Bonding

Bringing the atoms together

Until now, we have been consumed with describing individual atoms of elements. However, isolating individual atoms in most elements is an arduous task given the scale. Most matter is composed of many, many atoms.

Matter

Pure substances*

Elements

Compounds

Mixtures

Homogeneous

Heterogeneous*Pure is very hard to achieve in quantity

More than one atom

Pure substances – typically more than one atom

So what is holding the polyatomic elements together?

Image by E.B. Watson

Covalent bonds – the sharing of electrons

1s1 to 1s2 ([He])

1s1 & [He] 2s2 2p5

to [Ne]

[He] 2s2 2p5

to [Ne]

Two hydrogen atoms in close proximity can share their electrons so that each takes on an electronic structure similar to He – a noble gas.

The diatomic H-H system:

Covalent bonding

Images by E.B. Watson

Electron Swapping

Best with elements of nearly identical electronegativity.

e.g. H2

Hydrogen is 1s1

Another proton and electron would make He, a much more stable configuration- so when you bring two hydrogens together they share their electrons so each has 2 (sort of).

The Covalent Bond Model

This electron sharing is a very strong bond. This tends to by asymmetrical, and therefor difficult to pack into repeating lattices

H2 O2 Cl2 F2

Image from Gill, 1996

Image from Pauling, 1970

Image modified from Zoltai and Stout, 1984

Diamond’s excited state

Sharing an electron in 2p

Sharing an electron in two vacancies with 1s in 2p

Image after Zoltai and Stout, 1984

Electron distribution

Double bondingTwo electron pairs are shared

Triple bondingThree electron pairs are shared

Coordinate covalent bonds – the shared electron is donated by atom.

Most carry an overall negative charge(CO3)2-, (OH)-, (HCO3)-, (PO4)3-

lithium (Li) 1s22s1

The 2s electrons are delocalized – move around

For atoms with appropriate electron structure, electron swapping is quite easy when matter is condensed

Metallic bonding

Image by E.B. Watson

Image by E.B. Watson

Covalently bonded atoms have no charge, but most examples will orient themselves in an electric field

Couloumb’s law

So there must be an ionic character to the bond

Ionization - losing or gaining valence electrons

Can only attract so far – “solid spheres”

Ionic bonding

Electronegativity!

Ionic and covalent bonding are endmembers there is a range of between these two extremes. How do we know if the bonding is dominated by one form or another.

Measuring electronegativity

EAB > ½ E(A2) + ½E(B2)

EAB = ½ E(A2) + ½E(B2) +

is excess energy due to ionic attraction

(+ and -)

= 23(XA - XB) ---X is electronegativity --

Periodicity of electronegativity

Ionic-covalent character makes molecules dipolar

F, X = 4

H, X = 2.1

= 23|XA - XB|

Silcates Si-O Sulfides M-S

Fe 1.65 Fe-S: |1.8-2.5| = 0.7

S 2.5

Si 1.8 Si-O: |1.8-3.5| = 1.7

O 3.5

Silcates vs. Sulfides

A compound containing just two elements "-ide“.The metal is named first:

NaCl sodium chloride

Multiple valence stateFe3+ or Fe2+. Higher valence state with the suffix "-ic" and the lower with "-ous":

Fe2O3 ferric oxideFeO ferrous oxide

Today we tend to use a more explicit approachFe2O3 iron(III) oxideFeO iron(II) oxide

Ionic compoundsIonic compounds

More than two elements with polyatomic anions such as

hydroxide OH-

carbonate (CO3)2-

nitrate (NO3)-

phosphate (PO3)3-

The compound names follow pretty logically:KOH potassium hydroxideCaCO3 calcium carbonate

Polyatomic anions can have more than one configuration, e.g.

nitrate (NO3)-

nitrite (NO2)-

CO2 carbon dioxide (Greek "di" for 2)CO carbon monoxide (Greek "mono" for 1)CCl4 carbon tetrachloride (Greek "tetra" for 4)

Empirical Formulas

Always used in ionic compounds

NaCl CaF2 CH2O

Covalent compounds

Used for largely covalent compounds

While CH2O accurately describes the ratio of elements in glucose, it fails to characterize the whole molecule

Molecular Formulas

Structural formulas show the geometry and bonding

You are already familiar with atomic mass…

Recall that the atomic mass of an element is the mass of the individual isotopes proportionally distributed.

Molecular mass is obtained by summing the atomic mass for the number of atoms of each element.

CaF2 at. mass tot. mass

1 atom Ca 40.1 au 40.1 au

2 atoms F 19.0 au 38.0 au

m.m.m.m. 78.1 au78.1 au

Avogadro's number

Mg + ½ O2 MgO

A mole is the number of atoms or molecules (6.02 x 1023) needed to make a mass (g) equivalent to the atomic or molecular mass.

Image from Gill, 1996

Generally, directionality of bonds may be important in covalent species - bonds are generally weaker*

Directionality less important for ionic bonds - radius ratios determine structures.

* exception diamond

As atoms approach, there is a coulombic attraction

Ep (potential energy) = -e2/r

But as ions approach, their electron distributions overlap, so there is a repulsion.

Ep=-e2/r + (be2)/r12

Balance between the overall attraction of atoms and the inter-electron repulsions

Attraction F = kc q1 q2 r-2

Repulsion F is elastic rebound

Images by E.B. Watson

Image from Gill, 1996

NaCl vs. NaF

F:1s2 2s2 2p5

Cl:1s2 2s2 2p6 3s2 3p5

Both are strongly electronegative

So what differences might you expect?

As it tuns out, the ions are not hard spheres, but more squishy!

There is some variation allowed in the range of “acceptable” radius ratios (cation/anion) in this

configuration.

Image from Blackburn and Dennen, 1994

Ionic bonding is a reduction of excess energy because of (+) or (-) charges. Ionically-bonded compounds are charge balancedcontrols stoichiometry, or ratio of atoms in the compound

Na+ + Cl- = NaClCa++ + 2F- = CaF2

The Ionic Bond Model

Changing coordination

Bonding

The atoms are not stationary.

T Vibration

25oC 0.025 nm

600oC 0.060 nm

Image from Blackburn and Dennen, 1994

Coordination

Coordination

Certain anion/cation ratios produce a predictable polyhedra in IONIC bonding.

CN Type Rc/Ra

2 Linear <0.155

3 Triangle >0.155

4 Tetrahedron >0.225

6 Octahedron >0.414

8 Cube >0.732

12 Closest Packing 1

No Yes

Yes, but... Preferred

CN Rc/Ra

3 Tri 0.155-inf

4 Tetra 0.225-inf

6 Oct 0.414-inf

8 Cube 0.732-inf

Symmetrically-packed structures

• Atoms are spheres

• Bonds must be either non-directional or highly symmetical

Cubic packing

Hexagonal packing

Molecular structures

• Composed of atoms characterized by strongly directional bonding with low symmetry.

• Result is clusters, chains, and layers of atoms that are strongly bonded internally, but weakly bonded to one another.

• Examples: ice, organic molecules

Cubic Closest Packing

Colors here denote different layers of atoms

Hexagonal Closest Packing

Symmetrically-packed structures can be monatomic or multiatomic.

Symmetrical packing applies to the larger anions.

Monoatomic - Native Elements (Au, Ag, S)

Multiatomic - Most oxides and many silicates

Quartz: Two oxygens for every silicon.

Charge of Si = +4, O = -2

We then say the stoichiometery is 1:2

Important: Si, Ti, Al, Fe, Mg, Ca, Na, K, P, O, S

Today’s $10K question: how do we reconcile the overall stoichiometry (i.e. the chemical formula SiO2) with the coordination of SiO4?

The tetrahedra link together such that the oxygens are shared

This illustrates the general principles of the architecture of crystals

Endmember types

Polyhedra-frame structures

• Bonding dominantly ionic

• Anions group around cations to make coordination polyhedra

Silicates (SiO2 minerals) built of silicate tetrahedra which share corners with one another - this makes a framework. It imparts certain properties to the minerals: strong, hard, etc.

Image from Klein and Hurlbut, 1985

Halite (NaCl)

Two ways to model NaCl: left, atoms of Na and Cl shown, right, atoms of Cl shown with coordination polyhedra (octahedra)

How are these

related?

QUARTZ

Six-fold symmetrical arrangement of tetrahedra all joined by common oxygen atoms.

Rule 1. Interatomic Distance. A coordination polyhedron of anions is formed about each cat-ion. The cation-anion distance being determined by the radius sum and the coordination number of the cation by the radius ratio.

Rule 2. Electrostaic Valency Principle. In a stable coordination structure, the total strength of the valence bonds that reach an anion from all neigh-boring cations is equal to the charge of the anion.

Rule 3. Sharing of Polyhedral Elements I. The existence of edges. and particularly of faces, common to two coordination polyhedra decreases the stability of ionic structures.

Rule 4. Sharing of Polyhedral Elements II. In a crystal containing different cations, those with large valence and small coordination tend not to share polyhedral elements with each other.

Rule 5. Principle of Parity. The number of essentially different kinds of constituents in a crystal structure tends to be small.

Pauling's Rules