Triplet spin label and molecular dynamics

Journal of Luminescence 12/13 (1976) 389—395 © North-Holland Publishing Company

TRIPLET SPIN LABEL AND MOLECULAR DYNAMICS M.A. EL-SAYED and P. ZINSLI Department of Chemistry ~ University of California, Los Angeles, California 90024, USA

It is shown that the effect of low magnetic field on the net spin direction of an excited triplet sample at low temperatures depends on the zero-field parameters of the triplet state coupled to the lowest singlet state in the intersystem crossing process. Using this idea and double resonance techniques, the mechanism of the ISC in pyrazine, quinoxaline and benzophenone is determined. In nitrogen heterocyclics, the type of electronic excita1’ ~-‘ ir,ir1’ selection rules are followed). In benzotion is changed in mechanism the ISC process (i.e., singlet n, iT and triplet states of the modified n,ir1’ type phenone, a direct between in the nonpianar configuration is involved. The effect of nonpianarity on the spin orbit interaction in heterocyclics is discussed in detail.

1. Perturbation of spin alignment with a magnetic field [1,2] The net direction of the spin angular momentum in T 1 is determined by the magnetic forces coupling the electronic spin and orbital motion resulting from the transition between S1 and the triplet state involved in the ISC process in zero.laboratory magnetic field. Upon the application of an external magnetic field, the net spin alignment changes in a manner that depends on the field strength, field direction, the relative energies of the zero-field levels of the triplet state(s) coupled to Sj in the nonradiative ISC process as well as to T1 (as it decays to S0). It thus appears that the response of the direction of the net spin alignment to a magnetic field at low temperatures could be used as an experimental means by which the mechanism of the ISC process can be elucidated. Equations have been given previously [1,2] which give the field dependence of observed quantities that measure the field induced change in the net spin direction (the change in the relative population of the three spin levels of T1), e.g., the relative change in the phosphorescence microwave double resonance (PMDR) signal or simply the relative change in the phosphorescence intensity origination from a single zero-field level. The assumptions made in these derivations are also discussed [21.In practice, we assume that molecules go from S1 to isoenergetic vibronic level ofT1 that relaxes to the zero point energy ofT1, on which the experiments are performed. Assuming that spin-vibronic interactions are weak, then the measured magnetic pro*

Contribution No. 3527.

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ofT1 are used to determine the response to the magnetic field of the net spin alignment. Then the predicted behavior is compared with observation. If agreement is found, barring an involvement of aT’ with similar magnetic properties as T1, we could assume a direct spin orbit coupling. If predictions disagree with the observed results, then an upper triplet state(s) must be involved. A computor fit is then used and by making a “reasonable” guess at the zero field parameters of T’, we could find out the best set of values of the zero field paranieters of T It should be pointed out that these fits should not be taken very seriously, since they certainly are not unique due to our lack of knowledge of the magnetic axes and zero field parameters of the upper triplet states are not known. perties

2. Results 2.1. N-heterocyclics The method has been applied to test the proposal [3] that the ISC process in Nheterocyclics follows the section rules n, lr* ~ lr,lr* and n, ~ ~ and 7r,7r* ~hirir~ Previous PMDR results on quinoxaline [4], pyrazine [5,61 pyrimidine [6], and 2,3dichloroquinoxaline [7] had showed that the spin level populated with highest probability is the one that would be predicted from group theoretical prediction using the above selection rules. The above selection rules, however, are based on spin orbit interaction in a fixed molecular geometry. Neither static nor dynamic changes in geometry is taken into account. In fact, the PMDR results on aromatic hydrocarbons [8] can only be accounted for if an out-of-plane distortion is assumed. This raises the question: How good is the assumption of fixed nuclear geometry in the ISC nonradiative process? In the present work, we would like to use the Zeeman-effect on spin alignment to determine the exact mechanism in the prototype N-heterocyclics with different energy level schemes. The energy schemes for the molecules studied are: quinoxaline, S1(n,lr*), T2(n,1r*), Ti(7r,1r*);pyrazine, Si(n,n*), T2(~,ir*), T1(n, ii ). The spin level TB is found to be the fastest populated level in quinoxaline. Ac1B cording to group theory, the spin orbit coupling of the Si(n,1r*), 1,with Tl(7r,n*), 3B 2, takes place with the spin level B1 X B2 = A2 r7 or TB, where B is the in-plane magnetic axis along the C2 axis in quinoxaline. This observation is in agreement with direct spin orbit coupling. However, TB could very easily be populated via a direct ~ mechanism if the molecule 1B is distorted (dynamically or statically) along a normal coordinate of a2 symmetry since 1 X ~B1 X a2 A2 TB. It is thus essential to determine the type of zero-field pattern of the triplet state coupled with S1 in the ISC. In the first (direct) mechanism, the pattern of T1 should be concluded but in the latter (indirect) mechanism, zero-field patterns different from that known for T1 would have to be used to explain the observed magnetic field effects. ,

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The results on quinoxaline are shown in fig. 1. In this figure, the observed results are shown by (I). It shows the behavior for the IDI + El PMDR signal as a function of field strength along the C’ axis of the durene host. In this figure the solid curves give the calculated behavior assuming the direct mechanism while the broken curves are those for an indirect process involving a T’(fl~*)of similar zero-field parameters to those observed for pyrazine. From a comparison of the calculated and observed behavior, one concludes that the direct mechanism for quinoxaline satisfactorily explains the field effect on the spin alignment. It is interesting to point out that due to the stronger spin orbit interaction involved in the direct mechanism, this mechanism is favored over the indirect one in spite of the fact that the latter is favored on account of the smaller energy gap involved in the ISC process. The field effect on the PMDR signal of the IDI + IEI transition in pyrazine is shown in fig. 2 with the field applied along the a’ axis of the p-dichlorobenzene host crystal. Again, the results are shown by (I) and the calculated curves for the direct and indirect mechanisms are shown by broken and solid curves respectively. It is shown that the direct mechanism cannot fully describe the observed behavior. An indirect mechanism, S1(n,7r*)T—~~T~~* withT’ having zero-field parameters similar to those for substituted benzenes (ID!

=

4.8 and IEI

=

0.8 GHz) can satis-

QUINOXALINE IN DURENE 101+ tEl TRANSITION

U Z

/

/

/

I

/

INDIRECT PROCESS

/

W:

-,

~

/~ //

/

/

,-

—

0

,/)‘

tOO /

/ /

/

300

400

WASIETICFEL.D(SAUU) tic

/

II /1

Fig. 1. Observed (I) and calculated (— — —; —) dependence of the DI + IEI PMDR signal of quinoxaline in durene on the magnetic field strength (applied along the durene c’ axis).

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PYRAZINE IN P-DICHLORO-BENZENE ~O~JIlJ~V(

DIRECT ISC

w > -j

uJ 00

300

MAGNETIC FIELD ~RALLEL

500 a

(GAUSS)

Fig. 2. Observed (I) and calculated (———; —) dependence of the DI + El PMDR signal of pyrazine inp-dichlorobenzene on the magnetic field strength (applied along the a’ crystal axis).

factorily explain the field effect on the degree of spin alignment. It can thus be concluded that the strong spin orbit interaction between the n, ir’ and ~ ~ states of different multiplicity strongly determines the observed S1-~----~T1intersystem crossing process. Interestingly enough, it does also determine the T1 S0 radiative properties, not only in N-heterocyclics, but also in aromatic hydrocarbons (if a, 7r* states in the latter compounds are considered to be the equivalent of the n,lr* states in N-heterocyclics). —~

2.2.

Benzophenone

Benzophenone is known to have a very efficient ISC. It was proposed earlier [91 that it might result from having Si(n,lr*) nearby T2(lr,7r*). However, recent spectroscopic [10,111 work has shown that at low temperature, T2 must be (slightly) above Si. How much higher is still an “unresolved” spectroscopic problem. We have used the Zeeman effect on spin alignment (ZESA) to find out if direct process is indeed involved in benzophenone at low temperatures. The results [1] indeed show that a direct S1—~-~T1 mechanism can fully explain the ZESA results. The question thus arises: Does the conclusion reached in section for benzophenone present a violation of the n,lr* ~+ 7r7r* ~ ~ selection rules that we have just concluded in section 2.1 for N-heterocyclics? The answer is definitely NO. While we indicated that in benzophenone the ISC involves S1 and T1, it is when we mislabel them as ~ and ~ that we meet the “apparent” violation of the ISC selection rules. Had benzophenone been planar (of C2,,, symmetry) in S1 and T1, the 2.2

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classification of n,1r* states becomes correct and the direct mechanism would indeed constitute a violation of the n,ir” 4* n7T” selection rules, since the ISC process in benzophenone is known to be extremely efficient. In C2,,, point group, the spin orbit operator cannot couple states of the same orbital symmetry (or the same configuration). However, as the rings lose coplanarity with one another and with the plane containing the

~CO

atoms, the P orbitals defining the n and the

C ir systems lose their distinction. They both become a linear combination of P~and P~in the planar configuration (the Z-axis is the C~’Oaxis). In C2 symmetry, the classification of n, ir~and ir, it’ states is no longer valid, since both states have the same symmetry. Furthermore, states of the same configuration could mix by spin orbit interaction [101 in this point group. Both S1 and T1 in benzophenone belong to A1 symmetry and spin orbit coupling takes place with the spin state A1 X A1 = A1 = TZ. Indeed, the spin level of most favored ISC is the TZ level in benzophenone. To summarize, the difference between N-heterocyclics and benzophenone is that the former molecules have a plane and a C2 axis of symmetry distinguishing the n,ir’~’ states from the ir,ii’~’states. Furthermore, all the components of the angular momentum operator are antisymmetric with respect to the symmetry elements. As a result, spin orbit coupling between states of the same symmetry, e.g., two n,ir* states, is not symmetry allowed. In benzophenone, as well as other nonpianar molecules, this not the case; spin orbit coupling between states of the same symmetry, e.g., S1 and T1, is allowed by symmetry. In N-heterocyclics, it was further shown [3] that between the symmetry allowed n,ir* 4* ir,ir’~and ~ ÷~ ir,ir’~(the iT,? states must be of different symmetry), the former is more favored on account of the nonvanishing one center spin orbit coupling terms, which are vanishing for the latter [12]. It remains to determine whether or not the symmetry allowed spin orbit interaction between S1 and T1 in benzophenone has nonvanishing one center terms. By using a two electron model, one in orbital a and the other in orbital b, and expressing the spin orbit operator for two electrons [13] as (1~~ ±1(2)) (S~1)±S~2)) for each coordinate i, the operator with the negative sign wouTd mix singlets and triplets and in benzophenone i = z (the carbonyl axis) for mixing S1 and T1 states. Expressing singlet and triplet spin orbit functions for two electrons in a and b with ~ and i3 spins and using the form of the spin orbit operator mentioned, one gets two types of spin orbit matrix elements: 5Ia> and II: E(b~1~b). I: ~(.aI1 In planar benzophenone a P~,and b = ~ CkP~,where the sum is over the oxygen and carbon atoms in the molecule. Type I would go to zero as a result of angular momentum conservation (or angular momentum operator properties) in C 2,,, type symmetry and Type 11 contains only three center terms as shown for aromatomic hydrocarbons by McClure [121. As nonpianarity is introduced (i.e. a change to C2 or lower symmetry), Type I will no longer vanish. Furthermore, a and b will each

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contain a linear combination of P~and P~.Then in each type of matrix element above a nonvanishing one center term of the type (PxIFIPy) would appear. In Type I, this one center term would appear on the oxygen atom if the lone pairs of electrons are localized, and over additional carbon atoms if they are delocalized [14]. In case a change of geometry from a planar to a nonpianar geometry takes place in the ISC process (e.g., ~i is planar but T1 is nonplanar), the above types of integrals would be modified as follows: Type I:
and

Type 11: (bIlzIb’>

where a and b are the orbitals in one geometry while a’ and b’ are the orbitals in the other geometry. In the planar configuration a = l~on the oxygen atom (assuming localized orbitals) and b = it” orbital defined in the correct sense. However, in the nonplanar configuration, each of a’ and b’is a mixture of P.,, and Py on each atom. One thus concludes that even for planar compounds, spin orbit coupling between n,lr* states (or ir,ir’’ states) could arise which contains one center spin orbit coupling matrix elements if the molecule changes to nonplanar configuration during the ISC process.

Acknowledgement The authors wish to acknowledge the financial support of the United States Energy Research and Development Administration (Contract No. E(04—3)—-34). The use of UCLA’s Campus Computer Network for computer services is also acknowledged.

References Ill M.A. El-Sayed and R. Leyerle, J. Chem. Phys. 62 (1975) 1579. [2] P.E. Zinsli and M.A. El-Sayed, Chem. Phys. Letters 36 (1975) 290. 13] M.A. El-Sayed, J. Chem. Phys. 38 (1963) 2834. 141 M.S. de Groot, l.A. Hesselmann and J.H. van der Waals, Mol. Phys. 12 (1967) 259~

M.A. El-Sayed and L. Hall, J. Chem. Phys. 50 (1969) 3113. [6] D.M. Burland and J. Schmidt, Mol. Phys. 22 (1971) 19. [7] D.S. Tinti, M.A. El-Sayed, A.H. Maki and C.B. Harris, Chem. Phys. Letters 3 (1969) 343. 181 M.A. El-Sayed, W.R. Moomaw and J.B. Chodak, J. Chem. Phys. 57 (1972) 4061. [9] S.K. Lower and M.A. El-Sayed, Chem. Rev. 66 (1966) 199. [101 S. Dyrn and R.M. Hochstrasser, 1. Chem. Phys. 51(1969) 2458. [11] M. Batley and D. Kearns, Chem. Phys. Letters 2(1968)423. [121 D.S. McClure, J. Chem. Phys. 20 (1952) 682. [13] R.M. Hochstrasser, Molecular aspects of symmetry (Benjamin, New York, 1966) p. 269. [14] R.M. Hochstrasser, G.W. Scott and A.l-l. Zewail, I. Cheni. Phys. 58 (1973) 393. [51

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Discussion T. Azumi: The only thing I am somewhat worried about your beautiful work is that we have to assume the zero-field splitting parameters for higher triplet states. However, we do not know what the zero-field splitting parameters are for higher states. In the specific case*of benzophenone, about which you have talked, in view of the vibronic coupling between the ~r,ir second triplet 1’ second triplet state and n, lr* first triplet state, the zero field spiltting parameters of the ir, ir’ might be quite different from the known values for the ,r,ir~Kfirst triplet state. Have you considered about such a possibility? M.A. El-Sayed: In this method, we first do calculations assuming all molecules go from Sç”9T 5. Since we know the magnetic properties of T5, this calculation assumes that spin vibronic coupling is weak (i.e. crossing to a vibronic level of Ti isoenergetic with Si is assumed to have similar zero field parameters as in the zero point level of Ti). If we get agreement, the results thus suggest that is dominant, unless of course an upper triplet state that has similar zero-field parameters to T5 is involved. If we do not get agreement, the results show that triplet state or states other than T5 must be involved. You could stop here but if you know what other triplet states below S~are present you could try to computer fit the results using zero-field parameters based on assuming no change of geometry from Ti or S~.Of course these zero field parameters are computer fit values and in some cases the fit might not be unique and one should not take them seriously. But what the results show for sure in this case is that triplet state(s) other than T5 must be involved in the ISC. R.M. Hochstrasser: G.W. Scott and A.H. Zewail measured accurately the orientations of the magnetic axes in the lowest triplet state of benzophenone in DDE. Even if you can guess roughly the zero-field splittings the possible range of magnetic axis orientations for T2 is so large, how can you know which to choose? I believe that even for T5 the axis orientations change with the environment. M.A. El-Sayed: In this calculation we use the magnetic axis determined by your group. We could stop at this point since there is no need to carry calculations involving higher triplets. In cases when Ss—’.s.Ti prediction does not account for observations, then our fit about upper triplet states becomes a matter of computer fit with a number of assumptions, since as you sald, we have no knowledge about the magnetic properties of upper triplet states. But even in this case, we do indeed learn that upper triplets are involved in the mechanism of the intersystem crossing. ~i--~~1