Band structures for solid rare gases ͑Ne, Ar͒ have been calculated using the GW approximation. All electron and pseudopotential ab initio calculations were performed using Gaussian orbital basis sets and the dependence of particle-hole gaps and electron affinities on basis set and treatment of core electrons is investigated. All electron GW calculations have a smaller particle-hole gap than pseudopotential GW calculations by up to 0.2 eV. Quasiparticle electron and hole excitation energies, valence bandwidths and electron affinities are generally in very good agreement with those derived from optical absorption and photoemission measurements.

Absorption spectra, exciton energy levels and wave functions for solid Ne and Ar have been calculated from first principles using many-body techniques. Electronic band structures of Ne and Ar were calculated using the GW approximation. Exciton states were calculated by diagonalizing an exciton Hamiltonian derived from the particle-hole Green function, whose equation of motion is the Bethe-Salpeter equation. Singlet and triplet exciton series up to n = 5 for Ne and n = 3 for Ar were obtained. Binding energies and longitudinal-transverse splittings of n = 1 excitons are in excellent agreement with experiment. Plots of correlated electron-hole wave functions show that the electron-hole complex is delocalised over roughly 7 a.u. in solid Ar.

The inverse dielectric function and response function are key quantities in the dielectric response of materials. The Hermitian, inverse dielectric function can be diagonalised to yield the dielectric band structure (DBS) and a set of eigenpotentials for a crystalline solid. The response function can also be diagonalised to yield a set of eigenfunctions which are similar in character to the eigenpotentials for the solid. The DBS and response functions of argon and silicon are calculated and analysed. The most important eigenpotentials of solid argon and silicon are atom-centred monopolar and dipolar functions for argon and atom-centred monopolar and dipolar functions and bond-centred dipolar functions for silicon. These ab initio calculations provide insight into the success of discrete dipole models for optical properties of semiconductor surfaces.

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