To probe the dynamic nature of the hydrogen bond network in water, linear and nonlinear infrared spectra of dilute HOD in H2O are computed from many-body molecular dynamics simulations with the MB-pol potential, which have been shown to accurately predict the properties of water from the gas to the condensed phase. The effects of various approximations to the many-body expansion of the dipole moment surface on the OD-stretch absorption line shapes are analyzed at different levels of theory. The interplay between effects associated with the variation of the HOD dipole moment and instantaneous nuclear configurations causes qualitative differences in the absorption profiles, which are traced back to how induction contributions are treated within the many-body formalism. Further analysis of the multidimensional infrared spectra demonstrates that the spectral diffusion of the OD stretching frequencies depends explicitly on the level of truncation in the many-body expansion of the dipole moment in the short-time regime that is associated with intact hydrogen-bond dynamics. In contrast, the long-time evolution of spectral diffusion, describing collective rearrangements of the hydrogen-bond network, is effectively independent of the details with which many-body contributions to the dipole moment are represented.
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