We improve the Mermin-Penn algorithm (MPA) for determining the energy loss function (ELF) within the dielectric formalism. The present algorithm is applicable not only to real metals, but also to materials that have an energy gap in the excitation spectrum. Applying the improved MPA to liquid water, we show that the present algorithm is able to address the ELF overestimation at the energy gap, and the calculated results are in good agreement with experimental data.

We present an approach for introducing damping into the Penn algorithm by using the Mermin dielectric function instead of the Lindhard dielectric function. We find that for a damping of 1.5 eV, the electron inelastic mean free path calculated by the present algorithm for Al is in excellent agreement with experimental values in the energy range 5–9 eV. Meanwhile, for a damping of 2.0 eV, our result for Au is consistent with the GW+T ab initio calculation at several electronvolts. In particular, at an energy of 1 eV, our result for Au is 297 Å and lies within the range 220–330 Å obtained from measurements by ballistic electron emission microscopy.

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