Shielding and effective nuclear charge Z*

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Lecture 2
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Shielding and effective nuclear charge Z In
polyelectronic atoms, each electron feels the
attraction of the nucleus and the repulsion of
the other electrons (both n and l must be taken
into account) Each electron 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 Z Z S (Z is the nuclear
charge and S is the shielding constant)

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Shielding and effective nuclear charge Z Z
Z S (a measure of the nuclear attraction for an
electron)

• To determine S (Slaters rules)
• Write electronic structure in groups as follows
• (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f)
  (5s, 5p) etc.
• Electrons in higher groups (to the right) do not
  shield those in lower groups
• For ns or np valence electrons
• other electrons in the same n group 0.35
  except for 1s where 0.30
• is used.
• electrons in the n-1 group 0.85
• electrons in the n-2, n-3, groups 1.00
• For nd and nf valence electrons
• other electrons in the same nd or nf group
  0.35
• electrons in groups to the left 1.00
• S is the sum of all contributions

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Shielding and effective nuclear charge Z
There is a particular stability associated with
filled and half-filled shells
4s electrons are the first ones removed when a
1st row transition metal forms a cation
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Holds maximum of 5
4s electrons are the first ones removed when a
1st row transition metal forms a cation
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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
8 x 1 8 x 1 .35
0 18.7
For V 3d (1s) (2s, 2p) (3s, 3p)
(3d) (4s, 4p) 2 8 x 1
8 x 1 2 x .35 0
18.7
For V 4s (1s) (2s, 2p) (3s, 3p)
(3d) (4s, 4p) 2 8 x 1
8 x .85 3 x .85 .35
18.7
For V 3d (1s) (2s, 2p) (3s, 3p)
(3d) 2 8 x 1 8 x
1 3 x .35
18.7
For V (4s23d2) 4s (1s) (2s, 2p)
(3s, 3p) (3d) (4s, 4p) 2
8 x 1 8 x .85 2 x .85
.35 18.7
V V V V
Config Z Config Z
3d3 4.3 4s0 3d2 4.65
4s2 3.3 3d4 3.95 4s2 4.15
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Periodic trends
Generally, atoms with the same outer orbital
structure appear in the same column
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Ionization Energy (IE) Energy required to remove
an electron from a gaseous atom or
ion. 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 B (He2s22p1 ? He2s2) lower IE than Be
(He2s2 ? He2s1), O (He2s22p4 ?
He2s22p3) lower IE than N (He2s22p3 ?
He2s22p2) Similar for Al, S
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Maximum for noble gases Minimum for H and alkali
metals
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Special dips

B (He2s22p1 ? He2s2) lower IE than Be
(He2s2 ? He2s1), O (He2s22p4 ?
He2s22p3) lower IE than N (He2s22p3 ?
He2s22p2)
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    Electron affinity (EA) energy required to
remove an electron from a gaseous negatively
charged ion (ionization energy of the anion) to
yield neutral atom.

• Maximum for halogens
• Minimum for noble gases
• Much smaller than corresponding IE

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The size of atoms
Atoms are not spheres with defined limits !! How
can we measure them? How much can we squeeze
them?
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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
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The size of orbitals tends to grow with
increasing n. As Z increases, orbitals tend to
contract, but with increasing number of electrons
mutual repulsions keep outer orbitals larger
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Anion formation increases e-e repulsions so they
spread out more SIZE INCREASES
Cation formation vacates outermost orbital and
decreases e-e repulsions SIZE DECREASES
Ionic radii

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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 elements symbol plus
one dot per valence electron
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He
Li
Be
B
C
N
O
F
Ne
Generally, atoms with the same outer orbital
structure appear in the same column
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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
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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.

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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.

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Number of Bonds
Additional stabilization that can be provided by
some atoms
H 1 more electron H 2 more H- 0 more
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
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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)
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Bonding Patterns
Formal charge C N O
1
0
-1
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Lewis Diagrams
(3 4 6 1) / 2 9 bonds
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.
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Resonance forms
When several possible Lewis structures with
multiple bonds exist, all of them should be drawn
(the actual structure is an average)
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Expanded shells
When it is impossible to write a structure
consistent with the octet rule increase the
number of electrons around the central atom
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.
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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
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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

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Problem cases- expanded shells- generating
charge to satisfy octets
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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.
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Charges may generated so as to satisfy the octet.
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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

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ABn
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Removing atoms from one basic geometry generates
other shapes
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Similar for higher steric numbers
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Lone pairs are larger than bonding pairs
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Effect of lone pairs on molecular geometry
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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.
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Boiling Points and Hydrogen bonding
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Hydrogen bonding in ice
The density of water decreases when it
freezes and that determines the geology and
biology of earth
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Hydrogen bonding is crucial in biological systems
DNA replication
Secondary structure of proteins
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Symmetry and group theory
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Natural symmetry in plants
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Symmetry in animals
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Symmetry in the human body
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The platonic solids
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Symmetry in modern art M. C. Escher
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Symmetry in arab architecture La Alhambra,
Granada (Spain)
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Symmetry in baroque art Gianlorenzo Bernini Saint
Peters Church Rome
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Symmetry in Native American crafts
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7th grade art project Silver Star School Vernon,
Canada
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Re2(CO)10
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C60
C2F4
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Symmetry in chemistry

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

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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
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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
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5 types of symmetry operations/elements
Identity this operation does nothing, symbol
E Element is entire object
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Proper Rotation Rotation about an axis by an
angle of 2?/n
NH3
H2O
How about
NFO2?
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The Operation Proper rotation Cn is the movement
(2p/n) The Element Proper rotation axis Cn is
the line
180 (2p/2)
Applying C2 twice Returns molecule to original
oreintation C22 E
C2
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Proper rotation axes
NH3
H2O
How about
NFO2?
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Rotation angle Symmetry operation
60º C6
120º C3 ( C62)
180º C2 ( C63)
240º C32( C64)
300º C65
360º E ( C66)
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Proper Rotation Rotation about an axis by an
angle of 2?/n
PtCl4
Rotation 2?m/n
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2p/2 C2 2p/4 C4 Cnn E
The highest order rotation axis is the principal
axis and it is chosen as the z axis
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Reflection and reflection planes (mirrors)
s
s
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? (reflection through a mirror plane)
s
NH3
Only one s?
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H2O
s
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H2O
s
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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)
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Inversion not the same as C2 rotation !!
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Figures with center of inversion
Figures without center of inversion
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Improper rotation (and improper rotation axis)
Sn rotation about an axis by an angle
2?/n followed by reflexion through perpendicular
plane
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S42 C2
Also, S44 E S2 i S1 s
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Symmetry operations and elements
Operation Element
proper rotation axis (Cn)
improper rotation axis (Sn)
reflexion plane (s)
inversion center (i)
Identity Molecule (E)
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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
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To determine the point group of a molecule
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Groups of low symmetry
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