Molecular Geometry and

Bonding Theories

Brown, LeMay Ch 9AP Chemistry

29.1 – 9.2: V.S.E.P.R.

Valence-shell electron-pair repulsion theory Because e- pairs repel, molecular shape adjusts so the

valence e- pairs are as far apart as possible around the central atom.

Electron domains: areas of valence e- density around the central atom; result in different molecular shapes

Includes bonding e- pairs and nonbonding e- pairs A single, double, or triple bond counts as one domain

Summary of LmABn (Tables 9.1 - 9.3):L = lone or non-bonding pairs

A = central atom

B = bonded atoms

Bond angles notation used here:< xº means ~2-3º less than predicted

<< xº means ~4-6º less than predicted

3Tables 9.1 - 9.3

# of e-

domains&

# and type of hybrid orbitals

e- domain geometry

Formula &

Molecular geometry

Predicted bond

angle(s)

Example(Lewis

structure with

molecular shape)

2

Two sp hybrid orbitals

Linear

AB2

Linear

180ºBeF2

CO2

A|X

X

A|B

B

3

Three sp2 hybrid orbitals

Trigonal planar

AB3

Trigonal planar

120º

BF3

Cl-C-Cl< 120º

Cl2CO

LAB2

Bent

< 120º

NO21-

A|X

XX

A|B

BB

A|B

:B

5Example: CH4

Molecular shape = tetrahedral

Bond angle = 109.5º

H|

H—C—H|H

109.5º

109.5º

109.5º

109.5º

4

Four sp3

hybrid orbitals

or

Tetrahedral

AB4

Tetrahedral

109.5º

CH4

LAB3

Trigonal pyramidal

< 109.5º

Ex: NH3 = 107º NH3

L2AB2 Bent

<<109.5º

Ex: H2O = 104.5º

H2O

X

A

X

XX

X

A

X

XX

B

A

B

BB

:

A

B

BB

:

A

B

B:

7PCl5

Molecular shape = trigonal bipyramidal

Bond angles

equatorial = 120º

axial = 90º

:Cl: :Cl:\ /

:Cl—P—Cl:|

:Cl::

:::

:: :

120º

120º

90º90º

90º

5

Five sp3d

hybrid orbitals

Trigonal bipyramida

l

AB5

Trigonal bipyramida

l

Equatorial = 120º

Axial = 90º

PCl5

LAB4

Seesaw

Equatorial < 120º

Axial< 90º

SF4

X

X

X

A

X

|

X

B

B

B

A

B

|

B

:

B - A - BB B

5

Five sp3d

hybrid orbitals

Trigonal bipyramidal

L2AB2

T-shaped

Axial<< 90º

ClF3

L3AB2

Linear

Axial = 180º

XeF2

X

X

X

A

X

|

X

B

:

:

A

B

|

B

:

:

:

A

B

|

B

6

Six sp3d2

hybrid orbitals

Octahedral

AB6

Octahedral

90º

SF6

LAB5

Square pyramidal

< 90º

BrF5

6

Six sp3d2

hybrid orbitals

Octahedral

L2AB4

Square planar

90º

XeF4

L3AB3

T-shaped

<90º

KrCl31-

129.3: Molecular Polarity A molecule is polar if its centers of (+) and (-)

charge do not coincide. A bond’s polarity is determined by the

difference of EN between atoms in bond. Partial (+) and partial (-) on atoms in a polar

bond can be represented as + and -.

H-Cl:

::

H-Cl:

::

+ -

Bond polarity is most often represented by an arrow that points toward the - (most EN atom), showing the shift in e-

density.

13

The dipole moment () is a vector (i.e., has a specific direction) measuring the polarity of a bond which contains partial charges (Q) that are separated by a distance (r).

The sum of the bond dipole moments in a molecule determines the overall polarity of the molecule.

1. Draw the true molecular geometry.2. Draw each bond dipole.3. Add the vectors, and draw the overall dipole

moment. If none, then = 0.

= Q r

Ex: Draw Lewis structures, bond dipole moments, and overall dipole moments. Also, name the e- domain geometry and the molecular geometry.

CO2 BF3 H2O

CCl4 NH3 PH3

159.4: Covalent Bonding and Orbital Overlap

Valence-bond theory: overlap of orbitals between atoms results in a shared valence e- pair (i.e., bonding pair)

Energy

(kJ/mol)0

  -436

0.74 ÅH-H distance

Figure 9.13:Formation of bond in H2

a. As 2 H atoms approach, the 2 valence e- in the 1s orbitals begin to overlap, becoming more stable.

b. As H-H distance approaches 0.74 Å, energy lowers b/c of electrostatic attraction between the nuclei & the incoming e-.

c. When H-H distance = 0.74 Å, energy is at its lowest because electrostatic attractions & repulsions are balanced. (This is the actual H-H bond distance.

d. When H-H distance < 0.74 Å, energy increases b/c of electrostatic repulsion between 2 nuclei & between the 2 e-.

ab

c

d

169.5: Hybrid Orbital Theory Explains the relationship between overlapping

orbitals (valence bond theory) and observed molecular geometries (VSEPR theory).

17“sp” hybrid orbitals BeF2 (g): observed as a linear molecule with 2 equal-

length Be-F bonds. Valence bond theory predicts that each bond is an overlap of one Be 2s e- and one 2p e- of F. However, Be’s 2s e-

are already paired. So…

To form 2 equal bonds with 2 F atoms:1. In Be, one 2s e- is promoted to an empty 2p orbital.

2. The occupied s and p orbitals are hybridized (“mixed”), producing two equivalent “sp” orbitals.

3. As the two “sp” hybrid orbitals of Be overlap with two p orbitals of F, stronger bonds result than would be expected from a normal Be s and F p overlap. (This makes up for energy needed to promote the Be e- originally.)

Be (ground state) → Be (promoted) → Be (sp hybrid)

2p

2s

Energy →

Orbital “shapes”One s + one p → Two sp orbitals

(to bond with 2 F’s)

A central atom in a Lewis structure with exactly 2 e-

domains has sp hybrid orbitals.

F F

19“sp2” hybrid orbitals BF3 (g): observed as trigonal planar molecule with 3

equal-length B-F bonds. However, 2 valence e- in B are paired, and the s and p e- can’t make the observed 120º angle.

2p

2s

One s + two p → Three sp2 orbitals(to bond with 3 F’s)

A central atom with exactly 3 e- domains has sp2 hybrid orbitals.

B (ground) → B (promoted) → B (sp2 hybrid)

F F F

20“sp3” hybrid orbitals CH4 (g): observed as tetrahedral

2p

2s

One s + three p → Four sp3 orbitals (to bond with 4 H’s)

A central atom with exactly 4 e- domains has sp3 hybrid orbitals.

C (ground) → C (promoted) → C (sp3 hybrid)

H H H H

21“sp3d” hybrid orbitals (or dsp3) PCl5 (g): observed as trigonal bipyramidal; forms 5 bonds of equal

energy (* but not equal length: equatorial are slightly longer)

3d

3p

3s

One s + three p + one d → Five sp3d orbitals(to bond with 5 Cl’s)

A central atom with exactly 5 e- domains has sp3d hybrid orbitals.

P (ground) → P (promoted) → P (sp3d hybrid)

Cl Cl Cl Cl Cl

22“sp3d2” hybrid orbitals (or d2sp3) SF6 (g): observed as octahedral; forms 6 equal-length

bonds

One s + three p + two d → Six sp3d2 orbitals

A central atom with exactly 6 e- domains has sp3d2 hybrids.

23Non-bonding e- pairs Lone pairs occupy hybrid orbitals, too

Ex: H2O (g): observed as bent; but e- domain is tetrahedral

2p

2s

Four sp3 orbitals (2 bonding, 2 non-bonding)

O (ground) → O (sp3 hybrid)

2 non-bonding pairs(lone pairs)

2 bonding pairs

H H

249.6: Multiple Bonds

Draw Lewis structures. For C’s: label hybridization, molecular geometry, and unique bond angles

C2H6

C2H4

C2H2

C6H6

25Sigma and Pi bonds

Sigma () bond: Covalent bond that results from axial overlap of orbitals

between atoms in a molecule Lie directly on internuclear axis “Single” bonds

Ex: F2

Pi () bond: Covalent bond that results from side-by-side overlap of

orbitals between atoms in a molecule. Are “above & below” and “left & right” of the internuclear

axis and therefore have less total orbital overlap, so they are weaker than bonds

Make up the 2nd and 3rd bonds in double & triple bonds.Ex: O2 N2

26Sigma () bonds in C2H4

Ex: ethene; C-C and C-H -bonds result from axial overlap of H s-orbitals and C sp2-orbitals

27Pi () bonds in C2H4

Each C has 4 valence e-: 3 e- for 3 bonds 1 e- for 1 bond, which results from side-

by-side overlap of one non-hybridized p-orbital from each C

2pC

2s sp2 hybrids bond axially = bonds

p orbital bonds side-by-side = bond

28Sigma () bonds in C2H2

Ex: ethyne (a.k.a. acetylene) C-C and C-H -bonds result from axial overlap of H s-orbitals and C sp-orbital

29Pi () bonds in C2H2

Each C has 4 valence e-: 2 e- for 2 bonds 2 e- for 2 bonds, which result from side-by-side overlap of two non-hybridized p-

orbitals from each carbon

sp hybrids bond axially = bonds

2pC

2s

p orbital bonds side-by-side = bonds

30Sigma () bonds in C6H6

Ex: benzene; C-C and C-H -bonds result from axial overlap of H s-orbitals and C sp2-orbitals

31Localized vs. Delocalized Bonds

(localized) (delocalized)

32Delocalized bonds in C6H6

C-C -bonds result from overlap of one non-hybridized p-orbitals from each C

Delocalization of e- in -bonds results in a “double-donut” shaped e- cloud above and below the molecular carbon plane.

339.7: Molecular Orbital (MO) theory

So far we have used valence-bond theory (covalent bonds form from overlapping orbitals between atoms) with hybrid orbital theory and VSEPR theory to connect Lewis structures to observed molecular geometries.

MO theory is similar to atomic orbital (AO) theory (s, p, d, f orbitals) and helps to further explain some observed phenomena, like unpredicted magnetic properties in molecules like those in O2.

AO are associated with the individual atoms, but MO are associated with the whole molecule.

Combination of two 1s AO from each H forms two MO in H2 molecule.

Bonding MO: form between nuclei and are stable Antibonding MO: marked with *; form “behind” nuclei and

are less stable.

1s 1s

Molecular orbitalsE

1s

*1s

*AO & MO in H2

Atomic orbitals

Bonding orbital

Anti-bonding orbital

35*Types of MO

Sigma () MO: form from combinations of: Two 1s or 2s orbitals from different atoms;

written as 1s or 2s. Two 2pz orbitals from different atoms (axial

overlap); written as 2pz.

Pi () MO: form from combinations of: Two 2px or 2py orbitals from different atoms; written as

2px or 2py

.

Do not appear until B2 molecule

36*MO diagrams for “< O2”

Bond order =

½ (# bonding e-

- # antibonding e-)

B.O. (N2) = ½ (10 – 4) =6 / 2 = 3 (triple bond)

N2 has no unpaired electrons which makes it diamagnetic.

Resulting MO for diatomic molecules with < 16 e- (B2, C2, N2, etc.)

N atom N atom

37*MO diagrams for “≥ O2” Resulting MO for

diatomic molecules with ≥ 16 e- (like O2, F2, Ne2, etc.)

O atom O atom

Bond order =

½ (# bonding e-

- # antibonding e-)

B.O. (O2) = ½ (10 – 6) == 2 (double bond)

O2 has unpaired electrons which makes it paramagnetic.

38Liquid N2 and liquid O2

From U. Illinois:http://www.chem.uiuc.edu/clcwebsite/liquido2.html

N2 O2

39Magnetism

In an element or compound: Diamagnetism: all e-

paired; no magnetic properties Paramagnetism: at least 1 unpaired e-

* Drawn into exterior magnetic field since spins of atoms become aligned; unlikely to retain alignment when field is removed

Ex: N OSc MnO2

* Ferromagnetism: occurs primarily in Fe, Co, Ni Drawn into exterior magnetic field since spins of atoms

become aligned; very likely to retain alignment when field is removed (i.e., “a permanent magnet”)

Nd2Fe14B is very ferromagnetic