Local-Density Correlation Functional from the Force-Balance Equation.

The force-balance equation of time-dependent density-functional theory presents a promising route toward obtaining approximate functionals; however, so far, no practical correlation functionals have been derived this way. In this work, starting from a correlated wave function proposed originally by Colle and Salvetti [Theoret. Chim. Acta 37, 329 (1975)], we derive an analytical correlation-energy functional for the ground state based on the force-balance equation. The new functional is compared to the local-density correlation of the homogeneous electron gas, and we find an increased performance for atomic systems, while it performs slightly worse on solids. From this point onward, the new force-based correlation functional can be systematically improved.