ABSTRACT
The laws of classical mechanics, which we reviewed in the last chapter, are both incomplete and not suitable for applications to problems of chemical interest. Matter is composed of electrons and nuclei, which are both extremely small and extremely light on the laboratory scale. Light particles have been shown to obey the laws of quantum mechanics, a more complete theory from which classical mechanics emerges in the large mass limit. We introduce quantum mechanics later in the text; however, the typical experiment in chemical physics yields thermodynamic properties, like temperature, pressure, and volume. These variables can be understood as averages of dynamic variables, like the velocity and kinetic energy of samples of matter composed of a large number (on the order of Avogadro’s number) of particles. It is impossible to integrate the laws of motion for such large systems. Instead, one constructs a statistical theory based upon models for small fractions of the sample of matter (e.g., for a gas, a single molecule, more generally this fraction is called a system), and seeks probability distributions for the dynamic variables. These fractions are much more convenient to handle theoretically and numerically. Once such a model is constructed, and the probability distributions derived, statistical averages can be obtained by integration. In this manner, gases, liquids, solids, and clusters can be simulated to obtain experimentally observable properties.
