The Evolution of Matter:
From Simple to Complex
Prof. Jackson
CC105
Music
“Molecules” performed by
Chick Corea
Today’s Lecture
•
•
•
•
Regularities in chemical properties
The periodic table
Connection to quantum mechanics
Chemical bonds:
– Ionic
– Covalent
• Molecules in space
The Story of Stuff: So Far
• The Big Bang made hydrogen and
helium.
• Stars made heavy elements and
dispersed them through supernova
explosions.
• Gas clouds are filled with many different
elements.
General Principle:
• At low temperatures, particles tend to
prefer more binding energy and more
bound particles
• At high temperatures, particles tend to
prefer more spatial freedom and more
unbound particles.
• In cold interstellar clouds, particles
agglomerate into atoms and molecules.
The Atom in Physics and Chemistry
• Physics: electrons bound to a nucleus
• Chemistry: smallest chemical unit
Chemical Evidence for Atom
• Compounds combine with small, whole
number ratios of elements
• These ratios represent the number of
atoms that combine in each molecule of
a compound: for example
2 H2 + O2  2 H2O
• Atom: smallest unit to share in
chemistry
Crystals: Atoms packed together
• Atoms combine in particular geometrical
shapes
Water
Salt
• Reflects the geometry of how individual
atoms combine
Crystals
The Chemical Atom
• Combines in specific ratios
• Combines with particular
geometric configurations
The Periodic Table
• Elements are arranged in columns
according to chemical properties; rows
according to atomic mass.
• Successes
– Organized elements in rational scheme
– Predicted existence of new elements
• Shortcoming
– Empirical (how, not why)
Periodic Table
Evidence for the Physics Atom before
Quantum Mechanics
• Brownian motion---jiggles of small
particles in a liquid can be explained by
collisions with large numbers of atoms
• Gas laws---relations between density,
temperature, and pressure---can be
explained by colliding atoms (or
molecules)
Physics vs. Chemistry
How can physics account for
the chemical properties of
atoms?
?
Quantum mechanics: connecting the
physics and chemistry atom
The Schrödinger Equation

ħ2
2m
2
Ψ + VΨ = EΨ
Application of Schrödinger Equation
to Atom
• Predicts wave function for electron
orbiting nucleus (electric force)
• Standing waves occur only for particular
energies
Orbitals
Standing waves of probability
The chance of finding an electron is
given by the square of the wave
function at a certain location
Mathematical predictions from the
Schrödinger equation
Shapes of orbitals
S Orbital
Angular momentum = 0
Spherical
Shapes of orbitals
S Orbitals
Can have several
radial maxima
Shapes of Orbitals
P orbital
Angular momentum = ħ
Dumbbell
3 sets of p orbitals
y
y
z
z
px
x
x
x
z
y
py
pz
Orbital Shapes:
d orbitals
D orbital
Angular momentum = 2ћ
Orbital Shapes:
F orbitals
F orbital
Angular momentum = 3ћ
Since they are waves, orbitals
superpose
y
y
x
z
y
x
z
x
z
y
y
x
x
z
P orbitals
z
P and S orbitals
The Schrödinger Atom
y
x
z
The atom is a
nucleus
surrounded by a
“cloud” of
electron
probability
Comparison with the Bohr atom
y
x
z
Electrons in
orbit around
nucleus
Probability waves
in constructive
interference
How it all works
• Orbitals have different energies
• Orbitals have specific shapes
• Electrons in a system settle into the
lowest energy states available
• Pauli Exclusion Principle
Pauli Exclusion Principle
No two electrons can have the
same quantum state.
Quantum state: a solution of the
Schrödinger equation, which can be
identified by its set of labels called
“quantum numbers.”
Quantum numbers represent
(for electrons)
l : Angular momentum = l x ħ (orbital motion)
l = 0,1,2,3, …
ml : Alignment of l along z-axis = ml x ħ
ml = 0,+1,+2,+3,…. |ml| < l
s : Intrinsic angular momentum (“Spin”) = s x ħ
s=½
ms : Alignment of s along z-axis = ms x ħ
ms = +½, -½
Quantized Projection of ℓ
z
l
ml
x
y
The projection of l
along the z-axis, ml,
is quantized, it can
take only values
0,±1ћ, ±2ћ,…±nћ
Only certain orientations for l are possible
Orbital
Angular
Name momentum
S
0
Number of
possible l
orientations
1
P
ћ
3
D
2ћ
5
F
3ћ
7
“Spin”
• No classical analogue
• Intrinsic angular momentum
s
Two possible spin orientations
Spin up
ms = +1/2
Spin down
ms = -1/2
Orbital Properties
#
of
electron
Orbital Angular
states in
Name Momentum orientations
orbital
#l
S
0
1
2
P
ħ
3
6
D
2ħ
5
10
F
3ħ
7
14
Principal Quantum Number n
Number of nodes in standing wave
rΨ
n=1
r
n=2 rΨ
r
rΨ
n=3
r
Nomenclature
• nl
–n = principle quantum number
– l is called
• S (l = 0)
• P (l = 1)
• D (l = 2)
• F (l = 3)
Example
2p
Nomenclature
• nl
–n = principle quantum number
– l is called
• S (l = 0)
• P (l = 1)
• D (l = 2)
• F (l = 3)
Example
2p n=2,
l=1
Larger n : Higher energy and larger
size
1s orbital
superposed on
2s orbital
y
x
z
Build Atom
• Hydrogen 1 electron
• Helium
2 electrons
• Lithium
3 electrons
Etc. …
Electronic Configuration
Nomenclature: nl#
n principle quantum number
l orbital angular momentum
# number of electrons in orbital
Open and Closed Shells
• When all of the orbitals for a particular
n (called a “shell”) are full, the shell is
closed.
• When the shell has empty slots, it is
open.
• Only electrons in open shells participate
in chemistry.
• Atoms with closed shells are chemically
inert.
Energy Level Diagram
3s
3px
3p
3pz
y
E
2s
2px
2p
y
1s
2pz
Energy Level Diagram
3rd shell
3s
3px
3p
3pz
y
E 2nd
shell
2s
2px
2p
y
1st shell
1s
2pz
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Hydrogen
1s
1s1
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
y
1s
Helium
1s2
2pz
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
y
Lithium
1s
1s22s1
2pz
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Beryllium
1s
1s22s2
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Boron
1s
1s22s22p1
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Carbon
1s
1s22s22p2
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Nitrogen
1s
1s22s22p3
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Oxygen
1s
1s22s22p4
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Fluorine
1s
1s22s22p5
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Neon
1s
1s22s22p6
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Sodium
1s
1s22s22p63s1
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Magnesium
1s
1s22s22p63s2
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Aluminum
1s
1s22s22p63s23p1
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Silicon
1s
1s22s22p63s23p2
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Phosphorus
1s
1s22s22p63s23p3
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Sulfur
1s
1s22s22p63s23p4
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Chlorine
1s
1s22s22p63s23p5
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Argon
1s
1s22s22p63s23p6
Quantum Mechanics and the Periodic
Table
• All atoms with the same number of
electrons in open shells have similar
chemistry
• Number of columns is due to the
number of electrons allowed in orbitals
Orbital Properties
#
of
electron
Orbital Angular
states in
Name Momentum orientations
orbital
#l
S
0
1
2
P
ħ
3
6
D
2ħ
5
10
F
3ħ
7
14
Periodic Table
2
1
s
n
1
2
3
4
5
6
7
6
filled
s2
p1 p2 p3 p4p5
10
d
14
f
Chemical Bonds
• Atoms tend to minimize their energy by
obtaining a closed-shell configuration
• Two possibilities
– Lose or gain electrons (ion=charged atom)
“Ionic bond”
– Share electrons with other atoms
“Covalent bond”
Chemical Bonds: Ionic
• Ions --- atoms that have gained or lost
electrons beyond their neutral state
• Positive ions’ charge balances negative
ions
• Shape of crystal results from packing
together ions of different sizes
Sizes of Ions
Example: Salt = Sodium Chloride
How do sodium and chlorine
most easily obtain a closed-shell
structure?
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Sodium
1s
1s22s22p63s1
Energy Levels
3s
3px
3p
3pz
y
E
2s
2px
2p
2pz
y
Chlorine
1s
1s22s22p63s23p5
How does atom attain a closed shell?
• Sodium has one extra electron, so it
loses one.
• Chlorine needs one extra electron, so it
gains one.
Example: Sodium Chloride
+
Sodium: loses
electron
Chlorine: gains
electron
Structure of Sodium Chloride
• Ions pack together
as closely as
possible.
• Forms cubic
structure
Cubic crystal results from atomic structure
Other crystal structures
Depends on sizes of ions
Crystal forms
Which atoms form ionic bonds?
• Elements in first (second) column have one
(two) loosely bound electron(s).
• These atoms lose electrons and form positive
ions.
• Elements in last (next to last) column require
one (two) electron(s) to complete a closed
shell
• These atoms lose electrons and form negative
ions.
Periodic Table
+ ++
Salts
• Na (sodium) + Cl (chlorine)
– Na+ + Cl-  NaCl
• Ba (barium) + F (fluorine)
– Ba++ + 2F-  BaF2
• Cs (cesium) + I (iodine)
– Cs+ + I-  CsI
Chemical Bonds: Covalent
The wave function of an electron from
one atom overlaps that of an electron
from a different atom
Bonding orbital
Constructive
Interference
+
-
+
Negative charge screens one nucleus
from the other, and attracts nucleus
Anti-bonding orbital
Destructive
Interference
+
+
Negative charge screen is absent,
nuclei “see” each other, repel each
other, attracted to negative charge
opposite the nucleus
Shapes of s Molecular Orbitals:
Combine 2 s orbitals
Molecular Orbitals
Antibonding
First electron
unattached
Second electron
unattached
Bonding
Building Diatomic Molecules
Anti-bonding
2s
Bonding
Hydrogen
2 bonding electrons
0 antibonding electrons
Anti-bonding
1s
Bonding
H2 exists
Anti-bonding
2s
Bonding
Helium
2 bonding electrons
2 antibonding electrons
Anti-bonding
1s
Bonding
He2 does not
exist
Anti-bonding
2s
Bonding
Lithium
4 bonding electrons
2 antibonding electrons
Anti-bonding
1s
Li2 exists
Bonding
Anti-bonding
2s
Bonding
Beryllium
4 bonding electrons
4 antibonding electrons
Anti-bonding
1s
Bonding
Be2 does not
exist
Diatomic Molecules
• The following molecules have more
bonding than anti-bonding electrons
– H2, Li2, B2, C2, N2, O2, F2
– These molecules exist in nature
• The following molecules have equal
numbers of anti-bonding and bonding
electrons
– He2, Be2, Ne2, …
– These do not exist in nature
Larger Molecules: Water
H
H
O
Ice crystals
Ice Crystals have hexagonal symmetry
Larger Molecules
Overlapping p orbitals
Proteins
Built up of
20 amino
acids
Green Fluorescent Protein
Hemoglobin
The shapes of
biomolecules
determines
their function
DNA
Successes of Schrödinger Atom
• Explains patterns in periodic table
• Explains chemical properties of
elements
• Explains structure of crystals and
molecules
Molecules in the Interstellar Medium
Molecules in Space
• Supernova explosions enrich the
interstellar gas with heavy elements
• They become incorporated into gas
clouds
• Gas clouds can form molecules
– Mostly H2
– But many, many other molecules are seen
Molecular Lines in
Interstellar Clouds
Molecular Lines in Interstellar Clouds
Interstellar Molecules Detected So Far
Interstellar Molecules: Two Atoms
AlF AlCl C2 CH CH+ CN CO CO+ CP CS
CSi HCl HF H2 KCl NH NO NS NaCl OH
PN SF SO S0+ SiN SiO SiS
Carbon monoxide
Hydroxyl radical
Interstellar SiN
Interstellar Molecules: Three Atoms
C3 C2H C20 C2S CH2 HCN HCO HCO+
HCS+ HOC+ H20 H2S HNC HNO MgCN
MgNC N2H+ N20 NaCN OCS S02 c-SiC2
CO2 NH2 H3+ SiCN
Water!
Interstellar Molecules: Four Atoms
c-C3H l-C3H C3N C30 C3S C2H2 CH2D+?
HCCN HCNH+ HNCO HNCS HOCO+
H2CO H2CN H2CS H30+ NH3 SiC3
Formaldehyde
Ammonia
Interstellar Molecules: Many Atoms
CH3OH CH3C4H (CH3)20 CH3CH20H HC7N
(CH3)2CO HC9N HC11N
Alcohol!
Interstellar Molecular Gas Clouds
Interstellar gas clouds
contain many
complex, organic
molecules.
Presumably, these will
be deposited onto
the newly formed
earth.
Perhaps these
molecules are
responsible for
the origin of
life.