ORBITALS and MOLECULAR REPRESENTATION

by DR. STEPHEN THOMPSON MR. JOE STALEY

The contents of this module were developed under grant award # P116B-001338 from the Fund for the Improve- ment of Postsecondary Education (FIPSE), United States Department of Education. However, those contents do not necessarily represent the policy of FIPSE and the Department of Education, and you should not assume endorsement by the Federal government. ORBITALS AND MOLECULAR REPRESENTATION CONTENTS

2 Atomic Orbitals (n = 1) 3 Atomic Orbitals (n = 2) 4 Atomic orbitals (n = 3) 5 Hybrid Atomic Orbitals (sp) 6 Hybrid Atomic orbitals (sp2) 7 Hybrid Atomic Orbitals (sp2) 8 Hybrid Atomic Orbitals (sp3) 9 Overlapping Orbitals (Bonding And Antibonding)

10 Orbital Pictures For H And H2 11 Difl uorine 12 Carbon Orbitals (Methane And Ethane) 13 Carbon Orbitals (Ethene) 14 Carbon Orbitals (Ethene) 15 Carbon Orbitals (Ethyne) 16 Carbon Orbitals (Ethyne) 17 Carbon Orbitals (Benzene) 18 Carbon Orbitals (Benzene) 19 Several Representations Of Molecules 20 Several Representations Of Benzene 21 Representations Of Molecules 22 Representations Of Molecules 23 Representations Of Molecules ORBITALS AND MOLECULAR REPRESENTATION ATOMIC ORBITALS

While Lewis diagrams and energy level structures can show connectivity and energy relationships of mol- ecules, they do not show the shape of the molecules. For this we need to picture atomic and molecular orbitals.

n = 1 We denote the phase of the wave function by color, using light red for one phase and green for the opposite l = 0 phase. Many books assign these phases plus or minus 1s signs but the only real meaning is that they are oppo- The picture above shows the spherically symmetric 1s site. Neither phase is plus or minus anything on its own orbital in the ‘green’ phase. Sometimes it is more con- but they are only opposite to each other. Sometimes venient not to show the phase, in which case we can when we are not concerned with phase we will draw use a greyed representation, as shown below.. the orbitals as a slightly reddish gray.

1s

It is also possible to show the orbital as a simple loop. Here are some boxes for you to practice drawing s orbitals in, although you do not really need boxes. 1s

And if you are drawing his by hand, the loop does not have to be an exact circle.

1s

As we proceed developing atomic and molecular orbit- als we will show various forms of representation.

n = 2

You can draw the two loops for 2s in the box below.

l = 0

2s

2 ORBITALS AND MOLECULAR REPRESENTATION ATOMIC ORBITALS

n = 2

l = 1

2px

This is an accurate This is a common This simplifi ed xp orbital A hand drawn version does

representation of a picture of a px orbital is often useful. not have to be exact.

2px orbital.

2py

Use this box

2pz to draw a pz orbital.

We can combine all three p orbitals in a three dimensional display.

y y y

x x x

z z z

Use these axes to draw all three p orbitals. 3 ORBITALS AND MOLECULAR REPRESENTATION ATOMIC ORBITALS n = 3

3s Draw the 3s orbital l = 0 in the box at left.

Phase Picture Grayscale Loop Diagram

3px l = 1

3py

3pz

l = 2

3dxy 3dxz 3dyz 3dx2--y2 3dz2

3d 2 2 3dxy 3dxz 3dyz x --y 3dz2

4 ORBITALS AND MOLECULAR REPRESENTATION HYBRID ATOMIC ORBITALS sp sp orbitals are a combination, or hybrid, of an s and a p You will recall that our color convention is to show the orbital. In addition there will be two remaining unhy- phases of the atomic orbitals with red and green. We bridized p orbitals orthogonal to each other and to the shall show the phases of hybrid orbitals in blue and line joining the two hybrid sp orbitals. yellow.

+ +

2s 2p sp sp 2 x sp You will also see these orbitals in greyscale, without phases. We use reddish grey for unhybridized orbitals and plain gray for for hybridized orbitals.

2p sp sp 2 x sp 2s It is common to show hybrid orbitals We can also draw these orbitals as simplifi ed loops. without the small lobes.

+ +

2s 2p sp sp 2 x sp

It is useful to draw the sp hybrid orbitals yourself. An sp hybridized atom uses one s and one p orbital to make two sp hybrid orbitals; there are two remaining p orbitals. Next we show the phase pictures of combining the sp hybrid orbitals with fi rst one and then both of the Axes for you remaining p orbitals. to draw the loop diagram. Phase pictures. loop Diagram

2 x sp + 2p 2 x sp + 2 x 2p 2 x sp + 2 x 2p NOTE: When we write 2 x sp we mean two instances of sp and when we write 2p we mean one instance of a 2p orbital. 5 ORBITALS AND MOLECULAR REPRESENTATION HYBRID ATOMIC ORBITALS sp2 The pictures below sp2 hybrid orbitals are formed when are trigonal views of 2 one 2s orbital combines or hybridizes sp sp2. Trigonal means with two 2p orbitals in the shapes and arranged in triangular arrangement shown. form in a plane.

+ +

2s 2p 2p sp2

trigonal view of sp2 120º sp2 In greyscale: 120º

120º

+ +

2s 2p 2p

You will often see a simple presentation of the sp2 orbitals. You can also draw the sp2 hy- Thr important points to know about are that the three brid orbital as simple loops. bonds are in a plane and that they are 120˚ apart.

Draw the loop version of the trigonal set of sp2 orbit- als in the box at right.

6 ORBITALS AND MOLECULAR REPRESENTATION HYBRID ATOMIC ORBITALS sp2

In addition to the trigonal set of hybridized orbitals there is a remaining 2p orbital that will point above and below the trigonal plane.

First we show the phase orbitals.

+

planar view of sp2 2p sp2 + 2p

Here we show the grayscale.

z

120° 120° x

120° y

7 ORBITALS AND MOLECULAR REPRESENTATION HYBRID ATOMIC ORBITALS sp3 sp3 orbitals are formed by the hybridization of a 2s orbital and three 2p orbitals.

2s sp3

+

2p

+

2p

+ sp3 sp3

sp3 2p

sp3 orbitals have a tetrahedral structure.

8 ORBITALS AND MOLECULAR REPRESENTATION OVERLAPPING ORBITALS

BONDING ORBITALS ANTIBONDING ORBITALS

Chemical bonds are formed from the overlapping of Overlapping orbitals of opposite phase form antibond- atomic orbitals having the same phase. ing orbitals. s + s σ s - s σ*

s + p σ s - p σ*

p + p σ p - p σ*

p + p π p - p π*

9 ANTIBONDING ORBITAL ORBITAL PICTURESFORHAND ORBITALS ANDMOLECULARREPRESENTATION HYDROGEN ORBITAL We canalsomakeorbital energylevelsformolecules. BONDING ORBITAL 1s 1s A -1s A 1s +1s B B or 1s 1s 1s A A -1s +1s B B 10

ENERGY 2 1s H A A 1s 1s A A H +1s -1s 2 B B H B 1s B ORBITALS AND MOLECULAR REPRESENTATION DIFLUORINE

2pA - 2pB z y x σ* x y z

2pA5 2pB5

ENERGY σ

2sA2 2sB2 2pA + 2pB

2 2 1sA 1sB 1

FA FB

In picture 1 we show the molecular orbital structure of F2. In picture 2 we show the overlapping p orbitals, which form the bond between the two fl uorine atoms, in red and green gradients.

The dashed lines show the remaining p orbitals which do not take part in the bonding. 2

z z

Construct the molecular orbital diagram for dichlorine. x

y y 3 Showing the p orbitals.

z z

x

y y 4

Showing the s and p orbitals.

11 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

METHANE AND ETHANE

H

C H H H

1

Methane CH4 In methane and ethane, all of the bonds are σ−bonds, which means that they are formed by orbitals overlapping along a direct line between the nuclei of the two bonding atoms.

H H

H C C H C2H6

H H

2

Ethane CH6

Color conventions: Hydrogen atoms are shown in gray. Hybrid atomic orbitals are shown in blue and yellow. Atomic p orbitals are shown in red and green. Greyscale Conventions: Hybrid orbitals are shown in grey. Unhybridized atomic orbitals are shown in reddish-grey.

12 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

ETHENE C2H4

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3 Picture 3 shows the sigma bond formed by overlaping sp2 orbitals between the two carbon atoms of ethene. The other sp2 orbitals are shown in dashed outline.

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� �

4 Picture 4 shows the π bond between the p orbitals of the carbon atoms. The pi bond is the overlap of the two red spheres and is actually coming out of the plane of the paper.

900 rotation

5

Picture 5 is similar to picture 4 but rotated 900 around the σ bond, so that the overlapping p orbitals which form the π bond are shown with the red phase above the σ bond and with the green phase below.

13 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

ETHENE C2H4

6

Ethene from above the trigonal plane. The carbon atoms and orbitals are shown.

H H

C2H4 C C

H H

7

Ethene from above the trigonal plane with the hydrogen 900 rotation atoms shown. The bond angles and relative bond lengths are correct.

H C C H H H

8

Ethene in the trigonal plane. 14 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

ETHYNE C2H2

� ����

� �

9 This drawing shows the sigma bond between two carbon atoms.

� ����

� �

10

In this drawing we have added a pi bond to the ethyne.

� ����

� �

11 We have added the other π bond which, as it needs to be orthogonal to both the fi rstπ bond and to the σ bond, must be imagined as coming out of the paper.

15 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

ETHYNE C2H2

12

Ethyne in the trigonal plane, but with the hydrogen atoms added.

H C C H

13

Unlike ethene, ethyne has the same form and ap- pearance when rotated 900 around the C-C axis.

16 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

BENZENE C6H6

C C

C C

C C This is the ring of σ bonds 14 15 whose orbitals are shown in picture 15 The sigma bond ring of benzene. The sigma bond ring of benzene with the additional sp2 orbitals.

C C C C C C ↔ C C C C C C This is a former represen- tation of the resonance structure of benzene.

This is a contemporary representation of the resonance structure of benzene.

17 ORBITALS AND MOLECULAR REPRESENTATION CARBON ORBITALS

BENZENE C6H6

16

To which we have now added the pi orbitals above the ring.

900 rotation

17 Benzene carbon orbitals viewed from the side. This picture illustrates the delocalization of the six 2p electrons in the benzene molecule. These six electons are shared collectively among all six of the carbon atoms.

900 rotation

19 18 Benzene from the side, complete with hydrogen atoms. Adding the hydrogen atoms to picture 16 we view benzene from above, complete. 18 ORBITALS AND MOLECULAR REPRESENTATION SEVERAL REPRESENTATIONS OF MOLECULES

METHANE CH4 H 95nm 109.5º C H H H

All orbitals Textbook Structural Space Ball and tetrahedron fi lling stick ETHANE C2H6 109 nm 154 nm H H H C C H

H 111º H All orbitals Textbook orbitals Structural Space Ball and fi lling stick ETHENE C2H4

134 nm All orbitals Textbook orbitals H H looking down on the trigonal plane C C 120°

H 120° H Space Ball and Structural fi lling stick

All orbitals but no Textbook orbitals hydrogen (for clarity) Looking along the trigonal plane

ETHYNE C2H2

Textbook orbitals All orbitals Space Ball and 106 nm 120 nm fi lling stick

H C C H Structural

19 ORBITALS AND MOLECULAR REPRESENTATION SEVERAL REPRESENTATIONS OF BENZENE

BENZENE C6H6

Benzene showing all orbitals Benzene textbook Benzene textbook σ bonds σ and π bonds from the side

Benzene space fi lling Benzene ball and stick

H H 140 nm 110 nm C C C C

C 120º C H C C H

C C C C

H H

Benzene structural Benzene structural carbon ring carbon ring and hydrogens

20 ORBITALS AND MOLECULAR REPRESENTATION REPRESENTATIONS OF MOLECULES

You can easily draw orbitals, bonds and molecules.

Start by drawing a circle, like this: You draw a circle (an s orbital) in the box.

This is an s orbital.

Now draw one circle above You draw a p orbital. another one, like this: (two circles tangent)

This is a p orbital.

When two s orbitals from different atoms overlap, this is You draw two overlapping circles in the box below. σ called a (sigma) bond. This is a σ bond.

When an s and a p orbital overlap, this is a σ bond. You can draw the s and p overlap.

21 ORBITALS AND MOLECULAR REPRESENTATION REPRESENTATIONS OF MOLECULES

N DINITROGEN 2 110 nm

N N Textbook orbitals Structural Ball and stick Space fi lling All bonding orbitals

DIOXYGEN O2 π bond

Space fi lling π bond For clarity, only the orbitals which 121 nm form the π bonds are shown. O O Ball and stick Structural

SIMPLIFIED ORBITALS

We have shown molecular pictures which are as accurate as possible, however such orbitals are diffi cult to draw by hand. But a simplifi ed version of them is easy to draw an s orbital and shows much about mjolecular structure a px orbital and bonding.

+z

-y a pz orbital a py orbital

Draw the bonding orbitals for: -x +x

H2O

NH3 +y -z CO All three p orbitals CO2

22 ORBITALS AND MOLECULAR REPRESENTATION REPRESENTATIONS OF MOLECULES

There are three orthogonal p orbitals. They can be drawn like this. Draw your own set of p orbitals on the axes pro- vided.

Two p orbitals (on different atoms) in the same direction You draw two p orbitals side by side and overlapping, can overlap forming a π (pi) bond. forming a π bond.

You can draw hybrid orbitals like this:

You draw an sp hybridized atom in the box below.

You draw an sp2 hybridized atom.

23