Chemical Bonds, Molecular Geometry, and Bond Theory

Brown and LeMay

Chapters 8 and 9

Introduction to types of bonding

• Three basic types of bonds– Ionic

• Electrostatic attraction between ions.

– Covalent• Sharing of electrons.

– Metallic• Metal atoms bonded to

each other – involves delocalized electrons.

8.1 – Lewis Symbols and the Octet Rule

• Octet rule – when forming bonds, atoms try to achieve the s2p6 configuration of a noble gas

• Lewis symbols – dots represent the valence electrons (no pairs until more than four)

8.2 – Ionic Bonding Ionic bonds = electrostatic forces that hold cations and anions

together Ionic crystal = a highly ordered solid collection of ions Using Lewis Symbols to show ionic bonding:

• Properties of ionic compounds:1. Brittle2. High melting points3. Crystalline4. Can be cleaved (break apart along smooth surfaces)5. The strength of the ionic bond can be measured with lattice energy (the

energy required to completely separate a mole of a solid ionic compound into its gaseous ions). Lattice energies are positive values, so the reverse process (forming the ionic bonds) is exothermic.

6. Lattice energy increases with:– increasing charge on the ions– decreasing size of ions– The bigger effect on lattice energy is from the ionic charge

8.3 – Covalent Bonding

• Basic Lewis Structures– Lewis Structure = using Lewis symbols to represent covalent bonds

between atoms.– Bonding pairs = the shared pairs of electrons. Shown as dots between

the atoms sharing the electrons, or more commonly as a line for each shared pair

– Lone pairs (or nonbonding pairs) = the unshared pairs of electrons. Shown as dots.

– Coordinate covalent bond = when one of the atoms provides both electrons of the shared pair. Ex. H3O+, NH4

+

– Multiple covalent bonds: ex. CO2, N2

8.4 – Bond Polarity and Electronegativity

• The electrons in a covalent bond are not always shared equally.

• Ex. Fluorine pulls harder on the electrons it shares with hydrogen than hydrogen does.

• Therefore, the fluorine end of the molecule has more electron density than the hydrogen end.

Electronegativity• Electronegativity is the ability of an atom in a

molecule to attract electrons to itself.• On the periodic table, electronegativity generally

increases as you go– from left to right across a period.– from the bottom to the top of a group.

• Nonpolar covalent bond – when the electrons are shared equally (diff. in electroneg. is ~0.4)

• Polar covalent bond – when the electrons are not shared equally (diff. in electroneg. is between ~0.4 and ~2.0)

• We depict this as follows:

• + -

• H Cl or H Cl

Is a Compound Ionic or Covalent?

• Simplest approach: Metal + nonmetal is ionic; nonmetal + nonmetal is covalent.

• There are many exceptions: It doesn’t take into account oxidation number of a metal (higher oxidation numbers can give covalent bonding).

• The electronegativity table also doesn’t take into account oxidation number.

• Properties of compounds are often best: Lower melting points mean covalent bonding, for example.

8.5 – Drawing Lewis Structures

• Hints for drawing plausible Lewis structures: Draw a skeletal structure first H is always a terminal atom The central atom of a structure usually has the

lowest electronegativity In oxoacids, H is usually bonded to O, not the

central atom Molecules and polyatomic ion structures are

usually compact and symmetrical

• A method for drawing Lewis structures:1) Determine the total # of valence electrons in the

molecule or ion2) Draw a skeletal structure using the hints on the

previous slide and connect atoms with a single bond3) Complete the octets around all the atoms bonded

to the central atom4) Use any remaining electrons for lone pairs around

the central atom(s)5) If there’s not enough electrons to make an octet

around the center atom, form multiple bonds.

• Formal Charge = the difference between the # of valence electrons in an isolated atom and the # of electrons assigned to that atom in a Lewis structure (it’s a hypothetical charge).

• # of electrons assigned = # of lone pair electrons + ½ the # of electrons in bonds.

• Example:

• Try to draw Lewis structures so that the formal charge is 0, or with a minimum formal charge

• Formal charges of adjacent atoms should be of opposite sign

• The atoms with the greatest electroneg. should have neg. formal charges, if any

• The total of the formal charges must equal the charge of the molecule

• Example:

• The middle one would be the “dominant” Lewis structure

8.6 – Resonance Structures

• Resonance (9.8): When we can draw different Lewis structures for the same molecule that differ only in the distribution of electrons (resonance structures), the actual molecule is a hybrid of the different structures (resonance hybrid). These hybrids have delocalized electrons (electrons shared by multiple atoms).

• Ex.

• The organic compound benzene, C6H6, has two resonance structures.

• It is commonly depicted as a hexagon with a circle inside to signify the delocalized electrons in the ring.

8.7 – Exceptions to the Octet Rule

• 3 categories:1) Odd number of valence electrons – most of these

are free radicals (very reactive molecular fragments). A bold dot () is sometimes used to represent the unpaired electron.

• 2) Incomplete Octets – usually the central atom is Be, B, or Al

• The general rule is: If filling the octet of the central atom results in a negative formal charge on the central atom and a positive formal charge on the more electronegative outer atom, don’t fill the octet of the central atom.

3) Expanded Octets – happens with elements in Period 3 and higher, because a d sublevel is needed in

order to have more than 8 valence electrons.Ex. PF5

ex. Phosphate ion – dominant

structure is the one with less formal charges and an 5 bondson the phosphorous

8.8 – Strengths and Lengths of Covalent Bonds

• Strength of a Covalent Bond• The strength of a bond is measured by determining how

much energy is required to break the bond.• This is called the bond enthalpy.• For ex. the bond enthalpy for a Cl—Cl bond, D(Cl— Cl), is

measured to be 242 kJ/mol.• Bond enthalpies are positive, because bond breaking is an

endothermic process. Bond forming is exothermic, so the negative value of the bond enthalpy is used.

• Average bond enthalpies are used because the actual bond enthalpy is influenced by the other bonds in the molecule

• The greater the bond enthalpy, the stronger the bond. A molecule with strong bonds generally is less reactive than one with weak bonds.

• One way to estimate H for a reaction is to use the bond enthalpies of bonds broken and the new bonds formed:

• Hrxn = (bond enthalpies of all bonds broken) − (bond enthalpies of all bonds formed).

• Example: CH4(g) + Cl2(g) CH3Cl(g) + HCl(g)

• In this example, one C—H bond and one Cl—Cl bond are broken; one C—Cl and one H—Cl bond are formed.

H = [D(C—H) + D(Cl—Cl)] − [D(C—Cl) + D(H—Cl)]

= [(413 kJ) + (242 kJ)] − [(328 kJ) + (431 kJ)]

= (655 kJ) − (759 kJ)

= −104 kJ

• Bond Length• We can also measure an average bond length

(distance between the 2 nuclei) for different bond types.

• There’s a relationship between bond enthalpy, bond length, and number of bonds between 2 atoms.

• In general, as the number of bonds between 2 atoms increases, the bond grows shorter and stronger.

9.1, 9.2 – Molecular Shapes and VSEPR Theory

• Electron group geometry (or electron domain) = the arrangement of all the electron groups around the central atom.

• Electron group (or domain) = a collection of valence electrons in a certain region around the central atom. An electron group could be a single e-, a lone pair, a single bond, a double bond, or a triple bond.

• 2 groups = linear electron group geometry (has bond angles of 180°)

• 3 groups = trigonal planar (120°)• 4 groups = tetrahedral (109.5°)• 5 groups = trigonal bipyramidal (contains both 90° and 120°)• 6 groups = octahedral (90°)• see pg 345

• VSEPR Theory (valence-shell-electron-pair- repulsion)• Simply put, electron pairs, whether they be bonding or

nonbonding, repel each other.• By assuming the electron pairs are placed as far as possible

from each other, we can predict the shape of the molecule.• VSEPR notation: central atom = A, terminal atoms = B,

nonbonding electrons = E• Ex. AB3E is a molecule with 3 terminal atoms and a lone pair.

Ex. NH3

• Molecular geometry = the shape formed from the bonded atoms (nonbonding electrons are not included)

• Once you have determined the electron-domain geometry, use the arrangement of the bonded atoms to determine the molecular geometry.

• Tables 9.2 and 9.3 show the potential molecular geometries. We will look at each electron domain to see what molecular geometries are possible.

Linear Electron Domain

• In the linear domain, there is only one molecular geometry: linear.

• NOTE: If there are only two atoms in the molecule, the molecule will be linear no matter what the electron domain is.

Trigonal Planar Electron Domain

• There are two molecular geometries:

1) trigonal planar, if all electron domains are bonding

2) bent, if one of the domains is a nonbonding pair.

Tetrahedral Electron Domain

• There are three molecular geometries:

1. tetrahedral, if all are bonding pairs,

2. trigonal pyramidal, if one is a nonbonding pair, and

3. bent, if there are two nonbonding pairs.

Trigonal Bipyramidal Electron Domain

• There are two distinct positions in this geometry:– Axial– Equatorial

• Lone pairs occupy equatorial positions.

Trigonal Bipyramidal Electron Domain

• There are four distinct molecular geometries in this domain:

• 1. Trigonal bipyramidal (all bonding pairs)

• 2. Seesaw (1 nonbonding pair)

• 3. T-shaped (2 nonbonding pairs)

4. Linear (3 nonbonding pairs)

Octahedral Electron Domain• All positions are equivalent

in the octahedral domain.• There are three molecular

geometries:• 1. Octahedral (0

nonbonding pairs• 2. Square pyramidal (1

nonbonding pairs)• 3. Square planar (2

nonbonding pairs)

Effect of Nonbonding Electrons and Multiple Bonds on the Ideal Bond Angles

• Nonbonding pairs are physically larger than bonding pairs.• Therefore, their repulsions are greater; this tends to compress bond

angles.

• Double and triple bonds have larger electron domains than single bonds.

• They exert a greater repulsive force than single bonds, making their bond angles greater.

Shapes of Larger MoleculesFor larger molecules, look at the geometry about each atom rather than the molecule as a whole.

9.3 – Molecular Shape and Polarity• For a molecule to be polar, it has to meet 2 criteria:• 1. it has to have polar bonds, and• 2. it has to have a shape in which the bond dipoles don’t

cancel each other out (it has a dipole moment)

9.4 - 9.6: Valence Bond Theory (Hybrid Orbitals)

• Valence Bond Theory looks at a covalent bond in terms of the overlap of atomic orbitals of the bonded atoms. The overlap of orbitals allows the bonding electrons to share the space between the nuclei, and they are simultaneously attracted to both nuclei, forming a covalent bond.

• The picture below shows how the potential energy of 2 hydrogen atoms changes as they come together to form H2. As the electrons and nuclei come closer together, a balance is reached between the like charge repulsions and the electron-nucleus attraction.

• The internuclear distance at the lowest point of the PE curve is the bond length.

• Hybridization: the mathematical mixing of atomic orbitals. This happens with the central atom of molecules. Terminal atoms do not hybridize.

• Hybrid orbitals form by “mixing” of atomic orbitals to create new orbitals of equal energy, called degenerate orbitals.

• The shape of a hybrid orbital is different than the shapes of the original atomic orbitals. The shapes of the hybrid orbitals mesh with the molecular geometry that VSEPR determines.

• When 2 atomic orbitals “mix” they create 2 hybrid orbitals; when 3 atomic orbitals mix, they create 3 hybrid orbitals; etc.

sp hybrids• sp hybridization is the “mixing” of one s atomic orbital and

one p atomic orbital. It leads to linear e- pair geometry and 180o bond angles.

• This is consistent with the observed geometry of molecules like BeF2

sp2 hybridization

• sp2 hybridization is the “mixing” of one s atomic orbital and two p atomic orbitals. It leads to trigonal planar e- pair geometry and 120o bond angles.

sp3 hybridization

sp3 hybridization is the “mixing” of one s atomic orbital and three p atomic orbitals. It leads to tetrahedral e- pair geometry and 109.5o bond angles.

Multiple Bonds• Sigma () bond = an end-to-end overlap of simple or hybrid

orbitals along a line between the 2 nuclei (i.e. all the bonds we’ve talked about so far)

• Pi () bond = a side-to-side overlap of p orbitals, producing high e- charge density above and below a line between the 2 nuclei. Pi bonds are weaker than sigma bonds.

Single bonds are bonds. Double bonds consist of 1 and 1 bond. Triple bonds consist of 1 and 2 bonds.

A bond involves more overlap (i.e. is stronger) than a bond.

The shape of the molecule is determined only by the bonds.

Rotation about the double bond is very restricted.

• Geometric Isomers = organic molecules that differ in the positions of attachment of substituent groups at a double bond.

• Cis isomers have the substituent groups on the same side of the molecule

• Trans isomers have the substituent groups of opposite sides.

Localized or Delocalized Electrons

• Bonding electrons (σ or π) that are specifically shared between two atoms are called localized electrons.

• In molecules that have resonance structures, we have electrons shared by multiple atoms. They are called delocalized electrons. Example: benzene

9.7, 9.8: Molecular Orbital (MO) Theory

• Molecular Orbital Theory views a molecule as a whole instead of a collection of individual atoms.

• Uses the wave functions of a molecule• Molecular orbitals have many characteristics like atomic

orbitals:– maximum of two electrons per orbital– electrons in the same orbital have opposite spin.– have specific energy levels

• Whenever two atomic orbitals overlap, two molecular orbitals are formed: one bonding, one antibonding.

• Bonding orbitals are constructive combinations of atomic orbitals.• Antibonding orbitals are destructive combinations of atomic orbitals.

They have a new feature unseen before: A nodal plane occurs where electron density equals zero.

Whenever there is direct overlap of orbitals (the electron density is centered about the internuclear axis), forming a bonding and an antibonding orbital, they are called sigma (σ) molecular orbitals. The antibonding orbital is distinguished with an asterisk as σ*. Here is an example for the formation of a hydrogen molecule from two atoms.

MO Diagram: has the interacting atomic orbitals on the left and right, and the MOs in the middle. It shows how orbitals combine to form the molecule.

• In H2 the two electrons go into the bonding molecular orbital (lower in energy).

• Bond order = ½(# of bonding electrons – # of antibonding electrons) = ½(2 – 0) = 1 bond

• A bond order of 1 is a single bond.• A bond order of 2 is a double bond.• A bond order of 3 is a triple bond.• 1/2, 3/2, or 5/2 are possible

(molecules containing an odd # of electrons)

Can He2 Form? Use MO Diagram and Bond Order to Decide!

• Bond Order = ½(2 – 2) = 0 bonds

• A bond order of 0 means that the bond doesn’t exist.

• Therefore, He2 does not exist.

σ and π bonds

• Molecular Orbitals from 2p atomic orbitals:

• The p orbitals that face each other overlap in fashion, like the s orbitals.

• The other two sets of p orbitals overlap in fashion.

The MO diagram for the 2nd energy level

There are σ and σ* orbitals from the 2s and 2p atomic orbitals.

There are also π and π* orbitals from 2p atomic orbitals.

Since direct overlap is stronger, the effect of raising and lowering energy is greater for σ and σ*

For O2, F2, and Ne2, the order of energy for the 2p sublevel is σ2p < π2p < π*

2p < σ*2p

For B2, C2, and N2, the order of energy is π 2p < σ 2p < π*

2p < σ*2p

because of interaction between the 2s and 2p.

MO Diagrams for Diatomic Molecules of 2nd Period Elements

MO Diagrams and Magnetism

• Diamagnetism is the result of all electrons in every orbital being spin paired. These substances are weakly repelled by a magnetic field.

• Paramagnetism is the result of the presence of one or more unpaired electrons in an orbital. These substances are attracted to a magnetic field.

• Is oxygen (O2) paramagnetic or diamagnetic? Look back at the MO diagram! It is paramagnetic.

• Lewis structures would not predict that O2 is paramagnetic, but experimental evidence shows that it is.

Heteronuclear Diatomic Molecules

• Diatomic molecules can consist of atoms from different elements.

• How does a MO diagram reflect differences?

• The atomic orbitals have different energy, so the interactions change slightly.

• The more electronegative atom has orbitals lower in energy, so the bonding orbitals will more resemble them in energy.