Explaining and predicting the properties of materials using quantum theory

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omic and molecular structure Experimentalists discover nature’s secrets by measuring and reporting the properties of matter. Theorists explain these properties and attempt to predict new properties. This is similar to the cartoon depicting three cavemen discussing the invention of the wheel. The experimentalist says, “To be honest, I never would have invented the wheel if it were not for Urg’s groundbreaking theoretical work with the circle!” Condensedmatter theorists naturally side with Urg, who, as shown in the cartoon, makes several unsuccessful attempts before he finally discovers the right idea for the wheel. One of the most important concept in all of science is that macroscopic matter is composed of atoms. However, even at the beginning of the 20th century, this concept was not universally accepted by the scientific community, even though the ideas about atoms were first proposed by the ancient Greeks. Einstein’s PhD thesis on measuring the size of sugar molecules in 1905 helped verify the fact that molecules and atoms exist.1 Later, when scientists tried to explain the properties of atoms, they realized they needed to invoke quantum theory. They relied

partially on the example of Einstein’s (1921) Physics Nobel Prize winning work—an explanation of the photoelectric effect. This study showed that light could be viewed as a particle or wave, which was an important concept for establishing quantum theory. Our current picture of an atom can be modeled as a positive nucleus surrounded by electrons that are held close to the atom (core electrons) and outer valence electrons that can participate in chemical reactions to form molecules or solids. For example, in the case of silicon, the nucleus contains 14 positive charges with 10 core electrons, so the charge on the core is essentially +4. The core structure does not change much when building solids from atoms since the core basically remains intact. The objective of condensed-matter physics is to explain the properties of valence electrons and the way they must be arranged to form a solid and to give the resulting system its properties. Quantum mechanics shows that the properties of particles are often described in terms of probabilities. For example, only the probability associated with finding an electron precisely in a specific position can be predicted. An electron position precisely at a specific point cannot be determined.

Marvin L. Cohen, University of California–Berkeley and Lawrence Berkeley National Laboratory, USA; [email protected] DOI: 10.1557/mrs.2015.119

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MRS BULLETIN • VOLUME 40 • JUNE 2015 • www.mrs.org/bulletin

© 2015 Materials Research Society

EXPLAINING AND PREDICTING THE PROPERTIES OF MATERIALS USING QUANTUM THEORY

In 1929, P.A.M. Dirac, who contributed greatly to the development of quantum theory, posed what is sometimes referred to as Dirac’s challenge. He stated that “the underlying physical laws necessary for a large part of physics and all of chemistry are completely known, and the difficulty is only that the exact application of th