Range optimized theory of electron liquids with application to the homogeneous gas

A simple optimization scheme is used to compute the density-density response function of an electron liquid. Higher order terms in the perturbation expansion beyond the random phase approximation are summed approximately by enforcing the constraint that the spin density pair correlation functions be positive. The theory is applied to the 3-D homogeneous electron gas at zero temperature. Quantitative comparison is made with previous theory and data from quantum Monte Carlo simulation. When thermodynamic consistency is enforced on the compressibility, agreement with the available simulation data is very good for the entire paramagnetic region, from weakly to strongly correlated densities. In this case, the accuracy of the theory is comparable to or better than the best of previous theory, including the full GW approximation. In addition, it is found that the spin susceptibility diverges at a lower density ($r_s \approx 107$) than the current estimate for the liquid-solid transition. Application of the theory to inhomogeneous electron liquids is discussed.