|In the field of materials science and chemistry, one of the Grand Challenge problems for the next decade is the prediction and design of molecular and material properties with controllable accuracy, from first principles; that is, from the fundamental laws of quantum mechanics. This can be accomplished by using advanced quantum simulations (QS), which provide numerical solutions to the partial differential equations representing the laws of quantum mechanics. In QS, the interaction between electrons and ions is modeled in an approximate, non-empirical manner. The last thirty years has seen key progress in the fundamental theories of condensed matter and molecular systems, the development of algorithms implementing both mean field and stochastic approaches, and the creation of optimized simulation codes running on high-performance computers. All these advances have transformed QS into a powerful tool capable of addressing the complexity of materials and nanostructures at the microscopic level. Numerous material properties can now be inferred from the fundamental laws of quantum mechanics without any input from experiment, and in some cases one can even investigate conditions not yet accessible.
Over the next decade we expect QS to acquire a central role in materials science and chemistry, as further theoretical and algorithmic developments allow the simulation of a wide variety of condensed and molecular systems with specific, targeted properties. This will open up the possibility of predicting and designing optimized materials and nanoscale devices from first principles. Although this modeling revolution will be years in the making, its unprecedented benefits are already becoming clear. Indeed, QS applications are currently making key contributions to our understanding of nanoscale measurements, complex, disordered systems (including liquids and solids under extreme conditions), and composite organic/inorganic materials. A fundamental understanding of microscopic behavior is very much needed in the field of nanoscience, where experimental investigations are often controversial and cannot be explained on the basis of simple models. It is just as important in the study of materials under extreme conditions, for which experimental data are usually rather limited. Some examples of recent predictions obtained using QS are illustrated in figure 10, where we use the "ball and stick" representation of microscopic structure for solids (diamond under 1,000 GPa of pressure), liquids (liquid water), and recently synthesized nanostructures (silicon and carbon). For all these materials, QS applications have provided a deeper understanding of their structural, optical, and vibrational properties, and have guided the interpretation of key experimental data.