Raymond P. Scaringe

The Coupled Representation Matrix of the Pair Hamiltonian.

A complete treatment of the spin hamiltonian for a pair of exchange coupled metal ions is given. The results obtained through the use of the Wigner-Eckart theorem are unrestricted with respect to the relative orientation of the single-ion tensors, and appropriate for both the S 1 = S 2 and S 1 ≠ S 2 cases. The necessary constants are derived so that matrix elements within a given spin multiplet can be treated by ordinary operator algebra with the coupled representation state vectors, |SM>, as a basis set. Explicit algebraic formulae for matrix elements between spin multiplets are presented for the first time. Symmetry restrictions are discussed in general and illustrated for the simple case of two ions related by an inversion centre, pair symmetry Ci .

Exchange coupling in di-μ-hydroxo-bridged chromium(III) dimers

SummaryThe magnetic properties of a series of di-μ-hydroxo-bridged chromium(III) complexes of the general formula [CrLm(H2O)n(OH)]2q± are discussed in terms of the structural features of the molecules using extended Hückel molecular orbital formalism. The singlet-triplet splittings which arise from superexchange coupling correlate with the ratio Φ/r, where Φ is the angle at the bridging oxygen atom and r is the Cr-O(bridge) bond distance. Small deviations from the overall correlation result from other structural variations and electronic effects which are not treated. Data presented for three alkoxo-bridged chromium(III) complexes reflect enhanced exchange coupling as expected from the increased electron density in the orbitals of the bridging oxygens.

Magnetic and structural characterization of the chromium(III) dimer sodium diμ-hydroxobis[bis(oxalato)chromate(III)] hexahydrate, Na4[Cr(C2O4)2OH]2·6H2O

Abstract The crystal and molecular structure of the sodium di-μ-hydroxobis[bis(oxalato)chromate(III)] hexahydrate, Na4[Cr(C2)4)2·6H2O [or Na4[Cr(ox)2OH]2·6H2O], has been determined from three-dimensional X-ray diffraction data collected by counter methods. The material crystallizes in the monoclinic space group P21/c with four dimeric formula units in a cell of dimensions a = 19.530(12), b = 9.860(7), c = 12.657(10) A and β = 106.93(4)°: least-squares refinement of the structure has led to a final R-factor (on F) of 0.061 using 3278 independent intensities. The structure consists of two crystallographically independent dimeric [Cr(ox)2OH]4−2 anions which interact with sodium cations and water molecules in the cell. The geometry around each independent chromium(III) center is roughly octahedral. The bridging unit is strictly planar, there being an inversion center in the middle of each dimer. The CrOCr bridging angles are 99.6(2) and 99.7(2)°, and the CrCr separations are 2.999(3) and 3.001(2) A. There is extensive hydrogen bonding between the oxalate ligands and the water molecules. The magnetic susceptibility of a single crystal of the complex has been examined in the temperature range 2–70 K, and has been interpreted by means of application of the magnetization expression for coupled pairs of S = 3 2 ions with a small value of ∣J∣. The dimer exhibits a very small exchange interaction, the best fit to the magnetization expression yielding J = −0.31 cm−1 and γ = 0.28; the latter value gives an inter-dimer lattice interaction parameter, J′, of 0.034 cm−1 for the four nearest neighbors.

Structural and magnetic properties of di-µ-hydroxo-bis[bis(ethylenediamine)chromium(III)] dithionate

The crystal and molecular structure of the title complex [{Cr(en)2(OH)}2][S2O6]2 has been determined from three dimensional single-crystal X-ray counter data. The complex crystallizes In the orthorhombic space group Pbca with four molecules in a cell of dimensions a= 13.58(1). b= 18.42(2), and c= 10.02(1)A. The observed and calculated densities are 1.85(2) and 1.851 g cm–3, respectively. The structure has been refined by full-matrix least-squares techniques to a value of R(on F) 0.049. The complex consists of dimeric [{Cr(en)2(OH)}2]4+ units which are hydrogen bonded to the dithionate anions. The dimeric cation isolated is the meso form, there being a crystallographic inversion centre in the middle of the dimer. The geometry around each chromium(III) centre is approximately octahedral, the Cr–Cr separation and bridging Cr–O–Cr angle being 3.032(3)A and 100.0(2)°, respectively. The dithionate anion has the staggered conformation [S–S 2.127(3)A, S–O 1.435(6)–1.460(5)A]. The hydrogen bonding is extensive, with all the possible donor and acceptor atoms participating. The magnetic susceptibility of a powdered sample of the complex shows a maximum near 7.3 K, indicative of antiferromagnetic coupling between the metal centres. The best fit of the susceptibility data to the Van Vleck equation (modified by the inclusion of biquadratic exchange) yields values for g. J, j, and ΔE(the singlet–triplet splitting) of 1.947 (7), –1.08(2) cm–1, 0.234(7) cm–1, and –3.68 cm–1, respectively.

Magnetic studies on the nitrate and bromide salts of the cation di-μ-hydroxobis [di( 1, 10-phenanthroline)chromium(III) ]4+

Abstract The magnetic susceptibilities of powdered samples of di-μ-hydroxobis [di(1,10-phenanthroline)chromium(III)](NO 3 ) 2 ·7H 2 O, and the analogous bromide octahydrate salt have been determined in the temperature range 5 to 283 °K. The dimers exhibit antiferromagnetic exchange interactions with the best fits to the Van Vleck expression for exchange coupled S = 3/2 ions including biquadratic exchange yielding, for the nitrate salt, g = 1.98 ± 0.03, 2J = −42.2 ± 0.5 cm − , and J = 0 cm − and for the bromide salt, g = 1.95 ± 0.03,2J = −29.2 ± 0.6 cm −1 , and j = 0.5 ± 0.1 cm −1 .