The electronic properties and stereochemistry of mono-nuclear complexes of the copper(II) ion

Magnetochemistry: advances in theory and experimentation

Publisher Summary This chapter discusses quadrupole effects in nuclear magnetic resonance studies of solids. The first evidence that many nuclei possess magnetic moments came from the study of the hyperfine structure of atomic spectra in the visible region. The interaction of the nuclear magnetic moment with the magnetic field produced by the atomic electrons gives rise to a hyperfine spectrum that is relatively simple, being characterized by the well known “interval rule.” Marked departures from this interval rule do occur in a few cases, however, and some of the departures can definitely be attributed to the presence of a nuclear electric quadrupole interaction. The methods of radio-frequency spectroscopy are very well adapted for the investigation of the very small interaction energies to which nuclear moments give rise. They have led not only to much more precise determinations of nuclear magnetic moments, but also to a vastly increased knowledge of nuclear electric quadrupole effects. The first outstanding success along this line was the discovery, by the molecular beam resonance method, of the quadrupole moment of the deuteron. The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupole interactions.

Quadrupole Effects in Nuclear Magnetic Resonance Studies of Solids

It is shown that the dynamical Jahn-Teller effect in a complex having orbital degeneracy may partially quench spin-orbit interaction, the orbital parts of the Zeeman and hyperfine interactions, and other orbital operators governing response to perturbations such as strain or applied electric fields. Such dynamical quenching thus decreases the value of orbital reduction factors usually attributed in paramagnetic resonance studies to covalent bonding, without necessarily causing anisotropy in the spectrum of an individual complex. The dynamical Jahn-Teller effect may also substantially enhance various second-order effects. Such dynamic effects thus may make important changes in the parameters of the spin Hamiltonian without changing its symmetry. It is shown that the dynamical Jahn-Teller effect accounts qualitatively for unusual features in the spectra of interstitial transition-metal ions ${\mathrm{Cr}}^{0}$, ${\mathrm{Mn}}^{+}$, ${\mathrm{Mn}}^{0}$, and ${\mathrm{Fe}}^{+}$ in silicon and that it is probably of importance equal to or greater than that of covalent bonding in the interpretation of the spectrum of ${\mathrm{Fe}}^{2+}$ in MgO and CaO. A mathematical analysis of the dynamical effects is given for an orbital triplet state in interaction with a doublet or triplet vibrational mode, and some results are given also when the coupling is with the phonon continuum.

Dynamical Jahn-Teller Effect in Paramagnetic Resonance Spectra: Orbital Reduction Factors and Partial Quenching of Spin-Orbit Interaction

When two paramagnetic transition metal ions are present in the same molecular entity, the magnetic properties can be totally different from the sum of the magnetic properties of each ion surrounded by its nearest neighbors. These new properties depend on the nature and the magnitude of the interaction between the metal ions through the bridging ligands. If both ions have an unpaired electron (e.g. Cu2+ ions), then the molecular state of lowest energy is either a spin singlet or a spin triplet. In the former case, the interaction is said to be antiferromagnetic, in the latter case ferromagnetic. The nature and the order of magnitude of the interaction can be engineered by judiciously choosing the interacting metal ions and the bridging and terminal ligands, and, thus, by the symmetry and the delocalization of the orbitals centered on the metal ions and occupied by the unpaired electrons (magnetic orbitals). The first success in this “molecular engineering” of bimetallic compounds was in the synthesis of a Cu2+VO2+ heterobimetallic complex in which the interaction is purely ferro-magnetic. The same strategy could be utilized for designing molecular ferromagnets, one of the major challenges in the area of molecular materials. Another striking result is the possibility of tuning the magnitude of the interaction through a given bridging network by modifying the nature of the terminal ligands, which, in some way, play the role of “adjusting screws”. By careful selection of the bridging and terminal ligands, a very large antiferro-magnetic interaction can be achieved, even if the metal ions are far away from each other. Some sulfur-containing bridges are especially suitable in this respect.

Dinuclear Complexes with Predictable Magnetic Properties

The paramagnetic resonance spectrum of copper acetate is anomalous in that it resembles that of an ion of spin 1, and its intensity decreases as the temperature is lowered. The latter is correlated with the decreasing susceptibility found by Guha (1951). The following hypo­theses are suggested: (1) the crystalline field acting on each copper ion is similar to that in other salts such as the Tutton salts; (2) isolated pairs of copper ions interact strongly through exchange forces, each pair forming a lower singlet state and an upper triplet state, the latter only being paramagnetic. On this basis both the fine structure and the hyperfine structure of the spectrum have a simple explanation, and the theory also predicts a small initial split­ting of the triplet state of the same order as that found experimentally. The unit cell of the crystal contains two differently oriented pairs of ions, and, using an empirical value for the exchange parameter, fair agreement with the susceptibility measurements of Guha is obtained.

Anomalous Paramagnetism of Copper Acetate

The previous theory of Abragam & Pryce (1951) is extended to a special case of rhombic symmetry, and to include higher-order terms. The theory gives satisfactory agreement between the observed anisotropies of the g -tensor and the magnetic hyperfine structure, and shows that the size of the hyperfine structure is about 15 % smaller than would be expected on the assumption that the magnetic electron is confined to the copper ion. Comparison with the optical absorption spectrum suggests that the spin-orbit coupling is reduced by about the same amount, and the effects are explained by an overlap of the wave function of themagnetic electron on to neighbouring water molecules. The nuclear electric quadrupole moments are found to be (in units of 10 -24 cm 2 ) ; 63 Cu, — 0.16; 65 Cu, — 0.15, with an estimated maximum error in the theory of 20 % .

Paramagnetic Resonance in Diluted Copper Salts. III. Theory, and Evaluation of the Nuclear Electric Quadrupole Moments of 63 Cu and 65 Cu

The principal values of the g-tensor and the hyperfine structure (due to interactions with the magnetic dipole and electric quadrupole moments of the stable copper isotopes) have been determined in several copper Tutton salts diluted with the isomorphous zinc salts. At high dilution the residual line width is mainly due to interaction with the nuclear magnetic moments of the protons in the water of crystallization, and increased resolution is obtained by replacing these by deuterons. Crystals of the diluted copper potassium salt have been grown from heavy water, and a detailed study made of the electric quadrupole interaction. An investigation of the undiluted copper Tutton salts by means of paramagnetic resonance has been carried out by Bleaney, Penrose & Plumpton (1949). The principal axes of the copper ions were located, together with the principal values of the g-tensor. The variation of line width in the ac-plane was shown to be due in the main to dipole-dipole interaction with neighbouring copper ions, together with a contribution from some other cause whose anisotropy was determined by the principal axes of the ion. In a 'magnetically dilute' salt, obtained by growing a mixed crystal where most of the copper ions are replaced by diamagnetic magnesium or zinc ions, the line width due to magnetic dipole interaction can be largely eliminated. In this way Penrose (1949), working at Leiden University, discovered the presence of hyperfine structure due to interaction with the nuclear magnetic moment of copper. His initial results showed that this was the cause of the extra broadening observed in the concentrated salt, but his untimely death prevented a complete investigation. Measurements were therefore undertaken in this laboratory, which resulted in the discovery that the electric quadrupole moment of the copper nucleus played a major role in the nature of the spectrum observed perpendicular to the symmetry axis of the ion (Ingram I949). Investigation of copper ammonium, copper rubidium and copper potassium sulphates showed that the magnitude of the quadrupole interaction was nearly the same in all three salts (Ingram, Thesis, Oxford, 1951). It appeared also that the quadrupole moments of the two stable isotopes, of mass 63 and 65, were nearly equal, contrary to the deduc

Paramagnetic Resonance in Diluted Copper Salts. I. Hyperfine Structure in Diluted Copper Tutton Salts

An interesting transition in the paramagnetic resonance spectrum has been observed for a number of cupric salts with trigonal symmetry. At room temperature only a single nearly isotropic line is observed, with a small hyperfine structure. Below a certain temperature, which depends on the salt, the spectrum is that of three kinds of copper ion each with nearly axial symmetry about one of three mutually perpendicular directions. The behaviour of this spectrum is similar to that of the copper Tutton salts in the anisotropy of the g-tensor and magnetic hyperfine structure, and in the presence of a nuclear electric quadrupole interaction. A careful analysis of the spectrum is made for (Cu, Mg)$\_{3}$La$\_{2}$(NO$\_{3}$)$\_{12}\boldsymbol{.}$24D$_{2}$O.

Paramagnetic Resonance in Diluted Copper Salts. II. Salts with Trigonal Symmetry

Tinkham & Strandberg (1955a, b) have made a theoretical analysis of the paramagnetic resonance spectrum of molecular oxygen gas ($^{16}$O$^{16}$O), and obtained satisfactory agreement with their experimental results. Independent measurements at low field strengths, made by Hendrie & Kusch (1957), using a molecular beam method, yielded results which were not in agreement with those of Tinkham & Strandberg. The experiments of Tinkham & Strandberg have now been repeated to a higher accuracy and systematic discrepancies with their results have been observed. In these new measurements, the positions of the absorption lines have been fitted to values obtained by numerical calculations based on the theory of Tinkham & Strandberg and carried to an accuracy of two parts per million (2 p.p.m.). Agreement with the new experimental results to 6 p.p.m. is obtained with the following choice of the three Parameters: g$\_{s}^{\prime}$/g$\_{s}$ = 1 - (147 $\pm $ 10) $\times $ 10$^{-6}$, g$\_{l}$/g$\_{s}$ = (1$\cdot $405 $\pm $ 0$\cdot $015) $\times $ 10$^{-3}$, g$\_{r}$/g$\_{s}$ = (6$\cdot $3 $\pm $ 0$\cdot $6) $\times $ 10$^{-5}$, where g$\_{s}$, g$\_{s}^{\prime}$, g$\_{l}$ and g$\_{r}$ are the spectroscopic splitting factors for the free electron spin, the electron spin in the molecule, the molecular electronic orbital moment and molecular rotational moment respectively. These values are not in agreement with those of either Tinkham & Strandberg or Hendrie & Kusch within the experimental errors quoted. As an additional check, measurements and calculations have been made on five transitions within the even rotational states of $^{16}$O$^{18}$O; with the same parameters as above, appropriately modified to allow for the change in isotopic mass, agreement is obtained with experiment within 10 p.p.m. Evaluation of the relativistic and diamagnetic effects (Abragam & Van Vleck, 1953) within the molecule gives the correct order of magnitude for the departure of g$\_{s}$ from g$\_{s}$.

K. D. Bowers

Papers

Anomalous Paramagnetism of Copper Acetate

Paramagnetic Resonance in Diluted Copper Salts. III. Theory, and Evaluation of the Nuclear Electric Quadrupole Moments of 63 Cu and 65 Cu

Paramagnetic Resonance in Diluted Copper Salts. I. Hyperfine Structure in Diluted Copper Tutton Salts

Paramagnetic Resonance in Diluted Copper Salts. II. Salts with Trigonal Symmetry

Paramagnetic Resonance Absorption in Molecular Oxygen