Since Ceperley and Alder's QMC calculations for the Homogeneous Electron Gas (HEG)[13] in 1980 there has been a gradual increase in the use of QMC methods. [24] Successful application of QMC methods to inhomogeneous systems - those including atoms - is considerably more difficult than for the HEG.

The computational cost of QMC methods scale with the third power of
number of electrons in the system. However, in practice it has been
established that the *prefactor* for realistic calculations is
very large. Hence, the barrier to performing calculations has been the
large prefactor or *intrinsic variance* of the wavefunctions used
in the calculation as well as the number of particles (electrons).
The development of improved, more efficient
wavefunction forms and methods for their optimisation has led to a
considerable reduction in the prefactor.

A hidden scaling of QMC methods is their scaling with the atomic
number, , of the atoms included in the simulation. It has been
argued [23,35,36]
that the scaling of computer time, , with Z is,

(4.1) |

Fortunately, for most properties, the atomic cores are almost
unaffected by the valence (outermost) electrons and their
environment. This observation can be used to remove the core electrons
from the simulation, greatly reducing the problems of time and energy
scales. The removal is achieved by the incorporation of a
pseudopotential. This procedure, which is also common in DFT and
quantum chemical calculations,^{4.2} is described in section 4.5.