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 H 2 + O 2  2 H 2 O 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. Chemistry How can physics account for the chemical properties of atoms? ?

Quantum mechanics: connecting the physics and chemistry atom  ħ2ħ2 2m 2 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 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 pxpx pypy pzpz x y z y x z x y z

Orbital Shapes: d orbitals D orbital Angular momentum = 2ћ

Orbital Shapes: F orbitals F orbital Angular 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

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, … m l : Alignment of l along z-axis = m l x ħ m l = 0,+1,+2,+3,…. |m l | < l s : Intrinsic angular momentum (“Spin”) = s x ħ s = ½ m s : Alignment of s along z-axis = m s x ħ m s = +½, -½

Quantized Projection of ℓ x y z l mlml The projection of l along the z-axis, m l, is quantized, it can take only values 0,±1ћ, ±2ћ,…±nћ

Only certain orientations for l are possible Orbital Name Angular momentum Number of possible l orientations S01 Pћ3 D2ћ2ћ5 F3ћ3ћ7

“Spin” No classical analogue Intrinsic angular momentum s

Two possible spin orientations Spin up m s = +1/2 Spin down m s = -1/2

Example: How many S states? S orbital –l = 0 –m l = 0 –m s = +½ or -½ First state: l =0, m l =0, m s =+1/2 Second state: l =0, m l =0, m s = -1/2 } 2 states

A second example P orbital l = 1 m l = -1, 0, or 1 m s = +1/2, -1/2 How many states?

Six distinct p quantum states State # l mlml msms 11-1/2 21+1/ / / / /2

Orbital Properties Orbital Name Angular Momentum # l orientations # of electron states in orbital S012 Pħ36 D2ħ510 F3ħ714

Principal Quantum Number n Number of nodes in standing wave r rΨ r r n=1 n=2 n=3

Nomenclature n l –n = principle quantum number –l is called S ( l = 0) P ( l = 1) D ( l = 2) F ( l = 3) Example 2p

Nomenclature n l –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 x y z

Build Atom Hydrogen 1 electron Helium 2 electrons Lithium 3 electrons Etc. …

Electronic Configuration n principle quantum number l orbital angular momentum # number of electrons in orbital Nomenclature: n l #

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 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E

Energy Level Diagram 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E 1 st shell 2 nd shell 3 rd shell

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Hydrogen 1s 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Helium 1s 2

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Lithium 1s 2 2s 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Beryllium 1s 2 2s 2

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Boron 1s 2 2s 2 2p 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Carbon 1s 2 2s 2 2p 2

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Nitrogen 1s 2 2s 2 2p 3

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Oxygen 1s 2 2s 2 2p 4

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Fluorine 1s 2 2s 2 2p 5

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Neon 1s 2 2s 2 2p 6

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Sodium 1s 2 2s 2 2p 6 3s 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Magnesium 1s 2 2s 2 2p 6 3s 2

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Aluminum 1s 2 2s 2 2p 6 3s 2 3p 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Silicon 1s 2 2s 2 2p 6 3s 2 3p 2

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Phosphorus 1s 2 2s 2 2p 6 3s 2 3p 3

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Sulfur 1s 2 2s 2 2p 6 3s 2 3p 4

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Chlorine 1s 2 2s 2 2p 6 3s 2 3p 5

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Argon 1s 2 2s 2 2p 6 3s 2 3p 6

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 orientations # of electron states in orbital S012 Pħ36 D2ħ510 F3ħ714

Periodic Table pp s1s1 ss pp pp pp pp filled d f     n 7 6

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 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Sodium 1s 2 2s 2 2p 6 3s 1

Energy Levels 2p x 2p y 2p z 3p x 3p y 3p z 2s 1s 3s E Chlorine 1s 2 2s 2 2p 6 3s 2 3p 5

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 F -  BaF 2 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 Antibonding First electron unattached Second electron unattached Energy

Building Diatomic Molecules 1s 2s Hydrogen H 2 exists 2 bonding electrons 0 antibonding electrons Bonding Anti-bonding Bonding

1s 2s Helium He 2 does not exist 2 bonding electrons 2 antibonding electrons Bonding Anti-bonding Bonding

1s 2s Lithium Li 2 exists 4 bonding electrons 2 antibonding electrons Bonding Anti-bonding Bonding

1s 2s Beryllium 4 bonding electrons 4 antibonding electrons Be 2 does not exist Bonding Anti-bonding Bonding

Diatomic Molecules The following molecules have more bonding than anti-bonding electrons –H 2, Li 2, B 2, C 2, N 2, O 2, F 2 –These molecules exist in nature The following molecules have equal numbers of anti-bonding and bonding electrons –He 2, Be 2, Ne 2, … –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 H 2 –But many, many other molecules are seen

Molecular Lines in Interstellar Clouds

Interstellar Molecules Detected So Far

Interstellar Molecules: Two Atoms AlF AlCl C 2 CH CH+ CN CO CO+ CP CS CSi HCl HF H 2 KCl NH NO NS NaCl OH PN SF SO S0+ SiN SiO SiS Carbon monoxide Hydroxyl radical Interstellar SiN

Interstellar Molecules: Three Atoms C 3 C 2 H C 2 0 C 2 S CH 2 HCN HCO HCO+ HCS+ HOC+ H 2 0 H 2 S HNC HNO MgCN MgNC N 2 H+ N 2 0 NaCN OCS S0 2 c-SiC 2 CO 2 NH 2 H 3 + SiCN Water!

Interstellar Molecules: Four Atoms c-C 3 H l-C 3 H C 3 N C 3 0 C 3 S C 2 H 2 CH 2 D+? HCCN HCNH+ HNCO HNCS HOCO+ H 2 CO H 2 CN H 2 CS H 3 0+ NH 3 SiC 3 Formaldehyde Ammonia

Interstellar Molecules: Many Atoms CH 3 OH CH 3 C 4 H (CH 3 ) 2 0 CH 3 CH 2 0H HC 7 N (CH 3 ) 2 CO HC 9 N HC 11 N 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.