J. Am. Chem. SOC.1984, 106, 5941-5947
5941
Electronic Properties of the Linear Antiferromagnetically Coupled Clusters [ Fe3S4(SR),I3-, Structural Isomers of the [ Fe,S4]+ Unit in Iron-Sulfur Proteins J.-J. Girerd,ls.bG. C. Papaefthymiou," A. D. Watson,lPE. Gamp,ldK. S. Hagen,ls N. Edelstein,ldR. B. Frankel,lCand R. H. Holm*1P Contribution from the Department of Chemistry, Harvard Uni?ersity, Cambridge, Massachusetts 021 38, the Laboratoire de Spectrochimie des Elements de Transition, ERA CNRS 672, UniversitZ de Paris-Sud, F-91405 Orsay. France, the Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39, and the Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, California 94720. Received March 6, 1984
Abstract: The magnetic susceptibility, magnetization, and Mossbauer spectroscopic properties of the trinuclear clusters [Fe3S4(SR),13-(R = Et, Ph), containing the linear [Fe(p2-S)2Fe(p2-S)2Fe]+core with Fe-.. Fe separations of 2.71 A, have been examined in order to characterize this unique magnetic system. (Et4N)3[Fe3S4(SEt)4]follows the Curie-Weiss law xM = 4.268/( T + 0.58) at 5-300 K, with the average magnetic moment of 5.84 p B corresponding to an S = 5 / 2 ground state. The magnetization approaches p = gS = 5 pB per cluster at low temperature and provides an estimate of the zero-field splitting parameter ID1 5 1 cm-'. Mossbauer spectra reveal the presence of antiferromagnetically coupled, high-spin Fe(II1) atoms. Close resemblance of spectra in the solid and in DMF solution demonstrates retention of the linear structure in solution. Two magnetic subsites in a 2:l ratio are observed, with the more intense and less intense subsites corresponding to the hyperfine fields -310 f 5 and +230 f 5 kOe, respectively. It is shown that from these values the hyperfine interaction constants a/gn/3, = -153 & 3 and -137 & 3 kOe/spin can be calculated for the more intense and less intense subsites, respectively. The more intense subsite, with the larger hyperfine interaction, corresponds to the two end Fe(II1) atoms (1, 3), whose magnetic moments are parallel to each other and to the total moment of the cluster. The less intense subsite, with the smaller hyperfine interaction, is the central Fe(II1) atom (2) whose moment is antiparallel to the cluster total moment and hence to the moments of the other two Fe(II1) atoms. The estimates JI2= 3 2 3 ca. -300 cm-I and -100 5 J 1 3S 100 cm-l were obtained from susceptibility data. A theoretical treatment of three antiferromagnetically coupled S = 5/2 spins shows that when JI2= J23 IS2M2>JS3M3>, where Si = and IMi 5 5/2. The eigenvalue problem has been solved by Griffith.33 The energy surfaces of the lowest states of the antiferromagnetically coupled system (Ji, < 0) are schematically represented in the three-dimensional plot of Figure 3. Here we use the notation of eq 3 and 4. From the structure of cluster 3 (Figure l ) , it is expected
(32) Laskowski, E. J.; Reynolds, J. G.; Frankel, R. B.; Foner, S.;Papaefthymiou, G. C.; Holm, R. H. J. Am. Chem. SOC.1979, 101, 6562. (33) Griffith, J. S.Struct. Bonding (Berlin) 1972, 10, 87. (34) Kent, T. A.; Huynh, B. H.; Miinck, E. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 6574.
Paramagnetism”; Boudreaux, E. A., Mulay, L. N., Ed.; Wiley-Interscience: New York, 1976; Chapter 7 and references therein. (b) Ginsberg, A. P. Inorg. Chim. Acta, Reu. 1971, 5, 45. (37) (a) Takano, M. J. Phys. SOC.Jpn. 1972.33, 1312. (b) Yablokov, Y. V.;Gaponenko, V. A.; Zelentsov, V. V.; Suvorova, K. M. Solid State Commun. 1974, 24, 131. (c) Dziobkowski, C. T.;Wrobleski, J. T.; Brown, D. B. Inorg. Chem. 1981, 20, 671 and references therein.
i / X ~ = ( T - e)/c
(1)
C = 4.268 f 0.002 emu K/mol
0 = -0.58 f 0.08 K 5.842 f 0.001 pg
pav=
T - e)] were calculated at some 40 points in the interval 5.00-300.3 K. The average value of the magnetic moment is close to the value of 5.92 pg, the spin-only moment of an S = state. With the near-zero value of 0, these results establish that [Fe3S4(SEt),13- has a spin sextet ground state. Similar measurements have established the same state for [Fe,S4(SPh),l3-. For the former cluster below -50 K, deviations from the Curie that J I 2= J23 = J . Equation 2 can be rewritten as eq 5. For this law (eq 1, 0 = 0) become evident. The magnetization of case, unlike that of three unequal J values, thezigenvalue problem [Fe,S,(SEt),]* at 4.2 K deviates slightly from a Brillouin function can be solved an3lytically. We assumeihat SIand S3 couple to dependence on the applied field in approaching the saturation value produce a spin S’, which cpqA$s with ,S, to_forq the total spin of p = gS = 5 pg per cluster. At 80 kOe the magnetic moment S of the cluster; Le., S’= SI+ S3 and S = S’+ S2.The 27 spin per cluster is 4.73 pg. states and their occurrence numbers, obtained in this way, are Isomer shifts and quadrupole splittings of [Fe3S4(SEt),J3-, discussed in a following section, are consistent with three high-spin Fe(II1) atoms. Thus, indiyidua!iron_spins Si = 5 / 2 combine to (35) Fahil’berg, V. E.; Belinskii, M. I.; Tsukerblatt, B. S.Sou. Phys.produce a total spin I S 1 = IS1+ S2+ S31= ’12. Systems of three JETP (Engl. Trawl.) 1980, 52, 314. coupled high-spin Fe(II1) sites have been studied t h e o r e t i ~ a l l y ~ ~ - ~ ~ (36) (a) Hatfield, W. E. In “Theory and Applications of Molecular
5944 J. Am. Chem. SOC.,Vol. 106, No. 20, 1984
Girerd et al. Table 11. Mossbauer Spectral Data for (EtdN)lIFelSd(SR)dlat 77 K
R
r,e
6,” mm/s
mm/s
mm/s
0.23 0.25
0.52 0.55
0.60 0.72
Et solid DMF soh Ph solid DMF soh uRelative to Fe metal at h0.04.
0.29 0.63 0.68 0.24 0.60 0.72 room temperature; f0.03. bf0.05
[Fe,S4(SPh$-at
I
4.2K
I$a:: J S
0.88
I
I
I
I
-5.00
0.00
B.00
VELOCITY
fMM/SECI
Figure 5. Mossbauer spectra of polycrystalline (Et,N),[Fe,S,(SEt),] at (a) 77 K and (b) 4.2 K and (c) a 70 m M solution in D M F at 77 K. At 4.2 K the solution spectrum shows incipient hyperfine splitting.
listed in Table I. Equation 5 can be expressed in the form of eq 6. This Hamiltonian is diagonal in S, S’and in SI,S2,and
SJ-J
= (1/2)[52 - 5’2 - 5,21
+ ( ~ / 2 ) [ 5 ’ 2 - S12- S32] (6)
I
S 3 . The eigenvalues are given by E/-J
(1/2)[S(S + 1) - S’(S’+ 1) - Sz(S2 + I)] + (x/2)[S’(S’+ 1) - S1(S, + 1) - S3(S3 + l ) ] (7)
Since S, =
5/2,
Si(S, + 1) = 35/4 and eq 7 becomes
E(S,S’)/-J = (1/2)[S(S
+ 1) - S’(S’+
1) - 35/41 + (x/Z)[S’(S’+ 1) - 35/21 (8)
where S and S’ take the values
I S l - S 3 ( < S ’ < S+, S 3
IS’-S21
