This is an introduction to quantum mechanics as it relates to spectroscopy, the electronic structure of atoms and molecules, and molecular properties. A digital, living textbook, it provides opportunities not found in conventional textbooks—opportunities that allow students to develop skills in information processing, critical thinking or analytical reasoning, and problem solving that are so important for success.
- Our first chemical application of Quantum Mechanics is directed at obtaining a description of the electronic spectra of a class of molecules called cyanine dyes. We start with this set of molecules because we can use a particularly simple model, the particle-in-a-box model, to describe their electronic structure. This simple model applied to a real molecular system will further develop our “sense of Quantum Mechanics.”
- In this chapter we apply the principles of Quantum Mechanics to the simplest possible physical system, a free particle in one dimension. This particle could be an electron or, if we only consider translational motion, an atom or a molecule. Free means that no forces are acting on the particle. Since a force is produced by a change in the potential energy, the potential energy must be constant if there is no force. This constant can be taken to be zero because energy is relative not absolute.
- In this chapter we use the harmonic oscillator model and a combination of classical and quantum mechanics to learn about the vibrational states of molecules. The first section of the chapter introduces the concepts of normal modes and normal coordinates in order to deal with the complexity of vibrational motion found in polyatomic molecules. The second section of the chapter reviews the classical treatment of the harmonic oscillator model, which is very general.
- Molecules rotate as well as vibrate. Transitions between rotational energy levels in molecules generally are found in the far infrared and microwave regions of the electromagnetic spectrum.
- In this chapter you will learn several key techniques for approximating wavefunctions and energies, and you will apply these techniques to multi-electron atoms such as helium. You also will learn how to use the theoretical treatment of the electronic states of matter to account for experimental observations about multi-electron systems.
- Solving the Schrödinger equation for a molecule first requires specifying the Hamiltonian and then finding the wavefunctions that satisfy the equation. Since the wavefunctions involve the coordinates of all the nuclei and electrons that comprise the molecule, the complete molecular Hamiltonian consists of several terms. The nuclear and electronic kinetic energy operators account for the motion of all of the nuclei and electrons.