In this chapter, several Monte Carlo techniques for optimizing many-body wavefunctions are investigated. The development of statistically efficient and numerically stable optimization methods is important, as the cost of optimising a many-body wavefunction is high. The most commonly used techniques in the literature are evaluated and several variants are introduced. Two reasons why variance minimisation exhibits superior numerical stability to energy minimisation are identified by investigating a realistic model system. A robust and efficient variance minimisation scheme for optimising the wavefunctions of large systems is developed.
This scheme is applied to a series of real systems in the later chapters of the thesis, where the difficulties of optimisation are far greater. These successful applications demonstrate the scheme's practicality and efficiency. Wavefunction optimisation for the carbon clusters of chapter 8 would not be possible using some of the simpler optimisation techniques that have been used in the past.
The key issues and importance of wavefunction optimisation are briefly reviewed in section 5.2. Several different choices of objective function for optimisation schemes are then examined in section 5.3. In section 5.4 and higher, possible objective functions are analysed and tested numerically. A procedure for limiting the energy of ``outlying'' configurations is presented in section 5.8, which in practice enables the value of objective functions to be evaluated with an improved statistical accuracy. Conclusions and a summary of the proposed method are given in section 5.10.