Abstract

It was claimed that quantum mechanics could predict every property of any molecule or material – essentially that quantum mechanics explained the whole of physics, chemistry, materials science and biology – long before this claim could be tested. While there were the great early triumphs of quantum mechanics, such as the prediction of the energy levels of the hydrogen atom, the explanation of the covalent bond and the description of the lifetimes of radioactive nuclei, all these quantitative predictions were, effectively, for systems that consisted of a single particle. It is actually a formidable challenge to solve the equations of quantum mechanics for many interacting or entangled particles and it was 50 years before quantitative descriptions of many electron systems became feasible. Indeed, these first calculations were restricted to atoms or small molecules that contained only 2 or 3 electrons or to crystalline materials that contained only 1 or 2 atoms in the basic crystal unit cell.

Over the last 30 years the combination of more powerful computers combined with better theoretical and numerical methods has brought us to the point where we can routinely compute a vast range of properties of molecules and materials. For instance we can now determine the most stable crystal structure for a particular combination of atoms even when this is not known experimentally. In addition, we can calculate vibrational frequencies, activation energies of chemical reactions, surface energies and many more properties for systems containing hundreds of atoms, or more.

In this lecture I will briefly introduce quantum mechanics as the ultimate one-parameter theory and I will outline the mathematical challenges of solving the resulting equations. I will describe density functional theory, which is a reformulation of quantum mechanics that vastly reduces its computational complexity and has allowed predictive quantum mechanical simulations to become routinely possible. Finally, I will present applications of this simulation methodology selected from a range of scientific disciplines.