  Automatic Differentiation (AD) is a powerful tool that allows calculating
derivatives of implemented algorithms with respect to all of their parameters
up to machine precision, without the need to explicitly add any additional
functions. Thus, AD has great potential in quantum chemistry, where gradients
are omnipresent but also difficult to obtain, and researchers typically spend a
considerable amount of time finding suitable analytical forms when implementing
derivatives. Here, we demonstrate that automatic differentiation can be used to
compute gradients with respect to any parameter throughout a complete quantum
chemistry method. We implement DiffiQult, a fully autodifferentiable
Hartree-Fock (HF) algorithm, which serves as a proof-of-concept that
illustrates the capabilities of AD for quantum chemistry. We leverage the
obtained gradients to optimize the parameters of one-particle basis sets in the
context of the floating Gaussian framework.
