... found2.1
The solution found for the orbitals will be the ``best fit'' solution in a least-squares sense. 
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... wavefunctions.2.2
Methods to apply perturbative corrections to configuration interaction have been developed. Applying perturbative corrections to a configuration interaction-derived wavefunction can be an efficient way of improving accuracy at lower cost than performing a higher level configuration interaction-based calculation. Uses of these techniques are quite specialised and give a small non-variational correction to the CI energy. 
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...DMCeperleyPRL19802.3
Published in 1980, this is now one of the oldest, most widely referenced papers in the field of numerical electronic structure. 
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... experiment.2.4
An illustration of this point is found in chapter 8, where different functionals give significantly different energetic orderings compared with QMC calculations for carbon clusters up to $\mathrm {C}_{32}$. 
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... presented.4.1
This topic is studied further in chapter 5. 
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... calculations,4.2
Even within DFT and quantum chemical methods, the use of pseudopotentials is often unavoidable. Pseudopotentials allow the use of far smoother wavefunctions, greatly reducing the number of basis functions required. In the case of a plane-wave basis, most commonly employed in solid-state calculations, the use of pseudopotentials is almost essential. A hidden pseudopotential-like approximation is frequently made in quantum chemical calculations: that of neglecting selected core molecular orbitals from correlation calculations. This ``frozen-core'' approximation is almost essential for large-scale quantum chemical calculations. 
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...,4.3
Multiple determinants are particularly effective in systems with small gaps. For large gap systems, multiple determinants provide only a small (inefficient) improvement in the wavefunction. In the Be atom, a trial function consisting of $\approx 0.85$ of the $1{\rm s}^{2}2{\rm s}^{2}$ ground state and $\approx 0.15$ of the low lying $1{\rm s}^{2}2{\rm p}^{2}$ excited states and optimised Jastrow factor is found to obtain significantly more correlation energy ($\approx 20\%$) than a wavefunction consisting of the ground state determinant and an optimised Jastrow factor. In chapter 8, a 43 determinant wavefunction is used for a $\mathrm {C}_{26}$ ring. 
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... respectively.4.4
Due to basis set incompleteness, a subsequent projection onto a basis more suited to QMC applications is numerically treacherous. However, as we are only dealing with trial wavefunctions, this approach remains a potential area of future research. 
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... time.4.5
The proportion of time spent is very case-dependent, but proportions between $0.5\%$ and $25\%$ were observed during the calculations in this thesis. 
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... directly.4.6
In pseudopotential calculations, $T_{i}$ and $F^{2}_{i}$ were found to have worse statistics than the kinetic energy. However, in all-electron VMC calculations of the oxygen atom and water monomer using exact and near-exact HF orbitals respectively, the kinetic energy was found to have worse statistical errors by a factor of approximately 2. No mention of this was found in the literature. 
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... atoms,4.7
Arguably, sufficiently accurate wavefunctions may be constructed for all first row elements. Ref.[53] includes wavefunctions for first-row dimers obtaining $79\%$ or greater of the experimentally determined correlation energy. 
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... accuracy.4.8
In general, atoms with a large energetic separation of core and valence levels have cores that can be accurately represented by a pseudopotential. This is not always the case however: some third row elements maintain good core-valence separation, but in certain materials, such as Ga compounds, the occupied $d$-levels are found to significantly influence bonding. In these cases, additional electrons must be placed in the valence and a smaller core used. 
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... cell.6.1
The reduction of the problem to one within the primitive unit cell is only possible within independent particle theories; in a true many-body theory one has to solve over the entire simulation cell. 
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... shown.6.2
These results are similar to those given in Ref. [87], but they have been fully recalculated and corrected. 
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... ``cumulenic''8.1
Have only identical bond lengths. 
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... ``polyacetylenic''8.2
Have alternating bond lengths. 
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