Quantum chemistry – from the first steps to linear-scaling electronic structure methods

Abstract We first give a brief, incomplete overview over historic milestones leading to the emergence of quantum chemistry, starting from John Dalton’s earliest attempts to describe the atom in the early 19th century. After the formulation of the Schrödinger equation in 1926 and the first successful description of covalent bonding using the new theory, it became soon clear that the main challenge ahead was to find efficient approximations to the Schrödinger equation, as was famously stated by Paul A. M. Dirac in 1929. Since then, many quantum-chemical approximations have been introduced, with a key problem being the exponential increase of the computational cost with the system size when approaching the exact solution of the Schrödinger equation. In the second part, we will hence focus on selected techniques to overcome the scaling problem. Finally, we close with some insights into the new and challenging field of reaction network exploration, offering a glimpse into potential future directions of quantum chemistry.