Learning Objectives for Today

After today’s class you should be able to:• Define and compare ionic/covalent bonds• Predict properties of materials with different kinds of

bonds• Guess what kind of bonding should occur for specific

materials and back it up with things you’ve learned about bonding

• Reminder: Student talks next week (read rubrics)

Comparing Charge Densities

• We have characterized metals versus insulators by having partially full or full bands in k space

• Distinction in real space less clear (charge density)• Covalent crystals have large interstitial charge density

called bonds• Molecular crystals (noble gases) have filled shells, and

are extremely tight-binding solids (~spherical).• Ionic crystals composed of a metallic and a

nonmetallic element and share electrons (also bond)• Compare to metals (even distribution)

Bonding Type Affects PropertiesProperties are determined to a great degree by type of bonding

– Ionic: involves transfer of an electron between two atoms, resulting in a net electrostatic attractive force

– Covalent: involves sharing of an electron between atoms

The type of bonding is determined mainly by the degree of overlap between the electronic wavefunctions of the atoms involved.

Covalent to Ionic Transition

Purely Covalent

Purely Ionic

Cation: positive ion

Anion: negative ion

An ion is an atom in which the total number of electrons is not equal to the total number of protons, giving the atom a net electrical charge.

Perovskites and other structures(oxygen cation

or anion?)

Why do bonds form?Some molecules and their binding energies (i.e., energy released when molecule is formed). Binding energy = bond strength.

Bonding can be understood from coulomb energyAssume that charge (one electron) is completely transferred in an ionic molecule:

0

2

Rke

U - +

nm 2.00 R

eV 7nm 2.0

nm eV 44.1

If this potential energy is greater in magnitude than the energy required to ionize the atoms, a molecule will tend to form

Ionic Solids (Finding Binding Energy)

• Let’s find the energy required to transfer an electron from Na to Cl and then to form a NaCl molecule– To remove an electron from Na (ionize the atom) one

needs to “spend” 5.14eV (compare with the ionization energy of a hydrogen atom?)

Na + 5.14eV Na+ + e- – When a Cl atom captures an electron, 3.62eV

of energy is released (electron affinity of atom)

Cl + e- Cl- + 3.62eV

The energy cost to transfer the electron from the alkali to the halogen is

eV 5.1eV 6.3eV 1.5EA(Cl)(Na) IE E

X + e− → X− + energy

DANGER!

The Ionic Bond

eV 5.1eV 6.3eV 1.5EA(Cl)(Na) IE E

Rke

ERE2

)(

The ionic bond will form when E(R) becomes negative.

With a partner, find this R for NaCl.This happens when R is below the critical distance

E

keRC

2

at which E(R) = 0.

+Na+

-Cl-

R

(halogen)Affinity Electron (alkali)Energy Ionization E

• Since DE >0, this will not happen if the atoms are far away• As the atoms move closer, forming an ionic bond becomes

energetically favorable due to coulomb potential energy• Total energy of ion as a function of separation R is

Reminder: k=1/4o

The Ionic Bond

nm 96.0CR

In reality, ions will not get infinitely close to each because ? • repulsion between nuclei•electrons in the same region can not occupy the

same quantum states (Pauli exclusion principle), thus increasing the energy of the ion

A good approximation for the binding energy can be obtained from R0:

ER

keREBE

0

2

0 )(

•2nd term is repulsion between 2 electron clouds (two free parameters: B and 6<n<10)•This leads to a minimum energy as a function of R which defines distance between ions in molecule:

Effective potential nr

B

r

ke

2

NaCl critical distance is

Ionic crystals

• 3D crystals can be produced in this manner.• In NaCl, each chlorine atom is surrounded by

sodium neighbors, and vice versa.• The exact structure is determined by the

optimal use of space for the given ionic radii

Impenetrable Spheres

• Ionic crystals are often modeled as hard spheres

- +

nm 2.00 R

Due to Coulomb attraction

Due to Pauli exclusion

If the spheres touch, the sum of the two diameters is

approximately the lattice parameter (may not touch if

size very different)a

Types of Crystals

Closed-shell elements: molecular crystals

Closed-shell –plus one (alkali) elements: reactive due to loosely-bound outer electron in s-shell

Closed-shell–minus-one elements (halogens): elements with high electron affinity A (energy gained when an additional electron is added to a neutral atom); will easily form negative ions (take additional electron) in remaining p-shell state due to large nuclear charge; these elements are very reactive (e.g., F- with e.a.=3.4 eV)

I-VII ionic crystals

II-VI ionic crystalsIII-V crystals are more covalent and semiconducting.

Group IV prefer covalent.

Most ionic compounds are brittle; a crystal will shatter if we try to distort it. This happens because distortion causes ions of like charges to come close together then sharply repel.

Brittleness

Most ionic compounds are hard; the surfaces of their crystals are not easily scratched. This is because the ions are bound strongly to the lattice and aren't easily displaced.

Hardness

Solid ionic compounds do not conduct electricity when a potential is applied because there are no mobile charged particles. No free electrons causes the ions to be firmly bound and cannot carry charge by moving.

Electricalconductivity

The melting and boiling points of ionic compounds are high because a large amount of thermal energy is required to separate the ions which are bound by strong electrical forces.

Melting point and boiling point

ExplanationProperty

Ionic crystals have strong bonds

COVALENT BONDING

• The covalent bonding is formed by sharing of outer shell electrons (i.e., s and p electrons) between atoms rather than by electron transfer.

• Thus, the interaction between nearest neighbors is of prime importance!

Covalent Bonding of Multielectron Atoms

For multielectron atoms covalent bonding is more likely to occur if there are unpaired electrons in an orbital– Unpaired electrons can share the

same orbital with another unpaired electron of opposite spin

Example

Fluorine has one unpaired electron, thus acts like H in forming covalent bonds

e.g.: F2, HF

F: 1s22s22px22py

22pz1

Covalent Bonding of Multielectron Atoms

N: 1s22s22px12py

12pz1

In general, binding energy increases with number of bonds:

Valence: the number of electrons that an atom can share with other atoms in a covalent bond.

Molecule B (eV)F2 (1 bond) 1.6O2 (2 bonds) 5.1N2 (3 bonds) 9.8

• N in ground state has three unoccupied p-orbital states in order to minimize repulsion energy between electrons

• Nitrogen therefore has three electrons available for covalent bonding and can form molecules such as N2 and NH3 (ammonia)

• (Group) Discuss the electron configuration of the oxygen molecule O2.

• What does this tell you about the properties of the molecule?

• The oxygen molecule is formed when two half filled 2p-orbitals of each oxygen atom overlap with the 2p-orbitals, of the other oxygen atom to form a double bond

The Oxygen Molecule

Is oxygen atom happy?What to do?

What would that look

like?

Covalent network substances are brittle. If sufficient force is applied to a crystal, covalent bond are broken as the lattice is distorted. Shattering occurs rather than

deformation of a shape. Brittleness

They are hard because the atoms are strongly bound in

the lattice, and are not easily displaced. Hardness

Poor conductors because electrons are held either on the atoms or within covalent bonds. They cannot move through the lattice.

Electricalconductivity

Very high melting points because each atom is bound by strong covalent bonds. Many covalent bonds must be broken if the solid is to be melted and a large amount of thermal energy is required for this.

Melting point and boiling point

ExplanationProperty

Covalent Materials Also Strong Bonds

Which do you think is

more conducting?

METALLIC BONDING

Wave function amplitudes in Ni

• Metallic bonding is when electrons are accumulated between ion cores.

• Metallic bonding is the type of bonding found in metal elements. This is the electrostatic force of attraction between positively charged ions and delocalized outer electrons.

• In contrast to ionic bonds, the electrons now have wavefunctions that are very extended. (4s wavefunction at large r.) Thus, many neighbors are involved in bonding.

• The metallic bond is weaker than the ionic and the covalent bonds.

• All conduction e-s in a metal combine to form a sea of electrons that move freely between cores high electrical and thermal conductivity.

• More electrons=stronger attraction. Means melting and boiling points are higher, and metal is stronger and harder. 

• The free electrons act as the bond (or a “glue”) between the positive ions.

• This type of bonding is nondirectional and

rather insensitive to structure. • As a result we have a high ductility of metals:

the “bonds” do not “break” when atoms are

rearranged – metals can experience a

significant degree of plastic deformation.

+

+

+

+

+

+

+

+

+

METALLIC PROPERTIES

graphite

van der Waals Bond

• Arise from charge fluctuations in atoms due to zero-point motion (due to Heisenberg uncertainty principle); these create dipole moments that are attractive

• Depends on p2/r6, short ranged• Always present, but significant only when

other types of bonding not possible (closed electron shells, saturated molecules)

• Typical strength of 0.2 eV/atom ~1% of other bonds

• Because force results from dipole-dipole interactions, it is short range, varying as r -

6

Usually with oxygen, fluorine or nitrogen Hydrogen “Bonding”

• Comes from the fact that it’s really hard (13.6eV) to completely remove an electron from hydrogen

• In H20, hydrogen covalently bonds with nearby oxygen, but it also has a hydrogen bond with the next nearest neighbor.

• Since the electron is pulled toward the closer oxygen, the positive charge is on the outside and attracted to other negative oxygens.