Abstract
We study the energy gained for simple crystal structures by occupying the lower portion of tight-binding bands arising from one shell of atomic orbitals. We see that a Friedel model, based upon a rectangular density of states and the second moment of the bands, gives a reasonable account of the cohesive energy. It also predicts an equilibrium spacing proportional to the fourth root of the coordination but gives total energies independent of coordination. This depended upon an interatomic repulsion assumed to be proportional to the square of the interorbital coupling. When the variation in the repulsion is more rapid, as it tends to be lower in the periodic table, and in the simple metals, larger coordinations and simple close-packed structures are favoured. Going beyond this approximation, we find the energy lower when weakly coupled bond orbitals can be constructed, as for the [sgrave] bonds in tetrahedral semiconductors. Applying this correction to half-filled p bands favours the formation of right-angle [sgrave] bonds between three neighbours. This result, modified for the different filling of the p shell in the non-metal groups V, VI, VII and VIII of the periodic table, gives a good qualitative account of the observed structures. The same theory applied to half-filled f bands gives the same tendency for right-angle [sgrave] bonds, although for d bands it does not. Applying the theory to the light actinides, for fillings less than half, makes plausible the type of structures observed in plutonium and neptunium and is not inconsistent with those observed in uranium, protactinium and thorium.