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There exists a concerted and continual e ort to simulate systems of genuine biological interest to greater accuracy with methods of increasing transferability. More accurate descriptions of these systems at a truly atomistic and electronic level are irrevocably changing our understanding of biochemical processes. Broadly, classical techniques do not employ enough rigour, while conventional quantum mechanical approaches are too computationally expensive for systems of the requisite size. Linear-scaling density-functional theory (DFT) is an accurate method that can apply the predictive power of quantum mechanics to the system sizes required to study problems in enzymology. This dissertation presents methodological developments and protocols, including best practice, for accurate preparation and optimisation, combined with proof-of-principle calculations demonstrating reliable results for a range of small molecule and large biomolecular systems. Previous authors have shown that DFT calculations yield an unphysical, negligible energy gap between the highest occupied and lowest unoccupied molecular orbitals for proteins and large water clusters, a characteristic reproduced in this dissertation. However, whilst others use this phenomenon to question the applicability of Kohn-Sham DFT to large systems, it is shown within this dissertation that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Furthermore, practical solutions are demonstrated for ensuring a physical gap is maintained upon increasing system size. Harnessing these advances, the rst application using linear-scaling DFT to optimise stationary points in the reaction pathway for the Bacillus subtilis chorismate mutase (CM) enzyme is made. Averaged energies of activation and reaction are presented for the rearrangement of chorismate to prephenate in CM and in water, for system sizes comprising up to 2000 atoms. Compared to the uncatalysed reaction, the calculated activation barrier is lowered by 10.5 kcal mol-1 in the presence of CM, in good agreement with experiment. In addition, a detailed analysis of the interactions between individual active-site residues and the bound substrate is performed, predicting the signi cance of individual enzyme sidechains in CM catalysis. These proof-of-principle applications of powerful large-scale DFT methods to enzyme catalysis will provide new insight into enzymatic principles from an atomistic and electronic perspective.

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