In: Chemistry
what is the differences between semiempirical and ab-initio methods of electronic structure determinations?
Ab initio calculations are computational very expensive. Typically, they can only handle 102 atoms and, if Car-Parrinello dynamics is used, time scales on the order of 10ps. One problem with these methods is that the computational expense scales roughly as q ] where q is the number of basis functions (which must at least be the electrons). This arises due to the four-dimensional integrals that must be performed between basis functions. This can make ab initio studies prohibitive for even small molecular systems.
A number of approximate methods have been developed that achieve better performance and scaling than the Hartree-Fock and DFT approaches. These so-called semi-empirical methods only treat the valence electrons explicitly and incorporate parameters fitted to experimental data to make up for this lack of explicit detail in all of the electrons. These methods can treat ∼ 10d atoms and time scales up to 10 ns. The trade-off, however, is that large parameter sets are required from the experimental input.