Determination of the Surface Energy of a Metal by Molecular Orbitals

The electronic binding energy of a monovalent metal is calculated by means of the molecular approximation for the simple cubic lattice in one, two and three dimensions, and for the body-centred cubic lattice, in terms of the resonance integral β. The corresponding surface energy is deduced in each case. The effects of various improvements in the approximation are estimated, namely the inclusion of the overlap integral, the inclusion of next-nearest-neighbour interaction, and the modification of the coulomb terms of surface atoms due to their special environment. The bond orders in the neighbourhood of the surface are determined and the relation between them and the binding energy is discussed. Numerical values of the surface tensions of the alkali metals are calculated and compared with previous results. It is found that the theory underestimates the surface tension by a factor of about 2, and it is concluded that the coulomb term modification is the most important of the corrections studied.