  In electronic structure calculations, the correlation energy is defined as
the difference between the mean field and the exact solution of the non
relativistic Schr\"odinger equation. Such an error in the different
calculations is not directly observable as there is no simple quantum
mechanical operator, apart from correlation functions, that correspond to such
quantity. Here, we use the dimensional scaling approach, in which the electrons
are localized at the large-dimensional scaled space, to describe a geometric
picture of the electronic correlation. Both, the mean field, and the exact
solutions at the large-D limit have distinct geometries. Thus, the difference
might be used to describe the correlation effect. Moreover, correlations can be
also described and quantified by the entanglement between the electrons, which
is a strong correlation without a classical analog. Entanglement is directly
observable and it is one of the most striking properties of quantum mechanics
and bounded by the area law for local gapped Hamiltonians of interacting
many-body systems. This study opens up the possibility of presenting a
geometrical picture of the electron-electron correlations and might give a
bound on the correlation energy. The results at the large-D limit and at D=3
indicate the feasibility of using the geometrical picture to get a bound on the
electron-electron correlations.
