Bringing Density Functional Theory to other Realms of Physics and Chemistry
All the matter we see in our lives is composed of atoms. These are made of electrons and nuclei. Knowledge of how electrons behave around the nuclei is all we need to know to manipulate matter at our will in a lab. This idea seems quite pretentious, and many challenges exist that hinders our progress. Scientists in the last century have sought tools and methods to predict how electrons will behave in the presence of nuclei; which ultimately will explain the properties of matter. The laws that rule the electrons' lifes are described by the quantum theory. This offers a set of mathematical equations, quantum mechanics, to predict the outcome of any experiment we perform in a laboratory. However, the solution of those equations is a task of epic proportions. Not even our most modern computers are able to compute what it is required to solve the equations of quantum theory. This has motivated scientists to look for an alternative theory to understand molecules. One of the most used alternative theories is called density-functional theory (DFT). This theory uses the electronic density as its basic variable, which for large systems is the number of electrons per volume. The electronic density is enough to determine the state of lowest energy of a molecule. However, in principle, DFT offers no advantage over traditional quantum mechanics; but its approximations use a basic variable which is much easier to employ for computer calculations.
DFT is widely used by chemists and physicists in their research. However, approximations in DFT are still under development. Many technical challenges exist, and are needed to be solved. Some of these regard describing properly how chemical "bonds" are formed and broken between molecules and the energy changes involved in such processes. Questions like: "How electrons are transferred between molecules?", and "how molecules evolve in time?" are of paramount importance to us, DFT-ists. The purpose of my research is to explore and further develop partition density-functional theory (PDFT), a different version of DFT to study molecules that regards them as composite systems. For example, a molecule can be thought as an object made by smaller objects that are assumed to be isolated from one another (see "Partition Spin Density Functional Theory post"). This theory preserves the density as fundamental variable, but it is regarded as the sum of the smaller components' electronic densities. These densities are an outcome of PDFT and they are the densities that the molecular fragments would have as if they were isolated from one another. PDFT promises to solve problems related to static and dynamic correlation errors of common DFT approximations. Solving these little problems can help DFT to become an even more useful theory than it is nowadays.