Albert Sherman

Binding Energies in the Growth of Crystal Nuclei from Metallic Atoms

First order perturbation theory has been employed to compute the binding energies of various geometrical configurations of three to eight atoms of sodium. It has been assumed that in the metal lattice the binding is essentially homopolar. It has been shown that the growth of a unit cell probably proceeds via the diatomic molecule to a square, a fifth atom adding along a cube edge, a sixth at the body center and the cell completed by location of atoms at the remaining cube corners. The unit cell is still a very unstable unit, a result in agreement with high vapor pressures and solubility of finely divided particles, and with the concept of active centers on reaction surfaces. The fifth order secular equation employed to determine the energies of configurations of five and six atoms has been made more amenable to use in calculations. A fourteenth order secular equation, with similar characteristics, has been employed for the cases of seven and eight atoms. Approximate calculations with copper atoms instead ...

Addition of Symmetrical Diatomic Molecules to Benzene

The reaction of hydrogen and benzene to form 1,2‐dihydrobenzene is considered, and the activation energy of the reaction is calculated with various assumptions concerning directed valence. It is shown that one may calculate approximate heats of reactions by considering exchange integrals only between electrons on neighboring atoms in a molecule, but this is not possible in calculating activation energies. The hydrogenation of benzene is considered as an eight electron problem, and the system serves to illustrate the degree of simplification of the secular equation arising from the symmetry of the system. The matrix elements of the factored equation are calculated. Activation energies of the reactions involved in the adsorption of H2 and C6H6 on Ni have been calculated and lead one to expect that the reaction might be achieved more easily catalytically.

On the Symmetric States of Atomic Configurations

In the secular equations used by Eyring and his school the equations are of high order in general. When cognizance is taken of the symmetry of the configuration considered the secular equation may factor considerably. It is to be expected that the wave function for the lowest state will be invariant under the group which expresses the symmetry of the atomic configuration. This expectation is fulfilled in all cases considered. A general method is set forth upon which a derivation of such symmetric states may be carried out, and the reduced secular equation obtained. Several interesting applications of this method are carried through, including the case of eight identical orbits, centered at the corners of a cube, and eight orbits possessing tetrahedral symmetry, as in methane. The vector model is discussed and applied to the cases considered.

The Quantum Mechanics of Chemical Reactions Involving Conjugate Double Bonds

The various theories of conjugate double bonds are discussed on the basis of quantum mechanics. The potential energy surfaces for the addition of diatomic molecules to such bonds are calculated by the generalized Heitler‐London method. It is shown that various mechanisms are possible for such reactions and that such effects as the steric repulsions of the various inactive groups in the molecule and the nature of the catalytic surface on which such reactions often take place determine whether 1–2 or 1–4 addition takes place.