  As quantum computing approaches its first commercial implementations, quantum
simulation emerges as a potentially ground-breaking technology for several
domains, including Biology and Chemistry. However, taking advantage of quantum
algorithms in Quantum Chemistry raises a number of theoretical and practical
challenges at different levels, from the conception to its actual execution. We
go through such challenges in a case study of a quantum simulation for the
hydrogen (H2) and lithium hydride (LiH) molecules, at an actual commercially
available quantum computer, the IBM Q. The former molecule has always been a
playground for testing approximate calculation methods in Quantum Chemistry,
while the latter is just a little bit more complex, lacking the mirror symmetry
of the former. Using the Variational Quantum Eigensolver (VQE) method, we study
the molecule's ground state energy versus interatomic distance, under the
action of stationary electric fields (Stark effect). Additionally, we review
the necessary calculations of the matrix elements of the second quantization
Hamiltonian encompassing the extra terms concerning the action of electric
fields, using STO-LG type atomic orbitals to build the minimal basis sets.
