Many-body dispersion in model systems and the sensitivity of self-consistent screening

London dispersion is a weak, attractive, intermolecular force that occurs due to interactions between instantaneous dipole moments. While individual dispersion contributions are small, they are the dominating attractive force between nonpolar species and determine many properties of interest. Standard semi-local and hybrid methods in density-functional theory do not account for dispersion contributions, so a correction such as the exchange-hole dipole moment (XDM) or many-body dispersion (MBD) models must be added. Recent literature has discussed the importance of many-body effects on dispersion, and attention has turned to which methods accurately capture them. By studying systems of interacting quantum harmonic oscillators from first principles, we directly compare computed dispersion coefficients and energies from XDM and MBD and also study the influence of changing oscillator frequency. Additionally, the 3-body energy contributions for both XDM, via the Axilrod-Teller-Muto term, and MBD, via a random-phase approximation formalism, are calculated and compared. Connections are made to interactions between noble gas atoms as well as to the methane and benzene dimers and to two layered materials, graphite and MoS2. While XDM and MBD give similar results for large separations, some variants of MBD are found to be susceptible to a polarization catastrophe at short range, and the MBD energy calculation is seen to fail in some chemical systems. Additionally, the self-consistent screening formalism used in MBD is shown to be surprisingly sensitive to the choice of input polarizabilities.