  Highly accurate force fields are a mandatory requirement to generate
predictive simulations. Here we present the path for the construction of
machine learned molecular force fields by discussing the hierarchical pathway
from generating the dataset of reference calculations to the construction of
the machine learning model, and the validation of the physics generated by the
model. We will use the symmetrized gradient-domain machine learning (sGDML)
framework due to its ability to reconstruct complex high-dimensional
potential-energy surfaces (PES) with high precision even when using just a few
hundreds of molecular conformations for training. The data efficiency of the
sGDML model allows using reference atomic forces computed with high-level
wavefunction-based approaches, such as the $gold$ $standard$ coupled cluster
method with single, double, and perturbative triple excitations (CCSD(T)). We
demonstrate that the flexible nature of the sGDML framework captures local and
non-local electronic interactions (e.g. H-bonding, lone pairs, steric
repulsion, changes in hybridization states (e.g. $sp^2 \rightleftharpoons
sp^3$), $n\to\pi^*$ interactions, and proton transfer) without imposing any
restriction on the nature of interatomic potentials. The analysis of sGDML
models trained for different molecular structures at different levels of theory
(e.g. density functional theory and CCSD(T)) provides empirical evidence that a
higher level of theory generates a smoother PES. Additionally, a careful
analysis of molecular dynamics simulations yields new qualitative insights into
dynamics and vibrational spectroscopy of small molecules close to spectroscopic
accuracy.
