Liquid theory for band structure in a liquid. II. p orbitals and phonons

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Abstract
Surprisingly, the ground‐state quantum mechanical problem of calculating the set of single‐electron states available to a liquid (its electronic band structure) can be turned into an exercise in ordinary classical liquid theory. We generalize our previous findings by showing that this statement continues to hold for bands constructed from a basis of atomic p orbitals and we use this idea to provide a simple mean field theory useful for p bands in liquids. In addition, there is a natural way of thinking about the normal modes of vibration of a liquid (its phonons) that is accessible through virtually the same formalism. We discuss the significance of these ‘‘instantaneous normal modes’’ and show that the same kind of mean field theory is helpful in understanding both this phonon spectrum and its implications for liquid‐state dynamics.