Electron-nuclear Interaction Research Articles

The effect of correlation on the surface potential of a free electron metal

<dm:abstracts xmlns:dm="http://www.elsevier.com/xml/dm/dtd"><ce:abstract xmlns:ce="http://www.elsevier.com/xml/common/dtd" view="all" class="author" id="aep-abstract-id21"><ce:section-title>Publisher Summary</ce:section-title><ce:abstract-sec view="all" id="aep-abstract-sec-id22"><ce:simple-para id="fsabs010" view="all">This chapter discusses the effects of paramagnetism on nuclear magnetic resonances (NMR) of the ligand molecules by using lanthanide induced shift (LIS). Many lanthanide shift reagents are now available commercially, which are soluble in common organic solvents. Most of the reagents are lanthanide complexes of β-diketones having the basic 2,4-pentanedione structure. Some common reagents are Pr(fod)<ce:inf loc="post">3</ce:inf>, Eu(tfa)<ce:inf loc="post">3</ce:inf>, Yb(hfa)<ce:inf loc="post">3</ce:inf> and associated permutations. The shift reagents are tris-β-diketonates of lanthanides with a hexacoordinate structure and 3-fold symmetry axis. Nuclei of ligands in paramagnetic complexes are coupled to the electronic spin of the central ion by the electron-nuclear hyperfine interaction. As a result of this interaction, large chemical shifts in the NMR spectra of the ligands are observed. There are two independent mechanisms of hyperfine interaction: the contact interaction results from a finite probability of finding an unpaired electronic spin on an atomic s orbital, and the dipolar interaction takes place via space and causes shifts only if the magnetic susceptibility of the central ion is anisotropic.</ce:simple-para></ce:abstract-sec></ce:abstract></dm:abstracts>

TOPOLOGICAL ASPECTS OF THE CONFORMATIONAL STABILITY PROBLEM. PART I. DEGENERATE ELECTRONIC STATES1

: ? : 8 8 9 2 ; enner electronic potential energy surfaces of symmetric polyatomic systems is derived by means of group theoretic and permutational symmetry principles. Degenerate penturbation theory is utilized to obtain an explicit analytical expression of this topography. The dependence of the nuclear-electronic interaction matrix elements, which occur in the penturbation development, on the nuclear coordinates is shown to be precisely determinable by group theoretic and permutational symmetry technlques. The numerical coefficients which prefix the nuclear coordinates which appear in these interaction matrix arrays are regarded as phenomenological parameters in their subsequent topographical applications. It is demonstrated that the magnitudes of these parameters determine only the relative placements of the Jahn-Teller- Renner surface reliefs and not their basic character (in this sense, minimal and maximal domains are taken to be of the same character). The formulas derived by means of the penturbation theory (with and without the complication of spin-orbit interactions) are employed to describe the topology of the multiply degenerate electronic energy surfaces of the regular polygons (including the digon) and the regular polyhedra, as well as of a number of selected highly symmetric irregular polygons and polyhedra. The results obtained reveal a number ofmore » important maxims: (1) the Jahn- Teller- Renner behavior of a polyatomic group theoretic system is completely determined by that of its elemental subgroups (principle of mathematical inheritance); (2) isomorphous point groups exhibit isomorphous Jahn- Teller deportments (formation of Jahn- Teller families); (3) whereas the prime number groups produce a single unique Jahn- Teller- Renner topography, the non- prime number groups produce all those topographies which are required by the principle of mathematical inheritance (1) (law of prime numbers); (4) the dynamical quantization and the topography of the Jahn-Teller problem are completely specified by group theoretic and permutational symmetry precepts (symmetrical transcendence); (5) although not mathematically required, the symmetry of the stable Jahn- Teller conformation is always the highest symmetry which is yet compatible with the loss of the initial inherent degeneracy (mimimax rule); (8) the Jahn- Teller- Renner energy resolvants factor only at locations of high nuclear symmetry (factorization theorem); (7) certain nuclear structures can never be JahnTeller stabilized (exclusion principle); (8) it is impossible to distinguish between ordinary anharmonic elastic distortions and Jahn-Teller distortions in non-homologous series of compounds (indistinguishability theorem), (9) spin-orbit forces remove cuspidal Jahn-- Teller radial electroric energy singularities for geometries less regular than the cube (spin-orbit law); (10) ionic and covalent bonding forces always produce complementary Jahn- Teller deformations, whereas conjugate hole-electron electronlc configurations always produce the identical deformation, bonding forces being equal (complementarity rules); (11) pseudo-JahnTeller interactions make conformational isomerisms possible even for dispositions of low regularity (conformational isomerization tenet); (12) doubly degenerate electronic states possess continuous Jahn- Teller- Renner electronic energy surfaces, but triply degenerate electronlc states possess disjoint electronlc energy surfaces in centain directions (canon of dimensional variability); (13) tetragonal Jahn- Teller conformational interconversion takes place in two dimensions for doubly degenerate electronic states, and five dimensions for triply degenerate electronlc states (doctrine of dimensional impenetrability); (14) experimental proofs of Jahn- Teller- Renner consequences can only be obtained from studies of homologous series of compounds (criterion of probity). Panticular care was taken to graphically illustrate all the important consequences of the« less

Theoretical Interpretation of Carbon-13 Hyperfine Interactions in Electron Spin Resonance Spectra

A quantitative theory of the isotropic electron-nuclear spin interactions of carbon 13 in pi-electron radicals is presented and applied to the hyperfine splittings observed in the electron spin resonance spectra of these substances. The splittings arise from sigma-pi interactions which polarize both the 1s and 2s electrons. The 1s-orbital spin polarization is shown to contribute a term of negative sign with a magnitude comparable to that from the 2s electrons. For an sp2 hybridized carbon atom that is bonded to three atoms, Xi (i=1, 2, 3), the hyperfine constant aC has the form aC=(SC+ ∑ i=13QCXiC)ρπ+ ∑ i=13QXiCCρiπ,where ρπ and ρiπ(i=1,2,3) are the pi-electron spin densities on atoms C and Xi, respectively. The contribution of the 1s electrons is determined by SC and that of the 2s electrons by the Q's, where QBCA is the sigma-pi parameter for the nucleus of atom A resulting from the interaction between the bond BC and the pi-electron spin density on atom B. Calculations for a planar CHC2 fragment model yield SC= —12.7 gauss, QCHC=19.5 gauss, QCC′C=14.4 gauss, and QC′CC= —13.9 gauss. The theory predicts both the magnitude and sign of the hyperfine splittings and is readily applied to a variety of compounds. Excellent agreement is obtained with the available experimental data. For the methyl radical, the measured C13 splitting is shown to be consistent with a planar model and limits the deviation from planarity to ≲5°. The theory provides a useful criterion for the validity of approximate wave functions that is illustrated by a comparison of various theoretical treatments for the naphthalene negative ion and triphenylmethyl. The sigma-pi interaction parameters are shown to depend on the bond length, the type of hybridization (including the angles between sigma bonds), and on the nature of the bonding atoms. For pi-electron systems, the results demonstrate that the magnitude of the sigma-pi exchange energy is a small fraction of the total energy. It is also noted that the proton parameter QCHH is somewhat larger in CHC2 than in CH3, which suggests a theoretical justification for some of the variation in the experimental ``QCHH'' required to fit measured proton splittings. The form of the theory is readily extended to the treatment of hyperfine splittings from nuclei other than C13.

Effects of Hydrostatic Pressure on the Paramagnetic Resonance Spectra of Several Iron Group Ions in Cubic Crystals

The magnetic resonance spectra of ${\mathrm{Cr}}^{3+}$, ${\mathrm{Mn}}^{2+}$, ${\mathrm{Fe}}^{3+}$, and ${\mathrm{Ni}}^{2+}$ present as substitutional impurities in MgO crystals and powders, and of ${\mathrm{Mn}}^{2+}$ in cubic ZnS have been observed as functions of hydrostatic pressure at room temperature. The results are interpreted assuming the local compressibilities to be equal to those of the pure host lattices.The measured volume dependence of the orbital contributions to the magnetic moments of the $F$-state ions, ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Ni}}^{2+}$, are consistent with a point-charge model within the experimental error. This simple model can only crudely account for the observed magnitudes of the orbital singlet-triplet splittings, however.The pressure dependences of the cubic field splittings of the $S$-state ions, ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$, are identical in MgO and correspond roughly to a fourth power law if an ionic potential is assumed. The cubic field parameter for ${\mathrm{Mn}}^{2+}$ in ZnS varies half as rapidly with volume. These results are consistent with recent calculations of Powell, Gabriel, and Johnston if it is assumed that the volume dependence of the cubic potentials in these lattices are given by the ionic model, though the relative magnitudes are not.The hyperfine structure of the manganese spectra also proves sensitive to sample volume, particularly in the sulfide. The effect may be qualitatively understood in terms of the exchange-polarization theory of the strong electron-nuclear interaction.

A Thermal Motion Effect in the Electron Spin Resonance of a Free Radical in Solution

The electron resonance hyperfine triplet at 9.5 mm wavelength of the peroxylamine disulphonate ion has been measured in a series of solutions of water and glycerol from 20% to 72% glycerol by weight and over a temperature range from -46° to 65°C. There is a temperature and solution dependent broadening which affects the individuals of the triplet differently. The high field line is broadened first with falling temperature. The effect is thought to be due to the motionally attenuated anisotropic electron-nuclear interaction. The anisotropic interaction is estimated to be comparable with the isotropic one. The anisotropy of the g factor, δg/g, is 2 x 10-3. These parameters allow the prediction of a static spectrum of the ion in agreement with experiment (Weissmann and Banfill 1953). The effect of thermal motion of the ion is shown by the close relation between the value and temperature dependence of the thermal reorientation correlation frequency and the variation of the electron resonance signal with temperature and nature of the solvent.

Note on the Calculation of Saturation Effects in Magnetic Resonance

A simple method using diagrams is described for calculating saturation parameters in spin systems. Results are derived for the multiresonance case. The lattice is regarded as inducing transitions among the various spin levels and the transition probabilities are assumed known. The method is particularly useful in complicated spin systems as are found in organic free radicals. For a free radical in solution with one odd electron and N equivalent nuclei under conditions where the intramolecular electron nuclear dipole-dipole interaction and g factor anisotropy contribute to the relaxation, the dependence of the saturation parameters of the electron resonance spectrum on the nuclear quantum number mJ is given by an expression of the form AmJ2+BmJ+C. Such behavior has been found experimentally.

Spin-Spin Interactions in Nuclear Magnetic Resonance. Contact Contribution

A method for calculating the contact contribution to spin-spin interactions between nuclei in nonaromatic molecules is described. The method is based on the valence bond model. The equivalent Hamiltonian of the Dirac vector model is used for a perturbation calculation in a representation where the total spin of the two electrons in each bond in the molecule is a good quantum number. The Ramsey-Purcell contact term in the interaction is calculated by a double perturbation method where only terms linear in the electron-nuclear interactions are considered but the perturbation is carried to higher order in the exchange integrals. In this way the interaction constants can be obtained explicitly in terms of the exchange integrals, and the calculation of the valence bond wave functions is avoided. It is then possible to see how the signs and magnitudes of the interaction constants depend on these integrals and what the dominant interaction mechanisms are. The perturbation series is evaluated explicitly with the electron nuclear contact interaction and the results are compared with the results of a similar calculation based on Ramsey's closure formula. In this way the objections against the closure procedure can be avoided. It is shown that Ramsey's formula can be used when different average energy separations are used for terms of different order in the expansion. The results of Ramsey for H2 and of Karplus et al. for hydrogen atoms separated by two and three bonds and the justification of the method of calculation used by them are discussed in detail. It is found that only perturbation terms of one type are important in each of the cases discussed by these authors and therefore their procedure can be justified. The results previously obtained by the author for spin-spin interactions in the allyl group are also discussed.

Proton Spin Polarization of Water Adsorbed on Sucrose Chars

By saturating forbidden electron-nuclear double transitions in paramagnetic materials, it is possible to considerably enhance the nuclear polarization in a positive or negative sense. This effect has been investigated experimentally using the protons of water adsorbed on paramagnetic charred sucrose. The dependence of the enhancement on the saturating microwave power is derived for the case of overlapping allowed and forbidden transitions, and predicts a linear change in polarization at low power levels. The general features of the enhancement found are in agreement with those predicted by perturbation theory using a simple dipole-dipole electron-nuclear interaction. However, the plot of log (polarization change) vs log (power) has a slope of 0.82±0.04 instead of 1.0. In addition, the field separation between the points of maximum positive and maximum negative enhancement is too small in those chars for which inhomogeneous broadening is suspected.

Theory of ESR Linewidths of Free Radicals

A theory of ESR linewidths for substances in which the magnetic anisotropy is small and for which the orbital magnetism has been essentially quenched is developed. Nuclear quadrupole moments, zero field splittings, anisotropic Zeeman terms, and intramolecular electron-nuclear dipolar interactions, as well as motional and exchange effects are considered in the strong field case. The theory is developed in a manner that is particularly adaptable to the study of liquids but it is also applied to crystals since the resulting equations, though only applicable for small anisotropies, are particularly simple. The theory provides an extension of previous theories on ESR spectra in liquids. Several applications of the theory are discussed with particular emphasis on V4+ chelates. The theory of exchange in liquids, a phenomenon which is complicated by the noncommutivity of the motional and exchange Hamiltonians is considered in special detail. It is shown that this theory can be used to explain Hausser's results—the existence of an optimum viscosity for the observation of hyperfine structure.

Electronic Structure and Hyperfine Structure Constants of NO Molecule

The coupling constants of the magnetic hyperfine, electric quadrupole, and spin-orbit interaction have been calculated from the self-consistent field molecular orbitals formed by linear combination of atomic orbitals. The calculated values of the electron spin-orbit, nuclear spin-orbit, and nuclear-electronic spin-spin interaction constants agree reasonably well with experiment. The results for the nuclear quadrupole coupling constant and the Fermi contact term are less satisfactory, although the latter can be improved by configuration mixing. The relations of these coupling parameters to the electronic structure of the molecule are discussed.

Proton Spin Relaxation in Aqueous Solutions of Paramagnetic Ions. II. Cr+++, Mn++, Ni++, Cu++, and Gd+++

Nuclear magnetic relaxation times for protons in dilute aqueous solutions of chromic, manganous, nickel, cupric, and gadolinium ions were measured in the frequency range 1.9 to 60 Mc/sec. Results were interpreted in terms of Solomon's formulation of electron-nuclear dipole-dipole interaction and Bloembergen's expression for scalar coupling of electron and nuclear spins. In large magnetic fields relaxation times were found to be shorter than those expected on the basis of low field values, suggesting that the effective ion magnetic moments, electron spin relaxation times, and/or electron-nuclear spin exchange constants are field-dependent.

Theory of Ionization Probability Near Threshold

The behavior of the cross section for ionization by electron impact is investigated in the vicinity of threshold by means of the quantum theory of inelastic scattering. A Coulomb-modified form of the Born approximation is used to calculate the $S$-wave ionization cross sections for ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{He}}^{++}$. The electron-nuclear interaction is included in the unperturbed Hamiltonian for the problem while the interaction between the incident and atomic electrons is considered as the perturbation. It can be shown that the limiting law for the ionization of a hydrogen atom has a linear dependence on the excess incident energy. The absolute cross sections evaluated are in good agreement with experiment. Generalization of the excess energy dependence of the threshold law to the case of multiple ($n$-fold) ionization is found to yield the forms ${{E}_{\mathrm{ex}}}^{n}$ for ionization by electron impact and ${{E}_{\mathrm{ex}}}^{n\ensuremath{-}1}$ for photoionization.

The Franck-Condon Principle and Its Application to Crystals

The semiclassical Franck-Condon principle is shown to be related to the more rigorous (``exact'') quantum-mechanical perturbation formula in the following ways: (1) the Franck-Condon formula can be derived from the ``exact'' formula by using a mean value approximation or by neglecting certain commutators; (2) if the electric dipole moments are treated as approximately independent of position, the Franck-Condon and the ``exact'' absorption (or emission) spectrum have the same zeroth, first, and second moments, i.e., the same integrated spectrum, mean absorption frequency, and breadth; (3) the errors in higher moments than the second become relatively unimportant at high temperatures. If the electron-nuclear interaction is sufficiently strong the errors are unimportant even at absolute zero. The use of a quasi-molecular description in a many particle problem is found to be possible only if the masses or stiffnesses are allowed to be temperature dependent. A detailed analysis is made of the case in which the energy difference between the two electronic states is a linear function of the vibrational coordinates—and the latter are describable by normal modes. ``Exact'' formulas for the absorption and emission spectrum are obtained.

ZDependence and Angular Distribution of Bremsstrahlung from 17-Mev Electrons

The relative bremsstrahlung cross section for the upper portion of the spectrum as a function of $Z$, for 17-Mev electrons from a 22-Mev betatron, has been measured. The radiation was detected by means of the ${\mathrm{Cu}}^{63}(\ensuremath{\gamma},n)$ induced activity, which has a 10.9-Mev threshold. The effect of atomic screening is small for the quantum energies to which this detector responds, but was taken into account. The results are in agreement with the Bethe-Heitler theory for electron-nuclear interactions within 1 percent. Electron-electron interactions give 0.75 times the intensity for electron-proton interactions, as measured with a copper detector.The total cross section for radiative energy loss of electrons has been measured with an ionization chamber. The experimental $Z$ dependence of the relative cross section indicates that the yield from gold for a given $N({Z}^{2}+Z)$ is somewhat less than that from low $Z$ elements. This discrepancy might be accounted for by improved corrections for screening, and by more accurate consideration of the radiation produced by electron-electron impacts. Rough measurements of the absolute cross section are in agreement with the Bethe-Heitler theory.The intrinsic angular distribution of bremsstrahlung, produced in a small amount of cellophane and air, was measured by film and ion chamber, and was found to fit a $\frac{1}{{[1+{(\frac{E\ensuremath{\theta}}{\ensuremath{\mu}})}^{2}]}^{2}}$ distribution. The angular distribution was measured with three detectors, for one Be and several Au targets. The results are in agreement with calculations in which the above intrinsic distribution and Moli\`ere's multiple scattering theory are used.The central intensity of bremsstrahlung as a function of target thickness, measured with a small ion chamber, is in approximate agreement with a calculation in which the energy loss of the primary electrons has been taken into account.

The nuclear specific heat in paramagnetic cupric salts at temperatures below 1° K II. The nuclear specific heat

A theoretical discussion is given of the experimental results described in part I. Contributions to the low-temperature specific heat from dipole-dipole and exchange interaction are shown to depend linearly on the dilution factor when dilution has occurred in a purely random manner. From a comparison of the results for the diluted and undiluted salts it is shown that a part of the specific heat is independent of the degree of dilution. This part is identified with the nuclear specific heat expected from nuclear-electronic interaction within the atom. The interaction constants are evaluated and are of the order of 0.01° K. These results are in agreement with observations of the hyperfine structure in dilute copper salts made from paramagnetic resonance experiments.The effect of exchange interaction is also discussed.