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Intersystem Crossing in the 1nπ* and 1ππ* States Masaaki Baba* Division of Chemistry, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan ABSTRACT: Fast intersystem crossing is observed in the S1 1nπ* state of N-heterocyclic aromatic hydrocarbons and carbonyl compounds. It is attributed to spin-orbit coupling with the 3ππ* state in the same energy region. The strong singlet-triplet mixing was confirmed by large Zeeman splitting of rotational lines in a high-resolution spectrum. For the S1 1ππ* state of aromatic hydrocarbons, the observed Zeeman splitting was found to be considerably small, and intersystem crossing was considered to be minor. These facts are in accordance with El-Sayed’s rule, which states spin-orbit coupling is forbidden between the 1ππ* and 3ππ* states. The Zeeman splitting of several derivatives was also observed and the substitution effect on the intersystem crossing rate is discussed.
1. INTRODUCTION The excited triplet state plays a key role in dynamical processes of the electronically excited molecule,1,2 particularly for radiationless transitions such as internal conversion (IC) by nonadiabatic vibronic interaction and intersystem crossing (ISC) by spin-orbit interaction.3,4 In this article, we summarize recent experimental results of Zeeman splitting measurements and discuss ISC from the lowest excited singlet state (S1) to the triplet state of organic molecules with π bonds. The singlet-triplet optical transition is forbidden and very weak, because the electric dipole moment is independent of an electron spin. Spectroscopic studies have, therefore, started in the solid phase at low temperatures. Experiments on phosphorescence detection, electron spin resonance (ESR), and phosphorescence microwave double resonance (PMDR), for example, have been performed for the basic aromatic hydrocarbons such as benzene5 and naphthalene.6,7 Singlet-triplet mixing is fairly weak in these molecules, and the triplet lifetime is longer than 1 s. On the other hand, ISC was found to be appreciably fast in the S1 1 nπ* state of N-heterocyclic aromatic hydrocarbons such as pyrazine8 and quinoline,9 and carbonyl compounds such as benzophenone10,11 and benzaldehyde.12 The lifetime of the T1 3nπ* was found to be about 1 ms in these molecules. These results are in accordance with El-Sayed’s rule on spin-orbit coupling (SOC), which was derived through theoretical consideration.13 The molecular properties in the solid phase are affected by intermolecular interaction and the crystal field. It is of great importance to observe the phosphorescence from isolated molecules. Laser induced phosphorescence (LIP) has been observed in a supersonic jet for such key molecules as pyrazine,14 glyoxal,15 benzaldehyde,16 and oxalyl chloride.17 In contrast, the phosphorescence of the 3ππ* state of aromatic hydrocarbons has a long lifetime and it is impossible to detect in a supersonic jet where the molecule moves at a velocity of about 1000 m s-1. The T1 3ππ* state couples with the 1σπ* state. The excitation energy is, however, much higher, and the singlettriplet mixing is expected to be weak. Another powerful method is Doppler-free high-resolution spectroscopy of the isolated molecule in a supersonic jet. It is difficult to obtain the spectrum for the forbidden T1 r S0 r 2011 American Chemical Society
transition because the sensitivity is naturally low in high-resolution spectroscopy. On the contrary, rotationally resolved highresolution spectra have been successfully observed for the allowed S1 r S0 transition.18-32 The magnitude of the magnetic moment in the S1 state can be determined by Zeeman splitting of a rotational line in the external magnetic field. The magnetic moment of a molecule mainly arises from the orbital and spin motions of electrons. In nonlinear polyatomic molecules, the orbital angular momentum is almost quenched, and the spin angular momentum is zero in the singlet state. The magnetic moment in the S1 state is, therefore, expected to be very small. Singlet-triplet mixing by SOC, however, brings appreciable magnetic moment to the S1 level, so that Zeeman splitting of M sublevels is observed in the S1 r S0 high-resolution spectrum.19,22-32 Thus, the ISC rate in the S1 state can be evaluated by measuring the Zeeman splitting or magnetic moment and the singlet-triplet mixing at each rotational level. El-Sayed’s rule indicates that SOC is allowed between states of different symmetry and electronic configurations.13 ISC is expected to be remarkably fast in molecules with the low-lying nπ* states, where n represents a nonbonding electron of the nitrogen or oxygen atom. In contrast, ISC is expected to be slow in the S1 1 ππ* state of aromatic hydrocarbons with no nonbonding electrons. ISC to the triplet state has, nevertheless, been considered important in the S1-state dynamics of fundamental molecules such as benzene,33,34 naphthalene,35 and anthracene.36,37 In this article, we demonstrate that the main nonradiative relaxation process in the S1 1ππ* state is IC to the S0 state. The study of aromatic hydrocarbon derivatives in this context is of great interest. High-resolution spectra have already been observed and analyzed for derivatives containing halogen,38 oxygen,39-42 and sulfur atoms,43,44 and for methyl and alkyl groups.45,46 It has been demonstrated for several derivatives that Special Issue: David W. Pratt Festschrift Received: December 23, 2010 Revised: February 8, 2011 Published: March 14, 2011 9514
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the fluorescence lifetime is short and the fluorescence quantum yield is small in the S1 1ππ* state. ISC rates are discussed on the basis of the results of Zeeman splitting measurements.
2. INTERSYSTEM CROSSING (ISC) The excited S1 molecule relaxes through radiative and nonradiative processes. The important radiationless transitions are IC to the S0 state by nonadiabatic vibronic interaction and ISC to the triplet state by spin-orbit interaction. In this section, we summarize the theoretical backgrounds for ISC and singlet-triplet mixing. i. El-Sayed’s Rule on SOC. The spin-dependent term of the Hamiltonian is derived by the first-order relativistic treatment and is approximated by the sum over electron i as47,48 iep2 DV D DV D Hspin ¼ 2 ∑ σ x ðiÞ Dy Dz Dz Dy ð2mcÞ i i i i i DV D DV D þ σy ðiÞ Dzi Dxi Dxi Dzi DV D DV D þ σz ðiÞ ð1Þ Dxi Dyi Dyi Dxi Here V is the potential due to nuclei and electrons, and σx(i), σy(i), and σz(i) are Cartesian components of an electron spin. The spin-orbit Hamiltonian is given by HSO ¼ ¼
∑i ζi li 3 si ¼ ∑i ζi ðlxi sxi þ lyi syi þ lzisziÞ ∑i ζi
1 þ lzi szi þ ðlþ s- þ li si Þ 2 i i
ð2Þ
li and si are the orbital and spin angular momenta of the ith electron, respectively. ζi is the spin-orbit coupling constant. Nonvanishing -þ matrix elements arise from lþ i si þ li si , so that SOC is allowed between the states of different orbital symmetry and spin multiplicity. Group-theoretical arguments are helpful to understand the coupling scheme. The spin-orbit Hamiltonian belongs to the same irreducible representation as that of Rk(k=x,y,z), which is expressed by Γk. The direct product of irreducible representations of the singlet and triplet states, ΓS and ΓT must be identical to one of Γk. The Γk is nontotally symmetric for a planar molecule with a 2-fold symmetry axis. Consequently, the singlet and triplet states of identical symmetry cannot be coupled by the spin-orbit interaction. Although SOC between the 1ππ* and 3ππ* states of different symmetry are allowed, the value of the matrix element is considered to be very small because the one-center integral is vanishing.47 The nonvanishing matrix element is generally given by24 hΓS S ¼ 0vJKMjHSO jΓT S ¼ 1v0 J 0 N 0 K 0 M 0 i 0
¼ δJJ 0 δMM0 ð - 1ÞJ þ K ð2N 0 þ 1Þ1=2 ! ( J 1 N0 hΓS 0vjHSO jΓT 1v0 iδK 0 K - 1 K -1 -K þ 1 ! J 1 N0 hΓS 0vjHSO jΓT 0v0 iδK 0 K K 0 -K ) ! þ
J K
1 -1
N0 hΓS 0vjHSO jΓT - 1v0 iδK 0 K þ 1 -K - 1
ð3Þ
Figure 1. El-Sayed’s rule for spin-orbit coupling.
Figure 2. Coupling scheme for ISC in the S1 1nπ* state. SOC and VRC represent spin-orbit coupling and vibronic coupling, respectively.
ΓS and ΓT represent the singlet and triplet electronic states, and v and v0 are the vibrational quantum numbers, respectively. N is the quamtum number of the total angular momentum excluding an electronic spin. The selection rules are, therefore, N0 = J, J ( 1, and K0 = K, K ( 1 for the singlet-triplet mixing. Although the strength of the SOC is very low, the mixing becomes strong if the two coupling levels are close in energy. Here we treat planar aromatic hydrocarbons and their derivatives. The molecular orbitals are divided into σ and π orbitals, which are symmetric and antisymmetric, respectively, with respect to the molecular plane. The π electron can be excited by ultraviolet light, and the S1 state is the 1ππ* state because the σ bond energy is much greater. Singlet and triplet spin states exist for an electronic configuration, and the excitation energy of the triplet state is lower due to exchange interaction. ISC in the S1 state is always possible because the triplet levels exist at the same energy as a single rovibronic level of the S1 state. However, SOC between the singlet and triplet states of identical electronic configuration is forbidden. It is presumed that ISC is minor in the S1 1ππ* state of planar aromatic hydrocarbons. The N and O atoms possess n electrons. The energy of the n orbital is approximately identical to that of the 2p atomic orbital. The excitation energy of the nπ* state, in which one electron is excited from n to antibonding π* orbitals, is lower than that of the ππ* state. The S1 state, therefore, is the 1nπ* state, which cannot couple with the 3nπ*. The SOC between the 1nπ* and 3ππ* is allowed and strong, because the n orbitals of N-heterocyclic aromatic hydrocarbons and carbonyl compounds are along the molecular plane and overlap with the π* orbital by 90 rotation around the N or O nucleus, and the matrix element is expected to be considerably large. The SOC scheme between the singlet and triplet states is illustrated in Figure 1, which depicts El-Sayed’s rule. ii. S1 1nπ* State. The 1nπ* state does not couple with the 3nπ* state, and ISC is also expected to be slow. In many N-heterocyclic aromatic hydrocarbons and carbonyl compounds, however, the energy of n orbitals is significantly lowered by mixing with σ orbitals. As a result, the excitation energy of the nπ* state 9515
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approaches that of the ππ* state. In these molecules, the S1 state is 1nπ* and the 3ππ* state is located in the same energy region. In such cases, ISC occurs efficiently with strong SOC as illustrated in Figure 2. The molecules in the 3ππ* state are immediately relaxed to the T1 3nπ* state by nonadiabatic vibronic interaction. Eventually, strong phosphorescence can be observed from the T1 state, because the 3nπ* f S0 transition borrows the intensity from the strong 1ππ* f S0 allowed transition. In benzaldehyde, almost of all the S1 1nπ* molecules transit into the triplet state and no fluorescence can be observed from isolated molecule. iii. Isc Rate. In large molecules, the density of coupling triplet levels is sufficiently high, and the vibrational structure is a homogeneous quasi-continuum in the energy region of the S1 state (statistical limit). The ISC rate is given by4,49 kISC
2π ¼ jvSO j2 F h
ð4Þ
vso represents the SOC strength, which consists of the electronic part and the Franck-Condon factor. F is the density of coupling triplet levels. The spin-orbit coupling constant of an atom drastically increases with the principal quantum number. The strong singlettriplet mixing can be clearly seen in diatomic molecules of heavy atoms, such as ICl,50 Cs2,51 and I2.52 The level structure is approximately represented by Hund’s coupling case (c). In aromatic hydrocarbons, ISC has been found to be enhanced by substitution with Cl, Br, and S atoms, in what is called the heavy atom effect.2 Deuterium substitution, in contrast, reduces the SOC and ISC rates. Deuteration generally suppresses the radiationless transition; this effect is attributed to a smaller zero-point energy and narrower distribution of the vibrational wave function of the D atom compared with the H atom. The Franck-Condon factor is, therefore, smaller for the deuterated compound. The ISC rate is proportional to the density of coupling triplet levels. Consequently, ISC is normally fast in large molecules, because the density of vibrational and rotational levels is high. Methyl or alkyl group substitution also enhances ISC, which increases level density due to low-frequency large-amplitude motion.
3. ZEEMAN SPLITTING OF M SUBLEVELS To directly determine the ISC rate, it is necessary to measure absorption and phosphorescence intensities. The experiments, however, are difficult in a supersonic jet, where the molecular concentration is extremely low. High-resolution Zeeman spectroscopy is a very powerful method that enables us to evaluate the magnitude of magnetic moment for a single rovibronic level in the external magnetic field. Triplet mixing gives rise to magnetic moment in the S1 level. The Hamiltonian and matrix element of Zeeman interaction are given by25,53 HZ ¼ - ðm0 D100 - mþ1 D10 - 1 - m-1 D10 þ 1 ÞH hΓvJKMjHZ jΓ0 v0 J 0 K 0 M 0 i ¼ - δMM0 H "
ð5Þ
M fJðJ þ 1Þg1=2
K δK 0 K - hΓvjmþ1 jΓ0 v0 i fJðJ þ 1Þg1=2 ðJ þ KÞðJ - K þ 1Þ 1=2 δK 0 K - 1 þ hΓvjm-1 jΓ0 v0 i 2JðJ þ 1Þ # ðJ - KÞðJ þ K þ 1Þ 1=2 δK 0 K þ 1 ð6Þ 2JðJ þ 1Þ hΓvjm0 jΓ0 v0 i
where the magnetic field H is applied along the space fixed Z axis. mλ is the spherical compoment of magnetic moment, and D1Rβ is the rotation matrix of rank 1. |JKMæ is the symmetric-top rotational wave function. The selection rules for the Zeeman interaction are, therefore, ΔJ = 0, and ΔK = 0, (1. The M sublevels split in the magnetic field, and the energy shift is proportional to the magnitude of magnetic moment. i. S1 1nπ* State. The magnetic moment in the S1 1nπ* state of carbonyl compounds is produced by SOC with the T2 3ππ* state along the in-plane long axis (rotational a axis). For 1nπ* and 3 ππ* mixing, the magnitude of Zeeman splitting by SOC (Γso), which is defined by the energy difference between the M = J and M = -J levels, is given by25 ΓSO ¼ γSO Ka 2 =ðJ þ 1Þ where γSO ¼ 16Age μB H
j 1 nπjHSO j3 ππ j2 fEð1 nπÞ - Eð3 ππÞg3
ð7Þ
ð8Þ
Ka and A are the projection of the total angular momentum J and the rotational constant along the top axis (a), respectively. The Zeeman splitting is expected to be large for the large Ka level, and proportional to J for the J = Ka levels. In the case of a pure triplet state (S = 1, ge = 2.0023), the magnitude of Zeeman splitting is estimated to be about 1 cm-1 at the magnetic field of 1 T. Zeeman splitting of rotational lines was actually observed in the pyrazine and pyrimidine molecules with a magnitude of about 0.005 cm-1 at 0.01 T.19,22,23 In these molecules, the energy of the T2 3ππ* state is smaller than that of the S1 1nπ* state. The T2 3 ππ* levels are strongly coupled with the T1 3nπ* vibronic levels. The effective density of coupling triplet levels is expected to be considerably high at the S1 energy region; hence the S1 state possesses strong triplet character. The S1 single rotational level was actually observed to be perturbed by several triplet levels simultaneously. The reported high ISC yield can be explained by this coupling scheme. Considerable Zeeman splitting can be clearly observed in glyoxal, which is one of the prototypical carbonyl compounds.24,25 The ISC yield in the S1 1nπ* state is not very high in this molecule, however, because the energy of its T2 3ππ* state is slightly higher. Almost of all the rotational levels exhibit appreciable Zeeman splitting with a magnitude proportional to Ka2/(J þ 1), which is in accordance with eq 7. Significant Zeeman splitting could be seen for a number of specific singlet levels. Each level is strongly perturbed by a triplet level whose energy is accidentally very close (resonant limit). ii. S1 1ππ* State. The S1 state is 1ππ* for aromatic hydrocarbons. ISC is not expected to occur because the S1 state cannot be coupled with the 3ππ* state. In fact, Zeeman splitting was observed to occur at very low levels in benzene,27 and in polyacenes such as naphthalene28,29 and anthracene.30 Several rotational levels were found to exhibit low level of Zeeman splitting of about 0.005 cm-1 even at the strong magnetic field of 1 T. This phenomenon is attributed to J-L coupling (electronic Coriolis coupling) between the S1 and S2 states. The electronic orbital angular momentum is supposed to be mostly quenched in a nonlinear polyatomic molecule, so that the magnetic moment is small. The magnitude of Zeeman splitting by the J-L coupling (ΓJL) is given by25 ΓJL ¼ γJL Kc 2 =ðJ þ 1Þ 9516
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Figure 3. High-resolution spectra of the S2 1ππ* r S0 transition of azulene at magnetic fields of 0 and 0.9 T.
where γJL
j S1 1 ππjLZ jS2 1 ππ j2 ¼ 8CμB H EðS2 1 ππÞ - EðS1 1 ππÞ
ð10Þ
Kc and C are the projection of the total angular momentum J and the rotational constant along the c axis (out of plane), respectively. LZ is the z component of the electronic orbital angular momentum. The z axis is out-of-plane and is parallel to the rotational c axis. The Zeeman splitting is negligibly small in large molecules such as pyrene31 and perylene.32 In benzene and naphthalene, the magnitude of Zeeman splitting could be accurately determined for a number of completely resolved rotational lines, and was found to be proportional to Kc2/(J þ 1). On the basis of these results, it is concluded that the main radiationless transition in the S1 state of aromatic hydrocarbons is not ISC to the triplet state, but IC to the S0 state. Azulene is an interesting aromatic hydrocarbon, of which the nonradiative process is abnormally fast in the S1 1ππ* state but is relatively slower in the S2 1ππ* state. As a result, this S2 state is weakly fluorescent, which is a violation of Kasha’s rule that the emitting level is the lowest level of the spin multiplicity. The highresolution spectra of the S2 r S0 transition at magnetic fields of 0 and 0.9 T are shown in Figure 3. No change was seen in the spectrum with a magnetic field of up to 1.2 T, indicating that the main nonradiative process is also IC to the S0 state. The stable geometrical structure was shown to be similar in both the S1 and S2 states. The fast IC in the S1 state is considered to be due to its potential curve being different from that of the S0 state with respect to the normal coordinate of promoting mode.54 The S2 f S1 IC is relatively slow in spite of the small energy gap. It is due to the shallower and deeper potential curves in the S1 and S2 states, respectively. The vibrational overlap between these two states is expected to be small. iii. S1 1ππ* State of Substituted Compounds. It is wellknown that atom or group substitution enhances ISC in the S1 1 ππ* state of aromatic hydrocarbons in the solid phase.2 There have been high-resolution studies of the S1 1ππ* r S0 transition of jet-cooled substituted aromatic hydrocarbons. The coupling level density is expected to be remarkably increased by methyl substitution. The observed fluorescence lifetime of toluene, however, was not changed much with deuteration, although intramolecular vibrational redistribution (IVR) was found to be remarkably enhanced in the vibronic levels.45
The spin-orbit coupling constant of the Cl or Br atom is much larger than that of the H atom, so that ISC may be enhanced by the substitution through the heavy atom effect. In 2-chloronaphthalene, the fluorescence lifetime in the S1 1ππ* state is remarkably short; this has been shown by lifetime broadening in the high-resolution spectrum.38 We have found that Zeeman splitting is very small in the S1 zero-vibrational level, indicating that the heavy atom effect of this Cl substitution is not significant compared with the IC rate that dominates the decay of excited molecules in the S1 state. Dibenzo-p-dioxin and dibenzofuran are the O-atom derivatives and are the prototypes of toxic dioxins. The fluorescence quantum yield in the S1 state of dibenzo-p-dioxin is very low. The observed level of Zeeman splitting is very low, and the main nonradiative process in this case is not considered to be ISC, but predissociation.41 The p orbitals of nonbonding electrons are perpendicular to the molecular plane, and the π* orbital does not include the O atom. Consequently, in these molecules, there exists no nπ* state of the carbonyl type that induces strong singlet-triplet mixing in the S1 1ππ* state. It is noteworthy that this molecule is distorted out-of-plane with respect to the butterfly mode. ISC, however, is not expected to be enhanced much because the out-of-plane distortion is small. For dibenzofuran, the high-resolution spectrum has already been analyzed, and the molecule is considered to be planar in both the S0 and S1 1ππ* states.40,42 We observed Zeeman splitting for the spectral lines of the S1 r S0 000 band, and the result is shown in Figure 4. Zeeman splitting is strongly dependent on the rotational level, and the observed values are plotted against J0 and Kc0 in Figure 5. The magnitude of Zeeman splitting was proportional to Kc2/(J þ 1), indicating that the magnetic moment originates in J-L coupling with the S2 1ππ* state as found in benzene, naphthalene, and anthracene. It is concluded that the singlet-triplet mixing is also very small in the S1 1ππ* state of dibenzofuran. Next we consider the effect of substituting S-atoms, whose valence electrons have a structure identical to those of the O atom. Dibenzothiophene, therefore, has the same bond structure as dibenzofuran, and a larger heavy atom effect on ISC was expected in the S1 1ππ* state. In practice, it has been demonstrated by phosphorescence detection and PMDR experiments that ISC occurs efficiently in the S1 state of dibenzothiophene in the solid phase.55 The high-resolution spectrum of the isolated molecule has been analyzed, and the main nonradiative process has been suggested to be ISC to the triplet state.43 Zeeman splitting, however, could not be seen at up to 0.9 T. We obtained similar results for thioanisole. The rotational lines were found to be appreciably broadened due to its short lifetime even in the absence of a magnetic field. The Zeeman splitting, however, was shown to be negligibly small at up to 1 T.44 Further experimental studies are necessary to elucidate the effect of S-atom on ISC of the S1 1ππ* state.
4. SUMMARY ISC is very fast in the S1 1nπ* state of N-heterocyclic aromatic hydrocarbons and carbonyl compounds because of the strong SOC with the 3ππ* state. Singlet-triplet mixing gives rise to magnetic moment in the single rotational line of the S1 state; this can be experimentally proved by measuring Zeeman splitting for each rotational line in the high-resolution spectrum. The magnitude of the observed Zeeman splitting is about 0.005 cm-1 at a magnetic field of 0.01 T in pyrazine and glyoxal. In contrast, 9517
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Figure 4. High-resolution spectra of the S1 1ππ* r S0 transition of dibenzofuran at magnetic fields of 0 and 1.8 T. The assignments of rotational lines are shown below the spectrum.
Figure 5. Magnitude of Zeeman splitting of dibenzofuran (a) for the J = 26 levels against Kc at 1.2 T, and (b) for the J = Kc levels against J at 1.2 and 1.8 T. The solid lines indicate the calculated values assuming ÆS11ππ*|LZ|S21ππ*æ = -2.1p and E(S21ππ*) - E(S11ππ*) = 7450 cm-1.
Zeeman splitting is very small in the S1 1ππ* state of planar aromatic hydrocarbons such as benzene, naphthalene, anthracene, and azulene. The low level of Zeeman splitting was attributed to J-L coupling between the S1 and S2 states, but the triplet mixing is negligibly small. These facts are in accordance with El-Sayed’s rule that SOC is allowed between singlet and triplet states of different symmetry, for instance, between the 1nπ* and 3ππ* states. ISC is concluded to be minor in the S1 1ππ* state of aromatic hydrocarbons. It has been considered, however, that the main nonradiative process is ISC to the 3ππ* state. It should be noted that there have been many experimental studies of phosphorescence detection and PMDR in solid phase. Singlet-triplet mixing has presumably been believed to be strong in the isolated molecule. However, it has never been experimentally confirmed because it is hard to observe phosphorescence from the 3ππ* state with a lifetime of longer than 1 s in a gas phase or in a supersonic jet. On the basis of our experimental observation of small-scale Zeeman splitting, we
conclude that the main nonradiative transition is not ISC to the triplet state, but rather IC to the S0 state. To prove this, it will be necessary to utilize techniques that allow us to directly detect triplet molecules, such as sensitized phosphorescence56,57 and surface electron ejection by laser excited molecule (SEELEM).58,59 ISC is generally suppressed by deuteration in aromatic hydrocarbons but is possibly enhanced by substitution with Cl, O, and S atoms. We observed Zeeman splitting of rotational lines in the high-resolution spectra of substituted derivatives whose S1 states have considerably short lifetimes. Its magnitude, however, was found to be uniformly very small in the S1 1ππ* state. LIP experiments are in progress to elucidate the S-atom effect on ISC in a more quantitative manner.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. 9518
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