RealQM has been extended to molecules in general geometry by computing on a fixed mesh using a level set method to handle the free boundary, as described in a sequence of posts on my main blog under the labels RealQM and Real Quantum Chemistry including the following key posts:
This site describes a new model of atoms and molecules in terms of classical continuum mechanics in three space dimensions in the form of a free boundary problem for a system of partial differential equations in non-overlapping electron wave function/charge densities satisfying a free boundary condition involving continuity and a homogeneous Neumann condition.
The new model is referred to as realQM (real quantum mechanics) as a model with interpretation in physical terms, to be compared with the model presented in books referred to as stdQM (standard quantum mechanics) with non-physical interpretation as particle statistics (according to the Copenhagen Interpretation by Bohr-Born-Heisenberg).
realQM is computable while stdQM is uncomputable. realQM has physical meaning while stdQM has a statistical non-physical meaning.
realQM combines simplicity, generality and physicality. The question is to what extent realQM describes true physics.
One may argue that macroscopic physics may be complex/random as consisting of many interacting microscopic pieces, while microscopic physics consisting of few pieces can only be simple/deterministic. With such a realQM perspective, the ground state of an atom is simple and leaves no door to the randomness of stdQM.
To get an overview, browse the header menu. It is also helpful to try the following question:
The first live presentation of realQM to the World was given at the conference 50th Anniversary of Journal of Structural Mechanics, August 24-25, 2017, Vaasa, Finland as
We shall see that it is natural to apply the homogeneous Neumann condition for electron wave functions on the free boundary separating electrons, and also where the two electrons in the innermost shell (or the one electron for Hydrogen) meet(s) the kernel. This requires the kernel to have positive radius, which then can be used as a model parameter allowing perfect match to observation for two-electron ions, from which atoms with outer shells can be built, see Helium and Two-Electron Ions.
An alternative giving a similar effect is to use a Robin boundary condition of the form 
realQM thus opens to inspection of the inner mechanics of an atom, such as the effective radius of the kernel vs electrons, which is hidden to experimental inspection.
In particular, even the basic case of the Hydrogen atom gets a new model in realQM with the homogeneous Neumann condition on a kernel with small positive radius staying away from the kernel singularity, as compared to the model of stdQM with vanishing kernel radius keeping the singularity of the kernel potential. We here follow the device that physics without singularities may be more transparent and closer to reality than physics with singularities with hidden physics. Compare with this discussion.
Real Quantum Mechanics 