The importance and power of simulations has been recognized in various fields, and in particular in materials science. In addition to providing a conceptual framework to understand the different physochemical properties of materials, simulations can be used to aid in the rational design of materials with tailored properties using computational screening approaches. The confidence in the different levels of first-principles theories and the increase in computational power have allowed the validation and feasibility of these computational approaches.
Materials’ modeling has experienced a huge growth in the last two decades, which is due to new mathematical approaches, numerical techniques, and computational protocols, in addition to a vast increase in the computational power. It is hard to tell but it is unlikely that materials’ modeling has reached its peak and many more advances are yet to come. Based on what we know now, materials’ modeling has certainly come a long way; it was only 90 years ago that Schrodinger introduced his equation to describe the quantum state of a physical system. This was followed by seminal work by Hartree, Fock, Fermi, Dirac, and others for extending quantum mechanics to realistic electronic systems (atoms, molecules, and solids).
The major breakthrough in materials’ modeling was in 1964-1965 when Kohn, Hohenberg and Sham introduced the fundamentals of density functional theory (DFT), and transformed it into a practical scheme for describing the properties of materials from first principles without any parameters. This relatively new theory became the workhorse in materials modeling and simulations. Any material can be studied using a computer to asses its electrical, magnetic, thermal, optical, and catalytic properties. Despite the success of DFT, this theory is not exact. This is because Kohn and Hohenberg established that the total energy of any system depends only on the electronic density of the system, but the exact form for this dependence is not known. From a practical point of view, this limitation did not severely hinder the use of DFT for understanding or predicting materials properties. There are different approximations for this unknown functional that are of increasing complexity and often of better accuracy.
DFT is also the starting point for many methods that improves on the deficiencies of DFT such as many body perturbation theory, quantum Monte Carlo, dynamical mean field theory, density matrix renormalization group, or advanced quantum chemistry approaches. All of these theories are considered state-of-the-art but are of considerable computational cost for extended systems.
In our research lab for materials simulations we focus on using the right and most efficient approach for each problem. Our group has extensive expertise in different levels of theories in computational materials design that span a wide range of accuracy levels and length scales, including force-field, density-functional theory, quantum Monte Carlo and quantum chemistry methods.
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