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									        Atomic and Molecular Orbitals
Recall the following principles from General Chemistry
     The horizontal rows of the periodic table are called
      Periods.
     Each period represents a different quantum energy
      level.
     All of the atoms in a given row have a set of electrons
      at various energy levels (i.e. the principle quantum
      level; 1, 2, 3 etc.)
     The highest energy level is called the valence shell.
     Within each period there may be 1, 2, 3 or 4 sublevels,
      designated as s, p, d, and f. These are atomic orbitals.
5. Atomic and Molecular Orbitals

   One way to show the relative energies of the
   quantum levels and the atomic orbitals is the
   diagram below:

Quantum energy
level 3                                          3d
                  3s
                               3p
Quantum energy
level 2

Quantum energy    2s
                               2p
level 1
                  1s
  We are most interested in level 2, where carbon is. Note that
  when atomic orbitals are of the same energy, they are called
  degenerate. For simplicity, we refer to atomic orbitals and
  their quantum levels as 1s, 2s, 2p, 3s etc.
5. Atomic and Molecular Orbitals
   The three dimensional picture of an atomic orbital is
   actually a combination of all the individual equations
   which describe, in terms of energy, repulsive forces,
   etc., just where an electron is most likely to be
   found in relation to the nucleus at any given point in
   time. The calculations provide what is known as a
   probability distribution. This model is used for
   isolated atoms. So, pictures that you see that
   describe the “shape” of an orbital, are really
   probability distributions. For example, when we say
   that an s orbital is spherical, what we are really
   mean is that there is a 90% probability that you can
   find an electron in that spherical space at any given
   time.
5. Atomic and Molecular Orbitals

1. The location of an electron can be considered as a wave
   property. Different amplitudes are shown as different colors
   or by using + (positive) and - (negative) signs. Note that these
   do not signify charge. Nodes are areas where the probability
   of finding an electron is zero.
2. An atomic orbital is an area of high probable electron density.
                                               postive
positive amplitude                            amplitude

                        node       node
                  or                                                    2-D
 node    node
                                                            negative
                       negative amplitude                   amplitude
                                                             nucleus
                                                                 2 = 3-D
                                          "up wave"       "down wave"
    "up wave" "down wave"                   p orbitals; there are 3 of these
5. Atomic and Molecular Orbitals


When two atomic orbitals
overlap, and one electron from
each is shared between the
two nuclei, the new probability
distribution is called a
molecular orbital (MO).
When two atomic orbitals
overlap, we get two
molecular orbitals,
not one. This is called the
linear combination of
atomic orbitals (LCAO).
5. Atomic and Molecular Orbitals

The p MO‟s that we will
consider result from
side by side overlap of
two p AO‟s. Lobes of the
same wave amplitude can
line up (constructive
overlap), which give bonding
MO‟s. The lining up of lobes
with opposite amplitudes
(destructive overlap)
gives anti-bonding MO‟s.
The bond formed by the
constructive parallel
overlap of two p AO‟s is
a  bond.
5. Atomic and Molecular Orbitals



Using the AO and MO theory
that we have just reviewed, we
can draw an MO diagram for a         2s            2p
typical C-H bond. To do so, we
must consider the electronic
configuration of carbon. Since       1s
we are interested in the valence     Electron configuration for C
electrons, we look at quantum
number 2 electrons only, the 2s22p2. Based upon this, we
would expect C to form only two bonds, since only two
electrons, those in the p AO, are unpaired.
5. Atomic and Molecular Orbitals

                                         antibonding MO
The MO diagram for one C-H bond
using the classic AO model would
look something like the diagram to
the right. One of the p electrons from
C is bonding to the s electron from
H to form a C-H bond.                                     2p

This looks good on paper,
but we know from experimental 1s
evidence that C doesn‟t just form
two bonds, it forms four bonds!
Thus, our model needs to be
                                         bonding MO
changed. Experimental evidence
indicates that C forms 4
identical bonds to H.          Possible MO diagram for a C-H bond
5. Atomic and Molecular Orbitals



   We know that:
   1. Carbon always forms 4 bonds.
   2. But carbon can be bonded to 2,3 or 4 „things‟.
   3. If all the „things‟ are the same, like 4 H‟s, all the
      bonds are identical in length and strength.
   4. When bonded to three „things‟, one bond is
      shorter and stronger than the other two
      degenerate bonds.
   5. When bonded to two „things‟, one bond is
     even shorter and stronger.
5. Atomic and Molecular Orbitals

 To accommodate the experimental observations we need:
 Four degenerate AO‟s which will „mix‟ or combine to form
 four degenerate MO‟s. This mixing is also known as
 “hybridizing”. For carbon, we have an s and three p orbitals
 in the second energy level. This means that we have a
 total of four orbitals; one of them is s, and the other three
 are p‟s. When these four orbitals mix or hybridize, we get
 four degenerate sp3 orbitals.

                               hybridizes to


                 p
  s                                                       sp3
               Hybridization produces 4 AO, energy between s and p
5. Atomic and Molecular Orbitals

  When C has only three „things‟ bonded to it, we need three
  AO‟s to form those three bonds. This means that we have
  to combine one s and two p atomic orbitals, to give a total
  of three degenerate sp2 orbitals. Remember that there is a
  p AO that has not been pulled into this overlap. This
  unhybridized p AO has an unshared electron and it forms a
  bond, a second bond, to „something else‟. The situation when
  C is only bonded to two things is analogous.


                               hybridizes to
                                                                       p
             p          p
   s                                                     sp2
Hybridization gives 4 AO, 3 with energy between s and p and one unhybridized p
5. Atomic and Molecular Orbitals

    Sp3 Hybridized Orbitals: Tetrahedral Geometry
5. Atomic and Molecular Orbitals

   Sp2 Hybridized Orbitals: Trigonal Planar Geometry
5. Atomic and Molecular Orbitals

       Sp Hybridized Orbitals: Linear Geometry
5. Atomic and Molecular Orbitals

                      Single Bond:  bond
5. Atomic and Molecular Orbitals

                   Double Bond: 1  and 1 
5. Atomic and Molecular Orbitals

         Triple Bond: 1  bond and 2  bonds
5. Atomic and Molecular Orbitals

                                                         H
Tetrahedral geometry: bond angle = 109.5 0

Trigonal planar geometry: bond angle = 120 0             C           H
                                                   H
Linear geometry: bond angle = 180 0                             0H
                                                       109.5.

                                       O
                180 0
                                           120 0         C           H
                                       C           H
     H      C       C     H        H       H                    0H
                                                       107.3
                   Isomers
Isomers are different compounds with the same
molecular formula. For example, if you are given
the molecular formula C3H8, there are two possible
structures that you could draw:
        CH3     CH2      CH2     CH3     n-butane

                   and

                    CH3

             CH3    CH     CH3       isobutane
Isomers
  Also, whereas you can have rotation about single bonds,
  you cannot have rotation about double bonds. In other
  words, double bonds are rigid. One of the consequences
  of this is that there may be more than one way to draw a
  formula that contains double bonds. For example, there
  are two ways to draw the molecule CH3-CH=CH=CH3:
           H3C           CH3   H3C           H

                 C   C               C   C

             H           H      H            CH3

              cis-2-butene       trans-2-butene
   These two structures actually represent two completely
   different molecules. When the two identical groups are on
   the same side, it is called cis. When they are on opposite
   sides, it is called trans.
Isomers


   Cis and Trans isomers are called Stereoisomers.
   Stereoisomers are isomers that differ from one another
   only in terms of the spatial orientation of the atoms, not
   in the bonding order of the atoms. Cis and trans isomers
   are also known as geometric isomers.

   n-Butane and isobutane are constitutional isomers.
   Constitutional (structural) isomers differ in their bonding
   sequence. In other words, their atoms are connected
   differently.
          Molecular Dipole Moments
The polarity of an individual bond is measured as its dipole
moment. The symbol for dipole moment is , and it is
measured in units of debye (D). You already know how to
identify a polar bond, and how to determine the direction
of the bond polarity. But it is possible to consider the
dipole moment of the molecule as a whole. The molecular
dipole moment is the vector sum of all the individual bond
dipole moments. This vector sum reflects both the
magnitude and direction of         H
each individual bond dipole
                                            O      O      C   O
moment. Example: both
formaldehyde and CO2 have          H
the have polar C=O bonds,
but only formaldehyde has a
molecular dipole moment.         formaldehyde      carbon dioxide
                                     = 2.3 D            =0
         Dipole-Dipole Forces
Dipole-dipole forces are attractive intermolecular
forces resulting from the attraction of the positive
and negative ends of the molecular dipole
moments in polar molecules. Two types of
dipole-dipole forces are London Dispersion
Forces and Hydrogen Bonding.
             Hydrogen Bonding
Hydrogen bonding refers to a particularly strong inter-
molecular attraction between a nonbonding pair of
electrons and an electrophilic O-H or N-H hydrogen.
Note, however, that it is much weaker than a single bond.
To see examples of hydrogen bonding, refer to page
65 in your text book. Molecules capable of hydrogen
bonding have higher boiling points than molecules of
comparable size and molecular weights.

CH3   CH2     OH                CH3    O      CH3

ethanol, bp 78 0         dimethyl ether, bp - 25 0
               London Dispersion Forces
       London dispersion forces are intermolecular forces
       resulting from the attraction of coordinated temporary
       dipole moments induced adjacent molecules. It is the
       principle attractive force in nonpolar molecules. See page
       64 of your text book for examples of this phenomenon.
       The effects of London forces can be observed when
       examining the boiling points of simple hydrocarbons. The
       more highly branched isomeric alkanes are, the lower the
       boiling point because of decreased surface area.
                                     CH3                        CH3


CH3    CH2   CH2   CH2   CH3   CH3   CH    CH2   CH3      CH3   C     CH3


                                                                CH3

      n-pentane, bp 36 0C      isopentane, bp 28 0C    isopentane, bp 10 0C

								
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