  Automatic differentiation represents a paradigm shift in scientific
programming, where evaluating both functions and their derivatives is required
for most applications. By removing the need to explicitly derive expressions
for gradients, development times can be be shortened, and calculations
simplified. For these reasons, automatic differentiation has fueled the rapid
growth of a variety of sophisticated machine learning techniques over the past
decade, but is now also increasingly showing its value to support {\it ab
initio} simulations of quantum systems, and enhance computational quantum
chemistry. Here we present an open-source differentiable quantum chemistry
simulation code, DQC, and explore applications facilitated by automatic
differentiation: (1) calculating molecular perturbation properties; (2)
reoptimizing a basis set for hydrocarbons; (3) checking the stability of
self-consistent field wave functions; and (4) predicting molecular properties
via alchemical perturbations.
