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)
2x1
(2s, 2p)
8x1
(3s, 3p)
8 x .85
(3d)
(4s, 4p)
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
4s2
4.15
3.95
Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
For V: 3d
(1s)
2x1
(2s, 2p)
(3s, 3p)
(3d)
(4s, 4p)
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
4s2
4.15
3.95
Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
For V+ (4s23d2): 3d
(1s)
(2s, 2p)
2
8x1
(3s, 3p)
(3d)
8x1
.35
(4s, 4p)
0
18.35
V+
V
V+
Config Z*
Config Z*
Config Z*
3d3
4.3
4s0
3d2
4.65
4s2
3.3
3d4
4s2
4.15
3.95
Vanadium, Z = 23
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
For V+: 3d
(1s)
(2s, 2p)
2
8x1
(3s, 3p)
8x1
(3d)
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
4s2
4.15
3.95
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 4s
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.


E  IE1
A( g )  A ( g )  e

2
A (g)  A (g)  e

E  IE 2
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
Special “dips”
O: ([He]2s22p4  [He]2s22p3)
lower IE than
N: ([He]2s22p3  [He]2s22p2)
Due to instability of the 4th 2p
electron in O
B ([He]2s22p1  [He]2s2)
lower IE than
Be ([He]2s2  [He]2s1)
Due to 2p being further away
from nucleus.
Ga: ([Ar]4s2 3d104p1  ([Ar]4s2 3d10 )
lower IE than
Zn: ([Ar]4s2 3d10  ([Ar]4s2 3d9 )
Due to relative instability of the 4p
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
vacates outermost orbital
and decreases e-e repulsions
(usually decreased
shielding)
SIZE DECREASES
Ionic radii
Anion formation
increases e-e repulsions
(usually increased
shielding)
so they spread out more
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 .
.Be .
Li .
[He]2s1 [He]2s2 [He]2s22p1
.
.
.
..
..
..O ..
..F ..
..Ne ..
.C .
.N ..
.
.
.
.
..
[He]2s22p2 [He]2s22p3 [He]2s22p4 [He]2s22p5 [He]2s22p6
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)
:O
H
H
:
:
:O
C
:
Molecules share pairs of electrons in bonds
and may also have lone pairs
O:
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
electron
C: 4 more
H+ 2 more
H- 0 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
C2+ 6 more C- 3 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
charge
C
1
N
N
C
0
O
O
C
-1
N
N
C
O
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
H
C
H
H
9 – 8 = 1 bond left
How many bonds left to draw?
Put remaining bond(s) in any place where the octet rule is not violated.
H
H
C
C
H
H
C
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
O
N
N
N
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
P
Cl
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 electrons) - (2 non bonding + 3 bonding) = -1
N: (5 valence electrons) - (2 non bonding + 3 bonding) = 0
S
C
-1 -
-1
N
S
C
N
+1
S
-2 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
Cl
B
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 needed 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
H2O
How about:
C3
NH3
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
H2O
How about:
C3, 120º
NH3
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
C
m
n
Rotation 2m/n
C E
n
n
C2
C
C2
n 1
n
 Cn
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
B
If the plane contains
the principal axis it is called sv
F
F
If the plane is perpendicular
to the principal axis
it is called sh
sn = E (n = even)
sn = s (n = odd)
F
B
F
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