Theoretical Toolkits for Inorganic and Bioinorganic Complexes: Their Applications and Insights

Following Coulson's dictum, ‘give us insight, not numbers,’ we review in this chapter the theoretical methods that are currently available for studies of structure, spectroscopy, and reactivity of transition-metal complexes in inorganic/organic and bioinorganic chemistry, and the means of extracting insight from these calculations. As such, we describe herein methodologies of density functional theory (DFT), wave function theory, hybrid quantum mechanical/molecular mechanical approaches, and relativistic calculations. We appraise the weaknesses and strengths of these methods and provide wherever possible practical advice for conducting the calculations meaningfully. In addition, we highlight the essential use of orbitals in DFT – natural orbitals, natural spin orbitals, and corresponding orbitals – as the means for understanding the electronic reorganization in complex bioinorganic reactions. Lastly, we review the use of valence bond (VB) theory in modeling reactivity and of ‘VB reading’ of complex multireference/multiconfigurational wave functions.