Physical Chemistry A Very Brief Introduction Aleksey Kocherzhenko March 14, 2013

What Is Physical Chemistry? Physical Science is that department of knowledge which relates to the order of nature, or in other words, to the regular succession of events. All chemistry is a branch of physical science

What Is Physical Chemistry? The name of physical science, however, is often applied in a more or less restricted manner to those branches of science in which the phenomena considered are of the simplest and most abstract kind, excluding the consideration of the more complex phenomena. James Clerk Maxwell, “Matter and Motion”, 1876

What Is Physical Chemistry? Chemistry started out as an empirical science Synthetic chemists: think in terms of functional groups Biochemists: concerned with the functionality of large molecules Physical chemists: – often look at phenomena at an atomic and even subatomic level – describe phenomena in an abstract mathematical way

What Is Physical Chemistry? Traditionally included are: Thermodynamics Kinetics Quantum mechanics as applied to molecular-level phenomena

A Great Textbook D. A. McQuarrie and J. D. Simon Physical Chemistry: A Molecular Approach University Science Books, 1997

Quantum Mechanics and Chemistry ortho meta para Reactivity is determined by orbital symmetry… … in many cases, so are functional properties!

Orbits vs. Orbitals Planetary atomic model Plum pudding atomic model Ernest Rutherford J.J. Thomson Planetary atomic model Plum pudding atomic model

Orbits vs. Orbitals The absorption/emission spectra of atoms are discrete, not continuous! Rydberg’s formula:

Principal quantum number n = 1, 2, 3, … Orbits vs. Orbitals Niels Bohr Coulomb force Centripetal force: Angular momentum quantization: Principal quantum number n = 1, 2, 3, … Reduced Planck’s constant Model of an H-like atom where Bohr radius

Orbits vs. Orbitals Energy levels of a hydrogen-like atom: Rydberg constant, R Planck constant: Correct absorption frequency: to satisfy Rydberg’s formula: n = 1 n = 2 n = 3 n = ∞ E = 0 n = 4 E = –13.6 E = –3.40 E = –1.51 –0.85 E (eV) +

Orbits vs. Orbitals Photoelectric effect: light consists of particles? Interference: light is a wave Louis de Broglie Light (and everything else) has both particle-like and wave-like properties De Broglie wavelength: Or: (angular wavenumber) (angular frequency)

Particle-wave duality

Orbits vs. Orbitals Particle in centrosymmetric potential: “Old” quantum theory n = 1 n = 2 n = 3 n = ∞ E = 0 n = 4 E = –13.6 E = –3.40 E = –1.51 –0.85 E (eV) + Wave in centrosymmetric potential: “New” quantum theory

Orbits vs. Orbitals n = 1 n = 2 n = 3 n = ∞ E = 0 n = 4 E = –13.6 E = –3.40 E = –1.51 –0.85 E (eV) + Electrons in atoms are found in stable (time-independent) states Electrons behave as waves Stable electronic states (orbitals) are standing waves

What a Typical PChem/QMech Course Covers: 0) Mathematical background and notation Foundations of quantum mechanics Postulates, equation of motion, stationary states 2) Simple model systems Particle-in-a-box, harmonic oscillator, hydrogen atom, barriers 3) Multi-electron atoms Approximate methods, spin 4) Molecules Orbital hybridization, chemical bonding 5) Spectroscopy Degrees of freedom, types of spectroscopy to probe them 6) The paradoxes of quantum mechanics and its relationship to classical mechanics