When the electronic many-body problem is solved at any level of theory, its solution provides energies and atomic forces that allow for the determination of structural and thermodynamic properties. Forces also open the road to molecular dynamics simulation and the computation of dynamical properties. In addition, and at variance with classical force fields, any such theory would give access to electronic properties such as electronic energy levels or bands, electronic density, charge transfer, and, in principle, also optical and electronic transport properties.

It is clear that the simpler the treatment of the electronic variables, the more efficient the calculation. Therefore, larger systems can be studied, and longer MD simulations permit us to accumulate more reliable statistics and give access to dynamical phenomena occurring on longer time scales. If the information arising from the electronic degrees of freedom is not strictly necessary, then a strategy that removes the electrons altogether out of the picture by means of effective interatomic potentials (classical force fields) is a winning strategy. However, as long as electrons are treated explicitly, the determination of interatomic potentials requires the solution of the Schrödinger equation, and this is far more expensive than just replacing distances and angles in an explicit formula.

Linear scaling with the system size in the solution of Hartree–Fock or Kohn– Sham equations can only be achieved for very large systems. But even in that limit, when using an atom-centered basis set, the calculation of the matrix elements and the diagonalization of the Hamiltonian matrix require a major computational effort; the latter scales as N3.