The development of reliable methods for calculating forces is essential. As shown in chapter 8, there can be considerable energetic differences amongst DFT functionals, which leads to small differences in optimum geometries. Lingering doubts will always remain over geometries determined at a lower level of correlation treatment, even in small systems where quantum chemical techniques may be applied. Accurate methods for calculating forces would represent a considerable refinement in QMC methodology. Improvements in relative energies between structures of significantly different geometry and bonding would result, and it is in these systems where other methods are likely to suffer from the greatest errors. Methods based on VMC will require consistently accurate wavefunctions for different geometries to obtain reliable forces, which is a considerable technical challenge. For DMC based methods, the accuracy of the fixed-node approximation is likely to be critical.
Accurate and efficient methods of calculating excited state energies and properties is a large potential area of research. Although direct methods of calculating excited state energies exist, they are currently computationally very expensive, and satisfactory methods based on correlated sampling might be better.
All of the above developments and applications would benefit from improved wavefunctions and optimisation methods. Specifically, improvements in wavefunction quality are likely to substantially improve the achievable energy resolution, which is determined by wavefunction quality and computational resources. The optimisation of the orbitals in the Slater determinants appears most likely to deliver these improvements. Efficient and reliable methods of orbital optimisation for large systems will need to be developed. Transition metal systems are certain to require improvements over current methodology. Improved pseudopotentials will also need to be developed for these systems, [61] as the LDA and pseudopotentials derived from it are unreliable.
Quantum Monte Carlo methods are currently the only practical methods for large-scale benchmark accuracy electronic structure calculations. Their non-perturbative nature and real-space formulation is ideal for benchmark studies of electron correlation. The techniques are particularly suited to supercomputer architectures and their application will continue to grow as increased computer resources become available to the community. Although the methods will always be more expensive than DFT and HF-based calculations, the scaling of the methods places them substantially ahead of other correlated wavefunction methods for large systems. Therefore it is important that Quantum Monte Carlo techniques are considered in context, as one of a range of electronic structure methods of increasing accuracy, from tight-binding through density functional theory to Quantum Monte Carlo.