Coupled-cluster expansion applied to the electron gas: Inclusion of ring and exchange effects

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Abstract
The coupled-cluster expansion (or the Coester-Kümmel-Čižek method) is applied to the correlation problem in the uniform electron gas. Coupled nonlinear integral equations are developed for ring summations and the analytic structure of the expansion coefficients is examined. To facilitate the solution of the equations a technique is introduced to reduce the dimensionality of the problem. Numerical solution of the equations enable the evaluation of both ring and exchange effects. The direct random-phase-approximation (RPA) energy agrees with other work to the accuracy of the calculation. The screened exchange energy is evaluated for the first time and contributes about 30% of the RPA energy. The resulting correlation energy compares favorably with recent calculations using a dielectric formulation over the range of metallic electron densities.