Howard: Physical Chemistry
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- Mar 6, 2024
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This course is designed to introduce students to a thorough, research-oriented view of Physical Chemistry. This content builds on the introduction to quantum mechanics where Students will solve the Schrödinger equation in 1-, 2-, and 3-dimensions for several problems of interest in chemistry, including the particle-in-a-box, harmonic oscillator, rigid rotor, and hydrogen atom. Further topics include atomic structure, valence-bond and molecular orbital theories of chemical bonding and group theory. The concepts of quantum theory are applied to molecular spectroscopy and nuclear magnetic resonance.
- 1: Atoms and Photons - Origin of the Quantum Theory
- The introduction of quantum mechanics within the context of how classical mechanics fails to explain new phenomena is discussed in this section. The word "atom" comes from the Greek atomos, meaning literally "indivisible." It became evident in the late 19th Century, however, that the atom was not truly the ultimate particle of matter. Michael Faraday's work had suggested the electrical nature of matter and the existence of subatomic particles.
- 2: Waves and Particles
- Quantum mechanics is the theoretical framework which describes the behavior of matter on the atomic scale. It is the most successful quantitative theory in the history of science, having withstood thousands of experimental tests without a single verifiable exception. It has correctly predicted or explained phenomena in fields as diverse as chemistry, elementary-particle physics, solid-state electronics, molecular biology and cosmology.
- 3: Quantum Mechanics of Some Simple Systems
- The basic application of the Schrödinger equation to free particles, trapped particles (in 1D and 3D boxes) and free electron model are introduced.
- 4: Principles of Quantum Mechanics
- Here we will continue to develop the mathematical formalism of quantum mechanics, using heuristic arguments as necessary. This will lead to a system of postulates which will be the basis of our subsequent applications of quantum mechanics.
- 5: Harmonic Oscillator
- The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment of such diverse phenomena as elasticity, acoustics, AC circuits, molecular and crystal vibrations, electromagnetic fields and optical properties of matter.
- 6: Angular Momentum
- Angular momentum is the rotational analog of linear momentum. It is an important quantity in classical physics because it is a conserved quantity. The extension of this concept to particles in the quantum world is straightforward.
- 7: Hydrogen Atom
- Modern quantum theory was introduced with a quantitative prediction of the spectroscopy of hydrogen atomic emission. That was powered by Bohr, who sought to avoid an atomic catastrophe by proposing that certain orbits of the electron around the nucleus could be exempted from classical electrodynamics and remain stable. The Bohr model was quantitatively successful for the hydrogen atom, as we shall now show.
- 8: Helium Atom
- The second element in the periodic table provides our first example of a quantum-mechanical problem which cannot be solved exactly. Nevertheless, as we will show, approximation methods applied to helium can give accurate solutions in perfect agreement with experimental results. In this sense, it can be concluded that quantum mechanics is correct for atoms more complicated than hydrogen. By contrast, the Bohr theory failed miserably in attempts to apply it beyond the hydrogen atom.
- 9: Atomic Structure and The Periodic Law
- Quantum mechanics can account for the periodic structure of the elements, by any measure a major conceptual accomplishment for any theory. Although accurate computations become increasingly more challenging as the number of electrons increases, the general patterns of atomic behavior can be predicted with remarkable accuracy.
- 10: The Chemical Bond
- Extension of the quantum mechanics for atoms to polyatomic molecules is simple in principle, but complicated in practice. Two theories were developed to address this: Valence Bond theory and Molecular orbital theory. The introduction to both are discussed in this section.
- 11: Molecular Orbital Theory
- Molecular orbital theory is a conceptual extension of the orbital model, which was so successfully applied to atomic structure. As was once playfully remarked, "a molecule is nothing more than an atom with more nuclei." This may be overly simplistic, but we do attempt, as far as possible, to exploit analogies with atomic structure. Our understanding of atomic orbitals began with the exact solutions of a prototype problem – the hydrogen atom.
- 12: Molecular Symmetry
- In many cases, the symmetry of a molecule provides a great deal of information about its quantum states, even without a detailed solution of the Schrödinger equation. A geometrical transformation which turns a molecule into an indistinguishable copy of itself is called a symmetry operation. A symmetry operation can consist of a rotation about an axis, a reflection in a plane, an inversion through a point, or some combination of these.
- 13: Molecular Spectroscopy
- Our most detailed knowledge of atomic and molecular structure has been obtained from spectroscopy-study of the emission, absorption and scattering of electromagnetic radiation accompanying transitions among atomic or molecular energy levels. Whereas atomic spectra involve only electronic transitions, the spectroscopy of molecules is more intricate because vibrational and rotational degrees of freedom come into play as well.
- 14: Nuclear Magnetic Resonance
- Nuclear magnetic resonance (NMR) is a versatile and highly-sophisticated spectroscopic technique which has been applied to a growing number of diverse applications in science, technology and medicine. This chapter will consider, for the most part, magnetic resonance involving protons.
