The Importance of Atoms and The New Suspenders

In the introduction to his lectures on physics, Feynman points out the important scientific fact that matter is composed of atoms. While this may seem obvious today, proving the atomic nature of matter was actually quite difficult, and it was only around the beginning of the twentieth century that it was completely accepted by the scientific community. Feynman goes on to claim that the atomic nature of matter is the most important scientific fact that can be expressed in a single sentence. Part of this is simply that Feynman took great pleasure from imagining how 'jiggling atoms' could lead to all sorts of everyday phenomena, such as solids liquids and gases. You can follow this link to watch Feynman talk about how 'jiggling atoms' can explain things like surface tension and why bike pumps get hot when you use them.

Of course jiggling atoms are also critically important in chemical reactions. The fact that atoms cannot be created or destroyed in chemical reactions allows for all sorts of important predictions. Atoms form the smallest building blocks of chemistry, and they combine to form an infinite variety of more complicated structures, however it turns out atoms are not the smallest pieces of matter.

Every atom is composed of some number of electrons orbiting a heavy but small nucleus. An electron is around 2000 times less massive than a proton, and the nucleus may be composed of several protons and neutrons (neutrons have about the same mass as a proton). Chemical bonds form when an electrons are either transferred between atoms (ionic bond), or shared between two atoms (covalent bond).

While imagining whole atoms and molecules as little elastic balls governed by Newtonian mechanics can help explain a wide variety of behavior, to understand the behavior of electrons in atoms and molecules we need quantum mechanics. Newtonian mechanics is actually an approximation of quantum mechanics which becomes very accurate for large massive systems.

The laws of quantum mechanics were first worked out in the 1920’s, and in the 90 years since they were developed there has been no experimental evidence to doubt their validity. In fact Dirac is often quoted as saying that quantum mechanics has completely solved chemistry. Now that we know how electrons and nuclei behave we can describe exactly how chemical bonds form. However, his full quote sheds a little more light on the actual situation:

“The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.” (Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 123, No. 792 (Apr. 6, 1929), pp. 714-733).

The work of solving these difficult equations has been picked up by theoretical and computational chemists, developing methods and algorithms to handle and avoid the complexities of quantum mechanics and then employing computers to study the behavior of molecules. Our research group is focused on one particular approach to quantum mechanics called density functional theory. In this approach we treat each of the nuclei of a molecule as fixed in space, (called the Born Oppenheimer approximation) then our primary variable is the probability density of finding an electron at a given point in space. This probability can be visualized as cloud of varying density spread out over the molecule. It will clump up strongly around the nuclei because of the strong electrostatic attraction between protons and electrons, and will grow sparser as you look farther away from the molecule.

While it is not always as accurate as other quantum mechanical methods density functional theory has been very successful at describing the electronic structure of very large molecular systems which cannot be handled by other methods. The goal of the Suspenders is to extend the range and applicability of density functional theory. Part of this goal is to help push density functional theory calculations to handle larger and larger systems, but another part of this goal is to help us get more information out of a given density functional theory calculation.

The electron density is a continuous cloud which makes no distinction between the atoms in a molecule, but we know that the behavior of an atom in various chemical contexts remain similar. In other words a fluorine atom in two completely different molecules will often still behave in a similar way. Our research group works on developing partition density functional theory which allows us to define individual atoms within a molecule, and compare between different chemical contexts. In this way we like to share in Feynman’s fun of imagining how our little atoms in molecules can lead to wide variety chemical phenomena. We agree with him that atoms may be among the most important scientific ideas of all time.

Victor H Chavez