Accurate Total Energies from the Adiabatic-Connection Fluctuation-Dissipation Theorem

In the context of inhomogeneous one-dimensional finite systems, recent numerical advances [Phys. Rev. B 103, 125155 (2021)] allow us to compute the exact coupling-constant dependent exchange-correlation kernel $f^\lambda_\text{xc}(x,x',\omega)$ within linear response time-dependent density functional theory. This permits an improved understanding of ground-state total energies derived from the adiabatic-connection fluctuation-dissipation theorem (ACFDT). We consider both `one-shot' and `self-consistent' ACFDT calculations, and demonstrate that chemical accuracy is reliably preserved when the frequency dependence in the exact functional $f_\text{xc}[n](\omega=0)$ is neglected. This performance is understood on the grounds that the exact $f_\text{xc}[n]$ varies slowly over the most relevant $\omega$ range (but not in general), and hence the spatial structure in $f_\text{xc}[n](\omega=0)$ is able to largely remedy the principal issue in the present context: self-interaction (examined from the perspective of the exchange-correlation hole). Moreover, we find that the implicit orbitals contained within a self-consistent ACFDT calculation utilizing the adiabatic exact kernel $f_\text{xc}[n](\omega=0)$ are remarkably similar to the exact Kohn-Sham orbitals, thus further establishing that the majority of the physics required to capture the ground-state total energy resides in the spatial dependence of $f_\text{xc}[n]$ at $\omega = 0$.