The x‐ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom. These factors may be better suited for the least‐squares refinement of x‐ray diffraction data from organic molecular crystals than those for the isolated hydrogen atom. It has been shown that within the spherical approximation for the bonded hydrogens in H2, a least‐squares refinement of the atomic positions will result in a bond length (Re value) short of neutron diffraction or spectroscopic values. The spherical atoms are optimally positioned 0.07 A off each proton into the bond. A nonspherical density for the bonded hydrogen atom in the hydrogen molecule has also been defined and the corresponding complex scattering factors have been calculated. The electronic density for the hydrogen molecule in these calculations was based on a modified form of the Kolos—Roothaan wavefunction for H2. Scattering calculations were made tractable by expansion of a plane wave in spheroidal wavefunctions.

Coherent X‐Ray Scattering for the Hydrogen Atom in the Hydrogen Molecule

A new approximate ``absolute'' scale of electronegativity, or electroaffinity, is set up. The absolute electroaffinity on this scale is equal to the average of ionization potential and electron affinity. These quantities must, however, in general, be calculated not in the ordinary way, but for suitable ``valence states'' of the positive and negative ion. Also, the electroaffinity of an atom has different values for different values of its valence; in general the electroaffinity as here calculated (in agreement with chemical facts) is larger for higher valences. Electroaffinity values have been calculated here for H, Li, B, C, N, O, F, Cl, Br, I. They show good agreement in known cases with Pauling's electronegativity scale based on thermal data, and with the dipole moment scale. The present electronegativity scale (like the others) is rather largely empirical, especially as to its quantitative validity; and it remains to be seen whether or not the latter will be more than very rough when tested for a wider range of cases. Nevertheless the new scale has a degree of theoretical background and foundation which throws some new light on the physical meaning of the concept of electronegativity (or electro‐affinity). The basis of the present scale, it should be mentioned, is simpler and more certain for univalent than for polyvalent atoms.—The nature of valence states of atoms is briefly discussed. It is hoped that the tabulations of atomic valence state energies and valence state ionization potentials and electron affinities given at the end of this paper may be useful in problems of molecular structure.

A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities

An analytic semiempirical expression is developed for the ground‐state potential‐energy surface of the H3 system. Use is made of the valence‐bond formulation with the inclusion of overlap and three‐center terms. The diatomic Coulomb and exchange integrals are estimated from accurate values for the H2 molecule by a modified London—Eyring—Sato procedure, while the three‐center integrals are approximated by simple formulas. A linear, symmetric saddle‐point configuration of minimum energy is found that has properties in approximate agreement, though not identical, with other estimates from theory and experimental rate data. The details of the surface are presented in terms of contour maps for a variety of distances and angles. Because of the inclusion of overlap and three‐center terms, a more realistic energy is expected for the nonlinear configurations than could be obtained from previous potential energy formulas. The utility of the present method for dynamical studies of reaction cross sections is indicated.

Potential Energy Surface for H3

Theory of Orientation and Stereoselection

The current state of the theory and its application to low-energy electron-molecule collisions is reviewed. The emphasis is on elastic scattering and vibrational and rotational excitation of small diatomic and polyatomic molecules. New and traditional theoretical approaches are described, and the results of calculations are compared with existing experimental measurements.

The theory of electron-molecule collisions

A simple wave function for the normal state of the hydrogen molecule, in which both the atomic and ionic configurations are taken into account, was set up and treated by a variational method. The dissociation energy was found to be 4.00 v.e. as compared to the experimental value of 4.68 v.e. and Rosen's value of 4.02 v.e. obtained by use of a function involving complicated integrals. It was found that the atomic function occurs with a coefficient 3.9 times that of the ionic function. A similar function with different screening constants for the atomic and ionic parts was also tried. It was found that the best results are obtained when these screening constants are equal. The addition of Rosen's term to the atomic‐ionic function resulted in a value of 4.10 v.e. for the dissociation energy.

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The Normal State of the Hydrogen Molecule

A variation function constructed of hydrogen‐like 1s functions with different values of the effective nuclear charges for He: and He.+ is used in the treatment of the normal state of the helium molecule‐ion. The treatment leads to the values De=2.22 e.v. and re=1.097A for the dissociation energy and the internuclear distance, in good agreement with the experimental values.

Sidney Weinbaum

Papers

The Normal State of the Hydrogen Molecule

The Normal State of the Helium Molecule Ion, He2+