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). 1 M* M SECONDARY SPECIES LATER SPECIES FINAL PRODUCTS BIOLOGICAL EVENTS DE-ACTIVATION (RAD/NON-RAD) ABS

MODULE 21(701) 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.

MODULE 21(701) 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 O 2, 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.

MODULE 21(701) 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 m s represents the quantum number for the projection of the spin vector on the z-axis.

  MODULE 21(701) The magnitude of spin angular momentum vector is and the z component is m s ħ, 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

MODULE 21(701) The spin vector can take up 2s +1 = 2 different orientations with respect to the z-axis. One corresponds to m s = +1/2; the other m s = -1/2. These are also referred to as  ; , or spin-up; spin-down. Not only are the m s components opposed but also the vectors are shown out of phase by 180 o.  

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.

MODULE 21(701) ½ 1 S# of electrons

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 + 1Multiplicity 0 1singlet 1/2 2doublet 1 3triplet 3/2 4quartet 2 5quintet

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 Cu 2+ 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 M s = 0 level of the triplet state. Coupling the top vector in the Figure with the next down gives a pair of  spins, the M s =1 level, and coupling the bottom vector with the next up yields the M s = -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 M s = 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 S 1 (for example) to v’ > 0 of T 1. The excess vibr energy is subsequently lost by IC to T 1 (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.

MODULE 21(701) Photo-excitation to S 1 (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 T 1 (v’ = 0) is reached. The triplet is “metastable” because the downward path to S 0 is spin forbidden. S1S1 S0S0 T1T1 ISC Delayed Fluorescence

MODULE 21(701) The long-lived T 1 state can be thermally repopulated (subject to the Boltzmann condition) into an upper vibrational level of T 1. Then ISC can regenerate S 1, 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 S 1. 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"

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.

MODULE 21(701) Phosphorescence The radiative transitions are forbidden since total electron spin is not conserved. Values of k PT are very low ( 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 k T is the sum of the unimolecular rate constants that are deactivating the triplet state.

MODULE 21(701) The phosphorescence quantum yield The ratio of the number of phosphorescence photons emitted to the number of molecules excited into S 1, or nm ABSORPTIONFLUORESCENCEPHOSPHORESCENCE I

MODULE 21(701) The quantum efficiency of phosphorescence is the total number of emitted photons per photon absorbed. Just as we use the S 1  S 0 radiative process (fluorescence) to learn about the chemistry of S 1 states, so we can use the T 1  S 0 radiative transition (phosphorescence) to learn about the chemistry of T 1 states. BUT… and phosphorescence is very weak in comparison to fluorescence and in fluid solutions at room temperature the denominator in is dominated by k GT and phosphorescence signals are extremely weak and often blend into the baseline noise, or into the long red tail of the fluorescence Lorentzian.

MODULE 21(701) Because of the forbidden nature of the T  S 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.

MODULE 21(701) In low temperature (77 K) glassy matrices, k GT is diminished and k PT 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.

MODULE 21(701) M(S 0 ) + h P R +  M(S 0 ) +  Bimolecular processes 3 M* M 1 M* 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)]: k GT is the first order rate parameter describing all the intramolecular (except the radiative one) and solvent-induced processes deactivating T 1 k RT 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 :

MODULE 21(701) Singlet states are very short-lived species and in most cases Thus, with these limitations, T 1 decays exponentially with a rate constant k T When Q is added, the term k QM [Q] augments the rate of triplet decay and the multiplier of time in the exponential becomes: where k obs is the observed first order rate constant describing the triplet decay. k QM can be obtained by plotting k obs vs. [Q].

MODULE 21(701) BEWARE!! Under excitation conditions where high concentrations of 3 T* are generated (> M, 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/k T ) is particularly long.

MODULE 21(701) Triplet-triplet absorption spectrophotometry S1S1 S0S0 T3T3 T2T2 T1T1