  Molecular dynamics (MD) simulations employing classical force fields
constitute the cornerstone of contemporary atomistic modeling in chemistry,
biology, and materials science. However, the predictive power of these
simulations is only as good as the underlying interatomic potential. Classical
potentials often fail to faithfully capture key quantum effects in molecules
and materials. Here we enable the direct construction of flexible molecular
force fields from high-level ab initio calculations by incorporating spatial
and temporal physical symmetries into a gradient-domain machine learning
(sGDML) model in an automatic data-driven way. The developed sGDML approach
faithfully reproduces global force fields at quantum-chemical CCSD(T) level of
accuracy and allows converged molecular dynamics simulations with fully
quantized electrons and nuclei. We present MD simulations, for flexible
molecules with up to a few dozen atoms and provide insights into the dynamical
behavior of these molecules. Our approach provides the key missing ingredient
for achieving spectroscopic accuracy in molecular simulations.
