T. P. Das

Tunneling through High Periodic Barriers. II. Application to Nuclear Magnetic Resonance in Solids

Analytic formulas derived in an earlier paper for the frequency of tunneling through high periodic barriers are here used to derive from nuclear magnetic resonance data in solids the heights of the potential barriers hindering the rotational motion of molecules. The rotations of CH3 groups, NH3+ groups, benzene, NH2 groups and water molecules of crystallization are considered. The use of the barrier heights in correcting for the effect of torsional vibrations of molecules on molecular dimensions obtained from nuclear magnetic resonance data is illustrated. A possible explanation of an isotropic part of the splitting of the proton resonance in Li2SO4·H2O, reported earlier by Pake, is presented. Comments are made on the relative magnitudes of the barrier heights in the different molecules considered.

Simple Evaluation of the Paramagnetic Part of the Proton Magnetic Shielding Constant

General arguments are proposed to show that the second‐order paramagnetic susceptibility of a molecule is a minimum when the origin of the magnetic vector potential is chosen at the electronic centroid. It is shown that with this choice of gauge, it is possible to evaluate a major portion of the paramagnetic part of the proton magnetic‐shielding constant from a knowledge of the dipole moment, bond distances, and bond angles of the molecule alone. This formulation is applied to the molecules H2, HF, HCl, HBr, HI, LiH, HCN, C2H2, CH4, and NH3. Good agreement is obtained when the results are compared with available data from molecular‐beam experiments.

Crystalline Fields in Corundum‐Type Lattices

Dipole moments of the deformable O2— ions in the corundum‐type crystals Al2O3, Cr2O3, and Fe2O3 are calculated self‐consistently. The magnitudes and signs of the dipole moments depend sensitively on the crystal parameters and vary widely over the series Al2O3, Cr2O3, and Fe2O3. Using the calculated dipole moments, the dipolar contributions to the crystalline components B10, B20, B30, B33, C33, B40, B43, and C43 have been calculated at the metal ion sites. The dipolar contributions are found to be substantial and in some cases to alter the sign of the crystalline field components obtained from point charges alone. The modified values of B20, B40, and B43 are used to obtain expressions for the optical parameters v, v′, and Dq in terms of the expectation values 〈r2〉 and 〈r4〉 for the d electrons of Cr3+ ions in Cr2O3 and ruby, and Fe3+ ions in Fe2O3 and sapphire. The coefficients of 〈r4〉 in the expressions for v and v′ are substantially altered on including the effect of the dipoles. The effect of the dipoles...

Molecular Orbital Theory of Sulfur and Selenium Radicals

The electronic structures of various sulfur and selenium radicals were studied by semiempirical molecular orbital theory in the form of a parameter theory. The ESR data (g values) were used to determine the actual value of the parameter α, which is the coefficient of the s orbital in the bonding hybrid of the S(Se) atom in the radical. The physical significance of α so determined was studied by investigating some quantum chemical quantities such as valence state energies Ev and bond strengths B as functions of α. As a result, a criterion for the determination of the parameter value was deduced, namely, the selection of that value of α which maximizes B2 | Ev |.From theoretical considerations and experimental data in the literature, the relative signs of the principal values of the hyperfine‐structure tensor of selenium were determined, and the magnitudes of the isotropic and anisotropic components were evaluated.

NUCLEAR MAGNETIC SHIELDING OF ALKALI IONS IN CRYSTALS AND DILUTE AQUEOUS SOLUTIONS

The formulation for the Kondo—Yamashita overlap mechanism for the nuclear magnetic shielding in alkali halides developed earlier, is applied to the rubidium nucleus in RbCl, RbBr, and RbI crystals. The pertinent average energy denominators of perturbation theory are obtained using experimental pressure data on the magnetic shielding. Using these energy denominators, the calculated values of σRb, the chemical shifts for the rubidium nucleus in the crystal with respect to the free ion, are −2.17×10−4, −2.14×10−4, −2.11×10−4 for RbCl, RbBr, and RbI, respectively. When combined with Barons experimental data on the chemical shifts with respect to dilute aqueous solutions, we obtain for σRbaq, which represents the chemical shift between the Rb+ ion in aqueous solution and the free ion, the values −0.88×10−4, −0.63×10−4, −0.60×10−4 from the RbCl, RbBr, and RbI data, respectively. These values are in fair agreement with the result σRbaq=−0.65×10−4 that we have derived using a model of six oriented water molecule...

Magnetic Properties of Hydrogen Fluoride. II. Susceptibility

A method is outlined for the calculation of the magnetic susceptibility χ from the ground‐state wave function of 1Σ molecules. The diamagnetic contribution χd is obtained directly by first‐order perturbation theory and the paramagnetic contribution χp is determined by a variational technique based on minimizing the second‐order energy in an external magnetic field. When applied to an SCF—LCAO—MO function for hydrogen fluoride, the theoretical result is 〈χ〉Av=—8.74×10—6 erg gauss—2 mole—1, in excellent agreement with the experimental value of —8.6×10—6 erg gauss—2 mole—1. The separate contributions, with respect to the fluorine as origin, are somewhat more in error, with 〈χd〉Av=—9.58×10—6 erg gauss—2 mole—1 (exp: —9.2×10—6 erg gauss—2 mole—1) and 〈χp〉Av=0.855×106 erg gauss—2 mole—1 (exp: 0.609×10—6 erg gauss—2 mole—1, as obtained from the rotational magnetic moment). For the isoelectronic atoms F— and Ne (in which there is only a diamagnetic term), analytic Hartree‐Fock functions yield 〈χ〉Av values equal t...

Calculation of the Spin‐Spin and Spin‐Orbit Contribution to the Zero‐Field Splitting in Hemin

Earlier theoretical studies of the electronic structure of hemin [iron (III) protoporphyrin (IX) chloride] have been extended to include calculation of both the spin‐spin and spin‐orbit contributions to the observed zero‐field splitting in this molecule. The wavefunctions used for the calculations were obtained by the self‐consistent‐charge extended Huckel method. The iron‐based one‐center spin‐spin result for D is 0.0407 cm‐1. The two‐center spin‐spin contribution to D is 0.0345 cm‐1, and is dominated by chlorine‐3p‐iron‐3d interactions. The total spin‐spin result (0.0752 cm‐1) is much smaller than the observed zero‐field splitting of 6.95 cm‐1, and the major contribution is shown to arise from spin‐orbit effects. The spin‐orbit contribution is large and strongly dominant because of the low‐lying 4A2 electronic state in hemin. The accuracy of the spin‐orbit calculation is limited by difficulties in calculating the energy of excitation to the 4A2 state, but, with reasonable choices of parameters in terms ...

Remarks on the Determination of Electric Dipole Moments from Rotational Magnetic Moments. The Dipole Moment of Hydrogen Fluoride

The determination of electric dipole moments from isotopic variations of the rotational magnetic moment is considered. It is pointed out that appreciable errors in the dipole moment can result if one neglects the effects of vibrational motion on the high‐frequency part of the magnetic susceptibility. Thus, a current discrepancy in the dipole moment of HF determined from the rotational magnetic moments of HF and DF and by the molecular beam electric resonance method is resolved by such vibrational corrections. When these vibrational corrections are made, the dipole moment of HF as determined from the rotational magnetic moments of HF and DF is 1.83±0.05 D (H+F—) instead of 1.65 D, and is in good agreement with the value of 1.818±0.008 D obtained by electric resonance.

Core polarization contributions to hyperfine effects of paramagnetic centers in ionic crystals

Abstract The theory for exchange core polarization in hyperfine interactions is formulated using the moment perturbation method for the case when the original basis functions are not orthogonal. Such a situation is typical of a wide variety of paramagnetic systems in the solid state, such as color centers and iron group ions in ionic crystals. The procedure consists of collecting terms proportional to μ N in the total energy, including both one- and two-electron operators in the total Hamiltonian. After some manipulation, the core polarization contribution is shown to have the same form as for the orthogonal case with the valence orbital orthogonalized to the unperturbed core wavefunctions. We have applied our analysis to an example, namely the F-center in LiF. A positive contribution from the core polarization was found for both the isotropic and anisotropic hyperfine constants of the nearest neighbor Li + ions adding to the direct effects from overlap in both cases.