1. Introduction 92

2. Methods and models 93

2.1 Density Functional Theory 93

2.2 Chemical models 98

3. Examples of mechanisms studied 104

3.1 Photosystem II 105

3.2 Cytochrome c oxidase 108

3.3 Manganese catalase 112

3.4 Ribonucleotide reductase 114

3.5 Methane mono-oxygenase 119

3.6 Methyl coenzyme M reductase 122

3.7 Intra- and extradiol dioxygenases 124

3.8 Tyrosinase and catechol oxidase 126

3.9 Amino-acid hydroxylases 130

3.10 Isopenicillin N synthase 132

3.11 Cytochrome c peroxidase 134

3.12 Copper-dependent amine oxidase 136

3.13 Galactose oxidase 138

4. Summary and conclusions 138

5. Acknowledgements 140

6. References 140

The study of metalloenzymes using quantum chemical methods of high accuracy is a relatively new field. During the past five years a quite good understanding has been reached concerning the methods and models to be used for these systems. For systems containing transition metals hybrid density functional methods have proven both accurate and computationally efficient. A background on these methods and the accuracy achieved in benchmark tests are given first in this review. The rest of the review describes examples of studies on different metalloenzymes. Most of these examples describe mechanisms where dioxygen is either formed, as in photosystem II, or cleaved as in many other enzymes life cytochrome c oxidase, ribonucleotide reductase, methane mono-oxygenase and tyrosinase. In the descriptions below high emphasis is put on the actual determination of the transition states, which are the key points determining the mechanisms.