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Chemistry 3820 Lecture Notes Dr.R.T.Boer Page 14

2 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 ionicand covalentcompounds. 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 AB is generally

considered ionic if the difference in electronegativity between Aand Bis 2 units. Thus for H-F,= (3.9 2.2) = 1.7, and HF is

considered to be a (polar) covalent molecule. But LiF, 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 structureand symmetryof 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

electrons is taken directly off the periodic table, and can be had from the group numbers

directly. (Using the new numbering sequence, for p-block elements, subtract 10.) The

number of valence electrons includes all s electrons since the last noble gas configuration

plus the electrons of the block in which the element finds itself. Completely filled orbitals

(exceptsorbitals) 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 essentialpostulate 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 thi

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-, SO3

2-, NSF3, XeF4, IF5, PF5, SF6.

You were wondering

Why can we ignore previous

shells when counting the

number of valence electrons?

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4 tetrahedral sp3 2 2

angular

4 tetrahedral sp3 1 3 linear (e.g. HCl)

5 triangular-bipyramidal dsp3 5 0

triangular-bipyramidal


seesaw


T-shaped5 triangular-bipyramidal dsp

3 2 3

linear

6 octahedral d2sp

3 6 0

octahedral

6 octahedral d2sp

3 5 1

square-pyramidal

6 octahedral d2sp

3 4 2

square-planar

* using anyresonance isomer; doubleand triplebonds count as a single pair!

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3 Molecular symm etry

3.1 Symmetry operations and elements

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 Schnflies 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 C1rotation axis, i.e. rotation by 360, is thesameas the identity, so C1is never used.

b) Proper rotation axes Symbol: Cn (n = 2, 3, 4, 5, 6, 7,)

An axis about which the molecule may be rotated 2/n radians. A two-fold rotation axis means

rotation by 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 principalrotation axis. The graphics show a molecule possessing a C2axis at right, and a C3axis 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) Mirror planes Symbol: , v ,h, d

A non-specific mirror plane (possible only if this is the only symmetry element the molecule possesses.

v Vertical mirror plane is a plane of reflection containing the principle rotation axis.

h Horizontal mirror plane is a plane of reflection normal to the principle rotation axis.

d Dihedral mirror plane is a plane of reflection containing the principle rotation axis which also bisects two adjacent C2axes

perpendicular to the principle rotation axis.

d) 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 o

the molecule. In coordinate language, this means converting x, y, z to -x, -y, -z.

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e) Improper rotation axes Symbol: Sn (n = 3, 4, 5, 6, 7)

Also called rotation-reflection axes , which accurately describes this type of element. One rotates by 2/n radians, then

reflects through hto get the new representation. The lower orders of Snare 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 h, it is also considered to

contain the corresponding improper axis. The first graphic shows the presence of an S4axis in a true tetrahedral molecule, which

lies along the line of the C2axis (there are 3 of each in a tetrahedral molecule).

The second figure depicts the redundancy and hence non-use of S1and 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 wil

help you is assigning the point groups. Be sure to know how to correctly interpret each question along the path to the correc

assignment. Note that the questions often prompt you to look for symmetry that you may have missed. Therefore whenevera

question is asked that you have not yet considered, alwaysgo 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 notbelong to a D group of any kind, nor Td, Ohor Ih.

3.4 Chirality

In order to be chiral, a molecule must notposses an Snaxis, nor a mirror plane, nor an inversion axis. (The latter two are

equivalent to S1and S2).

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3.5 Examples of point groups

C?v H-Cl Linear, unsymmetrical

D?h O=C=O Linear, symmetrical

Td GeH4 Tetrahedral (butnotCH3F!)

Oh SF6 Octahedral (but notSF5Cl)

Ih [B12H12]2-

Icosahedral (rare)

C1 CHFClBr No symmetry elements except ECs NHF2 Only a plane

Ci no examples Only an inversion centre

Cn H2O2, S2Cl2 Only an n fold rotation axis

Cnv H2O, SF4, NH3, XeOF4, BrF5

Cnh B(OH)3

Dn [Cr(en)3]3+

Dnd Mn2(CO)10, Cp2Fe staggered

Dnh BF3, XeF4

Yes

No

Yes

No

Yes

No

Yes

NoNo

Yes

Yes

No

Yes

No

No

No

Yes

n= principal axis ?

Shortened Flowchart to Determine Point Group

Cv

, Dh

, Td, O

h, or I

h?

Cn?

Cn

Cnv

nv ?

Cnh

h?nC2Cn?

Dn

Dnd

nv ?

Dnh

h?

C1i?

CiCs

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Yes

No

Yes

No

Yes

No

Yes

h? 2d? Dn

D2d

Dnh

Cs

Yes Yes

No

i? C1

Ci

No

?

Td

Yes

YesYes

Noi? T

Th

No3S4?

No

3C4?

Yes

Yes

No

i?

O

Oh

No

3C2?

No

4C3?

Yes

Yes

No

nd?

S2n

Dnd

S2n || Cn?

Yes

No

i? Cv

Dv

Yes

No

Yes

No

No

Yes

h? nv? Cn

CnvCnh

Yes

No

Yes

No

No

Linear?No

Unique Cn?

n= principal axis

nC2Cn?

6C5? i?

I

Ih

Extended Flowchart To Determine Point Group Symmetry

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