# Book: Quantum Chemistry (Blinder)

- Page ID
- 20779

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.

- 2: Waves and Particles
- For all its relevance, the quantum world differs quite dramatically from the world of everyday experience. To understand the modern theory of matter, conceptual hurdles of both psychological and mathematical variety must be overcome. A paradox which stimulated the early development of the quantum theory concerned the indeterminate nature of light. Light usually behaves as a wave phenomenon but occasionally it betrays a particle-like aspect, a schizoid tendency known as the wave-particle duality.

- 3: Quantum Mechanics of Some Simple Systems
- The simplest system in quantum mechanics has the potential energy V=0 everywhere. This is called a free particle since it has no forces acting on it.

- 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
- Bohr 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. In contrast to the particle in a box and the harmonic oscillator, the hydrogen atom is a real physical system that can be treated exactly by quantum mechanics.

- 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.

- 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. Our understanding of atomic orbitals began with the exact solutions of a prototype problem – the hydrogen atom. We will begin our study of homonuclear diatomic molecules beginning with another exactly solvable prototype, the hydrogen molecule-ion

- 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. Early observations of absorption or emission by molecules were character