Chem 261: Inorganic Chemistry

The elements in the periodic table are often divided into four categories: (1) main group elements, (2) transition metals, (3) lanthanides, and (4) actinides.

How do we determine the electronic configuration of the central metal ion in any complex?

Try to recognise all the entities making up the complex and knowing whether the ligands are neutral or anionic, so that you can determine the oxidation state of the metal ion.

A simple procedure exists for the M(II) case.

22 23 24 25 26 27 28 29

Ti V Cr Mn Fe Co Ni Cu

Cross off the first 2,

2 3 4 5 6 7 8 9

Evaluating the oxidation state

Oxidation States and their Relative Stabilities:

Why do these elements exhibit a variety of oxidation states?

Because of the closeness of the 3d and 4s energy states.

The most prevalent oxidation numbers are shown in green.

Sc     +3

Ti +1 +2 +3 +4

V +1 +2 +3 +4 +5

Cr +1 +2 +3 +4 +5 +6

Mn +1 +2 +3 +4 +5 +6 +7

Fe +1 +2 +3 +4 +5 +6

Co +1 +2 +3 +4 +5

Ni +1 +2 +3 +4

Cu +1 +2 +3

Zn   +2

An increase in the number of oxidation states from Sc to Mn. All seven oxidation states are exhibited by Mn.

There is a decrease in the number of oxidation states from Mn to Zn.WHY?

Because the pairing of d-electrons occurs after Mn (Hund's rule) which in turn decreases the number of available unpaired electrons and hence, the number of oxidation states.

The stability of higher oxidation states decreases in moving from Sc to Zn. Mn(VII) and Fe(VI) are powerful oxidizing agents and the higher oxidation states of Co, Ni and Zn are unknown.

The relative stability of +2 state with respect to higher oxidation states, particularly +3 state increases in moving from left to right.

This is justifiable since it will be increasingly difficult to remove the third electron from the d-orbital.

Summary of Physical Properties

1. have large charge/radius ratio; 2. are hard and have high densities; 3. have high melting and boiling points; 4. form compounds which are often paramagnetic; 5. show variable oxidation states; 6. form coloured ions and compounds; 7. form compounds with profound catalytic activity 8. form stable complexes.

Coordination Chemistry

A coordination compound, sometimes called a coordination complex, contains a central metal atom or ion surrounded by a number of oppositely charged ions or neutral molecules (possessing lone pairs of electrons) which are known as ligands.

If a ligand is capable of forming more than one bond with the central metal atom or ion, then ring structures are produced which are known as metal chelates, the ring forming groups are described as chelating agents or polydentate ligands.

The coordination number of the central metal atom or ion is the total number of sites occupied by ligands. Note: a bidentate ligand uses two sites, a tridentate three sites etc.

Ligands:

molecular formula

Lewis base/ligand

Lewis acid

donor atom

coordination number

[Zn(CN)4]2- CN- Zn2+ C 4

[PtCl6]2- Cl- Pt4+ Cl 6

[Ni(NH3)6]2+ NH3 Ni2+ N 6

Mono-dentate

Multidentate Ligands

Chelating ligands bonded to metal – rings – chelate rings - any number of atoms in the ring.most common – five or six atoms, including metal.

Coordination Numbers and Geometries

Isomers

Primarily in coordination numbers 4 and 6.

Arrangement of ligands in space, but also the ligands themselves.

Ionization isomers

Isomers can produce different ions in solution e.g.

[PtCl2(NH3)4]Br2 [PtBr2(NH3)4]Cl2

Polymerization isomers

Same stoichiometry, different arrangement in space.

Eight compounds with formula Co(NH3)3(NO2)3.

Coordination isomers

[Co(NH3)6]3+ [Cr(CN)6]-3 and [Cr(NH3)6]+3 [Co(CN)6]-3

Linkage isomers

e.g. Nitro and nitito, N or O coordination possible

In compounds, both cation and anion are complex, the distribution of ligands can vary, giving rise to isomers.

Geometric isomers

Formula is the same but the arrangement in 3-D space is different e.g. square planar molecules give cis and trans isomers.

For hexacoordinate systems other species can also occur.

For M(X)3(Y)3 systems there is facial and meridian

Are “stereo” isomers also possible? An analogy to organic chirality. Molecules which can rotate light.

Enantiomers (non-superimposable mirror images)

Complex Stabilities

In aqueous solution a comparison of metal complexes and their affinity for the H2O molecule as a competing ligand has been studied. Here are some general observations:

• For a given metal and ligand, complexes where the metal oxidation state is +3 are more stable than +2.

• Stabilities of complexes of the first row of transition metals vary in reverse of their cationic radii (in general)

MnII < FeII < CoII < NiII > CuII > ZnII

• Hard and soft Lewis acid-base theory

• Chelate Effect - effect is the additional stability of a complex containing a chelating ligand, relative to that of a complex containing monodentate ligands with the same type and number of donors as in the chelate. 

Mainly an entropy effect.

Cu(H2O)4(NH3)2]2+ + en = [Cu(H2O)4(en)]2+ + 2 NH3

When ammonia molecule dissociates - swept off in solution and the probability of returning is remote.

When one amine group of en dissociates from complex ligand retained by end still attached so the nitrogen atom cannot move away – swings back and attach to metal again.

Therefore the complex has a smaller probability of dissociating.

The origin of colour - absorption

The colour can change depending on a number of factors e.g.• Metal charge• Ligand

Physical phenomenon

Are there any simple theories to explain the colours in transition metal complexes?

There is a simple electrostatic model used by chemists to rationalize the observed results

Covalent bonds by sharing pairs of electrons was first proposed by G. N. Lewis in 1902.

It was not until 1927, however, that Walter Heitler and Fritz London showed how the sharing of pairs of electrons holds a covalent molecule together.

The Heitler-London model of covalent bonds was the basis of the valence-bond theory.

The last major step in the evolution of this theory was the suggestion by Linus Pauling that atomic orbitals mix to form hybrid orbitals, such as the sp, sp2, sp3, dsp3, and d2sp3 orbitals.

Bonding in Transition Metal Complexes

How do we view this and do we really need to ?

Valence-Bond Theory

It is easy to apply the valence-bond theory to some coordination complexes, such as the Co3+ complexes below.

d2sp3- inner sphere complex low spin complex

sp3d2- outer sphere complex high spin complex

Note: Such a situation will not arise for d1, d2 and d3

ion configuration.

• Assumes that all d orbitals in a complex are equal in energy.

• The arbitrary use of 3d and 4d orbitals for bonding energy differential ignored.

• The theory is unable to adequately explain electronic and magnetic properties of complexes.

•VBT is widely used in organic and main group element chemistry.

•In TM metal chemistry VBT is superseded by the Crystal Field Theory (CFT).

Deficiencies of VB approach to bonding

Crystal Field Theory is based on the idea that a purely electrostatic interaction exists between the central metal ion and the ligands.

Covalent bonding is ignored.

Crystal field theory was developed by considering two compounds: manganese(II) oxide, MnO octahedral geometry, copper(I) chloride, CuCl tetrahedral geometry.

We will start with octahedral and then expand to tetrahedral and square planar complexes

The Crystal-Field Theory

The five d-orbitals in an octahedral field of ligands

Tsuchida noticed a trend in while looking at a series of Cobalt(III) Complexes.

With the general formula : [Co(NH3)5X]

He arrived a series which illustrates the effect of ligands on o (10Dq)

He called it:

The Spectrochemical Series

Tsuchida, R. Bull. Chem. Soc. Jpn. 1938, 13, 388

The magnitude of the splitting(ligand effect)

Strongfield

Weakfield

The spectrochemical series

CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2

- > OH- > Cl- > Br- > I-

The energy gap between t2g and eg levels is designated o or10Dq

The magnitude of the splitting(metal ion effect)

Strongfield

Weakfield

increases with increasing formal charge on the metal ion

increases on going down the periodic table

o

3/5 o

2/5 o

t2g

eg

Splitting of d orbitals in an octahedral field

E(t2g) = -0.4o x 3 = -1.2o

E(eg) = +0.6o x 2 = +1.2oCFSE(Oh) = (–0.4x + 0.6y )o + nP

Placing electrons in d orbitals

1 u.e. 5 u.e.

d5

0 u.e. 4 u.e.

d6

1 u.e. 3 u.e.

d7

2 u.e. 2 u.e.

d8

1 u.e. 1 u.e.

d9

0 u.e. 0 u.e.

d10

Q. Determine which of the following are more likely to be high spin complexes:

[Fe(CN)6]3-

[FeF6]3- [Co(H2O)6]

+3

[Co(CN)6]-3

[Co(NH3)6]+3

[Co(en)3]+3

Solution: Compare the ligands on the spectrochemical series. Since we want a high spin complex, we want weak field ligands. The weaker field ligands in the above are H2O and F-, so complexes 2 and 3 are more likely to be high

spin. (The cyanide complexes are least likely)

Crystal–Field Stabilisation Energy (CFSE)

d4

Strong field =Low spin

(2 unpaired)

Weak field =High spin

(4 unpaired)

< o > o

When the 4th electron is assigned it will either go into the higher energy eg orbital at an energy cost of 0 or be paired at an energy cost of , the pairing energy.

Notes: the pairing energy, P, is made up of two parts. 1) Coulombic repulsion energy caused by having two electrons in same orbital

Pairing Energy,

The pairing energy, , is made up of two parts.

1) Coulombic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of c for each doubly occupied orbital.

2) Exchange stabilizing energy for each pair of electrons having the same spin and same energy. Stabilizing contribution of e for each pair having same spin and same energy

= sum of all c and e interactions

The energy increase of the eg orbitals and the energy decrease of the t2g orbitals must be balanced relative to the energy of the hypothetical spherical field (sometimes called the barycenter)

The energy of the eg set rises by +3/5o = +6Dq while theenergy of the t2g set falls by –2/5o = –4Dq, resulting in nonet energy change for the system.E = E(eg)8 + E(t2g)9= (2)(+3/5o) + (3)(–2/5o)= (2)(+6Dq) + (3)(–4Dq) = 0

Another way to view the energy in textbooks

The magnitude of o depends upon both the metal ion and the attaching ligands

Magnitudes of o are typically ~100 – 400 kJ/mol (~8,375 –33,500 cm–1)

11 kJ/mol = 83.7 cm–1

Most aquo complexes are high spin, because H2O is a weak fieldligand.

Almost all Co3+ (d6) complexes are low spin, including[Co(H2O)6]3+, except [CoF6]3–, which is high spin.

Second and third row transition metal ions tend to have lowspin states - These ions tend to have larger o values

Larger 4d and 5d orbitals result in smaller P values, owingto lesser electronic repulsions

4d and 5d orbitals overlap with ligand orbitals, delocalizingelectron density onto the ligands - Can we calculate or guestimate o?

In comparing groups of similar ligands - rationalize the order.

These effects have been placed on a semi-quantitative basis by Jorgensen who assigned a factor g to a sampling of metal ions and a factor f:

Δo ≈ g x f x 1000 cm-1

High- spin d 4

t2g3 eg

1

Low- spin d 4

t2g4 eg

0

x = 3 , y = 1 x = 4 , y = 0

E = (0.4x – 0.6y)Δo = 0.6 Δo

E = (0.4x – 0.6y)Δo = 1.6 Δo + P

The spectrochemical seriesThe splitting of d orbitals in the crystal field model not only depends on the geometry of the complex, it also depends on the nature of the metal ion, the charge on this ion, and the ligands that surround the metal. When the geometry and the ligands are held constant, this splitting decreases in the following order.

Results and Observations

1. octahedral gets larger for increasing oxidation state

2. It increases down a group e.g. Co < Rh < Ir

3. With a given ligand and oxidation state octahedral varies irregularly across the first row transition metals

For metals the series is:

Pt4+ > Ir3+ > Rh3+ > Co3+ > Cr3+ > Fe3+ > Fe2+ > Co2+ > Ni2+ > Mn2+

When the geometry and the metal are held constant, the splitting of the d-orbitals increases in the following order

For ligands the series is:

I - < Br - < [NCS] - < Cl - < F - < - OH < NH3 < en < CN -

Weak field < Increasing O < Strong field

Tetrahedral Coordination

t = 4/9o

All tetrahedral compounds areHigh Spin

The difference results in an energy split between the two levels by t or10Dq'. Relative to the barycenter defined by the hypothetical spherical field" the e level is lower by –3t /5 = –6Dq'." the t2 level is higher by +2t /5 = +4Dq‘

In principle, both high and low spin configurations are conceivable for d 3–d 6 ML4 Td complexes

With extremely rare exceptions, only high spin configurations are observed." t is much smaller than o

For a given ligand at the same M-L distances, it can be shown that t = (4/9)o

" t << P in ordinary complexes, so high spin is favoured

The crystal field stabilization energy for tetrahedral complexes is calculated from the following equation:

CFSE(Td) = (–0.6x + 0.4y )t + nP

What is the LFSE for octahedral ions of the following configurations:

(a) d 3 (b) high-spin d 5

(a) electronic configuration : t2g3eg

0, x = 3, y = 0

Therefore, LFSE = (0.4x – 0.6y)Δo = [(0.4)(3) – (0.6)(0)]Δo = 1.2 Δo

(b) electronic configuration : t2g3eg

2, x = 3, y = 2

Therefore, LFSE = (0.4x – 0.6y)Δo = [(0.4)(3) – (0.6)(2)]Δo = 0

What is LFSE for both high- and low-spin d 6 configuration?

Δo is the difference in energy between eg and t2g.

LFSE = (0.4x – 0.6y)Δo

The net energy of a t2gx eg

y configuration relative to the barycentre is called the ligand field stabilization energy (LFSE).

Let us see what happens when we withdraw the 2 trans ligands in an Oh complex (let it be the z ligands)

When this happens, we have a tetragonally distorted octahedral complex.As soon as the distance from Mm+ to these 2 ligands becomes greater than the other 4 ligands, new energy differences are established.

z2 orbital becomes more stable than x2-y2 orbital.

yz and xz are equivalent more stable than xy

t2g

eg

EΔo

dx2

-y2

dxy

dz2

dzy , dzx

Whether this happens depends on the metal ion and the ligands concerned.

Square complexes of CoII, NiII and CuII lead to energy level diagrams shown as follows:

eg

t2g

Δo

octahedral square

MX6 MX4

Δo exactly

dx2

-y2

2/5 Δo

1/12 Δo

dz2

dyz , dzx

M = CoII, NiII and CuII

The spectrochemical series

The splitting of d orbitals in the CF model not only depends on the geometry of the complex, it also depends on the nature of the metal ion, the charge on this ion and the ligands that surround this ion.When the geometry and the ligands are held constant, this splitting decreases in the following order:

Pt4+ > Ir3+ > Rh3+ > Co3+ > Cr3+ > Fe3+ > Fe2+ > Co2+ > Ni2+ > Mn2+

When the geometry and the metal are held constant, the splitting of the d- orbitals increases in the following order:

I- < Br- < [NCS]- < Cl-< F- < OH- < H2O < NH3 < en < CN- < CO

The ligand- field splitting parameter, Δo varies with the identity of the ligand.In the series of complexes [CoX(NH3)5]n+ with X = I-, Br-, Cl- H20 and NH3, the colours range from purple (for X = I-) through pink (X = Cl-) to yellow (with NH3).

This observation indicates that energy of the lowest electronic transition increases as the ligands are varied along the series.

Ligand that give rise to high energy transition (such as CO) is referred to as a strong-field ligand.

Ligands that give rise to low energy transitions (such as Br-) referred to as weak-field ligand.

The Jahn‐Teller (J‐T) theorem states that in molecules/ ions that have a degenerate groundstate the molecule/ion will distort to remove the degeneracy

Stretching of the two atoms in z‐direction in an octahedron leads to an advantage for all orbitals with z‐components because the repulsion decreases

Splitting of the two energetic levels into four levels at all complexes with unsymmetric occupation of the higher level d‐orbitals often show

Tetragonally distorted complexes the Jahn Teller effect

Magnetic properties of metal complexes

Diamagnetic complexesvery small repulsive

interaction with external magnetic field

no unpaired electrons

Paramagnetic complexesattractive interaction with

external magnetic fieldsome unpaired electrons

)2( nns

The spin-only magnetic moment of a complex = µ

Defined as µ = 2 [ S(S+1)]1/2 µB

(µB = Bohr magneton = 9.274 x10-24 JT-1)

N.B. Each unpaired electron has a spin quantum = ½

Therefore for multi-electron systems S = ½ n, where n is the number of unpaired electrons

From this we get µ = [n(n+2)]1/2 µB

Experimentally [Fe(OH2)6]3+ which is paramagnetic is found to have a magnetic moment of 5.3 µ/µB

From the table this value corresponds to a value for 5 unpaired electrons i.e. a high-spin t2g

3eg2

configuration

The numbers are never exact

The spin-only magnetic moment of a complex = µ

Defined as µ = 2 [ S(S+1)]1/2 µB

(µB = Bohr magneton = 9.274 x10-24 JT-1)

N.B. Each unpaired electron has a spin quantum = ½

Therefore for multi-electron systems S = ½ n, where n is the number of unpaired electrons

From this we get µ = [n(n+2)]1/2 µB

Experimentally [Fe(OH2)6]3+ which is paramagnetic is found to have a magnetic moment of 5.3 µ/µB

From the table this value corresponds to a value for 5 unpaired electrons i.e. a high-spin t2g

3eg2

configuration

The numbers are never exact

Magnetic measurementsUsed to determine the number of unpaired spins in a complex, hence identify its ground-state configuration.

Compounds are classified as diamagnetic if they are repelled by a magnetic field and paramagnetic if they are accepted by a magnetic field.The spin-only magnetic moment, μ, of a complex with total spin quantum number is given by:

μ = 2 {S (S + 1)}½ μB

μB = Bohr magneton

Measured magnetic moments include contributions from both spin and orbital spin. In the first transition series complexes the orbital contribution is small and usually ignored.

The magnetic moment of a certain Co(II) complex is 4.0 μB . What is its d- electron configuration?

A Co(II) complex is d 7.

Two possible configurations: t2g5eg

2 (high-spin, S = 1½) with 3 unpaired electrons or t2g

6eg1 (Low-spin, S = ½) with 1 unpaired

electron.The spin-only magnetic moments are 3.87 μB and 1.73 μB.

Therefore, the only consistent assignment is the high-spin configuration t2g

5eg2.

The magnetic moment of the complex [Mn(NCS)6]4- is 6.06 μB. What is its electron configuration?