1 Topic 10 Molecular Geometry and Bonding Theory

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Topic 10

Molecular Geometry and Bonding Theory

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The subject of molecular geometry deals with shapes of molecules. Recall that a Lewis structure is a two-dimensional representation of a molecule or ion; its intent is to show how the valence electrons of atoms are distributed in the molecule. A Lewis structure does not necessarily have to depict the actual shape of the molecule or ion, but we can use it deduce what the actual shape is.

Since atoms are always in motion, when we talk about the shapes of molecules or ion, we mean the shape based on the average location of the atoms.

Molecular Geometry

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A description of the geometry of a molecule or ion involves the positions of all the atoms in the molecule relative to each other which includes the parameters of bond angles and bond lengths.

In a Lewis structure, two atoms are joined by a line. When more than two atoms are joined together, these lines intersect at a given central atom and forms angles with each other. These angles are called bond angles.

The line or bond joining two atoms connects the nuclei of the two atoms with the length or distance between those two nuclei being called the bond length.

Molecular Geometry

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The bond angles and bond lengths of a molecule or ion dictate the particular geometry of the species.

Lewis structures are two-dimensional representations of a molecule but because molecules are three dimensional, a picture of the molecular geometry must convey information about the third dimension as well.

Our drawing surface is flat; therefore, we use a projection which includes dashed line-wedges for bonds to indicate the three-dimensional molecule.

Molecular Geometry

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Bonds are represented as ordinary lines if they are in the plane of the paper; solid wedges if they are pointing out of the paper; dashed wedges or dashed lines if they are pointing into the paper.

Ammonia has a geometry that is triangular pyramidal (looks like a pyramid with N at the top and H at the base of the three corners). If the N atom is in the plane of the paper, one 3-D arrangement could have two H atoms pointing back into the paper with the third pointing out of the paper or vice versa.

Molecular Geometry

H N

H H

:

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To determine the shape of a molecule based on the bond angles and bond length, we use a simple theory called VSEPR (Valence Shell Electron Pair Repulsion Theory).

The basic idea behind VSEPR is that regions of high electron density (electron groups) around each atom in the molecule tend to be oriented as far away from one another as possible.

Depending on the number of electron groups around the central atom, there will be a particular geometry available that minimizes the electron repelling forces in the molecule.

Once we know how the electron groups around an atom are oriented, it becomes easy to imagine the shape of the molecule.

Molecular Geometry

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Let’s take a look at the following example:

Which orientation gives the most space between the two negative charges around the central positive charge; the 90o or the 180o?

Molecular Geometry

(-) ----(+)--

--

(-)

90o(-) ----(+) ---- (-)

180o

Obviously, the 180o orientation gives the best use of space and allows the two negative charges to get as far apart as possible.

This means that a central atom that has two electron groups around it will adapt a geometry that is linear in shape; electron groups will be 180o apart.

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Let’s look at another example:

Which orientation gives the most space between the three negative charges around the central positive charge?

Molecular Geometry

(-) ----(+)

----

(-)

90o

(+)

----(-) 120o

Obviously, the shape that has all three negative charges 120o apart gives the best use of space and allows the three negative charges to get as far apart as possible.

This means that a central atom that has three electron groups around it will adapt a geometry that is trigonal planar in shape; electron groups will be 120o apart.

---- (-)90o

180o ----

----(-)

(-)

120o 120o

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Bottom line: Depending on the number of electron groups around the central atom, there will be a particular geometry that allows all the electron groups to maximize their distance from each other.

The first step in figuring out the shape of a molecule is to determine the steric number of atoms that are bonded to at least two other atoms.

Steric number (SN) refers to the number of electron groups around an atom and gives us information on how these groups will orient relative to each other.

Molecular Geometry

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To determine the steric number, we must account for the following:

- a single bond is counted as one group- a double bond is counted as one group- a triple bond is counted as one group- a lone pair is counted as one group

Basically, each electron density region (group of electrons between atoms) around an atom counts as one group, and a lone pair counts as one group as well.

Steric Number

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To determine the steric number (SN), we must first draw the Lewis structure and then count the number of electron groups around an atom.

What are the steric numbers for the C atoms in the Lewis structures below?

Steric Number

CC

H

H

H

H

CC HH

Both carbons have three electron groups around them (2 single bonds and one double bond);

therefore, both have a SN of 3.

Both carbons have two electron groups around them (one single and one triple bond;

therefore, both have a SN of 2.

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What are the steric numbers for the O and N atoms in the Lewis structures below?

Steric Number

-

. .

H N H-H

-

-

. .. .H O H-

The O atom has four electron groups around it (2 single bonds and two lone pairs);

therefore, O has a SN of 4 in this structure.

The nitrogen atom has four electron groups around it (3 single bonds and one lone pair);

therefore, N has a SN of 4 in this structure.

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Once we have determined the steric number of an atom, we can predict the measure of the angle formed by the electron groups sticking out of that atom.

However, when the groups on the atom are not identical, we must realize that the bond angles will differ slightly. Bond angles are affected by the type of electron density regions (electron groups) around the atom.

Lone pairs (LP) repel other groups more strongly than bonded pairs (BP) and multiple bonds repel more strongly than single bonds. Repelling force interactions are greater in LPLP > LPBP > BPBP and cause the bond angles to decrease.

Bond Angles

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Many physical properties of molecules are directly related to whether they are nonpolar or polar. The overall polarity of a molecule depends not only on the polarity of its bonds but also on its geometry.

Each polar bond has a bond moment, but each molecule also has an overall molecular dipole moment that is approximately the sum of all its individual bond moments. This vector sum of bond moments must include not only the magnitude of the bond moments but also their direction.

To determine if a molecule is polar or nonpolar requires the examination of the bond moments and their orientations within the geometry of the molecule. If bond moments are oriented in such a way that it cancels each other out, the molecule is nonpolar.

Polarity

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Arrangement of Electron Groups About an Atom Based on Steric Number

2 groups: steric number, SN = 2 molecular geometry: linear

bond angles: 180o polarity (assuming all atoms the same around central atom): nonpolar

geometry involves: 2 atoms bonded (X) to central atom (A), AX2

i.e CO2

3 groups: SN = 3 molecular geometry: trigonal planar


geometry involves: 3 atoms bonded (X) to central atom (A), AX3

i.e NO3-

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3 groups: SN = 3 molecular geometry: bent or angular

bond angles: <120o polarity (assuming all atoms the same around central atom): polar

geometry involves: 2 atoms bonded to central atom which has one lone pair (E), AX2E

i.e NO2-

4 groups: SN = 4 molecular geometry: tetrahedral

bond angles: 109.5o polarity (assuming all atoms the same around central atom): nonpolar

geometry involves: 4 atoms bonded to central atom, AX4

i.e CH4

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4 groups: SN = 4 molecular geometry: triangular pyramidal

bond angles: <109.5o polarity (assuming all atoms the same around central atom): polar

geometry involves: 3 atoms bonded to central atom which has one lone pair (E), AX3E

i.e NH3

4 groups: SN = 4 molecular geometry: bent or angular

bond angles: <109.5o polarity (assuming all atoms the same around central atom): polar

geometry involves: 2 atoms bonded to central atom which has two lone pairs, AX2E2

i.e H2O

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5 groups: SN = 5 molecular geometry: triangular bipyramidal

bond angles: 90o, 120o, 180o polarity (assuming all atoms the same around central atom): nonpolar


i.e PF5

5 groups: SN = 5 molecular geometry: see-saw

bond angles: <90o, <120o, <180o polarity (assuming all atoms the same around central atom): polar

geometry involves: 4 atoms bonded to central atom which has one lone pairs, AX4E

i.e SF4

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5 groups: SN = 5 molecular geometry: T-shaped

bond angles: <90o, <180o polarity (assuming all atoms the same around central atom): polar


i.e ClF3

5 groups: SN = 5 molecular geometry: linear


geometry involves: 2 atoms bonded to central atom which has three lone pairs, AX2E3

i.e I3

-

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6 groups: SN = 6 molecular geometry: octahedral

bond angles: 90o, 180o polarity (assuming all atoms the same around central atom): nonpolar


i.e SF6

6 groups: SN = 6 molecular geometry: square pyramidal

bond angles: <90o polarity (assuming all atoms the same around central atom): polar

geometry involves: 5 atoms bonded to central atom which has one lone pairs, AX5E

i.e BrF5

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6 groups: SN = 6 molecular geometry: square planar

bond angles: 90o, 180o polarity (assuming all atoms the same around central atom): nonpolar


i.e XeF4

Note:

There are other molecular geometries with SN =6 (AX3E3, T-shaped; AX2E4, linear) as well as molecular geometries with SN>6, but we will not cover these in this course.

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Valence Bond ModelThe VSEPR model provides a way to predict molecular shapes but says nothing about the electronic nature of covalent bonds. To describe bonding, the valence bond (VB) model was developed.

The VB model provides an orbital picture of how electron pairs are shared in a covalent bond.

A covalent bond results when two atoms approach each other closely enough so that a singly occupied valence orbital on one atom overlaps a singly occupied valence orbital on another atom.

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Valence Bond ModelThese paired electrons located within the overlapping orbitals are attracted to the nuclei of both atoms forming a covalent bond between the atoms.

For example, the H-H bond in H2 results from the overlap of two singly occupied hydrogen 1s orbitals:

H H H H+

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Hybridization ModelAccording to this model, it would seem that for an atom to form a covalent bond, it must have an unpaired electron. However, experience tells us that this is not true.

To adapt the valence bond model to include bonding between atoms with no unpaired electrons, the hybridization model was developed.

This model accounts for the experimental evidence about molecular structure much better than the simple overlap VB model.

The hybridization model modifies the description of atomic orbitals when they overlap to form bonds.

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Hybridization ModelIn this model, we do not describe the orbitals by using simple s and p orbitals, but instead, we use hybrid orbitals which are combination orbitals formed by the mixing of simple atomic orbitals. The number of hybrid orbitals formed is equal to the number of atomic orbitals mixed.

Although it appears that hybrid orbitals are nothing more than a different way of describing electrons, there is an underlying physical reality that we are actually describing. The new orbitals are more suited for forming bonds.

A bond is the result of the overlap of two orbitals, one from each atom of the bond. The better the overlap, the stronger the bond. Pure atomic orbitals are quite symmetrical resulting in relatively little overlap before their nuclei approach close enough to begin repelling each other.

Hybrid orbitals are less symmetrical than unhybridized ones resulting in more effective overlap and stronger bonding.

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Hybridization ModelThe formation of the BeH2 molecule can be explained using the hybridization model.

It is assumed that as two hydrogen atoms approach Be, the atomic orbitals of the Be atom undergo a significant change:

a 2s orbital is mixed or hybridized with a 2p orbital to form two new sp hybrid orbitals that will have better overlap (bonding) with the 1s orbitals of H:

one s atomic orbital + one p atomic orbital two sp hybrid orbitals

The next slide describes the process using an orbital diagram.

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Be 1s22s2 ____ ____ “ground state”

1s 2s

____ ____ ____ ____ ____ valence state

2s 2s 2px 2py 2pz “excited state”

____ ____

sp sp

Hybridization ModelBeH2 H : Be : H

s sp

Be does not have unpaired e-; therefore, it must promote an electron to a p orbital to form the valence state before bonding will occur.

Hybridization process: 2s and 2p orbitals are mixed so as to form two hybrid (mixed) orbitals (sp) that are better suited for overlaping with the 1s orbitals of H.

sp s

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Hybridization Model

CH4 C: 2s22p2 ___ ___ ___ ___

2s 2px 2py 2pz

Four unpaired electrons are formed as an electron from the 2s orbital is promoted (excited) to the vacant 2p orbital to form the valence state.

A similar process occurs for all atoms bonded in molecules. They undergo hybridization to form new orbitals that allow for better overlapping and bonding.

The bonding in carbon might be explained as follows:

ground state

1s

C atom (ground state)

2s

2p

En

ergy

2s

2p

1s

C atom (promoted)

valence “excited” state29

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Hybridization ModelThis promotion would give four unpaired electrons available for bonding: one bond on carbon would form using the 2s orbital while the other three bonds would use the 2p orbitals.

However, this does not explain the fact that the four bonds in CH4 appear to be identical and not a single 2s and three 2p orbitals.

The hybridization model assumes that the four available atomic orbitals in carbon combine to make four equivalent “hybrid” orbitals.

The 2s, 2px, 2py, 2pz mix to form 4 new equivalent sp3 orbitals that are better suited for overlapping in bonding and containing an unpaired electron.

____ ____ ____ ____

sp3 sp3 sp3 sp3

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Hybrid OrbitalsHybrid orbitals are orbitals used to describe bonding that are obtained by taking combinations of atomic orbitals of an isolated atom.

In the carbon case, a set of hybrids are constructed from one “s” orbital and three “p” orbitals, so they are called sp3 hybrid orbitals.

The four sp3 hybrid orbitals take the shape of a tetrahedron. Each C-H covalent bond results from an overlap between a singly occupied hydrogen 1s orbital with a singly occupied carbon sp3 hybrid orbital.

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ssp3

sp3

sp3

sp3

s

s

s

sp3

1s

You can represent the hybridization of carbon in CH4 as follows.

C atom

(promoted or

excited state)

En

ergy

1s

2p

2s

sp3

1s

C atom

(hybridized state)

C atom

(in CH4)

C

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- H bonds

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Hybridization Correlated to Geometry

In general, we can correlate the steric number to the hybridization of the atom. There is a relationship between the type of hybrid orbitals and the geometric arrangement of those orbitals.

• If the steric number is 2, the hybridization is sp.• If the steric number is 3, the hybridization is sp2.• If the steric number is 4, the hybridization is sp3.• If the steric number is 5, the hybridization is sp3d.• If the steric number is 6, the hybridization is sp3d2.

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What are the molecular geometry, angles between bonded atoms, hybridization, and polarity of XeF2?

First, you will have to draw it’s Lewis structure (22e- available):

Xe

F

--

:

:

: :

: F :

:

:

:Next, we see that there are 5 electron groups around the central atom giving this structure a steric number of 5.

The molecular geometry for SN=5 with two bonded atoms and 3 lone pairs is linear.

The angle between bonded pairs is 180o.

Since this is a SN=5, the hybridization is sp3d.

All dipoles cancel each other out (all 3 lone pairs pull out from the center while the two bonded atoms pull in opposite directions); therefore, this is a nonpolar molecule.

Xe

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What are the molecular geometry, angles between bonded atoms, hybridization, and polarity of NH3?First, you will have to draw it’s Lewis structure (8e- available):

Next, we see that there are 4 electron groups around the central atom giving this structure a steric number of 4.

The molecular geometry for SN=4 with three bonded atoms and 1 lone pairs is triangular pyramidal.

The angles between bonded pairs is <109.5o. The lone pair causes the angles of the bonded pairs to decrease.

Since this is a SN=4, the hybridization is sp3.

All dipoles are additive (lone pair pulls out and all three bonded atoms pull toward the center resulting in an overall dipole moment for the molecule; therefore, this is a polar molecule.

H N HH

:

H

NH H

:

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1Steric No. 2Angles, XAX3Hybrid-ization

Lone Pairs4Molecular Geometry

5Sketch 6Polarity

2 180o sp 0 linear no

3 120o sp2 0 trigonal planar no

<120o sp2 1 angular or bent yes

4 109.5o sp3 0 tetrahedral no

<109.5o sp3 1 triangular pyramidal yes

<109.5o sp3 2 angular or bent yes

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1Steric No. 2Angles, XAX3Hybrid-ization

Lone Pairs4Molecular Geometry

5Sketch 6Polarity

5 90o 120o 180o sp3d 0triangular

bipyramidalno

<90o <120o

<180o sp3d 1 see-saw yes

<90o <180o sp3d 2 T- shaped yes

180o sp3d 3 linear no

6 90o, 180o sp3d2 0 octahedral no

<90o sp3d2 1 square pyramidal yes

90o, 180o sp3d2 2 square planar no

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Molecular Geometry Table Footnotes• 1Steric number equals the number of electron density regions.

Single bond, double bond, triple bond, and lone pair all equal one electron density region.

• 2Angles are affected by the type of electron density regions. Repelling forces are greater in LPLP>LPBP>BPBP (LP – lone pair, BP – bonding pair) and multiple bonds are greater than single bonds.

• 3Hybridization can be easily determined by the Steric number and remembering the combined s, p, and d orbitals

• 4Molecular Geometry gives the shape of the atoms in the molecule.

• 5Example sketch of electronic geometry around of central atom. • 6Polarity is given for case when all the ligands are the same.

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Multiple BondingInsofar as geometry is concerned, a multiple bond acts as if it were a single bond. In other words, the extra electron pairs in a multiple bond (double, triple) have no effect on the geometry of the molecule.

Insofar as hybridization is concerned, the extra electron pairs in the multiple bond are not located in hybrid orbitals.

According to the valence bond model, only one electron pair occupies one needed hybrid orbital for each bond (whether a single or multiple bond).

hybrid hybridunhybrid

Triple bond Double bond

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For example, consider the molecule ethene:

Each carbon atom is bonded to three other atoms and no lone pairs, which indicates the need for three sp2 hybrid orbitals with one electron pair in each orbital.

The third 2p orbital is left unhybridized and lies perpendicular to the plane of the trigonal sp2 hybrids.

The following slide represents the sp2 hybridization of the carbon atoms.

sp2

sp2

sp2

sp2sp2

unhybridized

2p

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C atom (ground state)

2s

2p

En

ergy

sp2

2p

1s 1s

C atom (hybridized)

(unhybridized)

1-2s and 2-2p orbitals form 3-sp2 hybrid orbitals leaving 1-2p orbital unchanged

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Multiple BondingTo describe the multiple bonding in ethene, we must first distinguish between two kinds of bonds.– A s (sigma) bond is a “head-to-head” overlap of orbitals

with a cylindrical shape about the bond axis. This occurs when two “s” orbitals overlap or “p” orbitals overlap along their axis (hybridized).

– A p (pi) bond is a “side-to-side” overlap of parallel “p” orbitals, creating an electron distribution above and below the bond axis (unhybridized).

C : C axis

C : C.. ..

.. ..axis

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axis

axis

head-to-head overlap, s

head-to-head overlap, s

axis

side-to-side overlap, p

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Multiple Bonding

Two of the sp2 hybrid orbitals of each carbon overlap with the 1s orbitals of the hydrogens and the remaining sp2 hybrid orbital on each carbon overlap to form s bonds.

There are 5 s bonds in ethene.

s

ss

s

s

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Multiple BondingThe remaining “unhybridized” 2p orbitals on each of the carbon atoms overlap side-to-side forming a p bond.

You therefore describe the carbon-carbon double bond as one s bond and one p bond.

Ethene has 5 s bonds and 1 p bond.

Bottom line: single bond – sdouble bond – 1s and 1p triple bond – 1s and 2p

s

p

ss

ss

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How many s and p bonds does acetylene, C2H2, have?

First, you must draw a Lewis structure:

Multiple Bonding

H – C C – H

HW 68

Since the C’s have a SN of 2, we know that we have a hybridization of sp on the carbons.

This gives us 1 sp-sp head-on overlap (C-C) and 2 s-sp head-on overlaps (H-C) giving us 3 s bonds.

We also have 2 unhybridized side-on overlaps (C-C) giving us 2 p bonds.

This gives us a total of 3s and 2p bonds.

––s ssp

p

code: geometry

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1 Topic 10 Molecular Geometry and Bonding Theory