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J. Phys. Chem. 1996, 100, 7298-7316
FEATURE ARTICLE Magnetic Field Effects on Fluorescence in Isolated Molecules with the Intermediate Level Structure of Singlet-Triplet Mixed States Nobuhiro Ohta Department of Molecular Chemistry, Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060, Japan ReceiVed: June 23, 1995; In Final Form: January 10, 1996X
A review is presented of external magnetic field effects on the fluorescence of isolated molecules which exhibit the intermediate level structure composed of singlet-triplet mixed states. Fluorescence intensity (quantum yield), decay profile (lifetime), and polarization are well affected by an external magnetic field, even when fluorescence is considered to be emitted from a diamagnetic singlet state. Effects of molecular rotation, molecular vibration, methyl internal rotation, and deuterium substitution are observed in magnetic field effects on fluorescence, and these effects are interpreted in terms of the level density of the triplet states coupled to a singlet state. It is also shown how intramolecular vibrational energy redistribution and dissociation via triplet states are related to the field dependence of fluorescence.
I. Introduction The intramolecular relaxation process from electronically excited states of polyatomic molecules such as intersystem crossing (ISC), internal conversion, or vibrational redistribution, which is regarded as a primary process of photochemical reactions, is strongly related to level structure and interstate interaction in the excited states.1-5 These processes are expected to be significantly affected if external perturbations which change a level structure are applied to excited molecules. The external magnetic field (H) is one such perturbation, and the magnetic quenching of emission resulting from the field-induced change in excitation dynamics has been reported in rather small molecules.6-12 The level structure of the triplet state isoenergetic with S1 and the nature and strength of the singlet-triplet (S-T) interaction have been precisely measured in glyoxal or propynal by Lombardi, Huber, and their co-workers13-16 with elegant techniques of anticrossing spectroscopy and quantum beat spectroscopy. Ultrahigh-resolution fluorescence excitation spectroscopy both in the absence and in the presence of a magnetic field has also been applied to rather large molecules such as pyrazine or pyrimidine for elucidation of the nature of the S-T interaction by Kommandeur, Majewski, Pratt, and their coworkers.17,18 On the basis of these results, the relation between level structure and excitation dynamics has been discussed. In this review, external magnetic field effects both on level structure and on relaxation dynamics in the electronically excited states of isolated polyatomic molecules are discussed, on the basis of the field dependence of intensity (quantum yield), decay profile (lifetime), and polarization of fluorescence following excitation into the individual rovibronic levels of the excited states under collision-free conditions. Special attention has been paid to azaaromatic molecules which exhibit the intermediate case behavior of fluorescence characterized by a biexponential decay composed of fast and slowly decaying portions. Those decays are interpreted in terms of strong interaction between a X
Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(95)01751-5 CCC: $12.00
zero-order singlet state carrying the absorption intensity and a number of isoenergetic zero-order triplet states.19-23 Molecular rotation as well as molecular vibration plays a significant role in intramolecular ISC of these molecules, as confirmed by the excited level dependence of fluorescence property.24-30 Fluorescence of these molecules is efficiently affected by H, though the fluorescence is considered to be emitted from the diamagnetic singlet state, and a number of interesting problems concerning the magnetic field effect on level structure of the S-T mixed states and its relation to ISC have been elucidated on the basis of the measurements of the field dependence of intensity and decay of fluorescence following excitation into the individual rovibronic levels of S1.31-40 Especially, magnetic quenching of fluorescence was confirmed to depend on the following: (1) molecular rotation; (2) molecular vibration; (3) methyl internal rotation; (4) deuterium substitution. These dependences are systematically interpreted in terms of the level density of the triplet state coupled to a singlet state. With excitation into a higher vibrational level, intramolecular vibrational energy redistribution to isoenergetic other vibrational levels of the singlet state occurs from the initially prepared level (IPL). In the results, a broad emission from the relaxed levels is observed besides the sharp fluorescence from the IPL.5 It is shown in s-triazine vapor that the sharp fluorescence and the broad fluorescence give a different magnetic field dependence from each other, and the mechanism which interprets the difference is proposed.41 In addition to the fluorescence intensity and decay, fluorescence polarization is also affected by H in these azaaromatic molecules.42,43 Further, the magnetic depolarization of fluorescence resulting from coherent excitation into the S-T mixed states with the intermediate level structure was found to be different from the one expected for molecular resonance fluorescence following excitation into a single rotational level. The elucidation of the magnetic field effects on level structure of the S-T mixed states will be important not only for a thorough understanding of the relation between excitation dynamics and level structure but also for providing a way to © 1996 American Chemical Society
Feature Article
J. Phys. Chem., Vol. 100, No. 18, 1996 7299
control photochemical reactions. In fact, there is a strong relation between magnetic field effect on fluorescence and dissociation via triplet states following ISC. Let me give an instance from acetaldehyde vapor. The magnetic field employed in the present work is as weak as less than 200 G, unless otherwise noted. Even when such a weak field is applied, fluorescence resulting from excitation into the S-T mixed states is affected by H. Many characteristics of magnetic field effects on fluorescence obtained in azaaromatic molecules and acetaldehyde seem to be common on molecules which show a strong S-T interaction, though the efficiency of the field effects depends on the size of the molecule and on the rovibronic level excited. II. Intermediate Case Behavior in Fluorescence Property 2.1. Level Structure and Fluorescence Property. Fluorescence properties are strongly related to the level structure of the excited states.44,45 In this section, a zero-order singlet state, |S〉, and a manifold of zero-order triplet states, {|Tj〉} are considered, and it is surveyed how the yield and decay of fluorescence are related to the level structure of the S-T mixed states. The total energy widths of |S〉 and |Tj〉 are assumed to be expressed as
γS ) ΓS + γnS
(1)
(2) γTj ) ΓTj + γnTj where ΓS and ΓTj are radiative width and γnS and γnTj are nonradiative widths. The coupling of |S〉 and {|Tj〉} leads to the following quasistationary mixed states: |n〉 ) an|S〉 + ∑bnj|Tj〉
(3)
j
where n ) 1, 2, ..., Neff + 1, and Neff is the number of the triplet levels effectively coupled to |S〉. The mixed states under consideration are eigenfunctions of the effective Hamiltonian (Heff ≡ H - iΓ/2), not of the total Hamiltonian H. Γ is the operator corresponding to the line widths of |S〉 and |Tj〉, which result from the interaction of these states other than S-T interaction, e.g., interaction with radiative field and/or interaction with other electronic states, and the eigenvalue (En) and the line width (γn) of the mixed states are given as follows:
En ) n - iγn/2
(4)
γn ) |an| γS + ∑|bn | γTj j 2
2
(5)
j
When Neff is very small, i.e., in the small molecule limit, fluorescence decays are expected to be superimposed by quantum beats in the exponential decay. The frequency of the beats corresponds to the energy separation between different S-T mixed states, and the fluorescence lifetime corresponds to the average energy width of the mixed states given by eq 5. When Neff is medium, i.e., in the so-called intermediate case, the first term of eq 7 gives the population decay whose lifetime corresponds to the line width of each mixed state and the second term gives the dephasing decay whose lifetime corresponds to the total width of the absorption profile. In the results, fluorescence decay of the intermediate case molecules is given by a biexponential decay composed of fast and slowly decaying portion as follows:
IF ) Cf exp(-t/τf) + Cs exp(-t/τs)
(8)
Here, the subscripts f and s indicate the fast and slow components, respectively. The preexponential factors Cf and Cs are roughly proportional to 2∑∑n>m|an|2|am|2 and ∑n|an|4, respectively. If all the coefficients an and am are assumed to be the same, i.e., R, ∑n|an|4 and 2∑∑n>m|an|2|am|2 are given by (Neff + 1)-1 and Neff(Neff + 1)-1, respectively, since |R|2 is given by (Neff + 1)-1. Then, the ratio of the preexponential factors is roughly given by
Cf/Cs ) Neff
(9)
When a mixed state, e.g., |n〉 , is optically excited, the quantum yield of the resulting fluorescence, Φn, is given by |an|2ΓS/γn. By assuming that the coherence width of the excitation light is large enough to cover all the mixed states, therefore, the quantum yield of the slow fluorescence, Φs, may be expressed by ∑nAnΦn/ΣnAn, where An is the absorption intensity of the nth mixed state proportional to |an|2. Since ∑n|an|2 ) 1, Φs is given by
Φs ) ∑|an|4ΓS/γn
(10)
n
If the decay rates of the mixed states, γn, can be substituted by the average value of γ, Φs is given by
Φs ) (ΓS/γ)∑|an|4
(11)
n
In a coherent excitation of a set of mixed states with an assumption that the absorption intensity is carried only by transition to |S〉, the subsequent time evolution of the nonstationary states, |Ψ(t)〉, is described by
With the assumption that all the values of an are the same and that Neff >>1, Φs is given as follows:
|Ψ(t)〉 ) ∑an*|n〉 exp(-iEnt/p)
With the assumption that Neff >>1 and that the line widths of the zero-order triplet states are the same, the lifetime of the slow fluorescence in the intermediate case molecules, τs, as well as the fluorescence lifetime of the small molecule limit is roughly given by
(6)
n
Then, the probability of finding the molecule in |S〉 at time t, denoted by PS(t), is given by PS(t) ) |〈S|Ψ(t)〉|2. Since 〈S|Ψ(t)〉 ) Σn|an|2 exp(-iEnt/p), the intensity of fluorescence, denoted by IF, emitted from |S〉 following excitation of these mixed states with light whose coherent width is large enough to cover all the mixed states is expressed as
IF ) ΓSPS(t) ) ΓS[∑n|an|4 exp(-iγnt/p) + 2∑∑n>m|an|2|am|2 × exp{-i(γn + γm)t/2p} cos{(n - m)t/p}] (7) The time evolution of fluorescence can be simulated with eq 7, and fluorescence properties are characterized by Neff.
Φs ) ΓS/(γNeff)
p/τs ) γ ) γS/Neff + γT
(12)
(13)
As in the case of the statistical limit, where Neff is very large, the quantum yield and lifetime of the fast component of fluorescence of the intermediate case molecules, denoted by Φf and τf , respectively, may be given by
Φf ) ΓS/∆S-T
(14)
1/τf ) 2πVS-T2/p ) 2πFΤVS-T2/p ) ∆S-T/p
(15)
7300 J. Phys. Chem., Vol. 100, No. 18, 1996
Figure 1. Fluorescence decays of pyrazine-d4 at zero field with excitation at the individual rotational lines of the 0-0 band belonging to the S0 f S1 transition in a jet. Excited rotational lines are shown, together with J′ of the excited level.
where FΤ is the level density of the triplet state coupled to |S〉 and VS-T is the average value of the interaction matrix element between |S〉 and |Tj〉 . Here, it is assumed that the coupling constants of the S-T interaction are the same for all |Tj〉 and that the energy separation between adjacent levels of |Tj〉 are the same, i.e., . Then, the absorption profile, i.e., the distribution of |an|2, nearly gives a Lorentzian shape with a width (fwhm) of 2πFΤVS-T2, and ∆S-T corresponds to the spectral width (fwhm) of the absorption profile. 2.2. Rovibrational State Dependence of Fluorescence of Azaaromatic Molecules at Zero Field. Pyrazine, pyrimidine, and s-triazine vapors show the intermediate case behavior in fluorescence properties as a result of strong spin-orbit interaction between singlet and triplet states.19-23 The significance of the S-T interaction in these azaaromatic molecules is known from the presence of phosphorescence following photoexcitation into a singlet state.46-48 The presence of a nonzero magnetic dipole moment at the photoexcited singlet state in pyrazine or pyrimidine also shows the presence of effective S-T interaction.18,31,49 Fluorescence of these azaaromatic molecules in the vapor phase is affected by H, depending on the rovibronic level excited.32-43 All the results of the magnetic field effects on fluorescence are strongly related to the fluorescence property at zero field, and so the fluorescence property at zero field is briefly described in this section with particular regard to rotational and vibrational state dependence of the yield and lifetime for each of fast and slowly decaying portions of fluorescence. τf at around the S1 origin was evaluated to be ∼100 ps, ∼3 ns, and ∼300 ps in pyrazine,50-52 pyrimidine,20,21 and s-triazine,53,54 respectively, and τf varies with the vibronic level excited. τs at low vibrational levels of S1 evaluated under collision-free conditions is approximately 400, 800, and 100
Ohta ns, respectively.28,34,55 Note that τs of s-triazine vapor remarkably depends on the rotational level excited.26,28,36 Fluorescence quantum yield of these azaaromatic molecules at low pressures in a bulk gas or in a supersonic jet abruptly decreases with increasing the excess vibrational energy above the S1 origin, denoted by ∆Evib.19,20,54,56,57 At high pressures where the slow component of fluorescence is quenched by a collision, on the other hand, the vibrational state dependence of the quantum yield is not so large as that at low pressures,20,54,58,59 indicating that only Φs markedly decreases with increasing ∆Evib. These results as well as the vibrational state dependence of the ratio of the preexponential factors, Cf/Cs, estimated from the decay show that the number of the triplet state effectively coupled to the excited singlet level, i.e., Neff , increases monotonically with increasing ∆Evib. In other words, FT increases with increasing ∆Evib since FT is given by Neff/ ∆S-T. These results are well understood since the total level density of the triplet states increases with increasing ∆Evib. If K, which specifies the projection of the total angular momentum of molecular rotation on the symmetric top axis, is regarded as a good “quantum number”, the spin-orbit selection rule of ∆J ) 0, ∆K ) 0, (1 restricts the interaction between the excited singlet state and isoenergetic triplet levels.60,61 At the moderately high energies in the triplet manifold reached via ISC, various nonrigid body couplings as well as asymmetry lead to extensive scrambling of the rotational states of different K', and the actual wavefunction of the triplet state is given by a linear combination of the zero-order wave functions of a symmetric top molecule. As a result, the zero-order wave function specified by J′ and K′ of a symmetric top is included in all the (2J′ + 1) wave functions for each J′; K scrambling occurs in the triplet manifold following ISC. Here, the prime refers to the excited state. Actually, the effective value of FT is expressed in the form
FT ) [(2J′ + 1)/σ]FTvib
(16)
where FTvib represents the vibrational level density of the triplet state effectively coupled to S1 and σ is the symmetry number of the molecule.62 In fact, Φs decreases with increasing J' in these azaaromatic molecules, and FT evaluated from the rotational state dependence of yield and decay of fluorescence at zero field shows the same J' dependence as the one given by eq 16.26-29,56,63-65 Rotational state dependence of fluorescence decay of pyrazine-d4 shown in Figure 1 is an example which shows that FT increases with J'. Actually, fluorescence decay profiles may be classified into three groups: (i) a nearly single exponential decay, sometimes superimposed by quantum beats; (ii) a “pseudo-biexponential” decay, where the initial decay of the fast component is followed by a fast rise-and-decay component and a subsequent slowly decaying portion; (iii) a biexponential decay composed of fast and slowly decaying portions. The decays at the P(1) and P(2) line excitations may be grouped into (i) and (ii), respectively, and the decays on excitation into levels with J' g 2 may be regarded as a biexponential decay, i.e., group (iii). Figure 1 shows that the decay changes from a single exponential one to a biexponential through a “pseudo-biexponential” decay and that Cf/Cs increases with increasing J' of the excited level, indicating that Neff increases with increasing J'. It was shown that the relation γS /Neff
