Physical Chemistry

A Very Brief Introduction

Aleksey Kocherzhenko

March 14, 2013

What Is Physical Chemistry?

All chemistryis a branch of physical science

Physical Scienceis that department of knowledge which relates to the order of nature, or in other words, to the regular succession of events.

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?

• Physical chemists:– often look at phenomena at an atomic and even subatomic level– describe phenomena in an abstract mathematical way

Chemistry started out as an empirical science

• Synthetic chemists: think in terms of functional groups

• Biochemists: concerned with the functionality of large molecules

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. SimonPhysical Chemistry: A Molecular Approach University Science Books, 1997

Quantum Mechanics and Chemistry

Reactivity is determined by orbital symmetry…

R

ortho

meta

para

… in many cases, so are functional properties!

Orbits vs. Orbitals

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:

Orbits vs. Orbitals

Niels Bohr

Model of an H-like atom

Coulomb force

Centripetal force:

Angular momentum quantization:

Principal quantum numbern = 1, 2, 3, …

ReducedPlanck’s constant

where

Bohr radius

Orbits vs. Orbitals

n = 1

n = 2n = 3

n = ∞ E = 0

n = 4

E = –13.6

E = –3.40E = –1.51

–0.85

E (eV)

+

Energy levels of a hydrogen-like atom:

Rydberg constant, R

Planck constant:

Correct absorption frequency:

to satisfy Rydberg’s formula:

Orbits vs. Orbitals

Louis de BroglieInterference: light is a wavePhotoelectric effect:light consists of particles?

Light (and everything else) has both particle-like and wave-like properties

Or: (angular wavenumber)

(angular frequency)

De Broglie wavelength:

Particle-wave duality

Orbits vs. Orbitals

n = 1

n = 2n = 3

n = ∞ E = 0

n = 4

E = –13.6

E = –3.40E = –1.51

–0.85

E (eV)

+

Particle in centrosymmetric potential:“Old” quantum theory

Wave in centrosymmetric potential:“New” quantum theory

Orbits vs. Orbitals

n = 1

n = 2n = 3

n = ∞ E = 0

n = 4

E = –13.6

E = –3.40E = –1.51

–0.85

E (eV)

+

1) Electrons in atoms are found in stable (time-independent) states2) Electrons behave as waves

Stable electronic states (orbitals) are standing waves

What a Typical PChem/QMech Course Covers:

0) Mathematical background and notation

1) 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

5) Spectroscopy Degrees of freedom, types of spectroscopy to probe them

6) The paradoxes of quantum mechanics and its relationship to classical mechanics

4) Molecules Orbital hybridization, chemical bonding