Over the past few years we have developed a rather intriguing, and conceptually simple, way to visualize the behavior of a single electron in the midst of many electrons.
The fundamental tools are the sharing amplitude and the sharing index. The former serves as a replacement for the wavefunction when considering a single electron amongst many while the latter is a quantitative measure of how a single electron is shared between two points in space.
The sharing amplitude plays the role of a wavefunction for the single electron while the sharing index behaves much like a probability density.
One of the beauties of the present approach to the description of electron behavior is that many contacts can be made with more traditional (and non-invariant) modes of interpreting electron behavior.
Some classes of molecules so far analyzed include the hydrides of the first row of eight in the periodic table and the dimers formed from HF, H2O, and NH3. The dimers have allowed an unambiguous classification of the behavior of the inter-molecular sharing into covalent and anti-covalent bonding.