  Infrared spectroscopy is key to elucidate molecular structures, monitor
reactions and observe conformational changes, while providing information on
both structural and dynamical properties. This makes the accurate prediction of
infrared spectra based on first-principle theories a highly desirable pursuit.
Molecular dynamics simulations have proven to be a particularly powerful
approach for this task, albeit requiring the computation of energies, forces
and dipole moments for a large number of molecular configurations as a function
of time. This explains why highly accurate first principles methods, such as
coupled cluster theory, have so far been inapplicable for the prediction of
fully anharmonic vibrational spectra of large systems at finite temperatures.
Here, we push cutting-edge machine learning techniques forward by using neural
network representations of energies, forces and in particular dipoles to
predict such infrared spectra fully at "gold standard" coupled cluster accuracy
as demonstrated for protonated water clusters as large as the protonated water
hexamer, in its extended Zundel configuration. Furthermore, we show that this
methodology can be used beyond the scope of the data considered during the
development of the neural network models, allowing for the computation of
finite-temperature infrared spectra of large systems inaccessible to explicit
coupled cluster calculations. This substantially expands the hitherto existing
limits of accuracy, speed and system size for theoretical spectroscopy and
opens up a multitude of avenues for the prediction of vibrational spectra and
the understanding of complex intra- and intermolecular couplings.
