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Magnetic properties of mixed-valence tetranuclear iron clusters: electron transfer versus exchange interactions
Journal of Magnetism and Magnetic Materials 104-107 (1992) 955-956 North-Holland
M m+ ?
M
x M
Magnetic properties of mixed-valence tetranuclear electron transfer versus exchange interactions J.J. Borras-Almenar
‘, E. Coronado
iron clusters:
‘, R. Georges b and C.J. Gbmez-Garcia
a
” Dept. Quimica Inorg&ica, ZJni[,. Valencia, 46100 Burjasot, Spain ’ Lab. Chimie du Solide, Unit. Bordeaux I, France cubane-type cluster, we develop a model that takes into In order to obtain the energy levels of a mixed-valence [Fe,S,13+ account the electron delocalization within the cluster as well as the superexchange interactions. Trends of level pattern are discussed as a function of the sign and magnitude of transfer intergrals, and compared with those obtained on mixed-valence dimers and trimers.
Tetranuclear mixed-valence iron clusters of the type [Fe,S,] are active sites of iron-sulfur proteins. These systems manifest a wide spin-state variability which is not well understood [l-3]. In fact, in such systems, the spin-state ordering may result from a delicate balance between electron delocalization within the cluster and intermetallic superexchange interactions. Here we develop a model that takes into account the interplay between these electronic effects, as well as the geometry of the cluster. We focus on oxidized [Fe,S,13+, which contains three Fe(III) and one Fe(H). We idealize the cubane-type structure in which each metal is located in a regular tetrahedral site FeS, sharing two sulfurs with each one of its neighbors (fig. 1). In their turn, the four metals form a regular tetrahedron. Due to crystal field effects, only the two e,-type metal orbitals will be involved in the delocalization process which can be described by the transfer Hamiltonian:
where i, j (= 1,2,3,4) refer to the four metal sites and m, n (= [r2], [x2 - y2]) to the e,-type orbitals. C,tn, creates an electron on orbital m of site i, while C,n
Fig. 1. Idealized
structure
0312.8853/92/$05.00
of the cubane-type
cluster
[Fe,.?,].
0 1992 - Elsevier Science Publishers
destroys an electron on orbital n of site j. The ti,m,j,,r’s are the corresponding transfer integrals. They depend on the geometry of the cluster since they are nearly proportional to the related metal-metal overlap integrals. In principle, there are twenty four transfer integrals belonging to three types, according to the nature of the involved eg orbitals: [x2-y2]-[x2-y2], [z’][z2], and [x2 -y’]-[z’]. We have solved the problem within a basis involving only the high-spin configurations on each metal ion, excluding so the high-energy low-spin ones. Moreover, two distinct approaches have been considered concerning the transfer integrals. In a first step, we neglect the transfer between nonequivalent (m # n) e, orbitals, and we attribute the same value (say T) to all the t ,,“,,,,m. As can be see from fig. 2, the energy values plotted vs. the spin multiplicity give rise to regular alignments. The structure of the ground level depends on the sign of T. For negative T it corresponds to the highest spin multiplicity S,,, = 19/2. As a result, except for strong enough antiferromagnetic superexchange interactions, the magnetic properties should reflect a large Curie constant value at low temperature. For positive T the ground level involves several multiplicities ranging from Smin = l/2 to S = 17/2. In that case, at low temperature, the compound should exhibit a nearly paramagnetic (free-spin) behaviour. However, any superexchange (antiferromagnetic) coupling should split the ground level, giving rise to a decreasing magnetic moment upon cooling down. This situation is closely similar to what is observed in the regular mixed-valence triangular clusters, under similar assumptions [4]. In both cases the energy splitting depends on the sign of T, and furthermore, an accidental degeneracy of levels is observed for positive T values. In the second approach we take advantage of the symmetries of the idealized cluster, and we deduce the relative values of the transfer integrals from the corresponding overlap integrals. These are obtained using the sulfur-metal p-e, transfer integrals and excitation energy, U. In this case we can express all the metalmetal overlap integrals S,,,,j,,, in terms of the transfer
B.V. All rights reserved
9%
J.J. Borrus-Almenar
et al. / Mixed-cwlence
integral between the d,z_,z metal orbital and the p, sulfur orbital, namely b. Notice that from Si ,,1,, ,1 we can know the relative magnitude of the transfer’integrals in the cluster, but this gives no information on their signs. It is reasonable to assume that the t, ,n, ,,‘s can be deduced from the S, ,)1, ,,‘s by merely multiplying them by a common cnergy’factor Q. Introducing the S,,,,, ,,,,,‘s (instead of the t, ,),, ,,‘s) in the transfer Hamiltonian and diagonalizing it ‘we obtain the energy diagram of the cluster in units of Qb”/27U 2 (fig. 3). We notice that the states appear to be distributed in well defined “energy bands”. Depending on the sign of Q, we have two very different types of ground states. Thus, for positive Q, the ground level takes the highest spin multiplicity (S,,,, = 19/2), in agreement with the usual double exchange expectation. Conversely, for negative Q, several spin multiplicitics (ranging from S = 9/2 to S,,,,) are almost degenerate. Such results closely resembles that found in the previous scheme if opposite signs are attributed to T and Q parameters. Hcncc, we can conclude that the introduction of different transfer integrals to account for the different transfer pathways expected in the cubane geometry, dots not modify the low-lying lcvcl trends of the cluster. One of the aims of this work was to explain the large spin-state variability of the mixed-valence cubanc clusters. Such observation was difficult to understand in terms of the elementary double exchange theory,
tetrunuclear
iron clusters
Fig. 3. Energy spectrum of the cubane cluster as a function of the spin multiplicity when different transfer pathways through the sulfur p-orbitals are considered. The shadowed areas represent the bands containing the spin-states.
L Eil
which, in a delocalized mixed-valence pair, predicts a ferromagnetic ground state well separated in energy from the first excited ones. As we have shown in the cubane cluster, the role of the electron transfer is not always to stabilize the ferromagnetic state: actually, in some casts a dcgencratc, or quasi-degcncratc ground state, formed by an admixture of different spin configurations is obscrvcd. In such situations minor cffccts, as for example superexchange interactions or distortions of the clusters, should become quite pregnant in determining the spin-state ordering of the cluster. Such a result is quite similar to what is found in triangular mixed-valence clusters. This work was supported by the Comision Interministerial de Ciencia y Tecnologia (MAT89-0177) and by a Program of Integrated Actions with France (182A). C.J.G.-G. and J.J.B.-A. are grateful for a fellowship from the Ministerio dc Education y Ciencia.
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References
. 2
4
6
8
20 2s+1
Fig. 2. Energy spectrum of the cubane cluster as a function of the spin multiplicity. Only the transfer integrals between are considered. In parentheses are equivalent eg orbitals given the degeneracies of the spin-states.
[tl E. Miinck, V. Papaefthymiou.
K.K. Surerus and J.J. Girerd, in: Metal Clusters in Proteins, ed. L. Que WCS Symposium Series No. 372, IYXX). [21 G. Blondin and J.J. Girerd. Chem. Rev. 90 (1990) 1359. Inorg. Chem. 27 (1988) 3677. [31 L. Noodleman. E. Coronado and G. Pourroy, J. Appl. [41 C.J. Gomez-Garcia, Phys. 67 (1990) 5992.
M m+ ?
M
x M
Magnetic properties of mixed-valence tetranuclear electron transfer versus exchange interactions J.J. Borras-Almenar
‘, E. Coronado
iron clusters:
‘, R. Georges b and C.J. Gbmez-Garcia
a
” Dept. Quimica Inorg&ica, ZJni[,. Valencia, 46100 Burjasot, Spain ’ Lab. Chimie du Solide, Unit. Bordeaux I, France cubane-type cluster, we develop a model that takes into In order to obtain the energy levels of a mixed-valence [Fe,S,13+ account the electron delocalization within the cluster as well as the superexchange interactions. Trends of level pattern are discussed as a function of the sign and magnitude of transfer intergrals, and compared with those obtained on mixed-valence dimers and trimers.
Tetranuclear mixed-valence iron clusters of the type [Fe,S,] are active sites of iron-sulfur proteins. These systems manifest a wide spin-state variability which is not well understood [l-3]. In fact, in such systems, the spin-state ordering may result from a delicate balance between electron delocalization within the cluster and intermetallic superexchange interactions. Here we develop a model that takes into account the interplay between these electronic effects, as well as the geometry of the cluster. We focus on oxidized [Fe,S,13+, which contains three Fe(III) and one Fe(H). We idealize the cubane-type structure in which each metal is located in a regular tetrahedral site FeS, sharing two sulfurs with each one of its neighbors (fig. 1). In their turn, the four metals form a regular tetrahedron. Due to crystal field effects, only the two e,-type metal orbitals will be involved in the delocalization process which can be described by the transfer Hamiltonian:
where i, j (= 1,2,3,4) refer to the four metal sites and m, n (= [r2], [x2 - y2]) to the e,-type orbitals. C,tn, creates an electron on orbital m of site i, while C,n
Fig. 1. Idealized
structure
0312.8853/92/$05.00
of the cubane-type
cluster
[Fe,.?,].
0 1992 - Elsevier Science Publishers
destroys an electron on orbital n of site j. The ti,m,j,,r’s are the corresponding transfer integrals. They depend on the geometry of the cluster since they are nearly proportional to the related metal-metal overlap integrals. In principle, there are twenty four transfer integrals belonging to three types, according to the nature of the involved eg orbitals: [x2-y2]-[x2-y2], [z’][z2], and [x2 -y’]-[z’]. We have solved the problem within a basis involving only the high-spin configurations on each metal ion, excluding so the high-energy low-spin ones. Moreover, two distinct approaches have been considered concerning the transfer integrals. In a first step, we neglect the transfer between nonequivalent (m # n) e, orbitals, and we attribute the same value (say T) to all the t ,,“,,,,m. As can be see from fig. 2, the energy values plotted vs. the spin multiplicity give rise to regular alignments. The structure of the ground level depends on the sign of T. For negative T it corresponds to the highest spin multiplicity S,,, = 19/2. As a result, except for strong enough antiferromagnetic superexchange interactions, the magnetic properties should reflect a large Curie constant value at low temperature. For positive T the ground level involves several multiplicities ranging from Smin = l/2 to S = 17/2. In that case, at low temperature, the compound should exhibit a nearly paramagnetic (free-spin) behaviour. However, any superexchange (antiferromagnetic) coupling should split the ground level, giving rise to a decreasing magnetic moment upon cooling down. This situation is closely similar to what is observed in the regular mixed-valence triangular clusters, under similar assumptions [4]. In both cases the energy splitting depends on the sign of T, and furthermore, an accidental degeneracy of levels is observed for positive T values. In the second approach we take advantage of the symmetries of the idealized cluster, and we deduce the relative values of the transfer integrals from the corresponding overlap integrals. These are obtained using the sulfur-metal p-e, transfer integrals and excitation energy, U. In this case we can express all the metalmetal overlap integrals S,,,,j,,, in terms of the transfer
B.V. All rights reserved
9%
J.J. Borrus-Almenar
et al. / Mixed-cwlence
integral between the d,z_,z metal orbital and the p, sulfur orbital, namely b. Notice that from Si ,,1,, ,1 we can know the relative magnitude of the transfer’integrals in the cluster, but this gives no information on their signs. It is reasonable to assume that the t, ,n, ,,‘s can be deduced from the S, ,)1, ,,‘s by merely multiplying them by a common cnergy’factor Q. Introducing the S,,,,, ,,,,,‘s (instead of the t, ,),, ,,‘s) in the transfer Hamiltonian and diagonalizing it ‘we obtain the energy diagram of the cluster in units of Qb”/27U 2 (fig. 3). We notice that the states appear to be distributed in well defined “energy bands”. Depending on the sign of Q, we have two very different types of ground states. Thus, for positive Q, the ground level takes the highest spin multiplicity (S,,,, = 19/2), in agreement with the usual double exchange expectation. Conversely, for negative Q, several spin multiplicitics (ranging from S = 9/2 to S,,,,) are almost degenerate. Such results closely resembles that found in the previous scheme if opposite signs are attributed to T and Q parameters. Hcncc, we can conclude that the introduction of different transfer integrals to account for the different transfer pathways expected in the cubane geometry, dots not modify the low-lying lcvcl trends of the cluster. One of the aims of this work was to explain the large spin-state variability of the mixed-valence cubanc clusters. Such observation was difficult to understand in terms of the elementary double exchange theory,
tetrunuclear
iron clusters
Fig. 3. Energy spectrum of the cubane cluster as a function of the spin multiplicity when different transfer pathways through the sulfur p-orbitals are considered. The shadowed areas represent the bands containing the spin-states.
L Eil
which, in a delocalized mixed-valence pair, predicts a ferromagnetic ground state well separated in energy from the first excited ones. As we have shown in the cubane cluster, the role of the electron transfer is not always to stabilize the ferromagnetic state: actually, in some casts a dcgencratc, or quasi-degcncratc ground state, formed by an admixture of different spin configurations is obscrvcd. In such situations minor cffccts, as for example superexchange interactions or distortions of the clusters, should become quite pregnant in determining the spin-state ordering of the cluster. Such a result is quite similar to what is found in triangular mixed-valence clusters. This work was supported by the Comision Interministerial de Ciencia y Tecnologia (MAT89-0177) and by a Program of Integrated Actions with France (182A). C.J.G.-G. and J.J.B.-A. are grateful for a fellowship from the Ministerio dc Education y Ciencia.
i-
iI51 (211 -
Z-
-
,241
(241 Cl1 (ICI -
-
l- lb! -(151 (211 -(241 -I241
II-
1211 114,
-(IO) ihi
-l-
(191 (32) ---------
0
(391
(40)
I351
041
iI51
(81
111
IO
I!
14
16
18
-131
References
. 2
4
6
8
20 2s+1
Fig. 2. Energy spectrum of the cubane cluster as a function of the spin multiplicity. Only the transfer integrals between are considered. In parentheses are equivalent eg orbitals given the degeneracies of the spin-states.
[tl E. Miinck, V. Papaefthymiou.
K.K. Surerus and J.J. Girerd, in: Metal Clusters in Proteins, ed. L. Que WCS Symposium Series No. 372, IYXX). [21 G. Blondin and J.J. Girerd. Chem. Rev. 90 (1990) 1359. Inorg. Chem. 27 (1988) 3677. [31 L. Noodleman. E. Coronado and G. Pourroy, J. Appl. [41 C.J. Gomez-Garcia, Phys. 67 (1990) 5992.