Chapter 10. Chemical Bonding II. Molecular Geometry

and Hybridization of Atomic Orbitals

10.1 Molecular Geometry (what, how, why)

General Summary -- Structure and Bonding Concepts

Lewis Electron DotFormula of Molecule

Electronic Configurationof Atoms

3-D Shape of Molecule

VSEPR Theory

Polarity of Molecule

and Bond Polarity

Electronegativity

Theory

Bonding Descriptionof Molecule

Valence Bond

Intermolecular Forcesand Bulk Properties

Chemical Reactivity

Octet Rule

Valence Shell Electron Pair Repulsion Theory

Hypothesis -- The structure of a molecule is that which minimizes the repulsions between pairs of electrons on the central atom.

"Effective Number" (EN) = (number of atoms attached to central atom) + (number of lone pairs on central atom)

(Using the number of atoms is simpler than the number of bonding pairs, because this accounts for double and triple bonds which essentially occupy the same space as a single bond.)

EN Arrangement of Electron Pairs Molecular Shape (Geometry)

Examples

2

linear

180°

linear BeCl2, CO2

3

trigonal planar

120°

trigonal planar

bent

BCl3, CH3+

SnCl2, NO2-

4

tetrahedral

109.5°

tetrahedral

pyramidal

bent

CH4, PO43-

NH3, ClO3-

H2O, SeF2

5

e

e

e

a

a

trigonal

bipyramidal

120° & 90°

trigonal bipyramid

"see saw"

T-shaped

linear

PF5, SeCl5+

SF4, BrF4+

ClF3, XeO32-

XeF2, ICl2-

6

octahedral

90°

octahedral

square pyramid

square planar

SF6, PCl6-

BrF5, SF5-

XeF4, IF4-

Important corollaries:

• In trigonal bipyramid structures, lone e- pairs adopt equatorial positions (e)

• Order of repulsions: Lp - Lp > Lp - Bp > Bp - Bp

(Predicts distortions from ideal geometries)

� Molecules with more than one central atom, e.g., CH3OH, methanol

C O

HH

HH

• C and H are "central"

• HCH and OCH ∠ 109 °

• O is like water with two lone pairs and two bonding pairs: ∠HOC = 105

10.2 Dipole Moments (Polarity of Molecules) predict from molecular shape

A. Bond Polarity e.g., HF molecule

• F is more electronegative than H, so there is partial charge separation in the H-F bond:

or

δ−δ+H FH F

• the H-F bond is described as "polar covalent bond" and is said to have a "dipole moment"

B. Molecule Polarity (Polar or Non-Polar?)

• Polar bonds do not always mean the molecule is polar

• In very symmetrical structures (e.g., CO2 or CF4), the

individual bond dipoles effectively cancel each other and the

molecule is non-polar.

O C O CF

F

FF

• In less symmetrical structures (e.g., SO2 and SF4), the

bond dipoles do not cancel and there is a net dipole moment

which makes the molecule polar.

SOO

..S

F

F

F

F..

Other examples for practice: Polar: H2O SnCl2 NH3 SeF2 PF3 BrF5 XeO3

Non-Polar: BeCl2 CH4 PF5 XeF2 XeF4 SO3

10.3 Valence Bond Theory

A. Why is additional theory needed?

• VSEPR predicts H2 and F2 are the same type of bond

• H2 bond dissociation energy = 436.4 kJ/mole

• F2 bond dissociation energy = 150.6 kJ/mole

• Need better theory to explain these types of differences.

B. Basic Concept Covalent Bonds result from overlap of atomic orbitals consider the H2 molecule

. .. .+

1s1sσ bond

H H H2

Figure 10.5 shows the change in potential energy with distance between atoms

• atoms distant - no interaction

• atoms approach - electron from one atom is attracted to nucleus of other

• atoms get very close - nuclei repel each other

F2 molecule

. . . .+

F F F2

2p2p σ bond

HF molecule

H

+.2p

F

..

H F

. ...σ bond

Two types of covalent bonds:

σ (sigma) bond: "head-to-head" overlap along the bond axis (as in previous pictures)

π (pi) bond: "side-to-side" overlap of p orbitals:

π bond

. + ...

2p 2p

• single bond -- always a σ bond

• double bond -- combination of one σ bond and one π bond

• triple bond -- combination of one σ bond and two π bonds

10.4 Hybridization of Atomic Orbitals

Problem: Describe the bonding in CH4 molecule.

• experimental fact -- CH4 is tetrahedral (H-C-H angle = 109.5°)

• VSEPR theory "explains" this with 4 e- pairs, ∴ tetrahedral

• however, if only s and p orbitals are used, the angles ought to be 90° since the p orbitals are mutually perpendicular!

Solution: Modify the theory of atomic orbitals and use:

Hybridization: combination of 2 or more atomic orbitals on the same atom to form a new set of "Hybrid Atomic Orbitals" used in bonding.

CH4 (methane) Energy Level Diagram

C ↑↓ ↑ ↑ ground state - valence shell orbital diagram

2s 2p 2p 2p • H electrons can only share with C p orbitals

• bond angles can only be 90° angles required

by p orbitals -- wrong, must be 109°

So try promoting

C ↑ ↑ ↑ ↑ Now have four orbitals, but still have three that

2s 2p 2p 2p are 90° apart

So try mixing the four into new orbitals

C ↑ ↑ ↑ ↑ hybridized state (mixing of s and p orbitals)

sp3 sp3 sp3 sp3 (gives 4 identical bonds that are 109.5° angles

-- right!)

So what do these new orbitals look like?

see Figures 10.7 and 10.8 and 10.9

Types of Hybrid Orbitals (see Table 10.4)

Atomic Orbitals

Hybrid Orbitals

Geometry

Unhybridized p Orbitals (left over)

one s + one p two sp linear (180°)

2

one s + two p three sp2 trigonal planar

(120°) 1

one s + three p four sp3 tetrahedral

(109.5°) 0

one s + three p + one d

five dsp3 trigonal bipyramid

90° & 120°

one s + three p + two d

six d2sp3 octahedral

90°

{ Note: combination of n AO's yields n Hybrid Orbitals)

Practice: Use valence bond theory to describe the bonding in H2O, NH3, CH4, PF3.

Draw clear 3-D pictures (method shown in class) showing orbital overlap, etc.

[Note: All use only simple σ bonds and lone pairs.]

10.5 Hybridization in Molecules Containing Double & Triple Bonds

ethylene: sigma + pi bond (see Figure 10.16)

C C

H

H

H

H

acetylene sigma + two pi bonds (see Figure 10.19)

PRACTICE on

• H2CNH (use double bond like H2CO and H2CCH2)

• HCN (use triple bond like HCCH)

10.6 Molecular Orbital Theory A. Comparison of VB and MO Theory

Valence Bond Theory ("simple" but somewhat limited)

• e- pair bonds between two atoms using overlap of atomic orbitals on two atoms

• sometimes fails to explain facts, e.g., O2 is paramagnetic indicating unpaired electrons, but VB theory would indicate that

electrons in the σ and π orbitals are paired. Molecular Orbital Theory (more general but "complex")

• all e-'s in molecule fill up a set of molecular orbitals that are made up of linear combinations of atomic orbitals on two or more atoms

MO's can be:

• "localized" -- combination of AO's on two atoms, as in the diatomic molecules

• "delocalized" -- combination of AO's on three or more atoms, as in benzene (C6H6) -- page 424

B. Bonding and Antibonding Molecular Orbitals

Molecular Orbitals for simple diatomic molecules (H2 and He2)

in H2 the 1s atomic orbitals on the two H atoms are combined into:

• a bonding MO -- σσσσ1s

• lower energy than the atomic orbitals from which it was formed, .i.e., greater stability

• more electron density between nuclei from constructive interference (wave properties of the electron)

• an antibonding MO -- σσσσ*1s

• higher energy and lower stability than the atomic orbitals from which it was formed

• no electron density between nuclei from destructive interference

MO energy level diagram for H2 (only the bonding MO is filled):

1s 1s

H HH2

σσσσ1s

σσσσ*1s

Figure 10.23 In contrast, the MO diagram for the nonexistent molecule, He2 shows that both bonding and antibonding MO's are filled:

1s 1s

He HeHe2

σσσσ1s

σσσσ*1s

Figure 10.25 Bond Order = ½ [(# bonding e-'s) - (# antibonding e-'s)] for H2 = ½ [2 - 0] = 1 (a single bond) for He2 = ½ [2 - 2] = 0 (no net bonding interaction)

C. Bonding and Antibonding Molecular Orbitals from p Atomic Orbitals Figure 10.24 - shows interaction to form

• σ bonds when atomic orbitals approach end to end

• π bonds when atomic orbitals approach side to side

10.7 Molecular Orbital Configurations/Rules

A. Rules 1. The number of MO's equal the number of AO's used to make the

MO's 2. The more stable the bonding MO, the less stable the antibonding

MO 3. MO's fill from low to high energies 4. In stable molecules, the number of

electrons in bonding MO's > electrons in antibonding MO's 5. Maximum of 2 electrons per MO (with opposite spins) 6. Follow Hund's rule - electrons do not pair until all MO's of the same

energy are half filled 7. The number of electrons in MOs equals sum of all of the electrons

in the atoms

B. MO's for 2nd Row Diatomic Molecules (e.g., N2, O2, F2, etc.)

MO energy level diagram -- Figures10.26 plus 10.27

σσσσ*1s

σσσσ1s

1s1s

2s 2s

σσσσ2s

σσσσ*2s

2p2p

ππππ2pz

ππππ2py

ππππ*2py

σσσσ2p x

ππππ*2pz

σσσσ*2p x

Examples -- Table 10.5 (Note the change at O2 and F2)

Fill in MO diagram for C2, N2, O2, F2, and Ne2 and determine bond order for each:

molecule C2 N2 O2 F2 Ne2

bond order 2 3 2 1 0

B. Electron Configurations valence electrons in blue Example: N2

(σ1s)2(σ*1s)2(σ2s)

2(σ*2s)2(π2py)

2(π2pz)2(σ2px)

2

Example: O2

(σ1s)2(σ*1s)2(σ2s)

2(σ*2s)2 (σ2px)

2 (π2py)2(π2pz)

2 (π*2py)1(π*2pz)

1

10.7 Delocalized Molecular Orbitals

By combining AO's from three or more atoms, it is possible to generate MO's

that are "delocalized" over three or more atoms

Examples:

Resonance in species like HCO32-, CO3

-2 and benzene (C6H6)

can be "explained" with a single MO description containing

delocalized π bonds.

• see Figure 10.28 sigma framework in benzene

C

CC

C

CCH

H

H

H

H

H

• see Figure 10.29 for pi framework

• see Figure 10.30 for the carbonate ion pi framework

Computer model:: HIV enzyme with buckeyball occupying the active site preventing enzyme from working as it usually does.

Carbonate Ion

Bonding in Solids -- Band Theory

An energy "band" is composed of a very large number of closely spaced energy levels that are formed by combining similar atomic orbitals of atoms throughout the substance

Metals and metalloids have a

• "conduction band" -- set of highly delocalized, partially filled, MO's that extend over the entire solid lattice structure

• "band gap" -- energy difference between filled "valence band" and the conduction band (Figure 20.10)