On the Wigner Monte Carlo method coupled to pseudopotential models

In applied atomic physics and quantum chemistry, one of the main goal is the calculation of the electronic structure or, in other words, the chemical properties of a system such as an atom, and a molecule. This involves the numerical simulation of the quantum many-body problem, one of the most computationally demanding and difficult problem in applied physics. A rather common practice to reduce the complexity of this problem is represented by the introduction of a pseudopotential model, essentially an effective potential consisting of a superposition of the core electrons and the nucleus potentials. This approach reduces the original problem to the simulation of the valence electrons only. While usually quantum chemistry is performed using the Schrödinger formulation of quantum mechanics, in this paper we show how a pseudopotential model can be coupled to the Wigner Monte Carlo method based on signed particles. For the sake of simplicity and clarity, we validate our proposed coupling technique against the time-dependent single-body Schrödinger equation, showing an excellent agreement for the electron probability density and the induced dipole. In this context, the extension to the many-body Wigner formalism becomes trivial. This opens the way towards applied quantum chemistry in the Wigner formalism.