In this chapter, the practical realisation of the VMC and DMC methods is described. Although the theoretical presentation of QMC methods in chapter 3 describes the methods and their physics in mathematical terms, further developments are required in order to perform accurate and efficient calculations using reasonable computer power.
Solid-state and quantum chemical investigations require convenient parameterised forms for trial functions that are suitable for optimisation. Forms of trial functions are briefly reviewed and a practical scheme for wavefunction optimisation is presented.4.1 The incorporation of pseudopotentials into the many-body framework and the use of the supercell approximation for extended systems is described. Data from actual calculations are given to help clarify and further illustrate the methods.
The details of implementation, although many in number, are important for the later applications in this thesis. In particular, efficient algorithms and implementation is essential for the calculations in chapters 7 and 8, where systems involving 216 and up to 128 valence electrons are simulated. At the time of writing, these calculations could be considered large even if electron-correlations were treated at a density functional level and are sufficiently large that quantum chemical methods cannot be applied.