CH2102 - VSEPR Theory and an Introduction to Coordination Chemistry

VSEPR – Valence Shell Electron Pair Repulsion

VSEPR offers a simple method for predicting the shape of molecular compounds. The combination of

p atomic orbitals may result in σ or π molecular orbitals, similarly d atomic orbitals may form σ, π or

δ molecular orbitals. These terms reflect the type of overlap between the atomic orbitals to produce

the molecular orbitals.

The basis of VSEPR theory is that the shape of the molecule is determined by the repulsion between

σ valence shell electron pairs.

The electron pairs will repel each other and thus move as far from each other as possible and the

molecular geometry is determined by the number of electron pairs.

VSEPR applies;

1) Only to valence shell electrons

2) To σ-bonding electrons (not π or δ)

3) To full orbital electrons (i.e. it is not applicable to unpaired electrons)

Using VSEPR Theory;

1. Count the number of valence electrons of the central atom

2. Add donated electrons from other atoms

3. Adjust for the charges on species

4. Calculate the total number of electrons and divide by 2 to find the number of electron pairs

5. Select the basic geometry

6. Determine which electron pairs are bonding or lone pairs

7. Modify the basic geometry to account for the electron pair interactions

In order of increasing repulsion;

bonding pair-bonding pair < bonding pair-lone pair < lone pair-lone pair

since lone pairs are localised on the central atom and act as a more concentrated source of

charge than the shared bonding pairs which are less localised.

It is important to note that when describing the shape of a molecule lone pairs are not ‘visible’,

and so ammonia, NH3, is pyramidal and not tetrahedral despite its co-ordination geometry being

based upon a tetrahedral arrangement. When determining the shape of a molecule, in the case

of several lone pairs, it is important to ensure the repulsions are minimised.

Since the coordination geometry is determined only using σ electrons it is necessary to disregard

the central atom electrons involved in π or δ bonds. Since each π bond is a shared electron pair

with one electron rising from each atom, subtract one electron from each π bond involving the

central atom. The π bond will affect the geometry, but only slightly, by pushing the angle to its

adjacent atoms slightly over the ideal amount.

i.e. in propene the Me-C=CH2 bond is 124.8⁰, slightly higher than the ideal angle of 120⁰.

As a d-orbital is essentially 2 π bonds and a σ bond, the overall effect is -1; again its effect on the

geometry is only to push adjacent atoms slightly further than the ideal angle.

For VSEPR any charge on the molecule is always assigned to the central atom, even if it would

seem better placed elsewhere. As such a negative charge is considered an extra electron for the

central atom, and a positive charge is shown as the subtraction of an electron from the central

atom electron count.

In the case of radicals there will be a non-integral number of electron pairs, in this case the

unpaired electron takes up its own orbital (i.e. 5 electrons, or 21

2 electron pairs would take up 3

orbitals). The orbital containing the unpaired electron exerts less repulsion than it would if full,

and so the bond angles change accordingly. If an electron were to be added, filling the half-filled

orbital, it would then act as expected and the angles would revert to those expected.

An Introduction to Co-ordination Chemistry

Werner postulated in the early 1900’s 3 things;

1) Most elements exhibit two types of valence, a) primary valence (or oxidation state) and b)

secondary valence (or co-ordination number)

2) Every element tends to satisfy both its primary and secondary valence.

3) The secondary valence is directed toward fixed positions in space (forming the basis of

stereochemistry for metal complexes)

We have since advanced this area of knowledge and as such there are several modern terms to

define;

Coordination chemistry – the area concerned with structures, reactivity’s and physical

properties of molecules formed by the combination of metal centres (Lewis acids) and

electron donors (Lewis bases),

Complex – a complex is a species formed by the association of two or more simpler

species, each, normally, capable of independent existence

Ligand – a ligand is any negative ion or polar(isable) neutral molecule bound to a metal

atom. This includes all Lewis bases (nucleophiles and reducing agents). Square brackets

are commonly used to denote the complex entity formed between a metal and its

ligands.

Oxidation number – this is the charge that the central atom in a coordination compound

would have if all of the ligands were to be removed along with the electron pairs they

donated. It is represented by a Roman numeral. Although not technically the same, the

term oxidation number is often used interchangeable with the term oxidation state (the

two are only usually different when the ligand atom is less electronegative than the

central atom).

Coordination number – commonly the number of donor atoms or ligands bound to the

metal. However this definition can be misleading when more complex ligands are

involved (such as the cyclopentadienyl ligand). It is therefore better to define the

coordination number as the number of two electron bonding pairs between a metal and

its ligands (the number of coordinate bonds).

Coordination bond – a covalent bond in which both electrons are supplied by one of the

two components (the ligand) of the bond.

The Coordinate Bond

In the case of metal-ligand interactions we use the concept of coordinate (or dative) bonds as

defined above.

Some characteristics of a coordination bond;

-coordination bonds have enthalpies of the same magnitude as those of other covalent bonds.

-one atom (the ligand) donates both of the electrons involved in the bond.

-the electron pair donor, or ligand, is a Lewis base.

the electron pair acceptor (typically a metal atom or ion) is a Lewis acid.

-the pair of electrons donated by the Lewis base is most often a lone pair.

In a neutral complex the ligands are listed in alphabetical order, followed by the metal atom. The

number of ligands is indicated by; bi, tri, tetra, penta, hexa, hepta, octa, nona, deca etc

In anionic complexes the metal ends in –ate, anionic ligands end in –ato

Molecular Structure of Coordination Compounds

In describing the structure of coordination compounds there are several key concepts, the

coordination number, the coordination geometry, the classification of ligands, isomerism and

electronic structure.

1) Coordination number – for metal complexes the most common coordination number is 4 or

6, though values from 1-14 are possible

2) Coordination geometry – also called the complex or coordination stereochemistry. This

describes the special distribution of ligands in a complex.

Each coordination number has an associated coordination geometry (or several) as follows

CN=2 – this coordination number is common for the late transition metal complexes e.g. Cu, Ag and

Au complexes.

The coordination geometry in this case is linear.

[H3N-Ag-NH3]+

CN=3 – this coordination number is rare, an example could be Pt(PPh3)3, the associated geometry is

trigonal planar

Ph3P

Pt – PPh3

Ph3P

CN=4 – a very common coordination number with two main geometries

Tetrahedral; very common, particularly with simple anionic ligands e.g. halides, all bond angles are 109.5o

Square planar; common particularly for late transition metals with d7, d9 and especially d8 configurations

CN=5 – this coordination number is rare for transition metal complexes, but important as many 4

coordinate complexes undergo ligand substitution reactions via 5-coordinate intermediates. Again

there are two main geometries

Trigonal bypyramidal Square pyramidal

120o

Square pyramidal and trigonal bypyradmidal are very close in energy and can easily interconvert

CN=6 – another very common coordination number for transition metal complexes, there are, again,

two associated geometries

Octahedral; in which the L-M-L angles are all 90o

Trigonal prismatic; much rarer

CN>6 – although possible the geometries of coordination numbers higher than 6 tend to be more

and more distorted, they’re most commonly found when considering lanthanides and actinides.

3) Classification of ligands – a ligand must be able to donate at least one pair of electrons to a

Lewis acid, they are classified according to the number of coordination bonds that are

formed with a metal centre

a) Monodentate ligands – from mono (one) and dentate (bite), also called unidentates. These

donate one pair of electrons to a metal centre. Ligands may be neutral, negatively charged

and very rarely positively charged.

Neutral ligands;

Other examples include ethers, thioethers, arsines etc.

Anionic ligands;

b) Bidentate ligands – these ligands donate two pairs of electrons to a metal centre and are

hence capable of forming two coordinate bonds.

These are known as chelate rings, and are very stable structures, one bidentate ligand will

form a more stable structure than two monodentate ligands, the enhanced stability is

known as the chelate effect, chelating ligands are classified by the size of the chelate ring

that they form.

4 member chelate rings;

5 member chelate rings

In many cases two/three molecules of this class of ligand can form two/three chelate rings at one

metal centre, forming bis and tris chelates respectively.

6 member chelate rings

c) Tridentate ligands – these ligands donate three pairs of electrons to a metal centre

There is also another class of tridentate ligand (and tetradentate etc.) known as a macrocylic ligand.

d) Tetradentate ligands – these donate four pairs of electrons, and are thus capable of forming

four coordinate bonds

e) Hexadentate ligands – these donate six electron pairs and therefore are capable of forming

six coordinate bonds

Isomerism in Coordination Compounds

There are several types of possible isomerism in coordination compounds;

Alternative coordination polyhedral – a very rare form of isomerism, it arises when a coordination

compounds can adopt two or more geometries (i.e. square planar and tetrahedral)

Coordination sphere isomerism – a common form of isomerism, this occurs where two complexes

of identical empirical formulae have differing sets of ligands attached to the central metal ion

e.g.

[Cr(H2O)6]3+Cl3

- -> [Cr(H2O)5Cl]2+Cl2-.H2O -> etc.

Violet Green

one water molecule

of crystallisation

Geometric isomerism – again very common, these are isomers which involve a different special

arrangement of ligands about a central atom

Ionisation isomerism – a rare form of isomerism, these isomers possess different combinations of

ligands in the coordination sphere and as a counter ion, they give rise to different ions when they

dissociate in solution and hence may have different conductivities

[Co(NH3)5Br]SO4 – violet [Co(NH3)5 SO4]Br – red

Linkage isomerism – common, ambidentate (those which have more than one type of donor atom)

ligands may bond to a metal atom through different atoms

Optical isomers – common, if the mirror images of a molecule are non-superimposable then they

form optical isomers, this is most commonly encountered in bis and tris chelates of octahedral

complexes

Polymerisation isomerism – rare, monomers and polymers may have the same empirical formula

e.g.

[Pt(NH3)2Cl2] and [Pt(NH3)4][PtCl4] (monomer and polymer respectively)

Crystal Field Theory

One of the most commonly used descriptions for bonding in transition metal complexes is derived

from the crystal field theory. In the crystal field theory the metal complex is represented as a point

positive charge surrounded by a set of point negative charges (representing the ligand electron

pairs). As well as assuming the charges to occupy points, crystal field theory assumes that

electrostatic interactions alone are responsible for the complex formation. Electrostatic repulsions

between the point negative charges of the ligands and the valence d-orbitals of the metal atom are

responsible for the energy splitting of the d-orbitals, making them no longer degenerate.

Crystal field splitting for an octahedral ML6 complex;

In the presence of an octahedral crystal field d-orbitals are split into a lower energy triply

degenerate set (the t2g orbitals) and a higher energy doubly degenerate set (the eg) separated by an

energy gap, ∆o, the crystal field splitting parameter varies with the identity of the ligand and metal,

and the charge of the metal atom.

The eg set of orbitals (the dz2 and dx

2d-y2) point directly along the Cartesian axis while the t2g axis (the

dxy, dxz, and the dyz) point in between the axis.

This leads to the following energy profile;

∆o is dependent on the metal, it’s oxidation state and the type of ligand involved.

Crystal field splitting for a tetrahedral ML4 complex;

In order to understand the crystal field splitting in a tetrahedral

ligand field it is easier to imagine that the four point negative

charge (ligands) are occupying the four opposite corners of a

cube. In this case the e (dz2, dx

2-y

2) orbitals are further from the

ligands than the t2 (dxy, dxz, and the dyz) orbitals and, as such, are

repelled less.

∆t is the crystal field splitting parameter in a tetrahedral field and

it is the energy difference between these two sets. Assuming

constant bond lengths for the same ligands the relationship

between ∆t and ∆o is ∆t= 4

9 ∆o due to the lower number of ligands

in a tetrahedral complex.

Counting Electrons in Transition Metal Complexes

Once the number of d-

electrons has been

determined the spin-state

for the ion can be

determined.

For d0, d

1, d

2, d

3, d

8, d

9

and d10

configurations

there is only one spin

state possibility, only one

way in which to fill d-orbitals regardless of crystal field strength.

For d4, d

5, d

6 and d

7 configurations two possibilities, high-spin and low-spin exist;

High spin; P>∆o (weak field case), here the pairing energy of electrons in the d-orbital is greater than

the crystal field splitting value (∆o) – hence electrons fill d-orbitals according to the Aufbau principle.

For most, but not all, first row transition metal complexes this situation applies.

Low spin; P<∆o (strong field case), here the pairing energy of electrons in the d-orbital is less than the

crystal field splitting value (∆o) – hence electrons fill t2g orbitals first and then the eg orbitals. Low-

spin complexes are common for 2nd and 3rd row complexes and for 1st row complexes with high field

ligands such as CN-)

Once ligand field splitting has been accounted for the t2gneg

m (octahedral coordination) or emt2n

(tetrahedral coordination) configuration can be assigned (where m and n represent the number of

electrons in each orbital set). To assign these configurations the number of d-electrons, the

coordination geometry and the spin-state must be known.

Once the d-electron configuration has been assigned the spin-only magnetic moment (µs.o.) can be

calculated (in units of Bohr magnetons);

µs.o. = 2 S S + 1 𝑤ℎ𝑒𝑟𝑒 S = total spin =1

2x the no. of unpaired electrons

µs.o. is also sometimes referred to as the effective magnetic moment, µeff.