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LIGAND FIELD ANALYSIS OF MÖSSBAUER DATA
FOR A SIX COORDINATE Fe(IV) COMPLEX WITH
DITHIOLATE LIGANDS
V. Petrouleas, A. Kostikas, A. Simopoulos, D. Coucouvanis
To cite this version:
Abstract. — The Mossbauer data of a new Fe (IV) complex, [Fe(IV) (S2CC(COOC2H5)2b]2-, are analysed in the framework of ligand field theory. The temperature dependance of the quadru-pole spectra are well reproduced on the basis of a ligand field model conforming to the low symme-try crystal field distortions known from crystallographic data. The results of this analysis support the presence of an Fe(IV) (3d4) electronic system. There appears, however, a large reduction of the spin orbit coupling constant, the Fermi contact factor and < /—3 > indicating significant charge derealization and covalency effects.
1. Introduction. — Mossbauer spectroscopy has t2g configuration in low symmetry crystal fields has been recently applied to a number of well documented been presented by Oosterhuis and Lang [7].
examples of iron complexes with the iron ion in the In this paper we report on a detailed ligand field uncommon Fe(IV) oxidation state. These include the analysis of both the temperature dependence of the class of complexes of the general formula quadrupole splitting and the magnetically perturbed
n tA- ^ v /Dc ^ m spectra of the complex anion
Fe(diars)2X2(BF4)2 [1]
u v m T, i- ^ , , ,_• ,.,• ^ [Fe(IV) (S2CC(COOC2H5)2)3]2-. where X = CI, Br, diars = O-phenylenebis (dimethy- L v 'v 2 v z 5J2 3 J
larsine) and the class of tris dithiocarbamato Fe(IV) The data are well reproduced on the basis of a ligand complex anions [2]. The synthesis and molecular field model conforming to the low symmetry crystal structure of an iron (IV) complex with a new 1,1 field distortions, which are indicated by the crystallo-dithiolate ligand [3] as well as preliminary Mossbauer graphic data [3],
data [4] have been also recently reported. As in the
more familiar cases of Fe(III) and Fe(II) compounds, 2. Experimental results. — The synthesis and Mossbauer data can be used to determine electronic molecular structure of the studied complex has been parameters which characterize the state of the iron ion. reported elsewhere [3]. The magnetic moment has been This information is not only generally interesting for found equal to 2.92 ± 0.02 BM, [3] which is close to the chemistry of iron but also more particularly for the spin only value of a 3d4, S = 1 configuration in assessing the evidence of the presence of Fe(IV) octahedral symmetry. This indicates a strong distor-active centers in biologically important compounds tion from cubic symmetry which was also observed in as e. g. some peroxidase derivatives [5, 6]. other Fe(IV) complexes [2].
Few detailed analyses of Mossbauer data in Fe(IV) Mossbauer spectra were obtained with a constant complexes have appeared until now. The results for acceleration spectrometer coupled with a multichannel the diarsine complexes in external applied fields have analyzer operating in the time mode. At zero applied been analyzed by Paez et al. [1] with a spin Hamilto- field the spectra in the temperature range of 1.4 K to nian formalism with effective spin S = 1. A general 300 K consist of a well defined quadrupole doublet. calculation of spin Hamiltonian parameters for a The temperature dependence of the quadrupole
LIGAND FIELD ANALYSIS OF MOSSBAUER DATA FOR A SIX
COORDINATE Fe(IV) COMPLEX WITH DITHIOLATE LIGANDS
V. PETROULEAS, A. KOSTIKAS and A. SIMOPOULOS Nuclear Research Center Demokritos, Athens, Greece
and
D. COUCOUVANIS
Department of Chemistry, University of Iowa, Iowa City, U. S. A.
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 12, Tome 37, Décembre 1976, page C6-507
Résumé. —• Nous analysons dans le modèle du champ de ligandes les données Môssbauer concernant un nouveau complexe : [Fe(IV) (S2CC(COOC2H5)2)3]2~. La variation thermique de l'interaction quadrupolaire s'interprète bien avec un champ de ligandes à basse symétrie, conforme aux données cristallographiques. Les résultats de cette étude confirment le caractère Fe(IV) (3d4) du système électronique. On observe cependant une réduction importante de la constante de couplage spin-orbite, du terme de Fermi et de < r-3 >, ce qui indique que la délocalisation de
charge et la covalence ont des effets significatifs.
C6-508 V. PETROULEAS, A. KOSTIKAS AND A. SIMOPOULOS splitting is given in Table I. The isomer shift was
0.19 mm/s at room temperature and 0.30 mm/s at L. N. with respect to iron. These values are very close to the values reported for the diarsine Fe(1V) com- plexes [l].
Temperature dependence of the quaa'vupole splitting of Fe(1V) in Fe(DED)
Measurements in applied transverse magnetic fields of 30 and 60 kG were obtained at 4.2 K using a split- coil superconducting magnet. The spectra are shown in figure 1.
FIG. 1. - Mossbauer spectra of the Fe(1V) complex obtained a t high transverse magnetic fields at 4.2 K. Solid lines represent best simulations of the spectra with the parameters given in
table 11.
3. Ligand field analysis.
-
Figure 2 shows the molecular structure of the F ~ ( D E D ) ~ - anion. The iron ion is located at the approximate center of a distorted octahedron formed by the six sulfurs. The local symmetry can be described with an octahedron as a reference system, assuming a severe twist of its triangular faces around the C , axes, followed by a twist of one of the sulfur chelate rings around the C; axis bisecting it. Alternatively, as suggested for other dithiolene transition metal complexes [S] the geometry of the FeS, core can be described as arising from individual twists of each of the three sulfur che-FIG. 2.
-
Molecular structure of Fe [S~CC(COOC~HS)~:]:-.late rings around the C , axes of a trigonal prism, one of which is more severe than the others. These two descriptions are illustrated in figure 3. The former approach has been adopted in the present calculation since it offers the advantage of direct comparison with the common octahedral cases.
I
5 10 Dq ",.",(G<b,b) --- =" U,.", ( b , = r )I
--- U," u (b,-G)
a U, --- F 6 s ' ,' ' . U1FIG. 3. -Description of the point symmetry of the iron site : a) Starting from a trigonal prism ; b) Starting from a n octahe-
dron.
LIGAND HELD ANALYSIS OF MOSSBAUER DATA FOR A SIX COORDINATE Fe(IV) C6-509
Je, includes the kinetic energy and the interaction with
an inner core potential of spherical symmetry and affects only the zero of the energy scale. V, is the
octahedral term, which induces the splitting of the single 3d electron orbital states to a lower triplet (t2$ and a higher doublet (e,) (Fig. 3a). The next, trigonal term, V,, which describes the twist around the C3 axis, induces a partial splitting of the t2, states and a mixing with the e, states. By choosing the C, axis to be the quantization axis and the C; axis the x-
axis (Fig. 2) we can express the one electron eigen- functions of the first three terms in (l) by the following combinations of the familiar octahedral real wave functions [9].
where b,, b2 are mixing coefficients. For
we obtain the appropriate eigenfunction for 0, symmetry. For b, = 1 (b, = 0) the trigonal prismatic limit (D,,) is obtained which corresponds to maximum twist angle. In the present analysis b, is varied between these two limits.
The next term describes the Coulomb repulsion of the four 3d electrons which has been assumed weaker than the trigonal term V, and stronger than the C, distortion. The main effect of this term is to induce an S = 1 ground term as demonstrated by the value of the magnetic moment p = 2.92
+
0.02 BM. The four electron S = l Slater determinants have been formed from the single electron wave functions. These determinants have been designated by U,,,, (i = 1,2, 3 ; m =-
1, 0, 1) where we have considered only the U,, U,, U, eigenstates by making the reasonableassumption that they lie well below the upper u4 and
U, states. The first index (i) refers to the orbital which is
doubly occupied and the second index (m) denotes the z component of the total spin, i. e.
etc. where
+
and-
refers to spin up and down respecti- vely for the individual electrons. The Coulomb term contributes also to the trigonal splitting inside the S = l term, without however producing any extra splitting or mixing of the states. In the following analysis of the Mossbauer data the ~rystal field splitt- i n g ~ are treated as adjustable parameters and therefore this effect is not taken into account explicitly.(twist around the C; axis) which lifts fully the orbital degeneracy inside the S = 1 term and mixes the U,,, and U,,, states. It is easily seen through group theore- tical arguments that the eigenfunctions of the first five terms of (1) can be expressed as follows :
at energies 0, A, and A, respectively. It should be noted that these splittings coincide with those of the one eleatron eigenstates if we neglect the Cou1ombi"c contribution to the trigonal splitting. The energy separations A , , A, and the mixing ooefficients c,
and b, are treated as adjustable parameters in the following analysis.
The calculation is completed by taking into account the last two terms of (l), namely the l-S coupling and the Zeeman interaction. Their effect is explicitly contained in the 9 X 9 matrix which is calculated
on the basis Ui,, by operator techniques. The spin- orbit coupling constant enters also as adjustable para- meter here. Diagonalization of the matrix gives the energy eigenstates which are used for the calculation of the thermal average values of the various obser- vable~ of the system (e. f. g. components, L., S, H
,,,,
etc.). 3.1 ANALYSIS OF THE TEMPERATURE VARIATION OFTHE QUADRUPOLE INTERACTION.
-
The temperaturevariation of the quadrupole interaction can be account- ed by the thermal population of the lower eigenstates of (1). This variation can be expressed'as follows [l01 :
where
2
AE, = eZ Q(1
-
R)<
r - lis the bare quadrupole coupling constant and U is the, temperature independent, lattice contribution to AE,. The parameter F(T) is determined in terms of the thermal averages of the expectation values of the e. f. g. components :
4 2 112
+?((<Vxy >av)2+(<Vyz>av)2+(< V,x>av)
]
(4) whereC6-510 V. PETROULEAS, A. KOSTIKAS AND A. SIMOPOULOS
the l-s coupling constant
c,
and the mixing coefficients b, and c,.A program has been written which diagonalizes the hamiltonian (l), calculates F(T) for each combina- tion of the above parameters and then ,adjusts AE, and U for best fitting to the quadrupole splitting data. Combination of parameters have been tried in the following ranges :
A,, A , : (
-
2 500,+
2 500 cm-'f
5
: { 200, 500 } cm-'
b , : ( ~ , 1 }
The low temperature behaviour of the quadrupole splitting could be accounted successfully only for the values of b , = 0.99 f 0.01 or bl = 0.96 f 0.005. The former value corresponds to the trigonal prismatic limit. For this range of values the crystal field splitting parameters adjust to A , % Ad, < 0. This result howe-
ver corresponds to a ground state 'with non zero orbital angular momentum which is inconsistent with the almost diamagnetic response of the system in a magnetic field (section 3b). In addition the value of AE, adjusts to 1 mm/s which is much lower than the free ion value. On the other hand the value
not only is consistent with the crystallographic data (geometry intermediate to octahedral and trigonal prismatic) but it explains also the almost diamagnetic behaviour of the system. The values of the adjustable parameters that give the best simulation of the tempe- rature variation of the quadrupole interaction are given in table 11. Estimates of the free ion values of some of these parameters are also given in the same Table. The free ion value for AE, was estimated by comparison with ferrous data taking into account. that
<
r - 3>
= 5.0 and 6.0 a. U. for the Fe(I1) and Fe(1V) ion respectively.Electronic Structure parameters for Fe(1V) in Fe(DED) and the free ion
A 1 cm-
'
A 2 cm-'5
cm-' bl C1 AEo mm/s U mm/s H, kG a.u. (a) Ref. [ I l l . Free ion-
-
-
-
5w")
-
-
4.5-
220 6.3The temperature variation of the quadrupole inte- raction calculated with the parameters of table I1 is shown in figure 4 together with the experimental data.
FIG. 4. - Temperature variation of the quadrupole interaction
calculated with the parameters of table 11.
3.2 ANALYSIS OF THE SPECTRA IN APPLIED MAGNETIC FIELDS. - A common feature of all the known Fe(1V)
compounds is that they exhibit an almost diamagnetic response even in large applied magnetic fields. The possibility of pure diamagnetic character of these compounds is ruled out either from the magnetic susceptibility data which give S = l or from the observed temperature dependence of the spectra in large applied fields [l]. The above behaviour can be therefore interpreted in terms of the quenching of the angular and spin momenta due to the low symmetry of the crystal field.
The magnetic interaction of the iron nucleus in the effective field approximation is
where g, p,I is the magnetic moment of either the excited or the ground state of the nucleus, H, is the applied field and H,, is appropriately expressed as the vector sum of the following three contributions :
Here, i labels the single 3d electron operators, H, is the Fermi contact constant which has a free ion value of approximately
-
200 kG per unit spin, V,, are the single electron e. f. g. components in units ofl
e-I
A
LIGAND FIELD ANALYSIS OF MOSSBAUER DATA FOR A SIX COORDINATE Fe(1V) C6-511
the corresponding axis.
< >,,
denotes Boltzmann averaging of the expectation values of the appropriate sum of single electron operators over the 9 eigenstates of (1). General relations were worked out for the calculation of these expectation values.As it was mentioned already, the eigenstates of (l), due to the low symmetry of the crystal field, are orbital and spin singlets in the absence of an external field. The expectation values in (7) vanish therefore and the magnetic interaction at the nucleus also vanishes. The application of a large external field however produces mixing of the states and induces nonvanishing compo- nents of the effective field. In view of the experimental results these components are expected to have compa- rable magnitudes with the applied field and to sum in such a way that the total hyperfine field averaged over the various directions in a polycrystalline absorber is approximately equal, though opposite in sign, to the applied field.
We have obtained a quantitative view of the above ideas by incorporating the Hamiltonians (1) and (6) in a computer program which performs a summation over the applied field directions and calculates the resulting specturm for gamma rays either parallel or transverse to the field. Briefly the calculation proceeds as follows : for each direction of the applied field relative to the crystal field axes, (1) is diagonalized and its eigenstates are used for the calculation of the thermal averages of the e. f. g. and H,,, components. The e. f. g. is then diagonalized and the various vectors, including the applied field, are transformed to its principal axis system. Hamiltonian (6), augmented with a quadrupole interaction term is then diagona- lized and its eigenfunctions are used for the calculation of the line intensities for gamma rays parallel or trans- verse to the applied field. The calculation is repeated for various directions of the applied field over the upper half of the unit sphere. The resulting spectrum is therefore a function of the fine structure parameters A,, A,,
c,
b,, c, as well as of the parameters H, and<
r - 3>,,
entering the calculation of the effective field components in (7). Direct comparison with the results of the Q. S. analysis is therefore possible. In addition, since the effect of all the eigenstates is taken into account, the calculation is applicable to high temperatures as well.In fitting the spectra of figure 1 we have adjusted only the parameters H, and
<
r - 3 > 3 d while the otherparameters were fixed to their values in table 11. The final values of these parameters are also listed in table 11. The best simulation to the spectra at 30 and 60 kG is drawn as a solid line in figure 1. The sign of the maximum e. f. g. component is negative and the value of is close to 0.2. It is interesting to note that this value of rj is significantly lower than the value
that would be obtained from a diamagnetic inter- pretation of the spectrum.
4. Discussion.
-
The major result of the present analysis is that both the temperature variation of the quadrupole interaction and the response of the Moss- bauer spectra to external magnetic fields is well accounted for by ligand field analysis. The successful reproduction of experimental results with this model is strong evidence that the electronic state of the iron ion in this complex can be satisfactorily described as a 3d4, S = 1 configuration. Covalency effects are indi- rectly taken into account by allowing several of the parameters entering in the calculation to assume lower values than the free ion values. As it is known from several studies in Fe(I1) compounds [l01 the parame- ters mainly affected are the spin-orbit coupling constant 5, the bare quadrupole coupling constant BE,, the Fermi contact factor H, and<
r - 3>.
As it is seen from table 11,
I
is reduced by about 40%
with regard to its free ion value, indicating significant effects of charge delocalization comparable to those found in some iron (11) compounds [10].The value of
<
r - ,>
obtained from the analysis of the magnetically perturbed spectra shows also a significant radial expansion of 3d orbitals although it must be pointed out that the value of table 11 includes implicitely an orbital reduction factor for the compo- nent H, in eq. (7). The reduction of the Fermi contact constant is in close agreement with the reduction inc
while for the bare quadrupole coupling constant AE, it is not possible to make any comment due to the uncertainty in estimating the free ion value. It may be concluded that the values of the electronic parameters derived from the present analysis show clear evidence of significant charge delocalization and covalency effects.Another interesting result is the sensitivity of the analysis to the value of the mixing parameter b , which is a measure of the deviation from the two limits of octahedral and trigonal prismatic geometry. The value obtained from the analysis, b, = 0.96
+
0.005 reflects the significant distortion of the structure towards the trigonal prismatic limit. This seems to be a typical feature also for other Fe(1V) compounds with an FeS, core which have been studied at our laboratory (l) (V. Petrouleas and D. Petrides, to bepublished). A full discussion of the structural implica- tions of these results and a detailed description of the structure will be given elsewhere.
(1) One of us (A. S.) would like to acknowledge the hospitality
V. PETROULEAS, A. KOSTIKAS AND A. SIMOPOULOS
References
[l] PAEZ, E. A., WEAVER, D. L. and OOSTERHUIS, W. T., J. [7] OOSTERHUIS, W. T., LANG, G., J. Chem. Phys. 58 (1973)
Chem. Phys. 57 (1972) 3709. 4757.
[2] PASEK, E. A. and STRAUB, D. K., Inorganic Chin. 11
(1972) 259.
.
, [8] MARTIN,.
J. L. and TAKATS, J., Inorganic Chem. 14 (1975)[3] HOLLANDER, F. J., PEDELTY, R., COUCOUVANIS, D., 1335.
J. A. C. S. 96 (1974) 4032. [g] BALLHAUSEN, C. J., Introduction to Ligand Field Theory
[4] PETROULEAS, V., KOSTIKAS, A. and SIMOPOULOS, A., (McGraw Hill 1962), p. 68. Note that the X, y axes
Intern. Conf on Miissbauer Spectroscopy, Cracow 1975, are different here than in this reference.
Vol. 1, p. 251.
l51 M ~T, ~H., EHREN~ERG, ~ , A. and BEARDEN, A. J., Bio- [l01 PETROUJ-EAS, V., KOSTIKAS, A. and SIMOPOULOS, A., Phys.
chemistry 8 (1969) 4159. Rev. B 12 (1975) 4666, and references therein.
[61 LANG, G., SPARTALIAN, K. and YONETANI, T. (These [l11 FIGGIS, B. N., Introduction to Ligand Fields (Wiley,
