Brian N. Figgis

The Crystallography and Paramagnetic Anisotropy of Potassium Ferricyanide

Single crystal X-ray analyses of the structure of potassium ferricyanide at ca. 300 and 95° K are reported. Least-squares refinements within the monoclinic space group, P21/c, have converged with the residuals R300°K = 0·092 and R95°K = 0·077. The unit cell dimensions at 300°K are: a = 7·06, b = 10·38, c = 8·40 Å, β = 107·0°, and at 95°K are: a = 7·03, b = 10·31, c = 8·35 Å, β = 107·2°. The coordination octahedra are only slightly distorted, both analyses independently revealing a small tetragonal elongation of the molecule along Fe-CN bonds lying nearly perpendicular to the crystallographic c axis. The principal crystal paramagnetic susceptibilities are characterized by an essentially unique, and lower, moment parallel to the c axis. These two observations are to be reconciled only in relation to the role of second-nearest neighbour effects of either antiferromagnetic or crystal-field character. Exchange is ruled out by earlier e.s.r. work and the present susceptibility dilution experiments. The crystal anisotropy appears to be dominated by the coulombic field set up by adjacent potassium ions in the lattice. While all potassium ions in the structure will play some role in this second-order perturbation, those forming ‘chains’ with the octahedra parallel to the c axis are likely to be the more important. A simple crystal-field approach, using symmetry-adapted, zero-order wavefunctions on the iron atoms, has shown how the correct direction and relative magnitudes of the crystal magnetic anisotropies may be predicted by this model. The splitting of the ground 2T2g term of the complexion is estimated as 150 to 300 cm-1.

Wavefunctions derived from experiment. IV. Investigation of the crystal environment of ammonia

Constrained Hartree-Fock calculations have been performed to obtain wavefunctions that reproduce experimental X-ray structure-factor magnitudes for crystalline NH3 to within the limits of experimental error. Different model densities using both a single molecule and clusters of NH3 in the calculation of X-ray structure-factor magnitudes have been examined. The effects of the crystalline lattice on the experimental wavefunction of the NH3 unit can be reproducibly recovered. The construction of structure-factor magnitudes based on normally distributed random perturbations of the experimental values has also been used to gauge the accuracy of integrated atomic properties obtained from the wavefunctions, the point at which the constraint procedure should be terminated, and the approximate error in the experimental sigma(k) values.

Atomic displacement parameters for Ni(ND3)4(NO2)2 from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Structural parameters derived from 9(1)K X-ray diffraction data and 13(1)K time-of-flight neutron diffraction data on perdeuterated tetraamminedinitro-nickel(II), Ni(ND 3 ) 4 (NO 2 ) 2 , are compared. It is shown that excellent agreement can be obtained for both positional and thermal parameters derived separately from the two experiments, provided that great care is taken in all steps of the process, including data collection, data reduction, and nuclear and electronic structure refinement. The mean difference in the thermal parameters, , is as low as 0.00034 A 2 and 1/2 = 1.92, showing that, even without any form of scaling between the parameters, the same values can be obtained. This, compared with other such studies, indicates that time-of-flight neutron diffraction data can give structural information of a quality comparable to monochromatic neutron diffraction. The excellent correspondence between the thermal parameters derived separately from X-ray and neutron diffraction data gives confidence in the deconvolution of the thermal motion from the X-ray diffraction data, which is necessary for any study of a static electron density distribution.

X–N study of the electron density in (ND4)2Cu(SO4)2.6D2O at 9 K: flexible radial functions are vital

Diammonium hexaaquacopper(II) disulfate-d 20 , [ND 4 ] 2 °u(D 2 O) 6 ](SO 4 ) 2 , M r =419.7, monoclinic P2 1 /a, a=9.393 (2), b=12.666 (2), c=6.061 (1) A, β=107.16 (1) o , V=689.0 (4) A 3 , Z=2, Mo Kα radiation, λ=0.71069 A, μ=2.01 mm -1 , F(000)=415.3 (414.0 without anomalous dispersion), T=9 (1) A, R(I)=0.013, R(F)=0.0095, χ 2 =0.89, 5134 reflections. Refinement of the X-ray data, using a radially augmented multipolar charge model, gave thermal and positional parameters agreeing with those derived from neutron diffraction data and the correct cell content of electrons

The Paramagnetic Anisotropies and Ligand Fields of the Tetrahedral Cobaltous Chlorides and Thiocyanate

The temperature dependence of the paramagnetic susceptibilities of single crystals of Cs3CoCl5, Cs2CoCl4 and K2Co(CNS) 4. 4H2O have been measured over the range 80 to 300 °K. The splitting of the excited 4T2 term by low symmetry crystal fields is of the order of 1000 cm-1, and the extent of t2g electron delocalization in each complex corresponds to a delocalization parameter k of approximately 0.9. The magnitudes of the observed 4T2 term splittings are calculated in a semi-quantitative way through a comparison of the details of the molecular geometry with crystal field theory for a distorted tetrahedron. Magnetic exchange effects in the complexes, corresponding to exchange integrals of several degrees, are sufficiently large that the zero field splitting effect is relatively unimportant. The geometrical arrangement of adjacent (CoCl4)2- tetrahedra taken with the delocalization parameters allows an order-of-magnitude calculation of anisotropic magnetic exchange in crystals of Cs3CoCl5 and Cs2CoCl4. A new X-ray analysis of the co-ordination geometry of Cs3CoCl5 is also summarized.

Can a multipole analysis faithfully reproduce topological descriptors of a total charge density

Total charge densities rho(r) of solid NH(3) have been derived using an ab initio crystalline molecular-orbital approach and also from multipole refinement of the structure factors obtained from the same charge density. Comparison of the topological features of these charge densities, as defined by the quantum theory of atoms in molecules, has been used to probe the ability of the multipole analysis to reproduce exactly known total charge-density distributions. For the most part, multipole refinement satisfactorily returns the features of the original density, although the fit to theoretical data is not as good as that to the experimental data. The one topological parameter that is poorly reproduced is the Laplacian nabla (2)rho(r(b)) at NH bond critical points.

Spin densities and covalency in transition-metal complexes: A comparison of discrete variational Xα calculations with polarised neutron diffraction data

Abstract Spin-unrestricted discrete variational Xα self-consistent charge (DVXα SCC) calculations for the cubic transition-metal complexes [CoCl 4 ] 2− , [CoBr 4 ] 2− , [FeCl 4 ] − , [CrF 6 ] 3− and [Cr(CN) 6 ] 3− are reported. The calculated covalencies exhibit the same trends predicted by empirical nephelauxetic parameters. However, agreement between the experimental ligand-field splittings and theoretical values determined via Koopmans theorem is poorer, particularly for the tetrahedral species. The computed spin densities are compared in detail with experimental results derived from polarised neutron diffraction (PND) studies and with unrestricted Hartree-Fock (UHF) calculations. The qualitative agreement with the PND data is good and for [CoCl 4 ] 2− and [CrF 6 ] 3− the DVXα SCC and UHF models give almost identical spin densities. However, quantitative agreement with experiment is not obtained because the calculations ignore the real molecular site symmetry, the crystalline environment and configuration interaction (CI). These features appear to influence significantly the experimental spin and charge densities and, except for CI, can be readily included in DVXα SCC calculations. The present work suggests that the DVXα SCC scheme gives a sufficiently accurate description of electron distributions to provide a useful tool for further examination of these effects.

Spin Density and Bonding in the CoCl

We report improvement in the precision of certain of the polarized neutron diffraction data for Cs3CoCl5. The improvement allows us to analyse the data using a chemically based model of the spin-density distribution that is equivalent to a conventional multipole treatment to fourth order on the cobalt, and to second order on the chlorine atoms of the CoCl2–4 ion. To test the completeness of the model and to understand the meaning of the parameters in terms of the wavefunction, we have used it to analyse a set of theoretical magnetic structure factors. These are obtained from the wave-function of a Hartree–Fock calculation on the CoCl2–4 ion. We obtain an excellent fit to the theoretical ‘data’ and a much improved fit to the experimental data when the new model is used. We confirm the main features of the spin- and charge-density distributions deduced in our previous study, and we are now also able to interpret the experimental parameters in terms of the wavefunction by analogy with the fit to the theoretical data. We find that there is ca. 3 % of the total spin delocalized onto each chlorine atom of the CoCl2–4 ion, dominantly via σ - rather than π-bonding. There is a well defined diffuse spin density on the cobalt atom of 4p symmetry, and strong evidence for 3d–4p mixing. The spin density, in this almost cubic ion, has distinct non-cubic symmetry, which may arise from longer-range effects due to the rest of the tetragonal crystal.

^{2-}_4

Abstract The measurement of X-ray diffraction from crystals of (ND 4 ) 2 Cu(SO 4 ) 2 ·6D 2 O at 9 K gives a set of Bragg intensities as the basic observable. It is shown that ab initio quantum-mechanical calculations on individual isolated ions, near the Hartree—Fock limit, based on nuclear positions from a neutron diffraction experiment, when assembled into the crystal unit cell, reproduce the data set for the complex at a level close to the experimental error limits. This is accomplished using only four adjustable parameters related to the experimental details. Our procedure avoids the biasing effects of multipole models, of which a typical one used one hundred and eighty four parameters.

Ion in Cs

A polarized neutron diffraction experiment on Cs2KFe(CN)6 gave 292 unique magnetic structure factors. These were analysed by using a model for the magnetization density of multipoles and valence functions on the iron and ligand atoms, with the dipole approximation for orbital effects. Neither the ligand nor the iron atom densities retain the cubic symmetry of the free ferricyanide ion. The natural axes of quantization of the iron atom are rotated by significant amounts from the Fe-CN vectors. The iron electronic configuration was found to be d-0.64(8)xyd0.78(6)xzd0.72(5)yzd-0.06(6)z2d0.17(7)x2-y2 corresponding to the cubic t52g configuration of the low-spin d5 FeIII ion perturbed to put all spin in the dxz and dyz orbitals. The negative spin in the dxy orbital and the 6% of negative spin on the carbon atoms conform with the qualitative predictions of previous ab initio theoretical calculations, although for dxy there are large manifestations of spin polarization. The 12% of spin delocalized onto nitrogen atoms reflects covalence. The ligand populations depart considerably from those for cubic symmetry, and can be understood in terms of spin occupation of molecular orbitals involving 3d-t2g orbitals with coefficients dxy < dxz < dyz. These observations can be rationalized by an empirical model in which the ligand field components exerted by the cyanide groups are influenced by details of the crystal structure.