One of the most fundamental assumptions in chemistry is that low lying core electrons are relatively inert, and are not perturbed by a molecular environment. This assumption is supported by the chemical similarity of elements in the same column of the periodic table. Most of the important chemical properties of atoms and molecules are determined by the interaction of their valence electrons with the valence electrons of other atomic or molecular species. For molecules containing heavy atoms, large computational savings may be realized if a particular mathematical form for the atomic orbitals is assumed, a priori, so that the total number of parameters which must be optimized in, say, the computation of a Hartree-Fock wavefunction may be reduced. This approximation on its own is known as the frozen core approximation and will be explored in some detail in chapter 3.
A more extensive savings may be achieved if, instead of simply assuming a particular form for the core orbitals, all terms describing the interaction of the electrons in these orbitals with each other and those outside the core region are simply replaced by a scalar ``effective potential''. This provides the additional benefit of reducing the basis set size requirements, since no basis functions are now needed to explicitly describe the core orbitals. This has the effect of drastically reducing the number of two-electron quantities, such as electron repulsion integrals, which must be considered.
In correlated electronic structure calculations, the molecular orbitals which correspond to atomic core orbitals are often excluded from the active orbital space. Even when such orbitals are included in the active space, the resultant contributions are typically small for most chemical properties. The use of effective core orbitals in these methods ideally should not significantly affect the quality of the resulting molecular property predictions. Because correlated methods scale higher than Hartree-Fock with respect to basis set size, the decreased basis set size resulting from the use of effective potentials will introduce in an even more dramatic computational savings over all-electron methods.