The colour of visible light absorbed by a TM complex depends on the magnitude of Δo This depends on the ligands bonded to the metal.

some ligands induce large Δo high energy absorption

others induce small Δo low energy absorption

Hence different complexes of the same metal in the same oxidation state may exhibit different colours have different absorption spectra.

The E of the light absorbed is used to promote an electron from a lower to higher energy d orbital.

Note that CFT can only predict the splitting pattern of the d-orbitals.

The value of Δo is however derived from electronic spectra.

Electronic Spectra

Types of transition

1. Charge transfer, either ligand to metal or metal to ligand. these are often extremely intense are generally found in the UV region but they may have a tail into the visible spectrum.

2. d-d or ligand field transitions are transitions between orbitals that are predominantly metal d orbitals

the separation is characterised by the strength of Δo.can occur in both the UV and visible region. transitions usually have small to medium intensities.

Electronic spectra of TM complexes

Spectrum of the d3 complex [Cr(NH3)6]3+.

A single transition t2g2eg

1 ←t2g

3 has resulted into two bands in the spectrum of the d3 complex [Cr(NH3)6]3+ due to electron-electron repulsions.

Why study the electronic spectra:Understand how to obtain Δo from electronic absorption spectrum of a TM complex with more than one d electron when e-e repulsions are important.

The key point is that the presence of e-erepulsions within d orbitals mean that absorption frequencies ≠ Δo because e-erepulsions result in multiple absorptions.

n = Principal QN size of orbital and its energyl = Azimuthal/Orbital QN shape of orbital 0, 1, 2, 3…..n-1ml = Magnetic QNms = Spin QN ±½ for a single electron

Revision on Quantum Numbers (QN)

L 0 1 2 3orbital s p d f

ml 1 3 5 7

ml is a subset of l, where ml take values from l…. 0….-l.

There are thus (2l +1) values of ml for each l value,

i.e. for the 1 s orbital (l = 0), 3 p orbitals (l = 1), 5 d orbitals (l = 2), etc.

The different ways in which electrons can occupy the orbitals specified in configuration are called microstates.

For example, one microstate of a 2p2 configuration is (1+ , 1-), this notation signifies that both the electrons occupy an orbital ml = +1 but do so with opposite spins.

+ indicates ms = +½ and – indicates ms = -½.

Another microstate of the same configuration is (-1+ , 0+).

In this microstate, both the electrons have ms = +½ but one occupies the 2p orbital with ml = -1 and the other occupies the orbital ml = 0.

The microstates of a given configuration will have the same energy only if electron-electron repulsions are negligible.

If we group together the microstates that have the same energy taking into account e-e repulsions , we obtain energy levels called TERMS.

Microstates

Russell-Saunders (R-S) coupling

The interactions that can occur are of three types:

• spin-spin coupling S • orbit-orbit coupling L• spin-orbit coupling J

There are two principal coupling schemes used: • Russell-Saunders (or L - S) coupling • j - j coupling.

It follows that we can identify the terms of light atoms and put them in order of energy by sorting the microstates according to their total spin quantum number S and then according to their total orbital angular momentum quantum number L.

This process called Russel-Saunders coupling.

By analogy with the notation s, p, d, … for orbitals with l = 0, 1, 2, …, the total orbital angular momentum of an atomic term is denoted by the equivalent upper case letter:

L = 0 1 2 3 4…….

S P D F G….(omitting J)

The total spin is normally reported as the value of 2S + 1, which is called the multiplicity of the term:

S = 0 ½ 1 3/2 2 5/2

2S + 1 1 2 3 4 5 6

singlet doublet triplet quartet quintet sextet

Russell- Saunders Coupling

The multiplicity is written as a left superscript representing the value of L and the entire label of a term is called a term symbol.

The Russell Saunders term symbol is then written as: (2S+1)L

Examples:For a d1 configuration: S= +½, hence (2S+1) = 2 ; L=2 and the ground term is written as 2D doublet dee

For an s1p1 configuration: S= both +½, hence (2S+1) = 3; or paired hence (2S+1) = 1 ; L=0+1=1 and the terms arising from this are 3P (triplet pee) or 1P (singlet pee)

For a p1d1 configuration: terms arising are 3F (triplet eff) or 1F (singlet eff)TRY THIS AT HOME

Russell Saunders term symbol

Symbol Meaning

a or A Non-degenerate orbital; symmetric to principal Cn

b or B Non-degenerate orbital; unsymmetric to principal Cn

e or E Doubly degenerate orbital or statet or T Triply degenerate orbital or state(subscript) g Symmetric with respect to centre of inversion(subscript) u Unsymmetric with respect to centre of inversion(subscript) 1 Symmetric with respect to C2 perp. to principal Cn

(subscript) 2 Unsymmetric with respect to C2 perp. to principal Cn

Mulliken symbols for atomic and molecular orbitals

For splitting in a tetrahedral crystal field the components are similar, except that the symmetry label g (gerade) is absent.

The Ground Terms are deduced by using Hund's Rules: 1) The Ground Term will have the maximum multiplicity.

2) If there is more than 1 Term with maximum multipicity, then the Ground Term will have the largest value of L.Thus for a d2 the rules predict 3F < 3P < 1G < 1D < 1S

A simple graphical method for determining just the ground term alone for the free-ions uses a "fill in the boxes" arrangement.

Note the idea of the "hole" approach:

A d1 configuration is treated as similar to a d9 configuration.

d1 has 1 electron more than d0 andd9 has 1electron less than d10 i.e. a hole.

Energies of the terms- Hund's Rules

To calculate L, use the labels for each column to determine the value of L for that box, then add all the individual box values together.

E.g. for a d7 configuration: in the +2 box are 2 electrons, so L for that box is 2 x 2= 4in the +1 box are 2 electrons, so L for that box is 1 x 2= 2in the 0 box is 1 electron, L is 0in the -1 box is 1 electron, L is -1 x 1= -1in the -2 box is 1 electron, L is -2 x 1= -2 Total value of L is +4 +2 +0 -1 -2 = 3 F term.

To calculate S, simply sum the unpaired electrons using a value of ½for each.For maximum multiplicity S = 2s+1 = 2[3(½)] + 1 = 4 Also possible is S = 2s+1 = 2[1(½)] + 1 = 2Note that for 5 electrons with 1 electron in each box then the total value of L is 0 L for a d1 configuration = L for a d9.

4F2P

d-orbital ground terms

dn 2 1 0 -1 -2 L S Ground Term

d1 ↑ 2 1/2 2Dd2 ↑ ↑ 3 1 3Fd3 ↑ ↑ ↑ 3 3/2 4Fd4 ↑ ↑ ↑ ↑ 2 2 5Dd5 ↑ ↑ ↑ ↑ ↑ 0 5/2 6Sd6 ↑↓ ↑ ↑ ↑ ↑ 2 2 5Dd7 ↑↓ ↑↓ ↑ ↑ ↑ 3 3/2 4Fd8 ↑↓ ↑↓ ↑↓ ↑ ↑ 3 1 3Fd9 ↑↓ ↑↓ ↑↓ ↑↓ ↑ 2 1/2 2D

d-orbital ground terms

The overall result shown in the Table is that: 4 configurations (d1, d4, d6, d9) give rise to D ground terms,4 configurations (d2, d3, d7, d8) give rise to F ground termsd5 configuration gives an S ground term.

The Russell Saunders term symbols for the other free ion configurations are given in the Table below.

Note that dn gives the same terms as d10-n

Terms for 3dn free ion configurations

Configuration

# of micro states

# of energy levels

Ground Term

Excited Terms

d1,d9 10 1 2D -d2,d8 45 5 3F 3P, 1G,1D,1Sd3,d7 120 8 4F 4P, 2H, 2G, 2F, 2 x 2D, 2P

d4,d6 210 16 5D3H, 3G, 2 x 3F, 3D, 2 x 3P, 1I, 2 x 1G, 1F, 2 x 1D, 2 x 1S

d5 252 16 6S4G, 4F, 4D, 4P, 2I, 2H, 2 x 2G, 2 x 2F, 3 x 2D, 2P, 2S

Q.What is the ground term of the configurations: (a) 3d5 of Mn2+ and (b) 3d3 of Cr3+?

Remember the first rule for a ground term maximum multiplicity

• S = 2½ 2S + 1 2 x 2½ + 1 = 6 A sextetL = 2 + 1 + 0 -1 -2 = 0 6S term

(b) S = 1½ 2S + 1 2 x 1½ + 1 = 4 A quartetL = 2 + 1 + 0= 3 4F term

Answer:If done correctly you should come up with (a) = 6S (a sextet ess term) and

(b) = 4F (a quartet eff term).

The ligand field splitting of TM complex ground terms

Thus far our discussion refer only to free atoms, we will now take it a step further to the domain of TM complex ions.

The treatment will be restricted to complex ions in an Oh crystal field.

The ground term energies for TM complexes are affected by the influence of a ligand field.

The effect of a ligand field d orbitals split into t2g and eg subsets.

By analogy the D ground term states split into T2g and Eg.

f orbitals are split to give subsets known as t1g, t2g and a2g.

By analogy, the F ground term when split by a crystal field will give states known as T1g, T2g, and A2g.

R-S term Number of states Terms in Oh symmetry

S 1 A1g

P 3 T1g

D 5 Eg , T2g

F 7 A2g , T1g , T2g

G 9 A1g , Eg , T1g , T2g

Correlating the splitting of spectroscopic terms in Oh ligand field

Note: The ground term for first-row transition metal ions is either:D, F or S which in high spin Oh A, E or T states.

Now back to the spectrum of [Cr(NH3)6]3+ & e-e repulsions.

Due to d-d transitions the spectrum shows two central bands with intermediate intensities.

How do we account for two bands in a single electron transition?

The terms of an octahedral complex are labelled by the symmetry species of the overall orbital state; a superscript prefix shows the multiplicity of the term:

The ground term of the d 3 Cr3+ discussed above is 4F which gives rise to 4A2g , 4T1g , 4T2g in the octahedral crystal field.

The two eg ← t2g transitions of the excited state are thus labeled:4T1g ← 4A2g and 4T2g ← 4A2g.

These are called molecular term symbols serves a function similar to atomic term symbols discussed earlier on.

IMPORTANT: DO NOT CONFUSE THE TERM SYMBOLS WITH ORBITALS ALL TERM SYMBOLS ABOVE ARISE FROM d-ORBITALS. WE ARE MERELY USING ANALOGY WITH ORBITALS FOR CONSISTENCY.

Spectroscopic terms

For ALL octahedral complexes, except high spin d5, simple CFT would predict that only 1 band should appear in the electronic spectrum and that the energy of this band should correspond to the absorption of energy equivalent to Δ.

In practice however, ignoring spin-forbidden lines, this is only observed for those ions with D free ion ground terms i.e., d1, d9 as well as d4, d6.

The observation of 2 or 3 peaks in the electronic spectra of d2, d3, d7

and d8 high spin octahedral complexes requires further treatment involving electron-electron interactions.

Using the Russell-Saunders (LS) coupling scheme, these free ion configurations give rise to F free ion ground states which in octahedral and tetrahedral fields are split into terms designated by the symbols A2g, T2g and T1g.

Ground state configuration of the octahedral d 3 complex [Cr(NH3)6]3+

t2g3 absorption near 25 000 cm-1 excitation t2g

2eg1 ← t2g

3.

There are 2 eg ← t2g transitions possible:

Ligand field transitions

The dz2 ← dxy transition, promotes

an electron from the xy-plane into the already electron-rich z-direction (the axis is electron-rich because both dyz and dzx are occupied large e-e repulsion).

The dz2 ← dzx transition merely

relocates an electron that is already largely concentrated along the z-axis.

Here there is no e-e repulsion.

21 550 cm-128 500 cm-1

Selection rules for electronic spectra of TM complexes.

The Selection Rules governing transitions between electronic energy levels of transition metal complexes are:

1. The Spin Rule ΔS = 0

2. The Orbital Rule (Laporte) Δl = +/- 1

The first rule states that allowed transitions must involve the promotion of electrons without a change in their spin.

The second rule states that if the molecule has a centre of symmetry, transitions within a given set of p or d orbitals (i.e. those which only involve a redistribution of electrons within a given subshell) are forbidden.

Relaxation of the Rules can occur through:

a) Spin-Orbit coupling gives rise to weak spin forbidden bands

b) Vibronic coupling - an octahedral complex may have allowed vibrations where the molecule is asymmetric

Absorption of light at that moment is then possible.

c) π-acceptor and π-donor ligands can mix with the d-orbitals transitions are no longer purely d-d.

Selection rules for electronic spectra of TM complexes.

Expected Values:

For M2+ complexes, expect Δ = 7500 - 12500 cm-1 or λ = 800 - 1350 nm.

For M3+ complexes, expect Δ= 14000 - 25000 cm-1 or λ = 400 - 720 nm.

Extinction coefficients for octahedral complexes are expected to be around 50-100 times smaller than for tetrahedral complexes.

For a typical spin-allowed but Laporte (orbitally) forbidden transition in an octahedral complex, expect ε < 10 m2mol-1.

Electronic Spectra

Example: The complex [(Co(NH3)6]+3 absorbs light with a wavelength of 437 nm. What is the splitting energy Δ?

Electronic Spectra

Solution: The complex absorbs light at the given frequency, so Δ must be equal to the light energy absorbed.

E = hc/υh = 6.626 x 10-34 Js ; c = 3.00 x 108 m/s and υ = 437 nm = 4.37 x 10-7 m.

E = (6.626 x 10-34 Js x 3.00 x 108 m/s) /4.37 x 10-7 m = 4.55 x 10-19 J

This is equal to 4.55 x 10-19 J/atom x 6.022 x 1023 atoms/mole

Therefore Δ = 274 kJ/mole.