Attaining a reliable complete basis set (CBS) limit remains a significant challenge in ab initio correlated electronic-structure calculations. Building on our previous work for atoms and diatomic molecules, we present a finite-element (FE) Delta-Sternheimer approach for numerically accurate random-phase approximation (RPA) calculations applicable to general molecules. This approach seamlessly integrates atomic orbital basis sets with FE grids, enabling an arbitrarily precise representation of the first-order variation of the wave function. As a result, the density response function and RPA correlation energies can be computed with fully controlled numerical precision. The Delta-Sternheimer approach thus provides direct access to RPA correlation energies at the CBS limit, eliminating reliance on conventional extrapolation schemes. We apply this approach to two problems: The energy hierarchy of 20 water-dimer configurations and the atomization energies of 50 molecules from the G2 set. For the water dimer, we examine the basis set dependence of the isomer energy ordering. For the G2 set, we investigate the residual numerical uncertainty in the conventional extrapolated CBS limit, both with and without correction for basis-set superposition error.

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• Electronic structure
• Electronic structure of atoms & molecules
• Density functional theory
• Electron-correlation calculations
• Random phase approximation