Electronic Coupling Interactions Research Articles

Electron Coupled Interaction in Solid Iodine

Hyperfine structure in the nuclear quadrupole resonance spectrum of solid iodine observed by Kojima, Ogawa, Hagiwara, Abe and Minematsu is analysed in terms of electron coupled interaction between nuclear spins. Theoretical expression for the Hamiltonian of the electron coupled interaction between two nuclei in an iodine molecule is derived, having the form of J I A z I B z + K ( I A x I B x + I A y I B y ), where z is the bond axis. Electron coupled interactions between nuclei belonging to different molecules in the crystal are neglected. Values of the coupling constants J and K are determined to be both equal to 3.0 kc from the comparison with the experimental data. Electronic structure of the chemical bond is discussed on the basis of the above coupling constants in combination with the previously known quadrupole coupling constants. It is concluded that the bond in an iodine molecule has 22% s character and 33% d character. It is also concluded that there are auxiliary bonds between neighboring molecu...

Nuclear Magnetic Interactions in the HF Molecule

Magnetic relaxation times of hydrogen and fluorine in anhydrous hydrofluoric acid cannot be accounted for on the assumption of a pure dipole-dipole interaction between the hydrogen and the fluorine nuclei in the same molecule. However, the introduction, in the Hamiltonian, of a scalar term AI·S resulting from the indirect electron-coupled interaction between the two nuclei removes all the discrepancies between the calculated and observed decay times. Although the splitting due to this scalar term is smeared out by the rapid chemical exchange of the protons with the traces of water present in the acid, the nuclear Overhauser effect provides the extra parameter required to separate the dipole-dipole interaction from the scalar interaction and to calculate separately the scalar splitting and the exchange rate of the protons. The value obtained for the splitting is A/h=615 cps. The same method has been applied to investigate the structure of the HF molecule in solutions. The experimental results can be explained qualitatively by the following picture: (a) The fluorine nuclei form long chains that move more slowly than the Larmor frequency of fluorine. (b) The chemical exchange with the relatively large quantity of water present makes the motion of the hydrogen nuclei fast with respect to the hydrogen Larmor frequency. The results are: Long relaxation times for hydrogen with T1 and T2 equal, relatively short relaxation times for fluorine resonance, with T2 shorter than T1. Solutions of salts of hydrofluoric acid (KF) show the same character as solutions of the acid.

Molecular Orbital Approximation to Electron Coupled Interaction between Nuclear Spins

The general formulas obtained by Ramsey for the indirect second-order magnetic coupling of nuclear spins by electron spin and orbital magnetic moments in 1Σ molecules are used together with an antisymmetrized product of molecular spin orbitals to obtain a set of general equations for nuclear spin couplings which only involve (a) the individual molecular orbitals, and (b) rotationally invariant one and two electron space operators. By approximating the molecular orbitals with linear combinations of atomic orbitals quite tractable formulas are obtained for ``long-range'' nuclear spin-spin couplings, i.e., couplings between nuclei separated by two, three, or more bond lengths. The application of these formulas are illustrated by the development of an approximate formula for proton-proton coupling constants in terms of interproton bond orders, the application of this formula to methane, as well as some qualitative considerations of F19—F19 coupling constants in tetrafluoroethylene. In general nuclear spin couplings between protons not directly bonded to one another arises primarily through hyperfine interactions between protons and pairs of electron spins. In hydrocarbons long-range bond orders between protons, ηHH′, can be estimated from observed proton spin couplings by the equation, ηHH′2 = 0.5 × 10—2 JHH′ (in sec—1). In fluorocarbons (and probably many other substances) nuclear couplings are due to the combined effects of hyperfine electron orbital and electron spin interactions with F19 nuclei. Electron exchange effects are important for both two-electron spin and orbital contributions to nuclear coupling.

Electron Coupled Interactions between Nuclear Spins in Molecules

In addition to the direct magnetic interaction between two nuclear spins in a molecule, the nuclei can have an effective mutual interaction as a result of the magnetic interactions between each of the nuclei and the electrons of the molecule. Although these indirect interactions are in general small, they are important in many cases, particularly as a result of the fact that the frequent collisions which characterize most nuclear paramagnetic resonance experiments cause the direct interaction to average to zero while this is not so for the indirect. In the present paper, the indirect interactions are evaluated. Contributions arise from a simple diamagnetic term, a closely related second-order orbital paramagnetism term, and terms due to the magnetic interaction of the nuclei with the electron spins. Expressions for each of these terms are given both for the general case and for the spherically symmetric case which arises when there are many collisions. Specific numerical calculations of the various effects are given for hydrogen deuteride. It is shown for HD that the diamagnetic terms are of the order of a few tenths of a cycle per second. On the other hand, if the suitable mean energy of the molecular excited states is given the reasonable value of 1.4 Rydbergs, the electron spin terms are 43 cps in agreement with experiment.