Molecular Geometry and Bonding Theories Brown, LeMay Ch 9 AP Chemistry Monta Vista High School Ch 9 PS #8, 10, 16, 20 (and draw overall dipole moments),

Molecular Geometry and

Bonding TheoriesBrown, LeMay Ch 9

AP ChemistryMonta Vista High School

Ch 9 PS #8, 10, 16, 20 (and draw overall dipole moments), 30, 34, 36, 41, 59, 73; Recommended #9, 11, 13, 19, 25, 31, 40, 55, 60

•Lewis structure is a flat drawing showing the relative placement of atoms, bonds etc. in a molecule, but does not tell anything about the shape of the molecule.

•VSEPR theory helps construct molecular shape (3-D) from the Lewis structures, which are 2-D structures.

Rationale for VSEPR Theory

Valence Shell Electron Pair Repulsion Theroy• The basis principal of VSEPR is that each group of valence

electrons (electron domains) around a central atom tend to be as far as possible from each other to minimize repulsions. These electron domain repulsions around the central atom determine the molecular geometry of a molecule.

• Electron domains: areas of valence e- density around the central atom;

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

• Repulsions between two e domains are : lone pair-lonepair >lone pair-bond pair> bond pair-bond pair

Valence-shell electron-pair repulsion theory– Why is lone pair- lone pair repulsion greater than bond

pair-bond pair repulsion?– Good Links:

Good Power point on VSEPR, Shapes of sp3, sp2, sp Carbon, VSEPR Lecture

Summary of ABE (Tables 9.1 - 9.3) on the next slide:

E = 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

Tables Link

# 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

Example: 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:

PCl5

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

L2AB3

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

or

Octahedral

AB6

Octahedral

90º

SF6

LAB5

Square pyramidal

< 90º

BrF5

X

X

A

X

|

X

X

X

B

B

A

B

|

B

B

B

B

B

A

B

|..

B

BA

X

|

X

XX

X

X

6

Six sp3d2 hybrid orbitals

or

L2AB4

Square planar

90º

XeF4

or

L3AB3

T-shaped

<90º

KrCl31-

A

B

|

B

BB

..

..B

B

A

..

|..

B

B

B

B

A

..

|..

..

B

A

..

|

B

BB

..

..

Limitations of VSEPR TheoryEven though the VSEPR model is useful in predicting the shapes of molecules, it does not differentiate between single, double and triple bonds and does not account for bond strengths.

9.3: Molecular PolarityTwo factors must be considered in the polarity of a

molecule:1. Are the individual bonds (joining different atoms in a

molecule) polar? Ex. HCl vs. H2. HCl is polar while H2 is not.

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.

• 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).

= Q r

2. If individual bonds are polar, then do individual dipole moments cancel out or not. A molecule is polar if its centers of (+) and (-) charge do not cancel out- generally happens in a distorted molecule (molecules with lone pairs of e on the central atom.)

How to determine if a molecule is polar?

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

1. Draw the true molecular geometry (3D geometry).2. Draw each bond dipole as an arrow3. Add the vectors, and draw the overall dipole moment. If none, then = 0.4. Generally, a distorted molecule (with lone pairs on the central atom) will have a dipole.

Exception: AB2E3 type

What is the big deal about polarity?• The polarity of a molecule will tell you a lot about

its solubility, boiling point, etc. when you compare it to other similar molecules. Water, for example, is a very light molecule (lighter than oxygen gas or nitrogen gas) and you might expect it would be a gas based on its molecular weight, however the polarity of water makes the molecules "stick together" very well. Hence water is present as liquid.

• Polar substances are soluble in water (which is polar) and non polar substances are soluble in non polar solvents such as benzene and oil.

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

CO2 BF3 H2O

CCl4 NH3 PH3

Rationale For Valence Bond Theory

• VB theory provides a basis for covalent bond formation based upon overlapping of atomic orbitals to share electrons.

• This theory successfully predicts bond strengths based upon orbital overlap (such as H2 bond being weaker than N2 bond)- sigma vs. pi bond strength

Covalent Bonding and Orbital Overlap: Valence Bond Theory

The basic principle of VB theory is that a covalent bond forms when the orbitals of two atoms overlap. Three central themes of VB theory derive from this principle:1. Opposing spins of e pairs: In accordance with Pauli’s exclusion principle, an orbital can have max of two e with opposite spins.2. Maximum overlap of bonding orbitals: The bond strength depends upon the attraction of nuclei for the shared e, so the greater the overlap, the stronger the bond.3. End to end overlap of the atomic orbitals form a sigma bond and allows the free rotation of the parts of the molecule. Side-to-side overlap forms a pi bond, which restricts rotation. A multiple bond consists of one sigma bond and rest pi bonds.

Sigma and Pi bondsSigma () bond:• Covalent bond that results from axial overlap of orbitals between atoms in

a molecule• Lie directly on internuclear axis• “Single” bonds, could form between s-s orbital or s-p orbital or p-p orbital

by axial overlappingEx: 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 inter nuclear axis and

therefore have less total orbital overlap, so they are weaker than bonds. Forms between two p orbitals (py or pz)

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

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 : 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

Limitations of VB Theory• Valence bond (VB) theory assumes that all

bonds formed between two atoms are localized bonds and are formed by the donation of an electron from each atom. This is actually an invalid assumption because many atoms bond using delocalized electrons.

Rationale for Hybrid Orbital TheoryGood youtube video

• Hybrid orbital theory is seen as an extension of VB theory, where atomic orbitals “hybridize” to form new hybrid orbitals. This hybrid orbital theory helps explains the bonding in terms of quantum mechanical model of atom (s,p,d,f orbitals).

9.5: Hybrid Orbital TheoryMovie on Hybrid Orbitals

Explains the molecular geometries in terms of s,p,d,f orbitals.

VSEPR explains that e domains must be farthest from each other around central atom, but fails to explain these in terms of orbitals as defined in wave mechanical model of atom.

Hybrid orbital theory of Linus Pauling proposed that the valence atomic orbitals in the molecule are very different from those in the isolated atoms.

The process of orbital mixing is called hybridization, and the new atomic orbitals are called hybrid orbitals. Animation on Hybrid Orbitals, Hybridization Movie

Hybrid Orbital Theory

• Two key points about the number and types of hybrid orbitals are that

1. The number of hybrid orbitals obtained equals the number of atomic orbitals mixed.

2. The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed.

“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

En

erg

y

→

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

“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 are the s and p e-

not at 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

“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

“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

“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.

Non-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

9.6: Multiple BondsDraw Lewis structures. For C’s: label hybridization, molecular geometry, and unique bond

angles

C2H6

C2H4

C2H2

C6H6

Sigma () bonds in C2H4

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

Pi () 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

2ssp2 hybrids bond

axially = bonds

p orbital bonds side-by-side = bond

Sigma () bonds in C2H2

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

Pi () 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

Sigma () bonds in C6H6

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

http://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/intro3.htm#strc8c

Localized v. Delocalized Bonds• Delocalized bonds are present in compounds

showing resonance structures, while electrons are localized in most other bonds.

Localized vs. Delocalized Bonds

(localized) (delocalized – MINIMUM OF 4 c’S)

Delocalized 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.

Limitations of Hybrid Orbital Theory

Hybrid orbital theory assumes that all bonds are formed with localized electrons, which is not true. MO (Molecular Orbital) theory explains bonding in terms of delocalized orbitals as well.

9.7: 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. However, VB theory does not explain the magnetic or spectral properties of a molecule.

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.

*AO & MO in H2

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

Atomic orbitals

Bonding orbital

Anti-bonding orbital

*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.(Some sources say 2 px orbitals?)

• 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

MO s from Atomic p-Orbital Combinations

P orbitals can interact with each other forming either sigma molecular orbitals, 2p , in a end-to-end overlap or pi molecular obrbitals, p, in a side-to-side overlap.

The order of energy for MO s derived from 2p orbitals is 2p < p < p*< 2p*

There are three perpendicular p orbitals, so two sigma p orbitals (one bonding and one antibonding) and four pi p orbitals (two bonding and two antibonding) are formed.

This energy order gives the expected MO diagram for most of the p-block elements for homonuclear diatomic molecules.

MO s for B, C and N The energy order of p orbitals results from the assumption that

since s and p orbitals have differences in energy, they do not interact with each other. (or mix)

However, when 2p atomic orbitals are half filled, such as in B, C and N, the repulsions between e are little and the energy of these p orbitals is not much different than the s atomic orbital, which leads to s and p orbital mixing. This mixing lowers the energy of the 2s bonding and antibonding orbitals and increases the energy of sigma 2p (bonding and antibonding) orbitals.The pi 2p orbitals are not affected. This mixing gives a different energy order:

2s < 2s*< p<2p < p*< 2p

*MO diagrams for “< O2”• Resulting MO for

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

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.

N atom N atom

*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.

Liquid N2 and liquid O2

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

N2 O2

MagnetismIn 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