Lecture 02 - PowerPoint by 51IOf8

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									Lecture 2
Placing electrons in orbitals
    Approximate order
    of filling orbitals
    with electrons

E   5p
    4d
    5s
    4p
    3d
    4s
    3p
    3s
    2p
    2s
    1s
E   5p
    4d
    5s
    4p
    3d
    4s
    3p
    3s
    2p
    2s
    1s
                  Shielding and effective nuclear charge Z*

          In polyelectronic atoms, each electron is attracted to the nucleus
     and repelled by the other electrons (both n and l must be taken into account)

                                Electrons acts as a shield
for electrons electrons farther away from the nucleus, reducing the attraction between
                          the nucleus and the distant electrons

                     Effective nuclear charge: Zeff = Z* = Z – s

               (Z is the nuclear charge and s is the shielding constant)


      **
                    Shielding and effective nuclear charge Z*:

                                    Z* = Z – s
                (a measure of the nuclear attraction for an electron)
To determine s (Slater’s rules):
1. Write electronic structure in groups as follows:
            (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
Note the order does not correspond to filling order. The shielding constant
      for each group is formed as the sum of the following contributions:
2. Electrons in higher groups (to the right) do not shield those in lower
      groups
3. An amount of 0.35 from each other electron within the same group except
      for the [1s] group where the other electron contributes only 0.30.
4. If the group is of the [s p] type, an amount of 0.85 from each electron with
      principal quantum number one less and an amount of 1.00 for each
      electron with an even smaller principal quantum number
5. If the group is of the [d] or [f], type, an amount of 1.00 for each electron
      in a lower group (to the left).

Note that (1) as Z increases so does Z* leading to smaller orbitals as we move to
    right in a period

s is the sum of all contributions
                  Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.


  For V: 4s
  (1s)     (2s, 2p)     (3s, 3p)     (3d)      (4s, 4p)
   2x1      8x1          8 x .85     3 x .85       .35             s = 19.7
  Z* = 23 -19.7 = 3.3


              V                      V+                            V+
    Config Z*               Config Z*                    Config Z*
    3d3         4.3         4s0                          3d2        4.65
    4s2         3.3         3d4         3.95             4s2        4.15
                    Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.

  For V: 3d
  (1s)     (2s, 2p)      (3s, 3p)    (3d)     (4s, 4p)
   2x1        8x1          8x1      2 x .35      0        s = 18.7
  Z* = 23 – 18.7 = 4.3



              V                      V+                        V+
    Config Z*                Config Z*               Config Z*
    3d3         4.3          4s0                     3d2        4.65
    4s2         3.3          3d4        3.95         4s2        4.15
                   Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.

For V+ (4s23d2): 3d
(1s)    (2s, 2p)       (3s, 3p)     (3d)     (4s, 4p)
 2         8x1           8x1         .35      0           18.35




              V                       V+                       V+
     Config Z*                Config Z*             Config Z*
     3d3         4.3          4s0                   3d2         4.65
     4s2         3.3          3d4          3.95     4s2         4.15
                       Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.

 For V+: 3d
 (1s)       (2s, 2p)     (3s, 3p)     (3d)
  2          8x1           8x1       3 x .35                  s = 19.05
 Z* = 23 – 19.05 = 3.95


                V                      V+                      V+
      Config Z*                Config Z*                Config Z*
      3d3          4.3         4s0                      3d2      4.65
      4s2          3.3         3d4           3.95       4s2      4.15
                    Shielding and effective nuclear charge Z*:



                        There is a particular stability
                  associated with filled and half-filled shells


                           Cr : [ Ar]3d 5 4 s
                           Cu : [ Ar]3d 10 4 s
                            Mo : [ Kr ]4d 5 5s
                            Ag : [ Kr ]4d 10 5s
                            Au : [ Xe]4 f 14 5d 10 6 s

4s electrons are the first ones removed when a 1st row transition metal forms a cation
                            Spin Multiplicity


Frequently there are several ways of putting electrons into a partially filled
subshell. For example, a p2 configuration.




or
                                   Both electrons in same orbital. Larger
                                   electron-electron repulsion. Pc, higher energy
                                   a positive quantity.
or
                                   Two electrons of same spin. Energy
                                   reduced by exchange energy, Pe, a
                                   negative quantity.
     Further Example, p4.




           Pc + 3Pe (1-3, 1-4, 3-4)

or

         Pc + 2Pe

or


           2 Pc + 2Pe
                                                                     Holds maximum of 5




4s electrons are the first ones removed when a 1st row transition metal forms a cation
            Periodic trends




Generally, atoms with the same outer orbital structure
              appear in the same column
Ionization Energy (IE):
Energy required to remove an electron from a gaseous atom or
ion.                    
            A( g )  A ( g )  e 
                                                       E  IE1
               
            A (g)  A (g)  e    2              
                                                       E  IE2
Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is
constant).

Tendency 2: IE1 increases along a period (Zeff increases, r decreases)

Exception: Half-filled or filled shell are particularly stable
Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is constant).


       Tendency 2: IE1 increases along a period (Zeff increases, r decreases)


                                                Maximum for noble gases
                                                Minimum for H and alkali metals
                                               B ([He]2s22p1  [He]2s2)
                                               lower IE than
                                               Be ([He]2s2  [He]2s1)
                              Special “dips”   Due to 2p being further away
                                               from nucleus.




O: ([He]2s22p4  [He]2s22p3)         Ga: ([Ar]4s2 3d104p1  ([Ar]4s2 3d10 )
lower IE than                        lower IE than
N: ([He]2s22p3  [He]2s22p2)         Zn: ([Ar]4s2 3d10  ([Ar]4s2 3d9 )
Due to instability of the 4th 2p     Due to relative instability of the 4p
electron in O                        electron in Ga
  Electron affinity (EA) = energy required to remove an electron
from a gaseous negatively charged ion (ionization energy of the
                   anion) to yield neutral atom.


                                     
    A (g)  A (g)  e                       E  EA

•Maximum for halogens (have maximum of Z*)
•Minimum for noble gases (minimum for Z* for elec in next
shell)
•Much smaller than corresponding IE (working against
smaller Z*)
Effective atomic radius (covalent radius)
                            covalent radius
                          =1/2(dAA in the A2 molecule)

                          Example:

                          H2: d = 0.74 Å ; so rH = 0.37 Å


 To estimate covalent bond distances e.g.:

 R----C-H:    d C-H = rC + rH = 0.77 + 0.37 =1.14 Å
 The size of corresponding orbitals tends to grow with increasing n.
As Z increases, orbitals tend to contract, but with increasing number of
             electrons shielding keep outer orbitals larger

        Tendency 1. Atomic radii increase on going down a group
        (Zeff ~ constant as n increases because of shielding).

         Tendency 2: Atomic radii decrease along a period
         (Zeff increases .)
Pictorially, here are the trends in radii…..
      Cation formation                           Anion formation
 vacates outermost orbital     Ionic radii   increases e-e repulsions
and decreases e-e repulsions                    (usually increased
     (usually decreased                             shielding)
         shielding)                          so they spread out more
   SIZE DECREASES                              SIZE INCREASES
             Simple Bonding Theories

Lewis electron-dot diagrams are very simplified but
very useful models for analyzing bonding in molecules

Valence electrons are those in the outer shell of an atom
    and they are the electrons involved in bonding

       The Lewis symbol is the element’s symbol
       plus one dot per valence electron
                             .. .
                            ...
                             S
                       [Ne]3s23p4
                         .           .           ..           .
                        .B .        .C .        .N .        ..O ..      .
                                                                       .F..
                                                                       ...
                                                                                     ..
                                                                                   .Ne .
                                                                                   . .. .
 Li .      .Be .
                                     .           .            .
[He]2s1 [He]2s2 [He]2s22p1      [He]2s 22p2 [He]2s 22p3 [He]2s22p4 [He]2s 22p5 [He]2s 22p6




                                                                         He
        Li Be                                         B C N O F Ne




                   Generally, atoms with the same outer orbital structure
                                appear in the same column
                The octet rule

     Atoms tend to gain, lose or share electrons
until they are surrounded by eight valence electrons
        (i.e., until they resemble a noble gas)

    Molecules share pairs of electrons in bonds
          and may also have lone pairs


        :O                      :O
         :




                                              :
                                        C     O:
                              :
    H          H
  Octet Rule, Lewis Structures
Electrons can be stabilized by bond
  formation.
H atom can stabilize two electrons in the
  valence shell.
CF can stabilize 8 electrons in the valence
  shell.
Two electrons around H; Eight electrons
  complete the octet of CF.
       Completing the Octet
Ionic Bonding: Electrons can be transferred
  to an atom to produce an anion and
  complete the octet.
Covalent Bonding: Electrons can be shared
  between atoms providing additional
  stabilization.
                Number of Bonds
   Additional stabilization that can be provided by some atoms:


         H: 1 more          H+ 2 more         H- 0 more
         electron
         C: 4 more          C2+ 6 more C- 3 more

         N: 3 more          N+ 4 more         N- 2 more

         O: 2 more          O+ 3 more         O- 1 more

         F: 1 more          F+ 2 more         F- 0 more

Bonds make use of the additional stabilizing capability of the atoms.
# Bonds = (Sum of unused stabilizing capability)/2
                 Formal Charge
 Formal charge may begiven to each atom
  after all valence shell electrons have been
  assigned to an atom.
     – Non-bonding electrons are assigned to the
       atom on which they reside.
     – Bonding electrons are divided equally
       between the atoms of the bond.
Formal charge = (# valence shell electrons in neutral atom)
                           - (# nonbonding electrons)
                    - ½ (# bonded electrons)
         Bonding Patterns
Formal     C       N        O
charge

  1                N

           C                O



  0            C   N        O




 -1                N
               C                O
                           Lewis Diagrams
Typical Problem: Given a compound of molecular formula CH3CHCH2 draw a Lewis bonding
structure.

How many bonds in the molucule?             (3 * 4 + 6 * 1) / 2 = 9 bonds

Draw a bonding structure making use of single bonds to hold the molecule together.

                                            H

                                   H
                                            C
                                                                H
                                       C            C

                                   H       H
                                                        H



How many bonds left to draw?                                            9 – 8 = 1 bond left


  Put remaining bond(s) in any place where the octet rule is not violated.
                                                            H

                                           H
                                                            C
                                                                            H
                                                C                   C

                                           H            H
                                                                        H
                      Resonance forms

When several possible Lewis structures with multiple bonds exist,
 all of them should be drawn (the actual structure is an average)




         O                    O                   O

         N                    N                   N

     O       O            O       O           O       O
                             Expanded shells

   When it is impossible to write a structure consistent with the octet rule
        increase the number of electrons around the central atom



                           Cl

                                 Cl
                     Cl    P                          10e around P
                                Cl
                           Cl



Only for elements from 3rd row and heavier, which can make use of empty d orbitals



                                      See also: L. Suidan et al. J. Chem. Ed. 1995, 72, 583.
                                Formal charge

 Apparent electronic charge of each atom in a Lewis structure


Formal charge = (# valence e- in free atom)
                       - (# unshared e- on atom) -1/2 (# bonding electrons to atom)

Total charge on molecule or ion = sum of all formal charges



         Favored structures
             •provide minimum formal charges
             •place negative formal charges on more electronegative atoms
             •imply smaller separation of charges


  Formal charges are helpful in assessing resonance structures and assigning bonding
                     To calculate formal charges

Assign
     •All non-bonding electrons to the atom on which they are found
     •Half of the bonding electrons to each atom in the charge

                                               -
                                   C       N


           C: (4 valence elec trons) - (2 non bonding + 3 bonding) = -1
           N: (5 valence elec trons) - (2 non bonding + 3 bonding) = 0


                -1 -          -1                   -       +1         -2 -
 S       C      N              S       C       N           S     C    N



               Favored structure
                   •provides minimum formal charges
                   •places negative formal charges on more electronegative atoms
                   •implies smaller separation of charges
Problem cases
- expanded shells
- generating charge to satisfy
octets
                             Formal charges and expanded shells
Some molecules have satisfactory Lewis structures with octets but better ones with expanded shells.
Expansion allows a atom having a negative charge to donate into a positive atom, reducing the charges.
     Charges may generated so as to
            satisfy the octet.


     Cl
                    Cl


     B
                    B
Cl        Cl
               Cl        Cl




                              +    2-   +

                              Cl   Be   Cl
          Valence shell electron pair repulsion (VSEPR) theory
     (a very approximate but very useful way of predicting molecular shapes)


•Electrons in molecules appear in bonding pairs or lone pairs

•Each pair of electrons repels all other pairs

•Molecules adopt geometries with electron pairs as far from each other as possible



 Electron pairs define regions of space where they are likely to be:
     •Between nuclei for bonding pairs
     •Close to one nucleus for lone pairs

                        those regions are called electron domains
                    the steric number is the sum of electron domains
Basic molecular shapes
Basic molecular shapes


              ABn
Removing atoms from one basic geometry generates other shapes
The geometries
of electron domains
Molecular
geometries
Molecular
geometries




                Note that lone pairs
             adopt equatorial positions
Molecular
geometries
Similar for higher steric numbers
Lone pairs are larger
than bonding pairs
Effect of lone pairs on molecular geometry
       Electronegativity Scales
• The ability to attract electrons within a
  chemical, covalent bond

  Pauling: polar bonds have higher bond strengths.
  Electronegativity assigned to each element such that the
  difference of electronegativities of the atoms in a bond can
  predict the bond strength.
Boiling Points and Hydrogen bonding
Hydrogen bonding in ice

                The density of water decreases when it freezes
             and that determines the geology and biology of earth
           Hydrogen bonding is crucial in biological systems




Secondary structure of proteins             DNA replication
Symmetry and group theory
Natural symmetry in plants
Symmetry
in animals
Symmetry in the human body
Symmetry in modern art
M. C. Escher
Symmetry in arab architecture
La Alhambra, Granada (Spain)
Symmetry in baroque art
Gianlorenzo Bernini
Saint Peter’s Church
Rome
     Symmetry in
Native American crafts

                                QuickTime™ and a
                            TIFF (LZW) decompressor
                         are neede d to see this picture.
7th grade art project
Silver Star School
Vernon, Canada
Re2(CO)10
C2F4   C60
        Symmetry in chemistry


•Molecular structures
•Wave functions
•Description of orbitals and bonds
•Reaction pathways
•Optical activity
•Spectral interpretation (electronic, IR, NMR)
...
                           Molecular structures

A molecule is said to have symmetry if some parts of it may be interchanged
   by others without altering the identity or the orientation of the molecule
                     Symmetry Operation:

 Movement of an object into an equivalent or indistinguishable
                         orientation




Symmetry Elements:

A point, line or plane about which a symmetry operation is
carried out
         5 types of symmetry operations/elements


Identity: this operation does nothing, symbol: E

Element is entire object
                  Proper Rotation:
      Rotation about an axis by an angle of 2/n

      C2                                 C3




                                              NH3
H2O


How about:                              NFO2?
The Operation: Proper rotation Cn is the movement (2/n)

The Element: Proper rotation axis Cn is the line


             180° (2/2)



                                      Applying C2 twice
                             Returns molecule to original oreintation
                                           C 22 = E




        C2
             Proper rotation axes

C2 180º                       C3, 120º




                                         NH3
H2O


How about:                          NFO2?
Rotation angle Symmetry
               operation
     60º                C6
    120º            C3 (= C62)
    180º            C2 (= C63)
    240º            C32(= C64)
    300º               C65
    360º            E (= C66)
                 Proper Rotation:
     Rotation about an axis by an angle of 2/n

             PtCl4
                   C2, C4

                                                  m
                                            C     n
                                           Rotation 2m/n


C2
                                            C E  n
                                                  n
                                                  n 1
                                            C     n       Cn
                            C2
            2/2 = C2
            2/4 = C4

             Cnn = E




The highest order rotation axis
     is the principal axis
 and it is chosen as the z axis
Reflection and reflection planes
            (mirrors)


               s



                                   s
s (reflection through a mirror plane)


                s



                                        NH3


                                        Only one
                                          s?
H2O


      s
H2O

      s’
     F              F
                             If the plane contains
           B            the principal axis it is called sv

           F


                                        F             F
If the plane is perpendicular
                                               B
     to the principal axis
         it is called sh
                                               F

sn = E (n = even)
sn = s (n = odd)
           Inversion: i

Center of inversion or center of symmetry
            (x,y,z)  (-x,-y,-z)


       in = E (n is even)
        in = i (n is odd)
Inversion not the same as C2 rotation !!
  Figures with center of inversion




Figures without center of inversion
Improper rotation (and improper rotation axis): Sn

      rotation about an axis by an angle 2/n
followed by reflexion through perpendicular plane
        S42 = C2




Also, S44 = E; S2 = i; S1 = s
     Symmetry operations and elements



   Operation                 Element
 proper rotation              axis (Cn)
improper rotation             axis (Sn)
    reflexion                plane (s)
    inversion                center (i)
    Identity               Molecule (E)
                    Symmetry point groups


  The set of all possible symmetry operations on a molecule
     is called the point group (there are 28 point groups)




The mathematical treatment of the properties of groups
                  is Group Theory




In chemistry, group theory allows the assignment of structures,
      the definition of orbitals, analysis of vibrations, ...

         See: Chemical applications of group theory by F. A. Cotton
 To determine
the point group
 of a molecule
Groups of low symmetry

								
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