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

1. Physical ChemistryA Very Brief IntroductionAleksey KocherzhenkoMarch 14, 2013

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

3. 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

4. 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

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

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

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

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

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

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

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

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

13. Particle-wave duality

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

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

16. 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