MODULE 21(701)

The Nature and Properties of Excited

States

The absorption of a photon by a

molecule can set in train a series of

processes, chemical or physical, that terminate when

thermal equilibrium has been regained

(unless a subsequent

biological change is possible).

1M*

M

SECONDARY SPECIES

LATER SPECIES

FINAL PRODUCTS

BIOLOGICAL EVENTS

DE-ACTIVATION (RAD/NON-

RAD)ABS

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All processes after the primary one may involve other species present in the sample

Reactions such as bond breaking, bond formation, atom transfer, energy transfer, electron transfer, proton

transfer, etc may be initiated.

To investigate this plethora of processes the experimental photoscientist employs a variety of tools and techniques in order to describe, evaluate and understand the various

steps between light absorption and final product formation.

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Questions that are addressed include:•What is the nature and reactivity of the primary excited states and states derived there from?•What are the final products, what are their yields, and what environmental factors determine these?•What are the identities of the intermediate species in the sequence and what kinetic and thermodynamic properties do they possess?•What factors, such as molecular structure influence the reactivity of the intermediates?•Are there any biological consequences?

MODULE 21(701)Up to this point we have been mainly concerned with the absorption of light itself and the nature and reactivity of the primary electronically excited state generated in the

absorption process.

Virtually all organic and many inorganic molecules and organometallic complexes exist as singlet (spin-paired) ground states (there are a few notable exceptions, such

as O2, NO, and complexes containing open shell transition metals).

The primary excited state generated by photon absorption is also of singlet multiplicity, and the nature of such singlet states has been the focus of our attention to

now. Now it is useful to remind ourselves of the concept of

multiplicity.

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Electrons, Spin and Multiplicity

The total angular momentum of an electron in an atom/molecule is composed of contributions from its

orbital motion and from its intrinsic angular momentum, conveniently referred to as spin.

The full description of an electronic state requires a quantum number for spin angular momentum, termed s.

The symbol ms represents the quantum number for the projection of the spin vector on the z-axis.

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The magnitude of spin angular momentum vector is

and the z component is msħ , and limited to 2s+1 values

according to

For electrons the only value of s that is allowed is 1/2.

Then the magnitude of the spin angular momentum is

1/ 2{ ( 1)}s s

, 1, 2...,sm s s s s

1 12 21 3 1{ ( 1)} ( x ) 3

2 2 2s s

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The spin vector can take up 2s +1 = 2 different

orientations with respect to the z-axis.

One corresponds to ms =

+1/2; the other ms = -1/2.

These are also referred to as ; , or spin-up; spin-down.

Not only are the ms components opposed but also the vectors are shown out of

phase by 180o.

MODULE 21(701)In multi-electron systems, the electrons occupy orbitals

according to energy requirements (aufbau principle) and to the Pauli exclusion principle (same orbital-spins

opposed).

We define a total spin angular momentum quantum number, S (never negative), which combines the

individual s values through a Clebsch-Gordon series:

For two electrons, S = ½ + ½ = 1, or S = ½ - ½ = 0.

For three electrons, we take the values of S for two electrons and combine them with s = ½ for the additional

one, and so on.

1 2 1 2 1 2, 1,...S s s s s s s

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121 1 1 1, 1 1,02 2 2 2 1 1 3 11 ,0 ,2 2 2 2

3 1 1 1, 2,1,02 2 2 2

1 1 1 5 3 12 ,1 ,0 , ,2 2 2 2 2 2

5

4

3

2

½1

S# of electrons

1 1 1 1, 1 1,02 2 2 2

1 1 3 11 ,0 ,2 2 2 2

3 1 1 1, 2,1,02 2 2 2

1 1 1 5 3 12 ,1 ,0 , ,2 2 2 2 2 2

MODULE 21(701)Multi-electron systems are frequently described by their

(spin) multiplicity. Multiplicity has never been designated with a label.

It takes values of 2S + 1

S 2S + 1 Multiplicity

0 1 singlet

1/2 2 doublet

1 3 triplet

3/2 4 quartet

2 5 quintet

MODULE 21(701)Thus, a system in which all the spins are paired except for a single electron (e.g., a free radical or a Cu2+ ion) has S

= 1/2 and is a doublet state. A system in which two electrons are unpaired has S = 1

and is a triplet state. However, this same system may have the possibility of the two spins being paired (if Pauli allows) when S = 0

and it becomes a singlet state. Most organic molecule ground states have all spins paired

(singlet). Causing one of the spins to invert (in a different orbital)

produces an S = 1 system, i.e., a triplet.

MODULE 21(701)Intersystem Crossing: a re-phasing

mechanism

The unique sub-state of the singlet was represented earlier and in an

analogous way the three sub-states of the triplet may be represented

vectorially. The center pair of vectors shows

similarity to the pair in earlier Figure, except now the vectors are in phase. This represents the Ms = 0 level of the triplet state. Coupling the top vector in the Figure with the

next down gives a pair of spins, the Ms =1 level, and coupling the bottom vector with the next up

yields the Ms = -1 level.

FIG. 21.2

MODULE 21(701) Thus the conversion of singlet to triplet (or the inverse) requires only a re-phasing of vectors in the Ms = 0 sub-

level. Nearby inhomogeneous magnetic fields, such as a heavy

metal center, can accomplish this re-phasing ISC. In an energy sense, ISC proceeds iso-thermally from v = 0

of S1 (for example) to v’ > 0 of T1. The excess vibr energy is subsequently lost by IC to T1 (v’

= 0). From there a spin inverting, forbidden radiative decay

(phosphorescence) can occur. However, the non-radiative process is usually more

efficient (in fluid solutions). ISC applies also to triplet-quintet and doublet-quartet

inter-conversions.

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Photo-excitation to S1 (v’ = n) is rapidly followed by IC to v’ = 0. Now fluorescence and ISC processes are in

competition. Following ISC there is internal conversion in the T manifold until T1 (v’ = 0) is reached.

The triplet is “metastable” because the downward path to S0 is spin forbidden.

S1

S0

T1ISC

Delayed Fluorescence

MODULE 21(701)The long-lived T1 state can be thermally repopulated (subject to the Boltzmann condition) into an upper

vibrational level of T1.

Then ISC can regenerate S1, which can then undergo the fluorescence process.

This triplet state deactivation path is termed "delayed fluorescence".

Requires singlet-triplet energy gaps that are small, and thus it is relatively easy to thermally repopulate S1.

Delayed fluorescence has the same spectrum as prompt version but its lifetime follows that of the triplet state (

).

This type of unimolecular-delayed fluorescence is "E-type"

M T

MODULE 21(701)Another delayed fluorescence mechanism is called "P-

type" (after pyrene). This arises from the bimolecular mutual annihilation of a

pair of triplet states.

The P-type mechanism requires the triplet states to have a lifetime that is long enough for the second order,

bimolecular event between two low concentration species to be able to effectively compete with the first order

decay of the triplet.

3 * 3 * 1 *

1 *F

M M M M

M M hv

3 * 3 * 1 *

1 *F

M M M M

M M hv

MODULE 21(701)Phosphorescence

The radiative transitions are forbidden since total electron spin is not conserved.

Values of kPT are very low ( 10-3 s-1 or less).

The triplet quantum yield is a property of the singlet state

(in the absence of quenchers)

The phosphorescence quantum efficiency is defined by

where kT is the sum of the unimolecular rate constants that are deactivating the triplet state.

0 1S T

/TM TM i ik k

/PT PT Tq k k

1 0T S

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The phosphorescence quantum yield

The ratio of the number of phosphorescence photons emitted to the number of molecules excited into S1, or

PT PT TMq

nm

ABSORPTION FLUORESCENCE PHOSPHORESCENCE

I

MODULE 21(701)The quantum efficiency of phosphorescence is the total

number of emitted photons per photon absorbed.

Just as we use the S1S0 radiative process (fluorescence) to learn about the chemistry of S1 states, so we can use

the T1S0 radiative transition (phosphorescence) to learn about the chemistry of T1 states. BUT…

and phosphorescence is very weak in comparison to fluorescence and in fluid solutions at room temperature

the denominator in

is dominated by kGT and phosphorescence signals are extremely weak and often blend into the baseline noise, or into the long red tail of the fluorescence Lorentzian.

0 0

( ) ( )PT FMq P v dv F v dv q

, ,PT PT FM FMk q k q

/ ( ...)PT PT PT GTq k k k

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Because of the forbidden nature of the TS transition, phosphorescence lifetimes are usually much longer than

fluorescence lifetimes, even in fluid media.

Thus time resolved experiments can be used to discriminate between the short-lived fluorescence and the

longer-lived phosphorescence.

Unfortunately signal-to-noise discrimination is usually poor.

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In low temperature (77 K) glassy matrices, kGT is diminished and kPT can become more significant.

Such measures lead to measurable phosphorescence signals and spectra are attainable which are very useful in

estimating the spectroscopic energy of triplet states.

However triplet state studies in immobilized media are not useful for bimolecular reaction studies since there is

no diffusion

We need another approach for detecting and measuring the time-dependent concentrations of triplet states.

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M(S0) + hP

R + M(S0) +

Bimolecularprocesses

3M*

M 1M*h VARIOUS PROCESSES INCLUDING FLUORESCENCE

Consider the excitation-decay scheme:

MODULE 21(701)Assume that we excite our sample with a flash of light of zero width, and [Q] = 0, and that we can measure [T(t)]:

kGT is the first order rate parameter describing all the intramolecular (except the radiative one) and solvent-

induced processes deactivating T1 kRT represents a putative intramolecular reaction that leaves the system on a product surface (e.g. a Norrish

type II reaction). The solution of the differential equation is :

3 * 1 * 3 *[ ] [ ] [ ]TM Td M k M k Mdt

...T PT GT RTk k k k

1 *3 * 0[ ][ ] (exp( ) exp( ))TM

t T MM T

k MM k t k tk k

MODULE 21(701)Singlet states are very short-lived species and in most

cases

Thus, with these limitations, T1 decays exponentially with a rate constant kT

When Q is added, the term kQM[Q] augments the rate of triplet decay and the multiplier of time in the exponential

becomes:

where kobs is the observed first order rate constant describing the triplet decay.

kQM can be obtained by plotting kobs vs. [Q].

M Tk k

3 * 1 *0[ ] [ ] exp( )TM

t TM

kM M k tk

[ ]obs T QMk k k Q

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BEWARE!!Under excitation conditions where high concentrations of

3T* are generated (> 10-5M, for example) then a bimolecular triplet-triplet annihilation reaction can also

contribute to the triplet decay.

This is a kinetically second order process so the observed kinetics will be mixed second and first order.

This effect is largest when the intrinsic triplet lifetime (T = 1/kT) is particularly long.

3 *

3 * 3 * 1 *

T

TT

M M k

M M M M k

MODULE 21(701)Triplet-triplet absorption spectrophotometry

S1

S0

T3

T2

T1