Chemistry 3820 Lecture Notes
2
Dr.R.T.Boeré
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Lewis dot diagrams and VSEPR structures
Review Lewis structures and VSEPR from General Chemistry texts, and consult S-A-L: 3.1-3.3
One of the basic distinctions you must learn to make is between ionic and covalent compounds. You will do much better in
this course, as well as in all other chemistry courses, if you know instinctively whether the material being discussed is one or the
other. So how can you learn this? Short of sheer memory work for millions of compounds, it is very possible to learn this
intuitive knowledge simply by developing the habit of asking yourself:
Is this compound covalent (i.e. a molecule) or ionic (i.e. composed of two or more ions)?
Even if the answer is not obvious, it can usually be deduced from the information given. Often it becomes very obvious if you
stop and think about it.
We start by considering simple binary compounds , for which this distinction is simple. A compound A–B is generally
considered ionic if the difference in electronegativity between A and B is ≥ 2 units. Thus for H-F, ∆χ = (3.9 – 2.2) = 1.7, and HF is
considered to be a (polar) covalent molecule. But Li–F, 6c = (3.9 – 1.0) = 2.9, and thus LiF is ionic. Note however that the ionic
character of LiF is predominantly observed in the bulk solid - gaseous LiF (at very high temperature) will contain some Li-F
molecules.
We now focus on the structure and symmetry of the common covalent molecules, including common covalent or molecular
ions (also known as complex ions), for which there are chemical bonds within the ionic unit. An example of the latter is an ion
such as the sulfate ion, SO42-, which has covalent S-O bonds.
2.1
Valence and Lewis diagrams
In Chem. 1000 you learned how to write Lewis structures. The number of valence You were wondering…
electrons is taken directly off the periodic table, and can be had from the group numbers Why can we ignore previous
directly. (Using the new numbering sequence, for p-block elements, subtract 10.) The shells when counting the
number of valence electrons includes all s electrons since the last noble gas configuration number of valence electrons?
plus the electrons of the block in which the element finds itself. Completely filled orbitals
(except s orbitals) sink to much lower energy, becoming unavailable for bonding to elements
in the subsequent block.
Although Lewis diagrams are not 100% reliable, they have the advantage of organizing
thousands of varied chemical compounds into a fast, easily understood diagrams which give
a lot of useful information about the structure and reactivity of the compound. The essential
postulate of this theory, first postulated in 1916 and still used today, is that bonds between
atoms are due to shared electron pairs. Unshared electrons form lone pairs. Multiple bonds
form between elements short of electrons. Double bonds have four shared electrons, triple bonds six. To write Lewis structures,
follow the step-by-step guidelines given in the text (S-A-L) on p. 51-52.
1. Decide how many electrons are to be included in the diagram by adding together all the valence electrons provided by
the atoms. Adjust for the ionic charge, if any.
2. Write the chemical symbols with the right connectivity (this cannot be deduced from the Lewis theory).
3. Distribute the electrons in pairs so that there is one pair of electrons between each pair of bonded atoms, and then
supply electron pairs (to form multiple bonds or lone pairs) until each atom has an octet.
4. The formal charge gives some indication of the electron distribution in the molecule, where this is not even. For each
atom, count the sum of the number of lone pair electrons and one from each bond-pair. The difference between this
count and the valence of the atom is its formal charge.
5. Resonance is invoked whenever there is more than one way to distribute the electrons according to the above rules.
The true structure is said to be a blend or hybrid of the various resonance isomers.
6. Finally, there are some elements for which exceptions to the octet rule occur. These include Be (4), B and Al (6 in some
cases), as well as the "heavy" elements of period three and beyond, which may have 10 or 12 valence electrons about
them. My rule of thumb in all such cases is to start from the outside and provide octets for the ligands first. If there are
deficient or excess electrons at the central atom, verify that the atom is one of the ones mentioned here, and leave the
diagram as produced..
Let's do some examples: CO2, NO3-, SO32-, NSF3, XeF4, IF5, PF5, SF6.
Chemistry 3820 Lecture Notes
2.2
Dr.R.T.Boeré
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15
VSEPR theory
Just as Lewis structures give us a fast road to mapping the electrons of molecules, the Valence Shell Electron Pair Repulsion
theory gives us a quick approach to determining molecular structure for many common main-group compounds. It is not much
use for transition metal complexes, except those of the metals in their highest possible oxidation states. This concept, which is
especially due to Prof. Ronald Gillespie of McMaster University (along with Prof. Nyholm of the U.K.), considers the electron
pairs in molecules to be bound regions of negative charge, which naturally repel each other. The basic arrangements which
minimize electron pair repulsions are:
# of pairs
basic shape
hybridization of the central atom
2
linear
sp
3
trigonal planar
sp 2
4
tetrahedral
sp 3
5
trigonal bipyramidal
dsp 3
6
octahedral
d 2sp 3
But since the central atom may have lone pairs, which do not contribute to the description of the shape of the molecule, there are
several derivatives of the above. Within the derivatives, the choice of structure is such as to minimize 90° interactions in the
order:
LP/LP repulsions stronger than
LB/BP repulsions, than
BP/BP repulsions.
The logic behind this is that LP are less constrained than BP, therefore are larger. This also accounts for deviations in bond
angle in structures such as water and ammonia.
Hybridization can also be used to re-configure the atomic orbitals of the atoms in the molecule according to the observed
geometry. Note that when angles deviate from the ideal values, the extent of hybridization also changes. thus while CH4 has
four sp3 hybrid orbitals on carbon, the two orbitals bonding to H in OH2 are not exactly sp3. They have marginally more "p"
character, and less "s". The associated lone pair orbitals have correspondingly more "s" character. Quantum chemistry texts
have formulae which express hybridization functions for given values of angles. These ideas on molecular structure are at best
imprecise. A much more exact and extremely powerful approach to describing molecular shape exists, using symmetry and point
group labels. We start by considering symmetry operations and elements. The following table summarizes the VSEPR structure
method, and includes some common examples of the different structures that are encountered. The precise names of the
structures are problematic, and indeed we need a better system. This can be done much more systematically using symmetry
labels, and that will be the next topic we turn to.
# of electron
pairs at
central atom*
2
shape family
linear
hybridization
of the central
atom
sp
# of bond
pairs
# of lone
pairs
2
0
2
3
linear
triangular-planar
sp
sp 2
1
3
1
0
3
triangular-planar
sp 2
2
1
3
4
triangular-planar
tetrahedral
sp 2
sp 3
1
4
2
0
4
tetrahedral
sp 3
3
1
actual molecule shape
linear
linear (e.g. BeH+ )
triangular-planar
angular
linear (e.g. AlCl2+ )
tetrahedral
triangular-pyramidal
Chemistry 3820 Lecture Notes
Dr.R.T.Boeré
Page
4
tetrahedral
sp 3
2
2
4
5
tetrahedral
triangular-bipyramidal
sp 3
dsp 3
1
5
3
0
5
triangular-bipyramidal
dsp 3
4
1
5
triangular-bipyramidal
dsp 3
3
2
5
triangular-bipyramidal
dsp 3
2
3
6
octahedral
d 2sp 3
6
0
6
octahedral
d 2sp 3
5
1
angular
linear (e.g. H–Cl)
triangular-bipyramidal
seesaw
T-shaped
linear
octahedral
square-pyramidal
6
octahedral
2
d sp
3
4
2
square-planar
* using any resonance isomer; double and triple bonds count as a single pair!
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Chemistry 3820 Lecture Notes
Dr.R.T.Boeré
3
Molecular symmetry
3.1
Symmetry operations and elements
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17
Symmetry operation:
The movement of a molecule relative to some symmetry element which generates an orientation of the
molecule indistinguishable from the original.
Symmetry element: A line, point or plane, with respect to which one or more symmetry operations may be performed. We
designate the symmetry elements by their Schönflies symbols. The following symmetry elements are found
in molecules:
a)
Identity
Symbol: E
This means do nothing. It represents the lowest order of symmetry. All molecules posses the identity symmetry element.
The inclusion of this element may seem silly, but it is vital to the correct mathematical description of symmetry by group theory.
Note that the C1 rotation axis, i.e. rotation by 360°, is the same as the identity, so C1 is never used.
b)
Proper rotation axes
Symbol:
Cn (n = 2, 3, 4, 5, 6, 7,…∞)
An axis about which the molecule may be rotated 2π/n radians. A two-fold rotation axis means
rotation by π radians, or 180°. A three-fold axis means rotation by 120°, etc. A molecule may have more
than one order of axis; that axis with the largest value of n (highest order) is called the principal
rotation axis. The graphics show a molecule possessing a C2 axis at right, and a C3 axis below. To
discover if a molecule has a given symmetry element, we perform the corresponding operation. If the
new orientation is indistinguishable from the original, then the molecule is said to posses that symmetry
operation.
c)
σ
σv
σh
σd
d)
Mirror planes
Symbol: σ, σ v , σ h, σ d
A non-specific mirror plane (possible only if this is the only symmetry element the molecule possesses.
Vertical mirror plane is a plane of reflection containing the principle rotation axis.
Horizontal mirror plane is a plane of reflection normal to the principle rotation axis.
Dihedral mirror plane is a plane of reflection containing the principle rotation axis which also bisects two adjacent C2 axes
perpendicular to the principle rotation axis.
Centre of symmetry
Symbol: i
Also called an inversion, it means simply that: invert the position of all the atoms with respect to the centre of symmetry of
the molecule. In coordinate language, this means converting x, y, z to -x, -y, -z.
Chemistry 3820 Lecture Notes
e)
Improper rotation axes
Dr.R.T.Boeré
Page
18
Symbol: S n (n = 3, 4, 5, 6, 7…∞)
Also called rotation-reflection axes, which accurately describes this type of element. One rotates by 2π/n radians, then
reflects through σh to get the new representation. The lower orders of Sn are redundant. Thus S1 = mirror plane, while S2 = centre
of symmetry, so that these are never used. Also, when a molecule possesses a proper axis and σh, it is also considered to
contain the corresponding improper axis. The first graphic shows the presence of an S4 axis in a true tetrahedral molecule, which
lies along the line of the C2 axis (there are 3 of each in a tetrahedral molecule).
The second figure depicts the redundancy and hence non-use of S1 and S2.
3.2
Point Groups
Point groups is short for point symmetry groups. They are collections of symmetry elements which isolated real objects
may possess. Clearly only certain symmetry elements will coexist in the same object. The names of the point groups are related
to the names of the symmetry operations, and in some cases the same symbol does for both. Be careful to distinguish the two!
With some practice, it is easy to assign the point groups of all but the most difficult cases. The flowchart shown at the right will
help you is assigning the point groups. Be sure to know how to correctly interpret each question along the path to the correct
assignment. Note that the questions often prompt you to look for symmetry that you may have missed. Therefore whenever a
question is asked that you have not yet considered, always go back to your picture or model and try to see if the indicated
symmetry element may be present.
3.3
Polarity
In order to have a permanent dipole moment, a molecule must not belong to a D group of any kind, nor Td, Oh or Ih.
3.4
Chirality
In order to be chiral, a molecule must not posses an Sn axis, nor a mirror plane, nor an inversion axis. (The latter two are
equivalent to S1 and S2).
Chemistry 3820 Lecture Notes
3.5
Dr.R.T.Boeré
Page
Examples of point groups
C?v
D?h
Td
Oh
Ih
C1
Cs
Ci
Cn
Cnv
Cnh
Dn
Dnd
Dnh
H-Cl
O=C=O
GeH4
SF6
[B12H12]2CHFClBr
NHF2
no examples
H2O2, S2Cl2
H2O, SF4, NH3, XeOF4, BrF5
B(OH)3
[Cr(en)3]3+
Mn 2(CO)10, Cp 2Fe staggered
BF3, XeF4
Linear, unsymmetrical
Linear, symmetrical
Tetrahedral (but not CH3F!)
Octahedral (but not SF5Cl)
Icosahedral (rare)
No symmetry elements except E
Only a plane
Only an inversion centre
Only an n fold rotation axis
Shortened Flowchart to Determine Point Group
C∞v , D∞h , Td , Oh , or I h ?
No
i?
No
Cn ?
n = principal axis
No
σh ?
Ci
Cs
Yes
No
C1
Yes
σ?
Yes
nC2 ⊥ Cn ?
No
No
nσv ?
No
Cn
Yes
Yes
No
nσv ?
σh ?
No
Yes
Dn
Yes
Yes
Dnh
Dnd
Cnh
Cnv
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Chemistry 3820 Lecture Notes
Dr.R.T.Boeré
Page
Extended Flowchart To Determine Point Group Symmetry
Linear?
i?
No
Yes
No
Unique Cn ?
n = principal axis
No
C ∞v
I
D∞v
No
Yes
6C5 ?
Yes
i?
Ih
No
No
4C3 ?
Yes
Yes
i?
Yes
Oh
No
S 2n
No
S 2n || Cn?
Yes
3C4 ?
O
No
No
3S 4 ?
Yes
n σd ?
No
i?
Yes
T
Yes
Th
Yes
Td
Dnd
No
3C2 ?
No
No
σ?
No
i?
Yes
C1
Yes
Ci
Yes
Cs
σh ?
Yes
nC2 ⊥ Cn ?
No
No
2 σd ?
Dn
Yes
No
D2d
Yes
σh ?
No
nσ v ?
No
Cn
Yes
Yes
Cnh
Cnv
Dnh
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