Chapter

9

Molecular Geometry Bonding Theories

Molecular Shape

• A

bond angle

is the angle defined by lines joining the centers of two atoms to a third atom to which they are covalently bonded • The

molecular geometry

or shape is defined by the lowest energy arrangement of its atoms in three dimensional space.

VSEPR Valence-Shell Electron-Pair Repulsion Theory

The geometric arrangement of atoms bonded to a given atom is determined

principally

by minimizing electron pair repulsions of bonding and non-bonding electrons.

Central Atoms without Lone Pairs

Steric number (SN) is the number of volumes of space occupied by electrons surrounding a central atom

Geometric Forms

1.

Predicting a VSEPR Structure

Draw Lewis structure.

2.

Determine the steric number of the central atom.

3.

Use the SN to determine the geometry around the central atom.

4.

The name for molecular structure is determined by the number of volumes of space occupied by bonding electrons.

Examples

• What is the molecular geometry of BF 3 ?

• What is the molecular geometry of CH 4

Examples

• What is the molecular geometry of BF 3 ?

Lewis Structure (exception to Law of Octaves)

F B F F • What is the molecular geometry of CH 4

Examples

• What is the molecular geometry of BF 3 ?

Lewis Structure (exception to Law of Octaves)

F B F Bond Angles = 120° Trigonal Planar F • What is the molecular geometry of CH 4

Examples

• What is the molecular geometry of BF 3 ?

Lewis Structure (exception to Law of Octaves)

F B F Bond Angles = 120° Trigonal Planar F • What is the molecular geometry of CH H 4 H C H H

Examples

• What is the molecular geometry of BF 3 ?

Lewis Structure (exception to Law of Octaves)

F B F Bond Angles = 120° Trigonal Planar F • What is the molecular geometry of CH H 4 Bond Angles = 120° H C H Tetrahedral H

Central Atoms with Lone Pairs

• Electron-pair geometry describes the arrangement of atoms and lone pairs of electrons about a central atom.

 The electron-pair geometry will always be one of the five geometries presented previously.

• The molecular geometry in these molecules describes the shape of the atoms present (it

excludes

the lone pairs).

• • • • •

Lone Pairs

Lone pairs

of electrons occupy more space around a central atom than do bonding electrons.

Lone pair-lone pair repulsion is the largest.

Lone pair-bonding pair repulsion is the next largest.

Bonding pair-bonding pair repulsion is the smallest.

In structures with lone pairs on the central atom, the bond angles are a little smaller than predicted based on the electron-pair geometry.

SN = 3, Electron-pair Geometry = Trigonal Planar No. of Bonded Atoms No. of Lone Pairs Molecular Geometry Bond Angles 3 2 0 1 Trigonal Planar Bent 120 o <120 o Like 119.6

o

Non-bonding Electrons & Shape

H B H H Angles = 120 Trigonal Planar H B H H Angles < 120 Bent

SN = 4, Electron-pair Geometry = Tetrahedral No. of Bonded Atoms No. of Lone Pairs Molecular Geometry Bond Angles 4 0 Tetrahedral 109.5

o 3 2 1 2 Trigonal Pyramidal Bent <109.5

o <109.5

o

Non-bonding Electrons & Shape

Non-bonding Electrons & Shape

Tetrahedral Trigonal Pyramid v-shape

SN = 5, Electron-pair Geometry = Trigonal Bipyramidal No. of Bonded Atoms No. of Lone Pairs Molecular Geometry Bond Angles 5 0 Trigonal Bipyramidal 120 o & 90 o 4 1 Seesaw <120 o & 90 o 3 2 T-shaped <120 o & 90 o 2 3 Linear 180 o The lone pairs of electrons are always found in the trigonal planar part of the structure to minimize repulsion.

SN = 6, Electron-pair Geometry = Octahedral No. of Bonded Atoms No. of Lone Pairs Molecular Geometry Bond Angles 6 0 Octahedral 90 o 5 4 1 2 Square Pyramidal Square Planar <90 o 90 o 3 2 3 4 Although these arrangements are possible, we will not encounter any molecules with these arrangements.

Hybrid Orbitals

You may have noticed that the electron pairs in molecules have different orientations in space compared to atomic orbitals. Wave equations mathematically generated volumes of space where electrons spend most of their time, but what about molecules?

Hybrid Orbitals

You may have noticed that the electron pairs in molecules have different orientations in space compared to atomic orbitals. Wave equations mathematically generated volumes of space where electrons spend most of their time, but what about molecules? This brings us to the concept of

hybrid orbitals

, combinations of atomic orbitals, or

molecular orbitals

(from wave equations of electrons in molecules)

Hybrid Orbitals

Hybridization is a concept you might be familiar with. For example a grapefruit is a hybrid of what two fruits?

Hybrid Orbitals

Hybridization is a concept you might be familiar with. For example a grapefruit is a hybrid of what two fruits?

Hybrid Orbitals

Hybridization is a concept you might be familiar with. For example a grapefruit is a hybrid of what two fruits? Lemon and orange

Hybrid Orbitals

How about a nectarine?

Hybrid Orbitals

How about a nectarine? Plumb and a peach.

Hybrid Orbitals

How about a nectarine? Plumb and a peach.

Broccoaflower? Broccoli and cauliflower

Hybrid Orbitals

How about a nectarine? Plumb and a peach.

Broccoaflower? Broccoli and cauliflower And a Cocapoo?

Hybrid Orbitals

How about a nectarine? Plumb and a peach.

Broccoaflower? Broccoli and cauliflower And a Cocapoo? Cocker spaniel and poodle

Hybrid Orbitals

On to Chemistry! How about an

s-

orbital and a

p-

orbital? Yes,

sp

orbital.

Hybrid Orbitals

On to Chemistry! How about an

s-

orbital and a

p-

orbital? Yes,

sp

orbital.

How about one

s

-orbital and two

p

-orbitals?

Hybrid Orbitals

On to Chemistry! How about an

s-

orbital and a

p-

orbital? Yes,

sp

orbital.

How about one

s

-orbital and two

p

-orbitals? Yes an

sp

2 orbital.

Hybrid Orbital Notation

In order to construct

hybrid orbital notation

, we need to separate the central atom from the surrounding electrons, usually the central atom is the largest, the most electronegative, or the one that there is one of.

Hybrid Orbital Notation

In order to construct

hybrid orbital notation

, we need to separate the central atom from the surrounding electrons, usually the central atom is the largest, the most electronegative, or the one that there is one of. When constructing a hybrid orbital diagram, all of the valence electrons of the central atom are used and only the single electrons of the atoms attached to the central atom are use.

Hybrid Orbital Example

Suppose we want to make a diagram of SF 6 First we separate the central atom from the other atoms. The central atom is A and the other atoms are called X’s

A

SF 6

X’s

Hybrid Orbital Example

Suppose we want to make a diagram of SF 6 First we separate the central atom from the other atoms. The central atom is A and the other atoms are called X’s

A

SF 6

X’s

Then we generate a set of degenerate hybrid orbitals to house the valence electrons

Hybrid Orbital Example

Suppose we want to make a diagram of SF 6 First we separate the central atom from the other atoms. The central atom is A and the other atoms are called X’s

A

SF 6

X’s

Then we generate a set of degenerate hybrid orbitals to house the valence electrons F F F F F F F Insert single electrons into the degenerate hybrid orbitals

Practice

What are the molecular geometries of the ions: SCN and NO 2 ?

Polar Bonds and Polar Molecules

• Two covalently bonded atoms with different electronegativities have partial electric charges of opposite sign creating a bond dipole.

• A molecule is called a polar molecule when it has polar bonds and a shape where the bond dipoles don’t offset each other.

Examples

Measuring Polarity

• The permanent dipole moment (  ) is a measured value that defines the extent of separation of positive and negative charge centers in a covalently bonded molecule.

Atomic Orbitals and Bonds

• • A tetrahedral molecule requires that four orbitals of the central atom must overlap with an orbital of an outer atom to form a bond.

The central atom would use its s orbital and its three p orbitals, but these orbitals would not yield the 109 ° bond angles observed in the tetrahedral molecule.

Valence-Bond Theory

• • Valence-bond theory assumes that covalent bonds form when orbitals on different atoms overlap or occupy the same region of space.

A sigma (  ) bond is a covalent bond in which the highest electron density lies between the two atoms along the bond axis connecting them.

Examples

Valence Bond Theory

• • Hybridization is the mixing of atomic orbitals to generate new sets of orbitals that are then available to overlap and form covalent bonds with other atoms.

A hybrid atomic orbital is one of a set of equivalent orbitals about an atom created when specific atomic orbitals are mixed.

Tetrahedral Geometry: sp

3

Hybrid Orbitals

A tetrahedral orientation of valence electrons is achieved by forming four sp 3 hybrid orbitals form one s and three p atomic orbitals.

Other sp

3

Hybrid Examples

sp

2

Hybridization

• In a covalent pi (  ) bond, electron density is greatest above and below the bonding axis.

sp Hybridization

• Pi bonds will not exist between two atoms unless a sigma bond forms first.

The Bonding in Carbon Dioxide

The carbon atom is sp hybridized and these orbitals form the two sigma bonds. The  bonds are rotated 90 ° from one another.

d

2

sp

3

Hybridization

dsp

3

Hybridization

Practice

What are the hybridizations of the central atoms of the ions: SCN and NO 2 ?

Delocalization of Electrons

• The electrons in the  system with alternating single and double bonds can be delocalized over several atoms or even an entire molecule.

Problems with Bonding Theories

• Lewis structure and valence bond theory help us understand the bonding capacities of elements.

• VSEPR and valence bond theories account for the observed molecular geometries.

• None of these models enables us to explain why O 2 is attracted to a magnetic field while N 2 is repelled slighty.

Molecular Orbital (MO) Theory

• The wave functions of atomic orbitals of atoms are combined to create molecular orbitals (MOs) in molecules.

 Each MO is associated with an entire molecule, not just a single atom. MOs are spread out, or delocalized over all the atoms in a molecule.

MOs for H

2 • The two 1s orbitals may be added or subtracted to yield two MOs.

Types of MOs

• Electrons in bonding orbitals serve to hold atoms together in molecules by increasing the electron density between nuclear centers.

• Electrons in antibonding orbitals in a molecule destabilize the molecule because they do not increase the the electron density between nuclear centers.

Bond Types

• A sigma ,  , bond is a covalent bond in which the highest electron density lies along the bond axis.

• A pi ,  , bond is formed by the mixing of atomic orbitals that are not oriented along the bonding axis in a molecule.

Bond Order

Bond Order = 1/2 (# bonding electrons - # antibonding electrons) The bond order is zero in He 2 and the molecule is not stable.

MO Guidelines

1.

2.

3.

4.

5.

The total number of MO formed equals the number of atomic orbitals used in the mixing process.

Orbitals with similar energy and shape mix more effectively than do those that are different.

Orbitals of different principal quantum numbers have different sizes and energies resulting in less effective mixing.

A MO can accommodate two electrons with opposite spin.

Electrons are placed in MO diagrams according to Hund’s rule.

Combinations of Atomic Orbitals to form MOs for N

2

and O

2

MO Diagrams for N

2

and O

2

MO Scheme for N

2 Figure 9.27

• Electron configuration for N 2 :  2s 2  2s *2  2p 2  2p 4 • Bond order = 1/2 (8 - 2) = 3  N 2 has three bonds  N 2 has no unpaired electrons

MO Scheme for O

2 • • Electron configuration for O 2 :  2s 2  2s *2  2p 2  2p 4  2p *2 Bond order = 1/2 (8 - 4) = 2  O 2 has two bonds  O 2 has two unpaired electrons in  2p *

Paramagnetism and Diamagnetism

• Paramagnetism - atoms or molecules having unpaired electrons are attracted to magnetic fields • Diamagnetism - atoms or molecules having all paired electrons are repelled by magnetic fields

Other Diatomic Molecules

• The 2s and 2p interactions are strong in Li 2 through N 2 but weaker in O 2 through Ne 2 .

Other Diatomic Molecules

• • The MO diagram illustrates how the effective nuclear charge alters the diagram.

The odd electron is more likely to be found on nitrogen since its in an orbital closer in energy to the atomic orbitals of the nitrogen atom.

Comparison of Theories

• MO theory may provide the most complete picture of covalent bonding, but it is also the most difficult to apply to large molecules and it does not account for molecular shape.

ChemTour: Partial Charges and Bond Dipoles

Click to launch animation PC | Mac Students learn that covalent bonds often include unequal distribution of electrons leading to partial charges on atoms, bond dipole moments, and molecule polarity. Interactive Practice Exercises ask students to calculate dipole moments of polar molecule.

ChemTour: Greenhouse Effect

Click to launch animation PC | Mac This unit explores how excess carbon dioxide and CFCs in the atmosphere contribute to global warming.

ChemTour: Vibrational Modes

Click to launch animation PC | Mac This tutorial illustrates the three vibrational modes: bending, symmetric stretching, and asymmetric stretching. Students learn that molecules can absorb specific wavelengths of infrared radiation by converting this energy into molecular vibrations.

ChemTour: Hybridization

Click to launch animation PC | Mac This tutorial animates the formation of hybrid orbitals from individual

s

and

p

orbitals, shows examples of their geometry, and describes how they can produce single, double, and triple bonds. Includes Practice Exercises.

ChemTour: Chemistry of the Upper Atmosphere

Click to launch animation PC | Mac This ChemTour examines how particles of the upper atmosphere absorb and emit electromagnetic radiation.

ChemTour: Molecular Orbitals

Click to launch animation PC | Mac This animated tutorial offers a patient explanation of molecular orbital theory, an alternative to the bonding theory depicted by Lewis dot structures. Includes Practice Exercises.

Ethylene, which has the molecular formula C 2 H 4 , is a rigid molecule in which all 6 atoms lie in a plane.

Which of the following molecules also has a rigid planar structure?

A) H 2 C=C=CH 2 B) H 2 C=C=C=CH 2 Planar Hydrocarbons C) Neither

Consider the following arguments for each answer and vote again: A. A combination of 3 carbons and 4 hydrogens can form the rigid planar molecule H 2 C=C=CH 2 .

B. The orientations of the π bonds in H 2 C=C=C=CH 2 alternate in such a way as to create a planar structure.

C. The hybridization of the atomic orbitals on the carbons prevents the retention of a planar structure in molecules longer than C 2 H 4 .

Planar Hydrocarbons

What is the bond order of the N-O bond in nitrate, NO 3 -?

A) 1 Bond Order of Nitrate B) 11/3 C) 2

Consider the following arguments for each answer and vote again: A. The majority of the bonds in NO 3 - are single bonds, so the bond order is 1.

B. The N-O bond is twice as likely to be a single bond as it is to be a double bond, so the bond order should be 11/3.

C. The bond order is dictated by the strongest bond, which in NO 3 - is a double bond. Bond Order of Nitrate

Which of the following species is not paramagnetic in its ground state?

A) NO+ B) NO C) NO Bond Order of Nitrate

Consider the following arguments for each answer and vote again:

A. NO+ is isoelectronic with N 2 , which has no unpaired electrons and hence is not paramagnetic.

B. NO has no electrical charge and thus cannot be paramagnetic.

C. By pairing an additional electron with the one unpaired electron in NO, a diamagnetic anion, NO-, is formed.

Bond Order of Nitrate

According to Valence Shell Electron Pair Repulsion (VSEPR) theory, 4 objects around a central atom will have the tetrahedral arrangement shown to the left with bond angles of ~109.5º. Which of the following compounds has a bond angle of ~109.5º?

A) SF 2 B) SF 3 C) SF 4 Molecular Geometry of SF 2 , SF 3 -, and SF 4

Please consider the following arguments for each answer and vote again:

A. SF 2 consists of a sulfur atom surrounded by 2 lone electron pairs and bonded to 2 fluorine atoms, therefore, it has an approximately tetrahedral bond angle.

B. The tetrahedral VSEPR arrangement of SF 3 - is formed by a sulfur atom surrounded by 3 fluorine atoms and by the additional electron (from the negative charge).

C. Sulfur tetrafluoride is the only molecule with a central atom (sulfur) surrounded by 4 additional atoms (4 fluorines) and so is the only molecule with a bond angle of ~109.5º.

Molecular Geometry of SF 2 , SF 3 -, and SF 4

Which of the following is true of the bond angle (θ 1 ) in BrF 2 + compared to the bond angle (θ 2 ) in ICl 2 ?

A) θ 1 = θ 2 B) θ 1 > θ 2 C) θ 1 < θ 2 Bond Angles of BrF2 and ICl2

Please consider the following arguments for each answer and vote again:

A. Both BrF 2 + and ICl 2 consist of a central halogen atom bonded to two halogen atoms, and therefore should have the same arrangement of atoms.

B. ICl 2 has 1 more lone pair of electrons than BrF 2 + , which forces the chlorine atoms closer together.

C. ICl 2 , with 3 lone pairs, is linear whereas BrF 2 + , with 2 lone pairs, is bent.

Bond Angles of BrF2 and ICl2

Boron trifluoride (BF 3 ), which has the structure shown to the left, is capable of reacting with an unknown compound to form a new compound without breaking any bonds.

Which of the following could be the unknown compound?

A) BF 3 B) CH 4 C) NH 3 Reaction of Boron Trifluoride

Please consider the following arguments for each answer and vote again:

A. BF 3 can dimerize to BF 3 -BF 3 boron single bond.

by forming a boron B. By forming a boron-carbon bond, the carbon atom in CH 4 will increase its steric number to 5, thus expanding its octet to compensate for boron's incomplete octet.

C. The nitrogen lone electron pair can form a nitrogen boron bond yielding BF 3 -NH 3 , isoelectronic with CH 3 -CH 3 .

Reaction of Boron Trifluoride

Pictured to the left is the planar molecule ethylene, C 2 H 4 , which does not have a permanent electric dipole moment. If chlorine atoms were substituted for two hydrogen atoms, how many of the possible structures would also not possess a dipole moment?

A) 0 B) 1 C) 2 Dipole Moments of Dichloroethylene

Consider the following arguments for each answer and vote again:

A. Chlorine atoms always draw electron density away from carbon atoms, so all possible structures will possess a dipole moment.

B. Only if the chlorine atoms are diagonally opposite will the two carbon-chlorine dipole moments cancel each other.

C. So long as the two chlorine atoms are on different carbon atoms, no permanent dipole moment will form.

Dipole Moments of Dichloroethylene

For which central atom "X" does the anion pictured to the left have a square planar geometry?

A) C B) S C) Xe Molecular Geometry of XF 4 2-

Please consider the following arguments for each answer and vote again:

A. CF 4 2 forms a structure in which the 4 fluorine atoms form a square plane with one negative charge on either side of the plane.

B. With 2 lone electron pairs on the sulfur in SF 4 2 , its steric number is 6.

C. To maximize fluorine-fluorine distances, the 4 fluorine atoms in XeF 4 2 will lie in a plane.

Molecular Geometry of XF 4 2-