

chemical reaction from the excited-state; or the process may involve interaction

with states on another system which acts as a quencher of the excited-state, e.g. by

energy transfer or bimolecular reaction. (The resultant electronic state(s) may

themselves deactivate non-radiatively or radiatively, e.g. the phosphorescence from

a triplet state formed from a higher singlet, emission from excimers and exciplexes

formed from ground-state excited state interaction (see Sect. 1.13.5.5), or emission

from quencher states produced by energy transfer or chemical reaction.)



1.13.3.1 Internal Non-Radiative Processes

In an isolated molecule, non-radiative processes are not a deactivation of energy,

but rather a redistribution of energy within the molecule to give a more probable

distribution within the rotational, vibrational and electronic energy levels available; a distribution which, for any individual molecule, will itself be constantly

changing, as nuclei and electrons move within the molecular framework. For

energy to be lost non-radiatively, there must be a mechanism for loss of energy to



72



P. Douglas et al.



other molecules or the surroundings. In gas and solution phases this is usually via

collisions, in the solid-state it is to thermal/vibrational states of the solid material.

In solution, the frequency of collision with solute is of the order of picoseconds,

and therefore thermal equilibration of vibrational states, i.e. the relaxation of nonBoltzmann high-energy vibrational states, vibrational relaxation, is usually faster

than all but the fastest photophysical processes (see Chaps. 3 and 15 for examples

where it is not). Hence, population of a higher vibrational level of an electronic

state is almost immediately followed by rapid deactivation (*10-14–10-11 s) to

the lowest vibrational level of that state. In gases at moderate pressures, collision

frequencies are of the order of ns–ps, but at low temperature and low pressures

collisional deactivation in gases can be very much slower than photophysical

processes.



1.13.3.2 Internal Conversion, Intersystem Crossing and Vibrational

Relaxation

Internal conversion (IC) is the transition to a state of the same spin multiplicity,

while intersystem crossing (ISC) is the transition to a state of different spin

multiplicity; in both cases the transition is often to high vibrational levels of the

final state. Internal conversion and intersystem crossing are normally immediately

followed by vibrational relaxation (vr) to the lowest vibrational level of the new

electronic state. IC is usually very fast from Sn to S1, and from Tn to T1, and this

along with fast vibrational relaxation is the basis of Kasha’s rule—that emission

occurs from the lowest excited-state of a given multiplicity [56]. Conservation of

angular momentum requires a mechanism to exchange the electron spin angular

momentum for orbital angular momentum during intersystem crossing. Overlap of

the vibrational wavefunctions of any two electronic states decreases rapidly as the

energy difference between the zero point vibrational levels of the states increases.

Because of this, the rate of non-radiative processes decreases rapidly as the energy

gap between the two electronic states increases. This means that non-radiative

processes are fastest between states which are close in energy, and slowest

between states which are very different in energy. This effect of the energy gap

between states on the rate of non-radiative processes is called the ‘energy gap law’.



1.13.3.3 Unimolecular Chemical Reactions

Ionisation, dissociation and isomerisation are the three unimolecular reactions

possible following absorption. Ionisation requires excitation with enough energy

for electron ejection (electron transfer also leads to ion formation but this is a

different process where an electron is transferred to another molecule).

Bond breaking in the excited-state can result in dissociation and isomerisation.

Dissociation is quite common for small molecules, where breaking a single bond is



1 Foundations of Photochemistry



73



sufficient to break the molecule. For example, hydrogen peroxide on photolysis

can photodissociate to form two hydroxyl radicals:

H2 O2 ỵ hv ! 2 OH



ð1:31Þ



For larger molecules held together by a network of bonds, and where transitions

are more delocalised, photodissociation is less likely, but isomerisation, made

achievable by bond breakage, is possible, e.g. breakage of one bond in a double

bond can lead to cis–trans isomerisation, such as the cis–trans isomerisation of

retinal in the photochemical step in vision (Fig. 1.1). Breakage of a single bond in

ring structures can lead to ring opening, as in the spiropyran photochromics, which

are discussed in detail in Chap. 4.



1.13.4 Competition Between Decay Routes and Quantum

Yield

All deactivation processes are competitive, so the rate constant for decay of the

excited state, kobs, (the observed decay rate constant) is given by the sum of rates

for all deactivation processes, i.e. if all decay routes are first order process:

X

kobs ẳ

kdeactivation :

1:32ị

The quantum yield of a process, event or reaction x, /x, relates the rate of

photon absorption with the rate of any process of interest, and by integration of

these over time, also gives the ratio of the total number of events of interest to the

total number of photons absorbed, i.e.

/x ¼



ðtotal number of processes, events or reaction, xÞ

:

ðtotal number of photons absorbed)



ð1:33Þ



According to the Stark–Einstein law, /x should be equal to unity or less.

However, if secondary processes occur, /x can sometime be greater than 1. Under

continuous illumination, a steady-state will be reached, such that the rate of

excited-state formation, Jabs, will be equal to the rate of deactivation by all

intramolecular processes, Jtotal, i.e.

Jabs ẳ Jtotal :



1:34ị



If we consider the vibrationally-relaxed S1 excited-state in Fig. 1.24 as an

example, the competing intramolecular photophysical process that can lead to its

relaxation are fluorescence, internal conversion and intersystem crossing, and Jtotal

is given by:

Jtotal ẳ dẵS1 =dt ẳ kF ỵ kIC ỵ kISC ịẵS1 ẳ ktotal ẵS1



1:35ị



74



P. Douglas et al.



where kF, kIC, kISC are the first-order rate constants for fluorescence, internal

conversion and intersystem crossing, respectively. Solution of Eq. 1.35 gives:

½S1 t ẳ ẵS1 0 exp( -t=1 sị



1:36ị



where [S1]0 and [S1]t are the concentration of excited S1 states at time t = 0 (i.e.

immediately after excitation) and time t following excitation, respectively and 1s is

the excited-state lifetime. Time-resolved fluorescence is a convenient technique by

which the lifetime of the excited-state may be measured (see Chaps. 14 and 15 for

experimental details). Note that 1s is the excited singlet-state lifetime in the

presence of all intramolecular deactivation pathways, i.e.

1



s ẳ 1=kF ỵ kIC ỵ kISC Þ ¼ 1=ktotal :



ð1:37Þ

1



In the absence of radiationless decay, the radiative lifetime s0 is given by:

1



s0 ẳ 1=kF :



1:38ị



The fluorescence quantum yield, /F, of a material will often determine its

suitability for a given application, for example /F should be high for display

technology (Chap. 4) but low for solar cells (Chap. 7). The experimental determination of /F (and other quantum yields) is discussed in Chap. 15. From

Eqs. 1.33 and 1.34, /F is given by:

/F ẳ JF =Jabs ẳ JF =Jtotal



1:39ị



where JF is the rate of fluorescence. This may be rewritten as:

/F ẳ kF ẵS1 =ktotal ẵS1 ẳ kF =ktotal :



1:40ị



Since kF = 1/1s0 and ktotal = 1/1s:

/F ¼ 1 s=1 s0 :



ð1:41Þ



1.13.5 Bimolecular Interactions, Quenching and Energy

Transfer

So far we have only considered the intramolecular processes which may lead to

the deactivation of an excited state. Intermolecular excited-state relaxation is also

possible. Any molecule or substance which upon interaction with an excited-state

leads to an increase in the rate of relaxation is known as a quencher. The quencher

may either be the same chemical species as the excited-state itself (self-quenching)

or a different one.



1 Foundations of Photochemistry



75



1.13.5.1 The Nature of the Quenching Processes

The first distinction comes between short range quenching, where overlap of the

orbitals of the quencher and excited-state molecule of interest is required, and long

range quenching, where there is a through space coupling between the deactivating transition of the excited-state being quenched and an excitation transition

on the quencher molecule. Quenching can also be classified by whether or not a

chemical change is caused; if there is, it is chemical quenching, if not, it is physical

quenching.



1.13.5.2 Long range dipole–dipole quenching: Förster Resonance

Energy Transfer (FRET)

Energy can be exchanged between molecules at a significant intermolecular separation by a process in which the transition dipole moments on the two molecules

couple through space. This was first observed by Franck and Cario between excited

mercury and thallium atoms in the gas phase [57], and subsequently studied for

molecules in condensed phases by Förster [58, 59]. The process is commonly termed

Förster Resonance Energy Transfer (FRET). It involves dipole–dipole coupling

between electronic energy donor and acceptor, as represented schematically in

Fig. 1.25. The rate constant, kFRET, can be calculated from the spectral properties of

the donor and acceptor, their separation, and their relative orientations:



kFRET ¼ KFRET /D JAD j2 n4 sD R6DA :

ð1:42Þ

Here, KFRET is a collection of various constants, /D is the donor emission

quantum yield; JAD is the overlap integral between the emission spectrum of the

donor and the absorption spectrum of the acceptor; j2 is the dipole orientation

factor, which depends upon the relative orientations of donor and acceptor; n is the

refractive index of the medium; sD the observed donor lifetime (note that /D/sD is

the radiative rate constant of the donor) and RDA is the donor acceptor separation.

The efficiency of FRET is often represented by the Förster distance (R0), which

is that separation at which the rate of FRET is equal to all other decay rates of the

donor, i.e. when 50 % of the initial excitation energy will be transferred to the

acceptor. The rate constant for FRET at any separation R is then given by:

kFRET ẳ 1=sD ịR0 =Rị6 :



1:43ị



Energy transfer is an isoenergetic process, hence the requirement for donor

emission and acceptor absorption band overlap. JAD is calculated from the area of

the overlap of the emission spectrum, normalised to an area of 1 and plotted in

frequency (usually cm-1) rather than wavelength, with the absorption spectrum,

plotted in terms of e vs frequency. In addition, FRET is most commonly

encountered when both transitions are highly allowed, e.g. in singlet–singlet

energy transfer these conditions are met by a high donor radiative decay rate



76



P. Douglas et al.



Fig. 1.25 Orbital

comparison of long- and

short-range quenching of an

excited state (D*) and a

ground state acceptor (A) by

a Förster energy transfer

(long-range), b Dexter energy

transfer (short-range) and

c photoinduced electron

transfer (short range)



constant, and large JAD arising from a high acceptor e. However, it is possible for

the donor transition to be forbidden and FRET to still be efficient, even if not fast,

provided the long lifetime of the donor is sufficient to compensate for the reduction

in the rate of FRET; thus triplet–singlet FRET is possible. Singlet–triplet and

triplet–triplet FRET are so slow that they are unimportant processes. Table 1.7

gives FRET distances for typical donor-acceptor pairs of molecules. FRET is

characterised by a reduction in both the donor emission quantum yield and donor

lifetime. However, if donor–acceptor distances are fixed, but not equal, then each

different donor–acceptor distance must be considered a different population for

kinetic analysis.



1.13.5.3 Short Range Quenching: Static and Dynamic Quenching,

Perturbation, Electron Transfer and Dexter Quenching

In these processes the two molecules must be at (or able to approach each other to)

the relatively short distances required for orbital overlap. This requires approach to



1 Foundations of Photochemistry



77



Table 1.7 Förster energy transfer distances for some typical donor–acceptor pairs

Donor

Acceptor



R0/nm



Anthracene

Benzene

Biphenyl

Biphenyl

Indole

Naphthalene

Naphthalene

Pyrene

p-Terphenyl



2.51a

1.93b

1.09b

2.81b

2.65a

2.50a

2.44a

3.00a

4.21b



Rhodamine 6G

1,3,5-triphenylbenzene

Naphthalene

2-Phenylnaphthalene

Rose Bengal

Quinine sulfate

Rhodamine 6G

Uranine (fluorescein)

1,4-bis(5-phenyloxazol-2-yl) benzene (POPOP)c



Data taken from Ref. [60]. The structures and photophysical data for many of these molecules can

be found in Chap. 4

a

In ethanol solution

b

In cyclohexane solution

c

1,4-bis(5-phenyloxazol-2-yl) benzene



typically *200–500 pm. If close approach is obtained by molecular diffusion, or

energy or exciton migration, then the lifetime of the excited-state, concentration of

quencher, and diffusion rate, are key parameters in determining the efficiency of

quenching. Thus the much longer lifetime of the triplet-state compared to singletstate means that collisional triplet quenching can be very effective in typical nonviscous solvents even at low (*10-6 mol dm-3) quencher concentrations,

whereas diffusional collisional quenching of singlets in typical non-viscous solvents requires quencher concentrations of * 10-2 mol dm-3.

The second-order rate constant for diffusion-controlled reactions, kdiff, depends

on the viscosity (g, in mPa s) according to the Smoluchowski equation:

kdiff ¼ 8RT=3g:



ð1:44Þ



The diffusion-controlled rate constant in water (g = 0.890 mPa s) is

7.4 9 109 mol-1 dm s-1; values in a variety of solvents are given in the literature

[34]. This equation is valid for reaction between neutral species of the same size.

The effect of charge and size is discussed in standard textbooks on chemical

kinetics [61]. Diffusional quenching is often termed dynamic quenching because it

involves movement. The effect of dynamic quenching is a reduction in both the

quantum yields of competing processes, such as emission from the donor, and the

lifetime of the donor excited-state.

If close approach is obtained by a random distribution of quenchers in a fixed

matrix then the excited-state lifetime is somewhat less important. The rate depends

on orbital overlap, and this decreases exponentially with distance, so only those

donors with a neighbouring acceptor will be quenched, and these quenched very

quickly, while those without a neighbouring quencher will remain unquenched.

This leads to the condition of static quenching in which the quantum yields of

competing processes, such as emission from the donor, are reduced by very fast



78



P. Douglas et al.



quenching of a certain fraction of donors, but the lifetime of the unquenched donor

remains the same as in the absence of quencher.

Three mechanisms of short range quenching can be identified: perturbation,

electron transfer, and energy transfer.

Perturbation quenching. Here, orbital overlap allows some property of the

quencher molecule to be shared with the donor excited-state. Heavy-atom

quenching and paramagnetic quenching are of this type. In heavy-atom quenching

orbital overlap with a heavy atom quencher introduces an element of spin–orbit

coupling into the orbitals of the excited-state donor and provides a mechanism for

deactivation via otherwise spin-forbidden routes, notably intersystem crossing.

Paramagnetic quenching is similar, but here the quencher is a paramagnetic ion

and it is the unpaired spins on the quencher which introduce otherwise spinforbidden deactivation routes.

Electron transfer quenching. Here, orbital overlap allows transfer of an electron

between the two molecules. As discussed earlier a molecule in an excited state is

simultaneously a better oxidant and reductant than the ground-state, and a

quencher with a HOMO or LUMO at the correct energy, which can overlap with

either the HOMO or LUMO of the excited-state will act as an electron transfer

quencher (see Fig. 1.25). The requirement for electron transfer quenching is

overlap of two orbitals, one from each participant. Transfer is most rapid, and

quenching most efficient, for those cases in which there is little nuclear rearrangement required in moving from neutral to oxidised/reduced species. The

theory of rates of ground state electron transfer reactions has been comprehensively developed notably by Rudolph Marcus [62], and similar considerations

apply to excited-state electron transfer. A detailed description is given in Chap. 15

of Ref. [61].

Collisional energy transfer quenching. In this case, simultaneous exchange of

two electrons occurs, requiring overlap of two pairs of orbitals, and orbital overlap

criteria are more demanding than for electron transfer quenching [63] (Fig. 1.25):

D ỵ A ! D ỵ A :



1:45ị



The process is often referred to as Dexter energy transfer, after David L. Dexter

who, following on from earlier work by Förster, developed a detailed quantitative

description of the various coupling mechanisms involved in electronic energy

transfer [64]. The relevant equation in its simplest form is:

kDEX ¼ KDEX JexpðÀ2RDA=LÞ :



ð1:46Þ



The key term is usually the exponential in which RDA is the mean distance

between the donor and acceptor, and L is the sum of their van der Waals radii, so

the rate constant decreases exponentially with increasing D-A separation and

Dexter energy transfer is only efficient when A and D are close. kDEX cannot,

generally, be so easily related to spectral features as is possible for Förster energy

transfer, and KDEX is a constant which usually has to be determined experimentally. Note that there are no constraints on the ‘allowedness’ of either D or A



1 Foundations of Photochemistry



79



transitions, all that is required is energy conservation (i.e. an isoenergetic energy

transfer) and overall spin conservation, so transitions to and from all multiplicities

are possible: singlet–singlet, singlet–triplet, triplet–singlet, and triplet–triplet, and

other combinations of D and A multiplicities, are all possible. JDEX is termed the

normalised spectral overlap integral (cf. JAD for FRET) and corresponds to the

overlap of the emission spectrum of the donor and absorption spectrum of the

acceptor, given in cm-1, with both normalised to an area of 1. The term spectral

overlap may seem something of a misnomer when describing Dexter energy

transfer, since the process is possible between species for which spectral data for

the transition(s) is impossible to obtain, such as highly forbidden S$T transitions

where neither absorption nor emission can be detected. The importance of the

spectral overlap term, however, is that it gives an estimate of the probability of

energy matching for the transitions on D and A. Where spectral data are not

available, estimation of the transition energies for transitions on A and D can be

used to assess whether energy transfer will occur or not. Generally, the relatively

high density of states for molecules means that energy matching is not limiting for

molecular energy transfer where the change in electronic energy on A is lower

than that on D. For atoms, which have a low density of states, energy matching can

limit kDEX, although for atoms in solids, energy matching can be enhanced if the

electronic transition is coupled with lattice phonon transitions, the solid effectively

generating higher densities of states than are present in isolated atoms.

It is important to note that the Dexter and Förster models involve a number of

simplifications, in particular in treating the systems as involving point dipoles.

More recent theoretical studies have concentrated on overcoming these limitations

[65, 66].



1.13.5.4 Quantification of the Quenching Process: The Stern–Volmer

Relationship

Quenching, by any of the mechanisms outlined above, will also compete with the

various intramolecular photophysical relaxation routes that deactivate the excitedstate. The presence of quenching, therefore, will lead to a reduction in the luminescence intensity (fluorescence or phosphorescence), which is related to the

quencher concentration [Q] by the Stern–Volmer equation [67]:

I0

ẳ 1 ỵ kSV ẵQ

I



1:47ị



where I0 and I are the luminescence intensity (at a given wavelength) in the

absence and presence of the quencher at concentration [Q], respectively and kSV is

the Stern–Volmer constant. For dynamic quenching, kSV is related to the bimolecular quenching rate constant, kq, and the excited-state lifetime: kSV = k1qs.

For dynamic quenching, the Stern–Volmer relationship may also by described

in terms of the excited-state lifetime:



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