Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero‐point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2.In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure on...

Determination of Molecular Structures from Ground State Rotational Constants

A new criterion for the determination of molecular structures from ground state rotational constants

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

Measurements of the nuclear magnetic shielding of F19 and H1 are reported for a number of their respective binary covalent compounds. The applied fields required for the F19 and H1 nuclear magnetic resonances, at fixed frequency, vary in these compounds over a range of 3.98 and 0.122 gauss, respectively, at fields of about 6365 gauss. These ranges are of the same order of magnitude as the theoretical internal diamagnetic corrections for the unbound fluorine and hydrogen atoms. The dependence of nuclear magnetic shielding on the electronic structures of the molecules is discussed qualitatively and some general correlations indicated. One such correlation is that the magnetic shielding of the F19 nucleus decreases with increasing electro‐negativity of the atom to which the fluorine is bonded. This and other correlations differ in degree for the proton. The differences may arise from the relatively greater importance of the diamagnetic shielding term for the proton. Specific information regarding molecular a...

Nuclear magnetic shielding in fluorine and hydrogen compounds

Introduction 781 III. Cerenkov Radiation in the Presence of Boundaries 782 1. Boundary Conditions 782 2. Radiation Produced by a Charge Moving Along the Axis of a Cylindrical Dielectric- Filled Channel 783 3. Motion of a Point Charge Parallel to the Axis of a Channel in a Dielectric 788 4. Radiation Produced by a Dipole Moving Along the Axis of a Cylindrical Channel 789 5. Cerenkov Radiation in Linear Periodic Structures 791 a) General Theory 791 b) Radiation of a Charge in an Iris-Loaded Waveguide 792 6. Cerenkov Radiation in Waveguides 793 a) Waveguide Filled with an Isotropic Dielectric 794 b) Waveguide Partially Filled with an Isotropic Dielectric 795 c) Waveguide Filled with an Anisotropic Dielectric 796 7. Field Produced by a Charged Particle Moving Parallel to the Boundary Between Two Media 799 Literature References 804

S. Geschwind

Papers

Čerenkov Effect at Microwave Frequencies

Limiting Sensitivity of a Microwave Spectrometer

Microwave Measurements on the Stable Selenium Isotopes in OCSe

Determination of atomic masses by microwave spectroscopy

Polarization of the Nucleus by Electric Fields