Abstract
We construct analytic formulas that represent the coupling-constant-averaged pair distribution function of a three-dimensional nonrelativistic ground-state electron gas constrained to a uniform density with density parameter and relative spin polarization over the whole range and with energetically unimportant long range oscillations averaged out. The pair distribution function at the physical coupling constant is then given by differentiation with respect to Our formulas are constructed using only known theoretical constraints plus the correlation energy and accurately reproduce the of the quantum Monte Carlo method and of the fluctuation-dissipation theorem with the Richardson-Ashcroft dynamical local-field factor. Our is correct even in the high-density and low-density limits. When the spin resolution of into and contributions is known, as it is in the high- and low-density limits, our formulas also yield the spin resolution of Because of these features, our formulas may be useful for the construction of density functionals for nonuniform systems. We also analyze the kinetic energy of correlation into contributions from density fluctuations of various wave vectors. The exchange and long-range correlation parts of our are analytically Fourier transformable, so that the static structure factor is easily evaluated.
- Received 10 June 2002
DOI:https://doi.org/10.1103/PhysRevB.66.165118
©2002 American Physical Society