The Evolution of Matter:From Simple to Complex

Prof. JacksonCC105

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

• Reflects the geometry of how individual atoms combine

Water Salt

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. ChemistryHow can physics account

for the chemical properties of atoms?

?

Quantum mechanics: connecting thephysics and chemistry atom

ħ2

2m2 Ψ + VΨ = EΨ

The Schrödinger Equation

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 probabilityThe 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 OrbitalAngular momentum = 0Spherical

Shapes of orbitals

S OrbitalsCan have severalradial maxima

Shapes of Orbitals

P orbitalAngular momentum = ħDumbbell

3 sets of p orbitals

px pypz

x

y

z

y

x

z

x

y

z

Orbital Shapes: d orbitals

D orbitalAngular momentum = 2ћ

Orbital Shapes: F orbitals

F orbitalAngular momentum = 3ћ

x

z

Since they are waves, orbitals superpose

x

y

z

x

y

z

P orbitals P and S orbitals

y

x

y

z

x

y

z

The Schrödinger Atom

The atom is a nucleus surrounded by a “cloud” of electron probability

x

y

z

Comparison with the Bohr atom

Electrons in orbit around nucleus

Probability waves in constructive interference

x

y

z

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 PrincipleNo 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

x

y

z

lml

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

Name

Angular momentu

m

Number of possible l

orientations

S 0 1

P ћ 3

D 2ћ 5

F 3ћ 7

“Spin”

• No classical analogue• Intrinsic angular momentum

s

Two possible spin orientations

Spin upms = +1/2

Spin down ms = -1/2

Orbital Properties

Orbital Name

Angular Momentum

#l orientatio

ns

# of electron states in orbital

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

r

rΨ

r

rΨ

r

rΨ

n=1

n=2

n=3

Nomenclature

•nl –n = principle quantum number– l is called

•S (l = 0)•P (l = 1)•D (l = 2)•F (l = 3)

Example2p

Nomenclature

•nl –n = principle quantum number– l is called

•S (l = 0)•P (l = 1)•D (l = 2)•F (l = 3)

Example2p n=2,

l = 1

Larger n : Higher energy and larger size

1s orbitalsuperposed on2s orbital

x

y

z

Build Atom

• Hydrogen 1 electron • Helium 2 electrons• Lithium 3 electrons

Etc. …

Electronic Configuration

n principle quantum numberl orbital angular momentum# number of electrons in orbital

Nomenclature: nl#

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

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Energy Level Diagram

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

1st shell

2nd shell

3rd shell

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Hydrogen

1s1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Helium

1s2

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Lithium

1s22s1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Beryllium

1s22s2

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Boron

1s22s22p1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Carbon

1s22s22p2

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Nitrogen

1s22s22p3

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Oxygen

1s22s22p4

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Fluorine

1s22s22p5

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Neon

1s22s22p6

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Sodium

1s22s22p63s1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Magnesium

1s22s22p63s2

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Aluminum

1s22s22p63s23p1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Silicon

1s22s22p63s23p2

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Phosphorus

1s22s22p63s23p3

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Sulfur

1s22s22p63s23p4

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Chlorine

1s22s22p63s23p5

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Argon

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

Orbital Name

Angular Momentum

#l orientatio

ns

# of electron states in orbital

S 0 1 2

P ħ 3 6

D 2ħ 5 10

F 3ħ 7 14

Periodic Table

ps1

s ppp pfilled

d

f

1

32

45

n

76

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

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Sodium

1s22s22p63s1

Energy Levels

2px 2py 2pz

3px 3py 3pz

2s

1s

3s

E

Chlorine

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: loseselectron

Chlorine: gainselectron

Structure of Sodium Chloride

• Ions pack together as closely as possible.

• Forms cubic structure

Cubic crystal results from atomic structure

Other crystal structuresDepends 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

Negative charge screens one nucleus from the other, and attracts nucleus

+ +-Constructive Interference

+ +

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 Molecular Orbitals: Combine 2 s orbitals

Molecular Orbitals

Bonding

AntibondingFirst electronunattached

Second electronunattached

Energy

Building Diatomic Molecules

1s

2sHydrogen

H2 exists

2 bonding electrons

0 antibonding electrons

Bonding

Anti-bonding

Anti-bonding

Bonding

1s

2sHelium

He2 does not exist

2 bonding electrons

2 antibonding electrons

Bonding

Anti-bonding

Anti-bonding

Bonding

1s

2sLithium

Li2 exists

4 bonding electrons

2 antibonding electrons

Bonding

Anti-bonding

Anti-bonding

Bonding

1s

2sBeryllium

4 bonding electrons

4 antibonding electrons

Be2 does not existBonding

Anti-bonding

Anti-bonding

Bonding

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

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 monoxideHydroxyl radicalInterstellar 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

FormaldehydeAmmonia

Interstellar Molecules: Many Atoms

CH3OH CH3C4H (CH3)20 CH3CH20H HC7N (CH3)2CO HC9N HC11N

Alcohol!

Interstellar Molecular Gas CloudsInterstellar 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.