Valence Electron Distribution Research Articles

Investigation of the Valence Electron Distribution in Mg‐Al Alloys

Investigation of the Valence Electron Distribution in Mg‐Al Alloys

Study of the Wurtzite-Type Binary Compounds. III. Valence Band Structure of BeO

The LCAO approximation is applied toward a description of the valence band in BeO, in which only the closed shell Be(1s)2O(2p)6 configuration is considered. Thus no account is taken of the deformation of the oxygen valence electron distribution by the polarization field along the c axis of the wurtzite-type crystal. The problem is solved along several lines of symmetry in the hexagonal brillouin zone. We find a band width of 18 ev with a depth of approximately 7 ev.

Fourier Coefficients of Crystal Potentials

A method is developed for the calculation of the Fourier coefficients of the electrostatic potential of a given distribution of valence electrons in a solid. The valence electron wave functions are expressed as combinations of orthogonalized plane waves. The treatment takes full account of the nonspherical character of the atomic polyhedron. Application is made to lithium.

Molecules with tetrahedral and octahedral symmetry

ABSTRACTThe modified Thomas-Fermi method reported in (2) has been applied numerically to calculate the distribution of valence electrons in CC14. Slater wave functions have been used to describe the Cl inner-shell electrons, whilst a description of the C ls electrons based on the Thomas-Fermi model for atoms has been adopted. The electron distribution thus found is compared with the two approximations discussed in part I of this series (3). The first of these, in which valence and inner-shell electrons are treated in the same way, is shown to give a distribution of valence electrons in good agreement with the present results. The second approximation, that of effective nuclear charges, is less satisfactory and could only lead to a distribution of valence electrons in reasonable agreement with the present work if the effective nuclear charges were considerably reduced. This seems to throw some light on the results of Bowers for the force constants of tetrachlorides and tetrabromides.The overall distribution of electrons obtained here seems to be the inevitable result of assuming the valence electrons to move in any plausible central field. It is, of course, by no means certain that such an approximation is near to the truth. In fact, the results of (3) and the present paper leave little doubt that the electron cloud obtained by such an approximate method will be too diffuse. This seems at least partly responsible for our finding that rather more than 20 of the 28 Cl valence electrons lie outside the sphere drawn through the Cl nuclei.

Molecules With tetrahedral and octahedral symmetry. IV. A modified Thomas–Fermi scheme for molecules with heavy atoms in the outer positions

ABSTRACTIn Part I of this series it was shown that for CCl4 the approximation of smoothing out the Cl nuclei over the surface of a sphere did not lead to reasonable results for the Thomas–Fermi distribution of electrons in the molecule. An alternative method in which the inner-shell Cl electrons were first compressed into the nuclei was not theoretically satisfactory because of the neglect of the exclusion principle. In this paper therefore a general scheme is presented in which we describe the inner-shell electrons of the outer atoms wave mechanically, assuming them to be undisturbed by molecular binding, but still use a Thomas–Fermi description for the valence electrons. A method by means of which the exclusion principle can be imposed is formulated. The following paper of the series deals with the application of the method described here to obtain an improved valence electron distribution in CCl4.

Evidence from Crystal Structures in Regard to Atomic Structures

The distribution of valence electrons in the diamond and similar crystals.---Because of the cubical symmetry, the equivalent scattering power of all the atoms, and the absence of pyro- and piezo-electric effect, the atoms in the diamond cannot be held together as a result of the transfer of electrons from atom to atom. Symmetry requirements also eliminate any cubical arrangement of electrons or orbits around each atom. The diamagnetism of ${\mathrm{H}}_{2}$ and of most organic compounds eliminates rotations of two electrons or orbits in the same direction about each atomic center-line as a means of holding the atoms together. Similar structures and numbers of valence electrons, together with interatomic distance comparisons, indicate that the atoms in BeO, ZnO, ZnS, CdS, AgI, etc., are held together in a manner similar to that in the diamond. If so, there cannot be four electrons rotating around each atomic kernel in the diamond, for ${\mathrm{Zn}}^{\ensuremath{-}\ensuremath{-}}$, ${\mathrm{Ag}}^{\ensuremath{-}\ensuremath{-}\ensuremath{-}}$, ${\mathrm{O}}^{++}$ etc., are chemically impossible. It is not possible for two electrons to be rotating about each two adjacent atomic kernels in crystals of NaCl, MgO, CdO, AgBr, etc., and since chemically and physically these are not very different from BeO, CdS, AgI, etc., the bonds in the last named crystals and so in the diamond are probably not of this type. The conclusion is therefore reached that in the diamond and crystals of similar structure, the electrons are in pairs at tetrahedron corners around each atom, each pair being held jointly by two atoms. This is as predicted from the Lewis theory of valence. A study of the other known crystal structures leads to the conclusion that in general the valence shells of electro-negative atoms are tetrahedra of electron pairs rather than cubes of single electrons.

Electromerism, a Case of Chemical Isomerism Resulting from a Difference in Distribution of Valence Electrons

Electromerism, a Case of Chemical Isomerism Resulting from a Difference in Distribution of Valence Electrons