  We introduce a formalism to describe fractional charging of a molecule due to
interactions with its environment. The interactions which induce fractional
charging are contained in the Hamiltonian of the full system (molecule and
environment). Such interactions can be singled out by expressing the
Hamiltonian in a local spin orbital basis, and they are the main focus of this
work. A reduced density operator for the molecule is derived starting from the
Liouville-von Neumann equation for the full system by employing an explicitly
constructed projection superoperator. By treating the molecule as an
electronically open quantum system, we obtain a Redfield equation where the
environment is included approximately. Phenomenological broadening of energy
levels is included to mimic finite lifetimes of electronic states. The
populations of the reduced density operator determine the mixture of different
redox states and, hence, the fractional charging of the molecule. To illustrate
the formalism, we use benzene physisorbed on a graphene sheet as a toy model.
The work presented in this paper constitutes an initial step toward
understanding molecules as electronically open quantum systems.
