The ionic structure of liquid sodium obtained by numerical simulation from ‘first principles’ and ab initio ‘norm-conserving’ pseudopotentials

Abstract

The physical properties of disordered matter depend on the ‘atomic structure’ i.e. the arrangement of the atoms. This arrangement is described by the structure factor S (q) in reciprocal space and by the pair correlation function g(r) in real space. The structure factor is obtained experimentally while the numerical simulation enables us to obtain the pair correlation function. Liquid sodium is one of the elements the most studied and one can wonder about new scientific contribution appropriateness. The majority of theoretical calculations are compared with the experiment of Waseda. However two other posterior measurements have been published and give different results, in particular with regard to the height of the first peak of the structure factor. Three models of pseudopotential are considered to describe the electron-ion interaction. The first is a local pseudopotential with the alternative known as ‘individual’ of the model suggested by Fiolhais et al. The second model considered is that of Bachelet et al. This one, ab-initio and ‘norm conserving’, is non local. The last model is that proposed by Shaw known as ‘first principles’ and ‘energy dependent’. Various static dielectric functions characteristic of the effects of exchange and correlation have been used and developed by Hellal et al. We calculated the form factors (pseudopotential in reciprocal space) and deduce the normalized energy-wave-number characteristic FN (q), the interatomic pair potential Veff (r), then the pair correlation function g(r) by molecular dynamics. The structure factor S(q) is obtained by Fourier transform and is compared with the experiment. Our calculations with the Bachelet and Shaw pseudopotentials are close to the last experiments of Greenfield et al. and of Huijben et al. Our results are discussed.