Paramagnetic susceptibilities

APPLICATION OF RESULTS OBTAINED FROM THE QUANTUM MECHANICS AND FROM A THEORY OF PARAMAGNETIC SUSCEPTIBILITY TO THE STRUCTURE OF MOLECULES By Linus Pauling... 

The spins of the electrons are opposed when the bond is formed, so that they cannot contribute to the paramagnetic susceptibility of the substance. 

Data for which no reference is given are from the Slrukturbericht of P. P. Ewald and C. Hermann. 6 R. W. G. Wyckoff, Z. Krisl., 75,529 (1930). W. H. Zachariasen, ibid., 71, 501, 517 (1929). d The very small paramagnetic susceptibility of pyrite requires the presence of electron-pair bonds, eliminating an ionic structure Fe++S2. Angles are calculated for FeS2, for which the parameters have been most accurately determined. The parameter value (correct value = 0.371) and interatomic distances for molybdenite are incorrectly given in the Slrukturbericht. 

S is the spin quantum number. The expected magnetic moments for a sextet and a doublet state are 5.91 and 1.73 respectively, measured in Bohr magnetons. The values calculated from the observed paramagnetic susceptibilities of the crystals are 5.88 for (NH aFeFg and 2.0 for... 

Pauling, L. (1931) The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules, J. Am. Chem. Soc. 58,1367-1400. 

I. Pauling, L. The Nature of the Chemical Bond. Application of Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules J. Am. Chem. Soc. 1931, 53, 1367-1400. 

Information about the structure of Pd and Pt is provided by the paramagnetic susceptibility of the metals, interpreted by the Weiss equation... 

Fig. 4. Curves showing the reciprocal of the molar paramagnetic susceptibility of Ni, Pd, and Pt as a function of the temperature.

The quantum mechanics treatment of diamagnetism has not been published. It seems probable, however, that Larmor s theorem will be retained essentially, in view of the marked similarity between the results of the quantum mechanics and those of the classical theory in related problems, such as the polarisation due to permanent electric dipoles and the paramagnetic susceptibility. f Thus we are led to use equation (30), introducing for rK2 the quantum mechanics value... 

For molecules I, III and VII, Table 4 also gives theoretical values corresponding to the fully-symmetrical equilibrium structures. It will be seen that double-bond fixation brings about a considerable decrease in paramagnetic susceptibility. Partial evidence for such reduced mag-... 

In principle it should be possible to determine the anisotropy of the paramagnetic susceptibility for some systems of pseudo-axial symmetry, but apart from the citation (74) of a private communication regarding the ferricenium cation, no experimental data are available for metal sandwich complexes. Such measurements should however be possible for at least some metallocenes and mixed sandwich complexes since these are found to crystallise in either a monoclinic (Fe(Cp)2 (6)) or orthorhombic (Ru(Cp)2, (Cp)V(Ch),... 

Van Vleck, J.H. (1932) The Theory of Electric and Paramagnetic Susceptibilities, Oxford University Press, Oxford. 

In [Co(Cp )2][Ni(dmit)2], where the [Co(Cp )2]+ cations are diamagnetic (S — 0), the paramagnetic susceptibility arises only from the contribution of the anionic network, where S — 1/2 for [Ni(dmit)2]. The magnetic behavior of this compound is dominated by weak FM interactions (6 — 0.5 K) [54]. The observed dominance of the FM interactions in this compound confirms that the FM interactions between the i(dmit>2 units in the dimers are stronger than the AF A A intrachain interactions. 

The initial product of the inhibition step is not known in this case and may be a molecular complex.8 The direct reaction of the ethane with the peroxy radical is an example of a covalent compound giving a reaction resembling that of a related free radical. The molecular weight determination by Gomberg was therefore a necessary part of the proof that he was dealing with radicals and not merely an unusually reactive hydrocarbon. The presence of free radicals has since been confirmed by measurements of the paramagnetic susceptibility and the paramagnetic resonance absorption.9-10 The latter evidence also rules out an alter-... 

The primary measure of the amount of free radical must depend on those properties unambiguously due to the unpaired electron. In the past the most common method has been the measurement of the paramagnetic susceptibility, now subject to difficulties of quantitative interpretation. The method of paramagnetic resonance absorption is... 

The partial orientation of the elementary dipoles in a paramagnetic solid is counteracted by thermal agitation, and it would be expected that at high temperatures the random motion of the atoms in the solid would cancel the alignment due to the magnetic field. The paramagnetic susceptibility would therefore be expected to vary with temperature. The temperature dependence is given by the Curie law ... 

Determinations of epr fine structure and paramagnetic susceptibilities are most often used. For characterization of higher spin orders, neutron diffraction and other physical methods may be useful. On the other hand, a successful measurement of normal high-resolution nmr spectra would serve as good evidence for singlet ground states of the chemical entities at issue. 

The average magnetization I is given by (15), where Bj a) is called a Brillouin function, and a by (16). When a 1, Bj(a) may be expanded, and, if we take only the first term, then (17) results. The paramagnetic susceptibility X is inversely proportional to the absolute temperature T. This relation is called the Curie law, and the proportionality constant C is the Curie constant. 

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