- Email: [email protected]
An EPR study of single crystals of three dinuclear sulfur-bridged derivatives of iron
JOURNAL
OF MAGNETIC
RESONANCE
19,283-293
(1975)
An EPR Study of Single Crystals of Three Dinuclear Sulfur-Bridged Derivatives of Iron J. A.
VAN
WYK
Department of Physics, University of the Witwatersrand, Johannesburg, Republic of South Africa Received January 28,1975 The EPR spectra of the compounds
KFe(~-C&) (COP G&M
W.&h
[(Fe(q-C5H5) (CO)S (t-C4H&]
B(C6H&,
and HWtl-GH3 (CW (C&N4 BFhhave
been investigated. With the magnetic field applied in an arbitrary direction two lines are observed in the first, four in the second, and one only in the last. The spectra are explained by an exchange interaction which couple magnetically nonequivalent ions. The energy of this interaction being, respectively, smaller, comparable to, and greater than the difference in the Zeeman energies in these compounds. INTRODUCTION
Because of the complexity of most biological systems, it is often advantageous to study the property of interest, first in more tractable model systems. A group of compounds which bear some resemblance to the biologically important ferrodoxins are the complexes {Fe(&H,) (CO)SR}, (R = CH3, C2H5, CC,H, or t-C,H,). These diamagnetic compounds can be oxidized by various oxidants (I, 2) to the structurally almost identical paramagnetic {Fe(q-C,H,) (CO)SRj: ions. The stereochemical structure (of this compound is shown in Fig. 1. The Fe& ring is almost planar (3,4) with the other ligands extending upwards or downwards from this plane.
FIG. 1. Geometry of iron-sulfur 283
Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
compounds.
284
J. A. VAN
WYK
In what follows the formula of the salts of ions above will be abbreviated to [{X(R)},]A, where A represents the anion involved in the salt. This paper will be concerned with the EPR spectra observed in single crystals of
EXPERIMENTAL
The EPR spectra were taken at the ambient room temperature on a Varian V-4502 spectrometer; the x-band microwave assembly of which has been replaced by a k-band (22 GHz) system. The cavity, operating in the TEoil mode, was of conventional design, except that it was oriented such that the sample could be rotated about a horizontal axis. The magnet could be rotated about a vertical axis around the cavity. THEORY
Many of the features of the EPR spectra in the iron-sulfur compounds suggest that the paramagnetic electron on one ion is coupled to similar electrons on other ions by exchange or dipolar interactions. In a crystal any one electron could in general be interacting with electrons on several ions in its neighborhood. To do an exact calculation would be a formidable, if not impossible, task, and would require a knowledge of the exact nature of the exchange interaction and also the crystallographic arrangement of the ions. It was found, however, that an exploration of the effects of the interaction between a single pair of ions, provides a useful contribution towards the understanding of the observed spectra. A summary of the results of such a calculation (5) in which it is assumed that the exchange energy is small compared to the Zeeman energies will now be given. Consider two s = 3 ions which are coupled by an exchange or dipolar type of interaction. The spin-Hamiltonian to be considered is of the form &’ = /!?H-G;S:, + ,8H*G,.S; + 27;.r-S;.
PI
The first two terms represent the Zeeman energies of the electrons a and b, and the last term represents the interaction between them. No assumptions will be made at this stage about the form of the tensors appearing in Eq. [l]. The secular equation of the Hamiltonian above is greatly simplified if the spin operators Sl are replaced by S, where S;=T,S,
PI
and -gwg,t --c!?,
T, =
gm --gaga, -g,, .-ii-
ga, gut
-gas
gar-
ga,
ga
gar
gm
gap
ga
0
gat Z.
where a is a or b and the g’s appearing in Eq. [3] are defined by
km gas,A= R, *Gas
131
285
IRON-SULFUR DERIVATIVES
where RH = [I&,, RHs, RHt] represent the direction cosines of the magnetic field. Also & = g:r + ds and gZ=d,+&. By means of Eq. [2], Eq. [l ] becomes [41 where J= T;J”*T,.
A
Ed Eb* J33
BE- J33
h (4
V
I I 1 1 I I V I I , I C4J3j+ I 1
A
; I I L I I
FIG.
&2AE+
S3
+4J35+ I
I
Ea’ Eb’ J33
0 1 8
V
I
-E,-Eb+ I
4
V
(b)
-AE-J33
I I I I
AE- J33
A
-AE- J33 V
I
I I
I
I
?Ea Eb+J33 I
+2AE-+ I
2. Energy level diagrams fir two exchange coupled s = 3 spins (a) AE > Js3 and (b) AE < J33.
Using the assumption that the exchange energy is small compared to the Zeeman energies, Eq. [4] yields the following energies E1=Eai-Et,i-J3s E,= AE-Js3 Es=-AE-Js3 Ed = -E. -Eb + Js3,
286
J. A. VAN WYK
where AE = [ jJz3 1’ + (E, - Eb)2]“2, J23 = $[(J,x 4
= 3/k,
+J~~) K
4
+6&y
-&)I
= --h
H
and 533
= +Jzz.
Two possible energy level diagrams and the possible transitions are shown in Fig. 2. The one diagram corresponds to the case where AE > J33 and the other to J33 > AE. It can be shown that the latter situation is possible only when 2 x J33 is very different from 15231. In the former the separation between the lines in each pair is 4 x J33 and the pairs are centred at g=-H&+&)
AE +pg
Calculation of the transition probabilities shows that the intensity of the inner lines is greater than or equal to that of the outer lines, and that the inner ones grow at the expense of the outer ones as the difference between g, and g, is decreased. When g, = g, the spectrum should consist of two lines, except when
2Jzz= KJ.xx+ Jw)’ + (Jx,- J,.x)21”2>
bl
in which case only one line will be observed. This condition is complied with if only the diagonal components of the J tensor are nonzero, and if these are equal to each other. This in turn implies that the interaction term in Eq. [l] can be written as J’S~*S~. RESULTS
The EPR spectra observed in frozen solutions at 77 K, yield the g values (6) given in Table 1. TABLE PRINCIPALS
VALWSOFIRON-SULFUR
1
COMPOUNDS AS MEASURED gVALUES+o.c@l
Compound I(C,H,)Fe(CO)S(CH,)},BF4 ((C,H,)Fe(CO)S(C,H,)}~B(C6H34
I(C,HS)Fe(CO)S(i-C3H,)}~B(CsH5)4 I(C,HI)Fe(CO)S(t-C,H~)}~B(CsH3*
INFROZENSOLUTIONAT
77 K. ALL
&?I
g2
g3
2.032 2.037 2.040 2.047
2.014 2.015 2.016 2.014
1.941 1.940 1.935 1.937
The EPR spectra in single crystals showed the following features. In all three compounds only one EPR line is observed in two planes perpendicular to each other; the spectra show mirror symmetry about one of the planes, which will be referred to as the mirror plane. With the magnetic field applied in directions outside these planes, two lines are observed for the first, four for the second, and one only for the last. The mirror symmetry of the spectra suggests that the unit cell contains at least two
lRON-SULFUR
287
DERIVATIVES
ions which are crystallographically related to each other by a mirror (or glide) plane. For EPR purposes it was convenient to choose in this plane as reference axes, Y and S, the directions along which the maximum and minimum g values, respectively, are observed. The third axis f was naturally chosen perpendicular to this plane. These axes are not necessarily parallel to crystallographic or morphological axes. The two line spectra observed in this compound Hamiltonian
can be described by the spin-
~=~PH~G;S,f~H~G,~S,,
[71
where the principal values of the g tensors G,, and Gb are identical, but the principal axes form mirror images of each other across the rs plane. TABLE PRINCIPAL,
g VALUES AND
AXES AS DETERMINEDFROMSINGLE CRYSTAL {x(t-C4H&B(C,H,),
Principal g values
gx gY
gz Angles of principal axes with rf:ference axes
4x”
2
2.043 2.013 1.941 21.0” 139.4” 85.5” 69.7”
[email protected],NJKd-M~ 2.041 2.016 1.942 18.7” 115.8” 79.2” 44.4”
MEASUREMENTS
{X(CH&BF4 2.033 2.016 1.942 3Vb 90” 90” 0”
’ 4 is measured in the rs plane from r, and the polar angle 0 is measured from the f axis. b r axis was chosen parallel to the axis corresponding to gI and I parallel to gl.
:2*00 9 1.98-
1.94 tr
0+H
+e H FIG. 3. Angular variation of g values of EPR lines in [{X(t-C,H,)}z]B(C,H,)+ tabulated using the parameters given in Table 2.
e-)H The solid lines were
288
J. A. VAN WYK
The g tensors have been determined by means of least square regression calculation and using EPR measurements obtained in different crystal planes. The principal values of the g tensors and corresponding axes are given in Table 2. The calculated angular dependence of the EPR spectra in the rs, st, and rt planes, together with some experimental results are shown in Fig. 3. Note that these g values agree well with those given in Table 1. In the latter the dilution of the solutions were deliberately made large enough to avoid any interaction between electrons on different ions. The agreement between the results in Tables 1 and 2 therefore suggests that dipolar or exchange interactions are unimportant in single crystals, at least as far as the position of the EPR lines are concerned. Considerable line width variation, with orientation of the magnetic field is however observed, and this may well be due to these interactions. I. g Tensor. The EPR spectra observed in this compound differed from those in the
previous one in that four lines instead of two are observed when the magnetic field is applied in directions outside the two one-line planes. A typical example of the EPR
FIG. 4. Typical example of EPR spectrum of [{X(C2H5)}2]B(C6H5),. pairs is due to DPPH.
The narrow line between the two
spectra is shown in Fig. 4. The qualitative features of the EPR spectra can, however, be explained if instead of Eq. [7], Eq. [l] is used as spin-Hamiltonian. The symmetry relation between the g tensors is of course retained. Experimentally the maximum splitting produced by this interaction is found to be about 120 G, and the energy difference corresponding to this splitting is certainly small compared to g/MZ at k-band frequencies. The approximate calculation given earlier should therefore apply. Inspection of Eq. [5] shows that if the separation between the pairs is large compared to the splitting within the pairs, then the centers of the pairs corresponds very nearly to g, and gb, the g values of the Zeeman lines in the absence of exchange interaction. It can also be shown that this condition is complied with best if the magnetic field is applied at 45” to the I axis. For this reason, the centers of the pairs were measured in a
289
IRON-SULFUR DERIVATIVE%
cone around the t axis making an angle of 45” with this axis. The g tensors were calculated from these measurements, again using a least square regression technique. The results are presented in Table 2 and Fig. 5. Again the principal g values agree well with those measured in frozen solution, giving confidence in the method of analysis of the results.
2.025 2.005
1.985 9 1.965
1.945 0
30
60
90
120
150
180
%I FIG. 5. Angular variation of g values of EPR lines in [{X(C2H5)}2]B(C6H5)4 axis. (Solid lines were calculated using the parameters given in Table 2.)
in 45” cone around f
2. The exchange interaction. The qualitative features of the intensities of the lines are in agreement with those predicted from the coupled-pair calculation. This theory however predicts the same splitting between the lines in each pair. Experimentally, the splitting between the lines occurring at the higher magnetic field is always slightly greater than that of the other pair. The single line observed in two crystal planes suggests that the condition in Eq. [6] must apply at least approximately. This could mean that the interaction is isotropic, but it is found that the splitting (away from the one-line planes) depends on the direction of the applied magnetic field. Empirically it was found, within the range 0.4 < cos 8 < 0.9 and -0.1 < cos c1< 0.9, that the splitting between the lines of the high-field pair is given by AH= (26.3 + 67.9cosO)~(l + cosu),
PI
where B the angle between the magnetic field and the t axis. The angle c1is defined by [91
where (R& RfrH,,,R&) and (Rk,, Riy, R&,) are the direction cosines of the magnetic field relative to the principal axes of ions a and b, respectively. (Since the anisotropy in the g value is small, these direction cosines may also represent the axis of quantization of the ions.) To conclude, we present the following remarks : (i) Equation [8] applies where the splitting between the lines of the pair is greater of the lines. In directions where the splitting becomes comparable to
than the line width
290
J. A. VAN WYK
the line widths, the splitting seems to drop off more rapidly than is predicted by Eq. [8]. (ii) When the field is applied close to the rs plane, the spectrum consists of an intense line and two weak lines; one on either side of the strong line. The splitting between these lines is somewhat larger than is suggested by Eq. [8]. (iii) Eq. [8] was derived for the high-field pair. The splitting between the lines of the low-field pair is always smaller, and a slightly different relation is required. (iv) No physical meaning is attributed to the angle CIin Eq. [8]. It can be shown that cos CI= 1.0 when the magnetic field is applied in the direction which is perpendicular to the principal y direction of both the interacting ions, which also turns out to be the axis perpendicular to the crystallographic ab plane (see Fig. 6). This angle may therefore be related to the angle between the magnetic field and some or other important intermolecular axis. 3. Correlation of some EPRfeatures with some crystallographicfeatures. It is probably fair to expect that the crystallographic structure of the compound [{X(C,H,)),] B(C6H&, if available, should provide some clues to the origin of the interactions responsible for the splitting of the EPR lines. Unfortunately, some data on the structure of the iron-sulfur complexes has been published (4) only for the compound [{X(CH,)},] BF,. EPR results showed that the crystal structures of all the compounds have some common features, but it was also evident that the C2H5-compound does not have the
270
FIG. 6. Axes in, or projections of axes on, the rs (or UC)plane: rr and ss reference axes; au and cc crystallographic axes; xx and zz projections of principal axes (y axis lies in ub plane); pp and nn axes parallel and perpendicular to the plane of the crystal. The solid curve represents line width, and the broken curve the “exchange” splitting in the 45” cone.
IRON-SULFUR
DERIVATIVES
291
orthorhombic structure found for the CH,-compound. From preliminary X-ray data, it was found that the crystal structure of the C,H,-compound is monoclinic, with a = 1.82 nm, b = 0.98 run, c = 2.06 nm, and /I = 138”. The unit cell contains four formula units of the compound and the space group can be either Pz,=or PC,depending on whether the stru.cture has a center of symmetry or not. No more is presently known about the structure. Most of the crystals of the C,H,-compound were obtained as diamond shaped platelets, with one axis slightly longer than the other. The b axis lies along the shorter axis and the X-ray results showed that the c axis is 8” away from the longer axis. The crystallographic a and c axes, the Y and s axes, two morphological axes, and the prqjection of the principal axes on the ac plane are shown in relation to each other in Fig. 6. Also depicted in this diagram is the line widths of the EPR line in the UCplane, and the splitting between the lines of the high field pair, observed in the 45” cone around the t (orb) axis.
Im this compound only one line was observed with the magnetic field applied in any direction. The crystals used were obtained in platelet form with three well-defined mutually perpendicular morphological axes, and the g values took on extreme values along these axes. The g value of the line, in any other direction could be calculated with a fa.ir degree of accuracy from the expression
where g,, g,, g, represents the g values along the morphological axis, and RI, Rz, R3 the direction cosines of the magnetic field relative to these axes. The values for g,, g,, and g, are g, = 2.0265 g, = 2.0223
g, = 1.9420. If these values are compared with those measured in the frozen solution, it is noted that g, is almost identical to g,, but g, and g2 differ significantly from g, and g,,. The single crystal and frozen solution results can, however, be reconciled, if as before, it is assumed that the unit cell contains at least two ions, oriented such that their principal axes are mirror images of each other across one of the crystal planes, and that the energy of the exchange interaction is much greater than the difference of the Zeeman energies of these ions. The g value measured in the single crystal in any direction will then be equal to the average of the g values of the individual ions. With this in mind it can be shown t.hat agreement with the experimental values can be obtained if it is assumed that g, represents one of the principal values (g,), the other two principal values are g, = 2.0331 and g, = 2.0157, and that axes corresponding to these latter values lie in theg, g, plane, with the x axis 38” from the axes corresponding tog,. These results are in agreement with what one would expect from crystallographic data. Connely and Dahl(4) determined the structure of this compound, and inspection
292
J. A. VAN
WYK
of the crystal structure shows that all ions have their Fe-Fe and S-S axes parallel to the crystallographic ab plane. All ions, therefore, have an axis parallel to the c axis, and this axis must correspond to the principal axes associated with g,. From symmetry considerations it is probable that the other two principal axes will be parallel to axes through the iron and sulfur atoms. Unfortunately, not enough information is presented in the paper by Connely and Dahl to pursue this any further. The line width in [{X(CH,)},]BF, has been found to vary almost axially about the c axis, and varies according to A = 16.0+ 11.2(3cos20-
l)“,
where 0 is measured from the c axis. DISCUSSION
The most interesting aspect of this probably is the effect of the exchange interactions. In an undiluted compound one would expect every paramagnetic electron to be interacting with electrons on several molecules in its neighborhood. One would therefore expect a more complicated spectrum, if resolved, than the one observed. Even if it is assumed that in the lattice pairs of ions are closer to each other than to other, or that the molecules are favorably oriented for exchange interaction, the spectra cannot be analyzed fully without a knowledge of the crystal structure. Not only do the dipole-dipole interactions depend on the intermolecular distances and the direction of the applied magnetic field but so does the exchange interactions, and may also depend on the orientation with respect to each other, of the interacting ions (7). Without the crystal structure then, one can only speculate about the interactions responsible for the observed spectra. The only result of this report that might be of biological importance are the principal values of the g tensor. It has been known for some time already that EPR spectra observed in ferrodoxins are due to paramagnetic electrons localized on iron-sulfur centers (8). The more important features of the EPR and other results can be explained by a model proposed by Gibson et al. (9). The principal values measured here do not differ significantly enough from those measured in other model compounds (10) to warrant further discussion. ACKNOWLEDGMENTS The crystals used in this study have been prepared by J. A. de Beer of the Research and Process Development Department, South African Iron and Steel Industrial Corporation, and R. J. Haines, formerly of the same address but now in the Department of Chemistry of the University of Cape Town. REFERENCES 1. R. J. HAINE.Y AND A. L. Du PREEZ, Znorg. Gem. 11,330 (1972). 2. J. A. DE BEER, R. J. HAINES, R. GREATREX, AND J. A. VAN WYK, J. C/tern. Sot. Dalton, 3. G. FERGUSON, C. HANNAWAY, AND K. M. S. ISLAM, Chem. Comm. 1165 (1968). 4. N. G. GZINNELLY AND L. F. DAHL, J. Amer. Chem. Sot. 92,7472 (1970). 5. Full treatments of two special cases can be found in A. ABRAGAM AND B. BLEANEY,
2341 (1973).
“Electron Paramagnetic Resonance of Transition Ions,” Chap. 9, Clarendon Press, Oxford, 1970. 6. EPR spectra in these compounds have been observed for the first time by M. CLARE AND H. A. 0. HILL, Chem. Comm., 1376 (1970).
IRON-SULFUR
293
DERIVATIVES
7. R. BAUMANN, H. U. BEYELER, AND W. KANZIG, Helv. Phys. Acru 44,252 (1971). 8. E.g., W. R. DUNHAM, G. PALMER, R. H. SANDS, AND A. J. BEARDEN, Biochim.
Biophys. Acta 253,
373 (1971). 9. J. F. GIBSON,
D. 0. HALL,
J. H. M. THORNLEY,
AND F. R. WHATLEY,
Proc. Nat. Acad. Sci. U. S. 56,
987 (1966). 10. E.g.,
K. A. RUBINSON
AND G. PALMER,
J. Amer. Chem. Sot. 94,83X
(1972).
OF MAGNETIC
RESONANCE
19,283-293
(1975)
An EPR Study of Single Crystals of Three Dinuclear Sulfur-Bridged Derivatives of Iron J. A.
VAN
WYK
Department of Physics, University of the Witwatersrand, Johannesburg, Republic of South Africa Received January 28,1975 The EPR spectra of the compounds
KFe(~-C&) (COP G&M
W.&h
[(Fe(q-C5H5) (CO)S (t-C4H&]
B(C6H&,
and HWtl-GH3 (CW (C&N4 BFhhave
been investigated. With the magnetic field applied in an arbitrary direction two lines are observed in the first, four in the second, and one only in the last. The spectra are explained by an exchange interaction which couple magnetically nonequivalent ions. The energy of this interaction being, respectively, smaller, comparable to, and greater than the difference in the Zeeman energies in these compounds. INTRODUCTION
Because of the complexity of most biological systems, it is often advantageous to study the property of interest, first in more tractable model systems. A group of compounds which bear some resemblance to the biologically important ferrodoxins are the complexes {Fe(&H,) (CO)SR}, (R = CH3, C2H5, CC,H, or t-C,H,). These diamagnetic compounds can be oxidized by various oxidants (I, 2) to the structurally almost identical paramagnetic {Fe(q-C,H,) (CO)SRj: ions. The stereochemical structure (of this compound is shown in Fig. 1. The Fe& ring is almost planar (3,4) with the other ligands extending upwards or downwards from this plane.
FIG. 1. Geometry of iron-sulfur 283
Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
compounds.
284
J. A. VAN
WYK
In what follows the formula of the salts of ions above will be abbreviated to [{X(R)},]A, where A represents the anion involved in the salt. This paper will be concerned with the EPR spectra observed in single crystals of
EXPERIMENTAL
The EPR spectra were taken at the ambient room temperature on a Varian V-4502 spectrometer; the x-band microwave assembly of which has been replaced by a k-band (22 GHz) system. The cavity, operating in the TEoil mode, was of conventional design, except that it was oriented such that the sample could be rotated about a horizontal axis. The magnet could be rotated about a vertical axis around the cavity. THEORY
Many of the features of the EPR spectra in the iron-sulfur compounds suggest that the paramagnetic electron on one ion is coupled to similar electrons on other ions by exchange or dipolar interactions. In a crystal any one electron could in general be interacting with electrons on several ions in its neighborhood. To do an exact calculation would be a formidable, if not impossible, task, and would require a knowledge of the exact nature of the exchange interaction and also the crystallographic arrangement of the ions. It was found, however, that an exploration of the effects of the interaction between a single pair of ions, provides a useful contribution towards the understanding of the observed spectra. A summary of the results of such a calculation (5) in which it is assumed that the exchange energy is small compared to the Zeeman energies will now be given. Consider two s = 3 ions which are coupled by an exchange or dipolar type of interaction. The spin-Hamiltonian to be considered is of the form &’ = /!?H-G;S:, + ,8H*G,.S; + 27;.r-S;.
PI
The first two terms represent the Zeeman energies of the electrons a and b, and the last term represents the interaction between them. No assumptions will be made at this stage about the form of the tensors appearing in Eq. [l]. The secular equation of the Hamiltonian above is greatly simplified if the spin operators Sl are replaced by S, where S;=T,S,
PI
and -gwg,t --c!?,
T, =
gm --gaga, -g,, .-ii-
ga, gut
-gas
gar-
ga,
ga
gar
gm
gap
ga
0
gat Z.
where a is a or b and the g’s appearing in Eq. [3] are defined by
km gas,A= R, *Gas
131
285
IRON-SULFUR DERIVATIVES
where RH = [I&,, RHs, RHt] represent the direction cosines of the magnetic field. Also & = g:r + ds and gZ=d,+&. By means of Eq. [2], Eq. [l ] becomes [41 where J= T;J”*T,.
A
Ed Eb* J33
BE- J33
h (4
V
I I 1 1 I I V I I , I C4J3j+ I 1
A
; I I L I I
FIG.
&2AE+
S3
+4J35+ I
I
Ea’ Eb’ J33
0 1 8
V
I
-E,-Eb+ I
4
V
(b)
-AE-J33
I I I I
AE- J33
A
-AE- J33 V
I
I I
I
I
?Ea Eb+J33 I
+2AE-+ I
2. Energy level diagrams fir two exchange coupled s = 3 spins (a) AE > Js3 and (b) AE < J33.
Using the assumption that the exchange energy is small compared to the Zeeman energies, Eq. [4] yields the following energies E1=Eai-Et,i-J3s E,= AE-Js3 Es=-AE-Js3 Ed = -E. -Eb + Js3,
286
J. A. VAN WYK
where AE = [ jJz3 1’ + (E, - Eb)2]“2, J23 = $[(J,x 4
= 3/k,
+J~~) K
4
+6&y
-&)I
= --h
H
and 533
= +Jzz.
Two possible energy level diagrams and the possible transitions are shown in Fig. 2. The one diagram corresponds to the case where AE > J33 and the other to J33 > AE. It can be shown that the latter situation is possible only when 2 x J33 is very different from 15231. In the former the separation between the lines in each pair is 4 x J33 and the pairs are centred at g=-H&+&)
AE +pg
Calculation of the transition probabilities shows that the intensity of the inner lines is greater than or equal to that of the outer lines, and that the inner ones grow at the expense of the outer ones as the difference between g, and g, is decreased. When g, = g, the spectrum should consist of two lines, except when
2Jzz= KJ.xx+ Jw)’ + (Jx,- J,.x)21”2>
bl
in which case only one line will be observed. This condition is complied with if only the diagonal components of the J tensor are nonzero, and if these are equal to each other. This in turn implies that the interaction term in Eq. [l] can be written as J’S~*S~. RESULTS
The EPR spectra observed in frozen solutions at 77 K, yield the g values (6) given in Table 1. TABLE PRINCIPALS
VALWSOFIRON-SULFUR
1
COMPOUNDS AS MEASURED gVALUES+o.c@l
Compound I(C,H,)Fe(CO)S(CH,)},BF4 ((C,H,)Fe(CO)S(C,H,)}~B(C6H34
I(C,HS)Fe(CO)S(i-C3H,)}~B(CsH5)4 I(C,HI)Fe(CO)S(t-C,H~)}~B(CsH3*
INFROZENSOLUTIONAT
77 K. ALL
&?I
g2
g3
2.032 2.037 2.040 2.047
2.014 2.015 2.016 2.014
1.941 1.940 1.935 1.937
The EPR spectra in single crystals showed the following features. In all three compounds only one EPR line is observed in two planes perpendicular to each other; the spectra show mirror symmetry about one of the planes, which will be referred to as the mirror plane. With the magnetic field applied in directions outside these planes, two lines are observed for the first, four for the second, and one only for the last. The mirror symmetry of the spectra suggests that the unit cell contains at least two
lRON-SULFUR
287
DERIVATIVES
ions which are crystallographically related to each other by a mirror (or glide) plane. For EPR purposes it was convenient to choose in this plane as reference axes, Y and S, the directions along which the maximum and minimum g values, respectively, are observed. The third axis f was naturally chosen perpendicular to this plane. These axes are not necessarily parallel to crystallographic or morphological axes. The two line spectra observed in this compound Hamiltonian
can be described by the spin-
~=~PH~G;S,f~H~G,~S,,
[71
where the principal values of the g tensors G,, and Gb are identical, but the principal axes form mirror images of each other across the rs plane. TABLE PRINCIPAL,
g VALUES AND
AXES AS DETERMINEDFROMSINGLE CRYSTAL {x(t-C4H&B(C,H,),
Principal g values
gx gY
gz Angles of principal axes with rf:ference axes
4x”
2
2.043 2.013 1.941 21.0” 139.4” 85.5” 69.7”
[email protected],NJKd-M~ 2.041 2.016 1.942 18.7” 115.8” 79.2” 44.4”
MEASUREMENTS
{X(CH&BF4 2.033 2.016 1.942 3Vb 90” 90” 0”
’ 4 is measured in the rs plane from r, and the polar angle 0 is measured from the f axis. b r axis was chosen parallel to the axis corresponding to gI and I parallel to gl.
:2*00 9 1.98-
1.94 tr
0+H
+e H FIG. 3. Angular variation of g values of EPR lines in [{X(t-C,H,)}z]B(C,H,)+ tabulated using the parameters given in Table 2.
e-)H The solid lines were
288
J. A. VAN WYK
The g tensors have been determined by means of least square regression calculation and using EPR measurements obtained in different crystal planes. The principal values of the g tensors and corresponding axes are given in Table 2. The calculated angular dependence of the EPR spectra in the rs, st, and rt planes, together with some experimental results are shown in Fig. 3. Note that these g values agree well with those given in Table 1. In the latter the dilution of the solutions were deliberately made large enough to avoid any interaction between electrons on different ions. The agreement between the results in Tables 1 and 2 therefore suggests that dipolar or exchange interactions are unimportant in single crystals, at least as far as the position of the EPR lines are concerned. Considerable line width variation, with orientation of the magnetic field is however observed, and this may well be due to these interactions. I. g Tensor. The EPR spectra observed in this compound differed from those in the
previous one in that four lines instead of two are observed when the magnetic field is applied in directions outside the two one-line planes. A typical example of the EPR
FIG. 4. Typical example of EPR spectrum of [{X(C2H5)}2]B(C6H5),. pairs is due to DPPH.
The narrow line between the two
spectra is shown in Fig. 4. The qualitative features of the EPR spectra can, however, be explained if instead of Eq. [7], Eq. [l] is used as spin-Hamiltonian. The symmetry relation between the g tensors is of course retained. Experimentally the maximum splitting produced by this interaction is found to be about 120 G, and the energy difference corresponding to this splitting is certainly small compared to g/MZ at k-band frequencies. The approximate calculation given earlier should therefore apply. Inspection of Eq. [5] shows that if the separation between the pairs is large compared to the splitting within the pairs, then the centers of the pairs corresponds very nearly to g, and gb, the g values of the Zeeman lines in the absence of exchange interaction. It can also be shown that this condition is complied with best if the magnetic field is applied at 45” to the I axis. For this reason, the centers of the pairs were measured in a
289
IRON-SULFUR DERIVATIVE%
cone around the t axis making an angle of 45” with this axis. The g tensors were calculated from these measurements, again using a least square regression technique. The results are presented in Table 2 and Fig. 5. Again the principal g values agree well with those measured in frozen solution, giving confidence in the method of analysis of the results.
2.025 2.005
1.985 9 1.965
1.945 0
30
60
90
120
150
180
%I FIG. 5. Angular variation of g values of EPR lines in [{X(C2H5)}2]B(C6H5)4 axis. (Solid lines were calculated using the parameters given in Table 2.)
in 45” cone around f
2. The exchange interaction. The qualitative features of the intensities of the lines are in agreement with those predicted from the coupled-pair calculation. This theory however predicts the same splitting between the lines in each pair. Experimentally, the splitting between the lines occurring at the higher magnetic field is always slightly greater than that of the other pair. The single line observed in two crystal planes suggests that the condition in Eq. [6] must apply at least approximately. This could mean that the interaction is isotropic, but it is found that the splitting (away from the one-line planes) depends on the direction of the applied magnetic field. Empirically it was found, within the range 0.4 < cos 8 < 0.9 and -0.1 < cos c1< 0.9, that the splitting between the lines of the high-field pair is given by AH= (26.3 + 67.9cosO)~(l + cosu),
PI
where B the angle between the magnetic field and the t axis. The angle c1is defined by [91
where (R& RfrH,,,R&) and (Rk,, Riy, R&,) are the direction cosines of the magnetic field relative to the principal axes of ions a and b, respectively. (Since the anisotropy in the g value is small, these direction cosines may also represent the axis of quantization of the ions.) To conclude, we present the following remarks : (i) Equation [8] applies where the splitting between the lines of the pair is greater of the lines. In directions where the splitting becomes comparable to
than the line width
290
J. A. VAN WYK
the line widths, the splitting seems to drop off more rapidly than is predicted by Eq. [8]. (ii) When the field is applied close to the rs plane, the spectrum consists of an intense line and two weak lines; one on either side of the strong line. The splitting between these lines is somewhat larger than is suggested by Eq. [8]. (iii) Eq. [8] was derived for the high-field pair. The splitting between the lines of the low-field pair is always smaller, and a slightly different relation is required. (iv) No physical meaning is attributed to the angle CIin Eq. [8]. It can be shown that cos CI= 1.0 when the magnetic field is applied in the direction which is perpendicular to the principal y direction of both the interacting ions, which also turns out to be the axis perpendicular to the crystallographic ab plane (see Fig. 6). This angle may therefore be related to the angle between the magnetic field and some or other important intermolecular axis. 3. Correlation of some EPRfeatures with some crystallographicfeatures. It is probably fair to expect that the crystallographic structure of the compound [{X(C,H,)),] B(C6H&, if available, should provide some clues to the origin of the interactions responsible for the splitting of the EPR lines. Unfortunately, some data on the structure of the iron-sulfur complexes has been published (4) only for the compound [{X(CH,)},] BF,. EPR results showed that the crystal structures of all the compounds have some common features, but it was also evident that the C2H5-compound does not have the
270
FIG. 6. Axes in, or projections of axes on, the rs (or UC)plane: rr and ss reference axes; au and cc crystallographic axes; xx and zz projections of principal axes (y axis lies in ub plane); pp and nn axes parallel and perpendicular to the plane of the crystal. The solid curve represents line width, and the broken curve the “exchange” splitting in the 45” cone.
IRON-SULFUR
DERIVATIVES
291
orthorhombic structure found for the CH,-compound. From preliminary X-ray data, it was found that the crystal structure of the C,H,-compound is monoclinic, with a = 1.82 nm, b = 0.98 run, c = 2.06 nm, and /I = 138”. The unit cell contains four formula units of the compound and the space group can be either Pz,=or PC,depending on whether the stru.cture has a center of symmetry or not. No more is presently known about the structure. Most of the crystals of the C,H,-compound were obtained as diamond shaped platelets, with one axis slightly longer than the other. The b axis lies along the shorter axis and the X-ray results showed that the c axis is 8” away from the longer axis. The crystallographic a and c axes, the Y and s axes, two morphological axes, and the prqjection of the principal axes on the ac plane are shown in relation to each other in Fig. 6. Also depicted in this diagram is the line widths of the EPR line in the UCplane, and the splitting between the lines of the high field pair, observed in the 45” cone around the t (orb) axis.
Im this compound only one line was observed with the magnetic field applied in any direction. The crystals used were obtained in platelet form with three well-defined mutually perpendicular morphological axes, and the g values took on extreme values along these axes. The g value of the line, in any other direction could be calculated with a fa.ir degree of accuracy from the expression
where g,, g,, g, represents the g values along the morphological axis, and RI, Rz, R3 the direction cosines of the magnetic field relative to these axes. The values for g,, g,, and g, are g, = 2.0265 g, = 2.0223
g, = 1.9420. If these values are compared with those measured in the frozen solution, it is noted that g, is almost identical to g,, but g, and g2 differ significantly from g, and g,,. The single crystal and frozen solution results can, however, be reconciled, if as before, it is assumed that the unit cell contains at least two ions, oriented such that their principal axes are mirror images of each other across one of the crystal planes, and that the energy of the exchange interaction is much greater than the difference of the Zeeman energies of these ions. The g value measured in the single crystal in any direction will then be equal to the average of the g values of the individual ions. With this in mind it can be shown t.hat agreement with the experimental values can be obtained if it is assumed that g, represents one of the principal values (g,), the other two principal values are g, = 2.0331 and g, = 2.0157, and that axes corresponding to these latter values lie in theg, g, plane, with the x axis 38” from the axes corresponding tog,. These results are in agreement with what one would expect from crystallographic data. Connely and Dahl(4) determined the structure of this compound, and inspection
292
J. A. VAN
WYK
of the crystal structure shows that all ions have their Fe-Fe and S-S axes parallel to the crystallographic ab plane. All ions, therefore, have an axis parallel to the c axis, and this axis must correspond to the principal axes associated with g,. From symmetry considerations it is probable that the other two principal axes will be parallel to axes through the iron and sulfur atoms. Unfortunately, not enough information is presented in the paper by Connely and Dahl to pursue this any further. The line width in [{X(CH,)},]BF, has been found to vary almost axially about the c axis, and varies according to A = 16.0+ 11.2(3cos20-
l)“,
where 0 is measured from the c axis. DISCUSSION
The most interesting aspect of this probably is the effect of the exchange interactions. In an undiluted compound one would expect every paramagnetic electron to be interacting with electrons on several molecules in its neighborhood. One would therefore expect a more complicated spectrum, if resolved, than the one observed. Even if it is assumed that in the lattice pairs of ions are closer to each other than to other, or that the molecules are favorably oriented for exchange interaction, the spectra cannot be analyzed fully without a knowledge of the crystal structure. Not only do the dipole-dipole interactions depend on the intermolecular distances and the direction of the applied magnetic field but so does the exchange interactions, and may also depend on the orientation with respect to each other, of the interacting ions (7). Without the crystal structure then, one can only speculate about the interactions responsible for the observed spectra. The only result of this report that might be of biological importance are the principal values of the g tensor. It has been known for some time already that EPR spectra observed in ferrodoxins are due to paramagnetic electrons localized on iron-sulfur centers (8). The more important features of the EPR and other results can be explained by a model proposed by Gibson et al. (9). The principal values measured here do not differ significantly enough from those measured in other model compounds (10) to warrant further discussion. ACKNOWLEDGMENTS The crystals used in this study have been prepared by J. A. de Beer of the Research and Process Development Department, South African Iron and Steel Industrial Corporation, and R. J. Haines, formerly of the same address but now in the Department of Chemistry of the University of Cape Town. REFERENCES 1. R. J. HAINE.Y AND A. L. Du PREEZ, Znorg. Gem. 11,330 (1972). 2. J. A. DE BEER, R. J. HAINES, R. GREATREX, AND J. A. VAN WYK, J. C/tern. Sot. Dalton, 3. G. FERGUSON, C. HANNAWAY, AND K. M. S. ISLAM, Chem. Comm. 1165 (1968). 4. N. G. GZINNELLY AND L. F. DAHL, J. Amer. Chem. Sot. 92,7472 (1970). 5. Full treatments of two special cases can be found in A. ABRAGAM AND B. BLEANEY,
2341 (1973).
“Electron Paramagnetic Resonance of Transition Ions,” Chap. 9, Clarendon Press, Oxford, 1970. 6. EPR spectra in these compounds have been observed for the first time by M. CLARE AND H. A. 0. HILL, Chem. Comm., 1376 (1970).
IRON-SULFUR
293
DERIVATIVES
7. R. BAUMANN, H. U. BEYELER, AND W. KANZIG, Helv. Phys. Acru 44,252 (1971). 8. E.g., W. R. DUNHAM, G. PALMER, R. H. SANDS, AND A. J. BEARDEN, Biochim.
Biophys. Acta 253,
373 (1971). 9. J. F. GIBSON,
D. 0. HALL,
J. H. M. THORNLEY,
AND F. R. WHATLEY,
Proc. Nat. Acad. Sci. U. S. 56,
987 (1966). 10. E.g.,
K. A. RUBINSON
AND G. PALMER,
J. Amer. Chem. Sot. 94,83X
(1972).