physical chemistry -...

Physical Chemistry

A Very Brief Introduction

Aleksey Kocherzhenko

March 14, 2013"

What Is Physical Chemistry?"

All chemistryis a branch of physical science"

Physical Science"is 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. Simon!Physical 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!"

1

�vac= RZ2

✓1

n21

� 1

n22

◆Rydberg’s formula:"

Orbits vs. Orbitals"

Niels Bohr"

Model of an H-like atom"

)

E = � Ze2

4⇡"0r| {z }U

+mev2

2| {z }T

= �1

2

Ze2

4⇡"0r

mev2

r=

Ze2

4⇡"0r2Coulomb force

Centripetal force:"

Angular momentum quantization:" mevr = n~Principal quantum number

n = 1, 2, 3, … Reduced

Planck’s constant

where" r =n~mev

=

✓4⇡"0~2e2me

◆n2

Z

Bohr radius rB ⇡ 0.529 A

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)"

+  

Energy levels of a hydrogen-like atom: "

Rydberg constant, R

E = �✓e4me

8"20h2

◆

| {z }⇡13.6 eV

Z2

n2 Planck constant:

�E = E2 � E1 = h⌫

Correct absorption frequency:"

h = 2⇡~

to satisfy Rydberg’s formula:"

(�vac⌫ = c)

1

�vac= RZ2

✓1

n21

� 1

n22

◆

Orbits vs. Orbitals"

Louis de Broglie"Interference: light is a wave"Photoelectric effect:"light consists of particles?"

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

Or:" p = ~k, k = 2⇡/�

E = ~!, ! = 2⇡⌫

(angular wavenumber)"

(angular frequency)"

� =h

pDe Broglie wavelength:"

Particle-wave duality"

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)"

+  

Particle in centrosymmetric potential:"“Old” quantum theory "

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)"

+  

1)  Electrons in atoms are found in stable (time-independent) states"2)  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"