RealQM vs QTAIM

Here is a quick comparison between Real Quantum Mechanics RealQM and Quantum Theory of Atoms In Molecules QTAIM developed by Richard Bader in the 1960-90s, to be added to the discussion with leading chemist in previous post.

• QTAIM is based on the linear multidimensional Schrödinger equation of Standard Quantum Mechanics.
• RealQM is based on a new Schrödinger equation as a non-linear system of non-overlapping one-electron densities in 3d meeting at a Bernoulli free boundary with continuity and zero normal derivative.
• QTAIM requires advanced preprocessing to reduce multidimensional wave functions to electron density including parameters. Computational cost increases quickly with number of atoms.
• RealQM is ab initio parameter-free. Computational cost scales linearly with number of atoms.
• In QTAIM atomic kernels have main role to divide a molecule into basins of attraction.
• In RealQM electrons have main role to divide molecule into non-overlapping electron densities. 
• QTAIM works with general multi-electron densities.
• RealQM works with one-electron densities.

Both QTAIM and RealQM divide the volume of a molecule into subdomains filled by electron densities, but in different ways. 

Zero normal derivative of electron densities plays a key role on both QTAIM and RealQM, but in different ways. 

Both QTAIM and RealQM connect to Density Functional Theory, but in different ways.