Page "Computational chemistry" Paragraph 3

Both ab initio and semi-empirical approaches involve approximations.

These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system ( for example, periodic boundary conditions ), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all.

For example, most ab initio calculations make the Born – Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation.

In principle, ab initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced.

In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains.

The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable.