Correlation energy of a two-dimensional electron gas

Extending the Hedin-Lundqvist approximation, originally developed for the three-dimensional electron gas, we derive the correlation energy ${\mathit{E}}_{\mathit{c}}$ for the two-dimensional electron gas as a function of electron density ρ. A simple two-parameter function ${\mathit{E}}_{\mathit{c}}$(ρ) reproduces very well the first-principles numerical results in the whole density range. We also present a simple and accurate form of the correlation part of the chemical potential, which can be used, e.g., as a correlation part of the effective potential in the local-density approximation for two-dimensional electron systems.