J. Phys. Chem. 1984,88, 4223-4228
4223
Line-Shape Analysis of Translent Triplet Electron Paramagnetic Resonance Spectra. Application to Porphyrins and Chlorophylls in Nematic Uniaxial Liquid Crystalst 0. Gonen' and H. Levanon** Deportment of Physical Chemistry and the Fritz Haber Research Center f o r Molecular dynamic^,^ The Hebrew University, Jerusalem 91 904, Israel, and Radiation Laboratory, University of Notre Dame,4 Notre Dame, Indiana 46556 (Received: November 23, 1983)
A study of the transient triplet EPR line shape of H2TPP and chlorophyll a dissolved in a nematic liquid crystalline phase is reported. The analysis is carried out by unifying the theory of triplet spin dynamics together with the anisotropic orientational distribution of the porphyrin guest in the liquid crystal.
Introduction Liquid crystals represent an intermediate state exhibiting order properties higher than glass and lower than single crystals. The fluidity and orientational properties can be utilized to incorporate guest molecules into the liquid crystalline phase and impose its orientation on the guest solutes. Indeed, liquid crystal host-guest dye systems have been used in magnetic resonance5-I2and optical spectro~copy~"'~ studies to determine the order and orientational properties of these systems. It is well-known that EPR spectroscopy is a sensitive tool in probing anisotropic systems, in particular the triplet state whose spectral features are highly dependent on the mutual orientation between the external magnetic field and the dipolar interaction tensor. Obviously, such orientation is best defined in single crystals which have the further advantage of providing highly sensitive and resolved spectra. Unfortunately, growing single crystals is not feasible or extremely difficult in many cases such as large molecules of biophysical interest, e.g., porphyrins and chlorophylls.18-20 On the other hand, the detection of EPR spectra in glass matrices is well established despite the unavoidable difficulty that the random nature of the triplet distribution decreases the sensitivity as compared to single crystals. Nevertheless, many molecular systems, in particular those which are directly related to primary photosynthesis, namely porphyrins and chlorophylls, exhibit intense triplet EPR spectra in glass matrices. This is mainly due to the selective nature of the intersystem crossing mechanism which gives rise to nonthermal distribution within the triplet sublevels.21 This effect, known as electron spin polarization (ESP),z2,23results in emission and enhanced absorption lines in the EPR spectrum and subsequently highly sensitive spectra. EPR line-shape simulations of randomly and partially oriented triplets and paramagnetic centers have been reported previously by several l a b o r a t o r i e ~ . ~ ~ ~In, *all ~ -cases ~ ~ where triplet line shapes have been simulated, it was assumed that thermal distribution has been established within the triplet sub state^^-^^^^-^^ or that spin-lattice relaxation is negligibly small.28 In the present study we report on the EPR triplet line-shape analysis of randomly and partially oriented triplet spectra which exhibit ESP phenomenon. Such analysis enables deduction of molecular and kinetic parameters associated with the triplet state. For partially oriented molecules, order parameters can also be extracted. We demonstrate this method on H2TPP and Chl-a, compounds that have been extensively studied.21 Since their triplet kinetic parameters are already known, they can be compared with the results obtained in the present work. Theory Spin Hamiltonian. The spin Hamiltonian of a triplet state in a magnetic field is of the form29
The first term in eq 1 is the electronic Zeeman interaction and Dedicated to the late Dr. Moshe Zidon.
0022-3654/84/2088-4223$01.50/0
D and E are the zero-field splitting parameters related to the principal elements of the diagonalized dipolar interaction tensor via the relations
X = D/3 -E
Y = D/3
-E
Z = -?3D
(2)
(1) In partial fulfillment of the requirements for a Ph.D Degree at the Hebrew University of Jerusalem. (2) Permanent address: The Hebrew University of Jerusalem. (3) The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, GmbH, Munchen, BRD. (4) The research described herein was supported by grants of the Israel Council for Research and Development, the Israel Academy for Sciences and Humanities, and partially supported by the Office of Basic Energy Sciences of the Department of Energy. This is document no. NDRL-2509 from the Notre Dame Radiation Laboratory. (5) Mobius, K.; Haustein, H.; Platon, M. Z . Naturforsch. A 1968, 23, 1626. (6) Krebs, P.; Sackmann, E. J . Magn. Reson. 1976, 22, 359. (7) Swartz, J. C.; Hoffman, B. M.; Krizek, R. J.; Atmatzidis, D. K. J . Magn. Reson. 1979, 36, 259. (8) L!ckhurst, G. R., Gray, G. W., Eds. "The Molecular Physics of Liquid Crystals ; Academic Press: New York, 1979. (9) Grebel, V.; Levanon, H. Chem. Phys. Lett. 1980, 71, 218. (10) Meirovitch, E.; Igner, 0.;Moro, G.; Freed, J. H. J. Chem. Phys. 1982, 77, 3915. (11) Goldfarb, D.; Luz, Z.; Zimmermann, H. J . Phys. (Paris) 1981, 42, 1303. (12) Gonen, 0.;Levanon, H. J . Chem. Phys. 1983, 78, 2214. (13) Kelker, H.; Hatz, R.; Sinzing, 2. Anal. Chem. 1974, 267, 161. (14) Zannoni, C. Mol. Phys. 1979, 38, 1813. (15) Levanon, H. Chem. Phys. Lett. 1982, 90, 495. (16) Subramanian, R.; Patterson, L. K.; Levanon, H. Chem. Phys Lett. 1982, 104, 2972. (17) Anderson, V. C.; Craig, B. B.; Weiss, R. G. J. Am. Chem. SOC.1982, 104, 2972. (18) Goncalves, A. M. P.; Burgner, R. P. J . Chem. Phys. 1974, 61, 2975. (19) Michel, H. J . Mol. Eiol. 1982, 158, 567. (20) Gast, D.; Wasielewski, M. R.; Schiffer, M.; Norris, J. R. Nature (London) 1983, 305, 451. (21) For general reviews on triplet states in photosynthesis see, e.g.: (a) Levanon, H.; Norris, J. R. Chem. Reu. 1978, 78, 175. (b) Thurnauer, M. C. Reu. Chem. Intermed. 1979, 3, 197. (c) Levanon, H.; Norris, J. R. In "Light Reaction Path of Photosynthesis"; Fong, F. K., Ed.; Springer-Verlag: West Berlin, 1982; pp 153-95. (22) Levanon, H.; Weissman, S. I. J . Am. Chem. SOC.1981, 93, 4309. (23) For general reviews on ESP see, e.g.: (a) Hawser, K. H.; Wolf, H. C . Adv. Magn. Reson. 1976,8, 85. (b) Levanon, H. In "Multiple Electronic Resonance"; Dorio, M., Freed, J. H., Eds.; Plenum Press: New York, 1979; Chapter 13. (24) (a) Kottis, P.; Lefebvre, R. J. Chem. Phys. 1963,39, 393. (b) Kottis, P.; Lefebvre, R. [bid. 1964, 41, 379. (25) Wasserman, E.; Snyder, L. C.;Yager, W. A. J . Chem. Phys. 1964, 41, 1763. (26) (a) van Willigen, H. Ph.D. Thesis, University of Amsterdam, Amsterdam, The Netherlands, 1965. (b) Shain, A. L. Ph.D. Thesis, Washington University, St. Louis, MO, 1969. (c) Scherz, A,; Levanon, H. J . Phys. Chem. 1980, 84, 324. (d) van Willigen, H.; Weissman, S.I. Mol. Phys. 1966, 11, 175. (27) Freed, J. H.; Bruno, G. V.; Polnaszek, C. J . Chem. Phys. 1971, 55, 5270. (28) Frank, H. A,; Friesner, R.; Nairn, J. A,; Dismukes, G. C.; Sauer, K. Eiochim. Biophys. Acta 1979, 547, 484. (29) For general textbook and references on the triplet state see: McGlynn, S. D.; Azumi, J.; Kinoshita, M. "Molecular Spectroscopy of The Triplet State"; Prentice-Hall: Engelwood Cliffs, NJ, 1969.
0 1984 American Chemical Society
Gonen and Levanon
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984
4224
With evaluations of the commutator^^^^^^ (6) in the rotating frame and making the steady-state slow passage assumption, p = 0, one obtains for the two transitions -A + 2C(D,E,fi,cp) + i/T2 P2l = W l h l - P22) (1/T2)2 + [A - 2 C ( D 3 , f i , d l 2 -A - 2C(D,E,S,cp) + i/T2 (8) P32 = ul(P22 - P33) (1/T2I2 + [A + 2C(~,E,fi,cp)l2
-
where
L
Figure 1. (a) Schematic representat@ of cylindrical distribution of porphyrin molecules about the director L (parallel configuration), X,Y,Z (insert) and x,y,r are the molecular and laboratory coordinate systems, respectively. As discussed in the text this configuration describes an ideal case where the molecular (X,Y) planes are parallel to J? wit) an equal probability for? acd Y to be aligned in the direction of L and zero probability for L 11 2. (b) Same as in a except that the sample is rotated (in the frozen stat_e)by x = a / 2 such that the cylindrical distribution is perpendicular to B (perpendicular configuration). At this configuration any molecular axis can be parallel to B.
The Hamiltonian of eq 1 in terms of the high-field spin eigenfunctions II), IO), 1-1) isz5 D / 3 +gPBn (gpB/21/2)(1- im) E (gpB/2l/’)(I + im) -2D/3 (gpB/2’/’)(I - im) Cp;eB/2”’)(1 + im) D / 3 -gpBn (E
)
(3)
where I, m, n are the direction cosines between the external magnetic field and the principal axes X , Y,2 fixed in the molecular system (Figure 1). Since the dipolar interaction in the-molecules being studied in the present work is generally about 1 order of magnitude smaller than the Zeeman term, it may be regarded as a small perturbation on the latter interaction. The eigenvalues of eq 1 become hgpB, 0 and the corresponding eigenfunctions are given by Wasserman et al.25 Introducing D and E as the perturbation, the energy levels to first order are the elements of the diagonalized Hamiltonian matrix25 (!OB
)
0 - W J ,0 , ~ ) 0 2 C(D.E, 6 , ~ )0 (4) -gPB - C(D,E,O,P) 0
where
- 3n2) -
- m2) 2 EPR Triplet Line Shape. An EPR spectrum is a measure of the transverse component of the total magnetization of the s+mple under study, namely the expectation value of S+ = S, + is,. A convenient way to calculate this is via the density matrix formalism as shown by Alexander30b and applied to triplet EPR by van Willigen and Weissman26a*d in which (using the Zeeman eigenfunctions as basis) C(D,E,t9,9) = :(l
The density matrix itself can be obtained from its equation of motion ~
i
=j i [ ~ * % l l j -(l/Tz)PIj
A =B-~ / y
~1
= yBl
Thus, for an arbitrary orientation of 3 in the molecular frame, defined by 29,9 the absorption line shape I(B,d,p) is given by the imaginary part of (pZl p32). To obtain the line shape one needs to know the population differences (pi,- plJ). We shall assume the transition-inducing field is sufficiently weak (ulT1
