Formally `exact' first-order Taylor series expansion for density functional theory

Details Formally `exact' first-order Taylor series expansion for density functional theory Formally `exact' first-order Taylor series expansion for density functional theory

Jun 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002njph....4...36z&link_type=abstract

New Journal of Physics, Volume 4, Issue 1, pp. 36 (2002).

Physics

17

Scientific paper

The functional expansion of the non-uniform first-order direct correlation function (DCF) around the bulk density was truncated at the first order, then the functional counterpart of the Lagrangian theorem of differential calculus was employed to make the truncation formally exact. The actual procedure is as follows. According to the Lagrangian theorem and the definition of the DCF, the original expansion coefficient, i.e. the uniform second-order DCF, was replaced by the non-uniform second-order DCF whose argument is the appropriate mixture of the density distribution and the bulk density with an adjustable parameter determined by a hard-wall sum rule. With reference to an earlier paper (Khein A and Ashcroft N W 1999 Phys. Rev. E 59 1803), the non-uniform second-order DCF was then approximated by its uniform counterpart with a weighted density as its density argument. The truncated expansion was incorporated into the density functional theory formalism to predict the non-uniform hard-sphere fluid density distribution - in very good agreement with simulation data for three confining geometries: a single hard wall, a spherical cavity and a bulk hard-sphere particle whose resulting external potential leads to a radial distribution function of the bulk hard-sphere fluid whose prediction by the present theory was also in good agreement with the corresponding simulation data.

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