  Machine learning has emerged as an invaluable tool in many research areas. In
the present work, we harness this power to predict highly accurate molecular
infrared spectra with unprecedented computational efficiency. To account for
vibrational anharmonic and dynamical effects -- typically neglected by
conventional quantum chemistry approaches -- we base our machine learning
strategy on ab initio molecular dynamics simulations. While these simulations
are usually extremely time consuming even for small molecules, we overcome
these limitations by leveraging the power of a variety of machine learning
techniques, not only accelerating simulations by several orders of magnitude,
but also greatly extending the size of systems that can be treated. To this
end, we develop a molecular dipole moment model based on environment dependent
neural network charges and combine it with the neural network potentials of
Behler and Parrinello. Contrary to the prevalent big data philosophy, we are
able to obtain very accurate machine learning models for the prediction of
infrared spectra based on only a few hundreds of electronic structure reference
points. This is made possible through the introduction of a fully automated
sampling scheme and the use of molecular forces during neural network potential
training. We demonstrate the power of our machine learning approach by applying
it to model the infrared spectra of a methanol molecule, n-alkanes containing
up to 200 atoms and the protonated alanine tripeptide, which at the same time
represents the first application of machine learning techniques to simulate the
dynamics of a peptide. In all these case studies we find excellent agreement
between the infrared spectra predicted via machine learning models and the
respective theoretical and experimental spectra.
