Previous calculation of the ground‐state energy of H2 has been extended to include large internuclear distances and accurate potential‐energy curve for 0.4≤R≤10.0 a.u. is presented. For 0.4≤R≤4.0 a.u. expectation values of several operators have also been calculated. The calculation was made using a wavefunction in the form of an expansion in elliptic coordinates. The wavefunction depends on the interelectronic distance but, in contrast to the James—Coolidge expansion, is flexible enough to describe properly the dissociation of the molecule. Extensive calculations have also been made for the repulsive 3Σu+ state (1.0≤R≤10.0) and for the 1Πu state (1.0≤R≤10.0). In the former case a van der Waals minimum has been found at R=7.85 a.u. and 4.3 cm−1 below the dissociation limit. For the 1Πu state the computed binding energy De=20 490.0 cm−1 and the equilibrium internuclear distance Re=1.0330 A are in a satisfactory agreement with the experimental values De=20 488.5 cm−1 and Re=1.0327 A. In this case a van der ...

Potential‐Energy Curves for the X 1Σg+, b3Σu+, and C 1Πu States of the Hydrogen Molecule

Publisher Summary In an idealized picture, an ionic crystal is regarded as composed of spherical, nonoverlapping ions, bearing net charges of integral amount. The electrostatic interactions of these pointlike charges give rise to a net binding (Madelung energy), as each ion is preferentially surrounded by ions of opposite charge. In typical ionic crystals, the Madelung energy is in fact quite close to the observed cohesive energy. The Born model was originally proposed for the purpose of evaluating the lattice energy of crystals, which approach this idealized picture, and because of its success and simplicity it has subsequently been applied to the description of a variety of physical properties of ionic crystals, with varying degrees of success. In the framework of the Born model, it is convenient to describe the lattice energy of an ionic crystal as composed of energy terms arising from interactions between the ions. In addition to the net binding provided by the electrostatic interactions of point-like ionic charges, the binding arising from a synchronization of the electronic motions in the ions is considered explicitly in some versions of the model. The contribution of this so-called “van der Waals interaction” to the lattice energy is small, of the order of a few per cent. The ratio between the polarization energy that is connected with the mutually induced electronic dipoles on a pair of ions and the Coulomb interaction energy of the net charges of the ions is definitely less than the ionic polarizability per unit volume. The attractive forces in the crystal are balanced by the so-called overlap repulsive forces, which oppose the interpenetration of the ions.

Cohesion of Ionic Solids in the Born Model

Permanent and Induced Molecular Moments and Long‐Range Intermolecular Forces

Van der waals forces

Values of the diamagnetic anisotropy of benzene and other aromatic hydrocarbon molecules are calculated on the basis of the assumption that the p_z electrons (one per aromatic carbon atom) are free to move from carbon atom to adjacent carbon atom under the influence of the impressed fields. When combined with the assumed values for the contributions of the other electrons (‐2.0×10^(‐6) for hydrogen, ‐4.5×10^(‐6) for aromatic carbon, ‐6.0×10^(‐6) for aliphatic carbon) these lead to principal diamagnetic susceptibilities of molecules in approximate agreement with the available experimental data. The diamagnetic anisotropy of graphite is also discussed.

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The Diamagnetic Anisotropy of Aromatic Molecules

The Dependence of Interatomic Distance on Single Bond-Double Bond Resonance1

The van der Waals interaction energy of two hydrogen atoms at large internuclear distances is discussed by the use of a linear variation function. By including in the variation function, in addition to the unperturbed wave function, 26 terms for the dipole-dipole interaction, 17 for the dipole-quadrupole interaction, and 26 for the quadrupole-quadrupole interaction, the interaction energy is evaluated as ${W}^{\ensuremath{'}\ensuremath{'}}=\ensuremath{-}\frac{6.49903{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{6}}\ensuremath{-}\frac{124.399{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{8}}\ensuremath{-}\frac{1135.21{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{10}}\ensuremath{-}\ensuremath{\cdots},$ in which $\ensuremath{\rho}=\frac{R}{{a}_{0}}$, with $R$ the internuclear distance. Some properties of the functions ${F}_{\ensuremath{\nu}\ensuremath{\lambda}\ensuremath{\mu}}(\ensuremath{\xi},\ensuremath{\vartheta},\ensuremath{\phi})$, which are orthogonal for the volume element $\ensuremath{\xi}d\ensuremath{\xi}sin\ensuremath{\theta}d\ensuremath{\theta}d\ensuremath{\phi}$, are discussed, and their usefulness in atomic problems is pointed out.

J. Y. Beach

Papers

The Dependence of Interatomic Distance on Single Bond-Double Bond Resonance1

The van der Waals Interaction of Hydrogen Atoms

The Electron Diffraction Investigation of Phosgene, the Six Chloroethylenes, Thiophosgene, α-Methylhydroxylamine and Nitromethane1