1146
J. Phys. Chem. 1992,96, 1146-1 151
these doublets seemed to depend on the partial pressure of PF3, suggesting weak interactions between Ag atoms and PF3. In the absence of P hfi, however, assignment could not be made. Lines Occurred at the Same position as the = and lines from the two equivalent Ag "' lei Of Ag730'31and are
assigned to this cluster that may or may not have been perturbed by association with PF,. Acknowledgment. We thank Dr. P. L. Timms for providing us with details of the preparation of PF, and Drs. J. R. Morton and K.F, Preston for their computer programs and helpful discussions. We also thank Professor Lon B Knight, Jr. (Furman RWhy NO. AgPFS, 138009-37-7.
(31) Howard, J. A.; Mile, B. Electron Spin Reson. 1989, IIB, 136-174.
Zeeman Effects in Randomly Oriented Triplet States. 2. Optical Zeeman Spectra E. M. McCauley, C. L. Lasko, and D.S . Titi* Department of Chemistry, University of California, Davis, California 95616 (Received: August 12, 1991) The optical Zeeman spectrum associated with a tripletsinglet transition in a randomly oriented solid sample is described. The results indicate that, if the zero-field splittings and the radiatively active spin level of the triplet state are known, then the sign of the principal fine structure splitting constant, D,can be determined. If only the zero-field splittings are known, the Zeeman spectrum can restrict the sign of D and the radiative activity of the spin levels. Example experimental spectra are presented and analyzed for xanthione, chromyl chloride and pmethylbenzaldehydein polycrystalline hosts to yield parameters of the lowest triplet state of the guests.
Introduction The Zeeman effect has been widely used to probe molecular electronic spectra involving triplet-singlet transitions in solids. Typically single crystals are employed with the magnetic field oriented along known crystal directions. Analysis of the spectra for various orientations of the field and the electric vector of the light can then yield in favorable cases the exciton interactions, the signs and magnitudes of the fine structure splitting constants, the transition moment direction and its relative magnitude for the individual spin levels, and a symmetry assignment for the triplet state.'" That optical Zeeman spectra are also useful in probing randomly oriented triplet states is less well recognized. The information obtainable in this case is more limited but not inconsequential. Resolved optical Zeeman spectra of triplet states in randomly oriented solids have been reported previously, for example, for metal-complexed phthalocyanines in n-alkane matricesa7 The influence of magnetic fields on the singlet state of free-base porphine in amorphous solids has also been studied at high resolution by hole-burning techniques with the expected hole shapes discussed in detail.* However, to our knowledge no detailed characterization of the resulting Zeeman spectrum has been presented for a randomly oriented triplet state in terms of the triplet-state parameters. Since more triplet states can be studied as polycrystalline samples or in Shpolskii solvents than in oriented single crystals or hosts, an understanding of the optical Zeeman spectrum expected in such cases is potentially useful. (1) Hochstrasser, R. M. J . Chem. Phys. 1967, 47, 1015. Castro, G.; Hochstrasscr, R. M. J. Chem. Phys. 1968,48,637. Hochstrasser,R. M.; Lin,
T . 4 . J . Chem. Phys. 1968,49,4929. Hochstrasser, R. M.; Lin, T . 4 . Symp. Faraday Soc. 1969.3, 100. (2) Hochstrasser, R. M. In MTP International Review of Science: Physical Chemistry, Buckingham, A. D., Ramsay, D. A,, Eds.; Series 2; Butterworths: Washington, DC,1976; Vol. 3 and references therein. (3) Wiersma, D. A. Ber. Bunsen-Ges. Phys. Chem. 1976, 80, 226. Aartsman, T. J.; Wiersma, D.A. Chem. Phys. 1973, I , 211. (4) Van Egmond, J.; Burland, D. M.; van der Waals, J. H. Chem. Phys. Lett. 1971, 12, 206. van Dijk, N.; Noort, M.; Voelker, S.; Canters, G. W.; van der Waals, J. H. Chem. Phys. Lett. 1980, 71, 415. (5) Arrington, J. P.; Tinti, D. S.Chem. Phys. 1979.37, 1. Tinti, D. S. Mol. Phys. 1984, 51, 461. (6) Gliemann, G. Comments Inorg. Chem. 1986,5, 263. (7) Chen, W.-H.; Huang, T.-H.; Rieckhoff, K. E.; Voight, E. M. Mol. Phys. 1989.68, 341. ( 8 ) Van den Berg, R.; van der Laan, H.; Vblker, S. Chem. Phys. Lett. 1987, 142. 535.
We discuss herein the expected optical Zeeman spectrum of a triplet-singlet transition for a randomly oriented solid sample. The results show that if the mo-field splittings and the radiatively active spin level of the triplet state are known, from, e.g., zerefield ODMR studies9J0in a randomly oriented solid, then the high-field optical Zeeman spectrum of the same system can determine the sign of the principal fine structure splitting constant, D. If only the zero-field splittings are known, the Zeeman spectrum can restrict the sign of D and the radiative activity of the spin levels. The determination of the magnitude of the splitting(s) and of the spin-level radiative activity in the triplet state is only possible in particular systems. Example experimental spectra are presented for several systems. The results arc interpreted to yield parameters of the triplet state involved in the transition. k r y
We consider the perturbation of a triplet state in the high field basis (Ms= 0, f l ) due to the fine structure interactions. The fine structure axes and splitting parameters are chosen such that DIE 1 3 with D = -3212 and E 1 (Y-412,so that the relative order of the spin levels at zero field is T,,> T, > T,. The fmt-order energies of the electron spin states in a Zeeman field of magnitude B become
E(o)= D(l - 3n2)/3 E(*') = fg&,,B
+ E(m2 - 12)
- D(l - 3n2)/6 - E(mZ- 12)/2
(la) (lb)
where the g tensor is assumed isotropic with the free electron value, g,, be is the Bohr magneton, and 1, m, and n are the direction cosines of the field with respect to the x, y, z fine structure axes, respectively. Averaging over all orientations for a randomly = ( d )= 1/3)yieldsthetrivialresult oricntedsample((P) = (d) ( E(o))= 0 and (E(*')) = f g y $ for the mean energies. However, the mean energies alone are misleading and hide the important spectroscopic details. First, eqs 1 show that at zero line width the energy spread of the Ms = f l levels is half that of the Ms= 0 levels. The energy extrema correspond to orien(9) Clarke, R. H.. Ed. Triplet Stare ODMR Spectroscopy; Wiley: New York, 1982. Kwiriam, A. L. In MTP International Review of Science: Physical Chemistry, McDowell, C. A,, Ed.;Series 1; Butterworths: London, 1972; Vol. 4. (10) McCauley, E. M.; Lasko, C. L.; Tinti, D. S. Chem. Phys. Lett. 1991, 178, 109.
0022-365419212096-1146%03.00/0 Q 1992 American Chemical Society
Zeeman Effects in Randomly Oriented Triplet States. 2.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1147
TABLE I: Peak Energies, Asymmetries, and Relative Shifts of the M s= -1 Components for the Level Densities a d Spectral Intensities of the Zeemrn Compoaeats for an AwWly Symmetric Tridet State in a RIlldomlv Oriented SPmDle
N
4
'XJ
a
113 -213 113
-116 -116 -116
-1 1 -1
-112 112
0 -41 15 4/30
0
0 -1115 1/30
-115 2/5
0 -91 15 9/30
-215 115
Energies relative to M s g d r g ; in units of D. Energy relative to the mean of the fine structure splitting in units of D.
tations with the magnetic field parallel to they and z axes and yield spreads of ID El and ID E112 for Ms = 0 and f l , respectively. Second, in a randomly oriented ensemble, the density of levels for a given Msis generally asymmetric about its mean energy and strongly peaked. The peaks are associated with Bllx and occur at ( D -3E)/3 and f g y B B- ( D - 3 E ) / 6 for Ms = 0 and f 1, respectively, at zero line width. We define thc asymmetry of a Zeeman pattern as
+
+
6P I (E(+')P - (E(o)p(2) where the subscripts signify evaluation at the peak of appropriate distributions. For the distributions given by the level densities, 6 = -D + 3E to first order at zero line width. Third, spectroscopic observation of the Zeeman pattern by transition with, for example, the ground singlet state will weight the preceding distributions in terms of the relevant transition probabilities for the individual Mslevels. The result is easily predicted when just one of the spin levels is radiatively active at zero field, in which case no cross terms can arise in evaluating the squared transition moments for the Mslevels. For example, if at zero field only the T,spin level is active, spectroscopic observation selects mainly the BII z region of Ms = 0 and the B l z regions of Ms = f l . This causes a differentiation among possible spectra based on the radiative activity. We consider first the case where E = 0, obtaining analytical solutions in the perturbation limit for the above qualitative ideas. The case where E is nonzero is discussed afterward. E = 0. Expressing the energies as shifts from M a y @ , eqs 1 for E = 0 simplify to E(') = D(l - 3 COS' 6)/3
(3a)
- 3 cos2 6 ) / 6
(3b) where 6 is the angle between the field and the z spin axis. The level densities are proportional to sin 6/(dE(M)/d6) and become E(*')
-D( 1
No) [4D(D - 3E(o))/3]-'/2 Nfl)= [D(6E(*')+ D ) / 3 ] - 1 / 2
(4a)
(4b)
where E(O) ranges between -2013 and 0 1 3 and E(*') between -016 and D / 3 from eqs 3 with 0 I 6 I x . Equations 4 indicate that the shapes of the densities for Ms = f 1 are "mirror images" of that for Ms = 0 at half the energy spread. Evaluation of the peak energies associated with these distributions depends on the zero-field line width, r. Three limiting cases are particularly simple. In the limit of small line width, r
