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Orbitals and mouecular

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					                         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   Difluorine
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 simplified px 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




         3dxy            3dxz             3dyz               3dx2--y2          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 simplified 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 first 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
one 2s orbital combines or hybridizes                                     sp2                          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+sσ                                                    s - s σ*




s+pσ                                                    s - p σ*




p+pσ                                                    p - p σ*




p+pπ                                                    p - p π*




                                                    9
ORBITALS AND MOLECULAR REPRESENTATION
ORBITAL PICTURES FOR H AND H2

We can also make orbital energy levels for molecules.


HYDROGEN ORBITAL


                     or


          1s                    1s


ANTIBONDING ORBITAL




                                                             ENERGY
                                                                            1sA - 1sB


     1sA - 1sB                       1sA - 1sB
                                                                      1sA                    1sB

BONDING ORBITAL

                                                                            1sA + 1sB

                                                                      HA      H2        HB

       1sA + 1sB                     1sA + 1sB




                                                        10
ORBITALS AND MOLECULAR REPRESENTATION
DIFLUORINE




                                                        2pA - 2pB
                                                              σ*
     ENERGY




                         z         y     x                              x         y           z
                2pA5                                                                              2pB5
                                                               σ
                2sA2                                                                              2sB2
                                                        2pA + 2pB


                1sA2                                                                              1sB2
     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 fluorine 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      C 2H 6


                                                                       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           C 2H 4




                                                       � ����

                                              �    �



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.




                                                       � ����

                                              �    �

 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          C 2H 4




 6

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




                                                               H                  H
                                                                                           C 2H 4
                                                                   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                       H
                                                                    C        C
                                                               H                       H




 8

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

ETHYNE          C 2H 2




                                              � ����

                                     �    �


 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 first π bond and to the σ
bond, must be imagined as coming out of the paper.


                                                         15
ORBITALS AND MOLECULAR REPRESENTATION
CARBON ORBITALS

ETHYNE          C 2H 2




 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         C 6H 6




                                                                                       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         C 6H 6




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                                                               filling     stick
ETHANE           C 2H 6
                                                                109 nm         154 nm
                                                           H                     H
                                                       H         C             C       H

                                                            H           111º           H
       All orbitals         Textbook orbitals                    Structural                           Space        Ball and
                                                                                                      filling      stick
ETHENE           C 2H 4




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


                                                           H            120°       H
                                                                                                      Space        Ball and
                                                                        Structural                    filling      stick


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

ETHYNE            C 2H 2




                               Textbook orbitals
          All orbitals                                                                     Space                Ball and
                                          106 nm                         120 nm            filling              stick

                                                   H   C             C         H
                                                       Structural

                                                           19
ORBITALS AND MOLECULAR REPRESENTATION
SEVERAL REPRESENTATIONS OF BENZENE
BENZENE        C 6H 6




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




                                 Benzene space filling   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.
called a σ (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

DINITROGEN          N2
                                                              110 nm

                                                  N     N
                         Textbook orbitals       Structural
                                                                                                Ball and stick
                                                                          Space filling
All bonding orbitals



DIOXYGEN           O2
                                            π bond




                                                                                                         Space filling
                                                                                              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 difficult to draw by hand. But a
simplified 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
                                                                   H 2O

                                                                   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

				
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