## Introduction to the colour and magnetism of 1st row transition metal complexes

Before beginning a more detailed examination of the spectroscopy and magnetism of transition meal complexes, it is worth while reviewing how far a simple CFT approach will take us.

When electromagnetic radiation is absorbed by atoms or molecules it promotes them to an excited state. Microwave and infrared radiation correspond to lower energy quanta and so initiate rotational and vibrational excitation. Visible and UV light have much higher frequencies and can cause excitations characterstic of electronic excitation: the promotion of an electron from one orbital to another. We expect therefore that molecules will absorb light when the energy corresponds to the energy differences between occupied and unoccupied orbitals. For transition metal ions, the simplest case is Ti(III), solutions of which appear violet.

Absorption of light of frequency ~20,000 cm-1 excites the electron from the t2g subset to the eg subset. This is described as a eg ← t2g transition.
Absorption of green light, i.e. transmission of blue and red, gives a purple solution

ν ~20,000 cm-1
λmax ~ 500 nm
E = hν = hc/λ
Δ ~ 240 kJ mol-1

Rough guide to absorbance and colour
Wavelength Absorbed (nm) Frequency (cm-1) Colour of Light Absorbed Colour of Complex
410 24,400 violet lemon-yellow
430 23,300 indigo yellow
480 20,800 blue orange
500 20,000 blue-green red
530 18,900 green purple
560 17,900 lemon-yellow violet
580 17,200 yellow indigo
610 16,400 orange blue
680 14,700 red blue-green

In spectroscopy it is usual to measure either the amount of light that is absorbed or transmitted through the sample. For UV/Vis, absorbance is given by the Beer-Lambert expression:
A = ε c l
where A is the Absorbance
ε is the molar absorbance (extinction coefficient)
c is the concentration
and l is the path length of the cell

The most common (and cheapest) sample cells have a 1 cm path length and since A is unitless then we can see that the units of ε are mol-1 l cm-1. To move this to an acceptable SI set of units requires converting ε to units of m2 mol-1 and this involves a factor of 1/10.

Thus an ε of 5 mol-1 l cm-1 is equivalent to ε of 0.5 m2 mol-1.

Given that the separation between the t2g and eg levels is Δ then whether there is 1 d electron or several d electrons the simple Crystal Field Theory model would suggest that there is only 1 energy gap hence all spectra should consist of 1 peak. That this is not found in practise means that the theory is not sophisticated enough. What is required is an extension of the theory that allows for multi-electron systems where the energy levels are modified to include electron-electron interactions. This can be achieved by looking at the various quantum numbers for each of the electrons involved and using a system called the Russell-Saunders coupling scheme to describe an electronic state that can adequately describe the energy levels available to a group of electrons that includes these interactions.

## Magnetism

In CHEM1902 (C10K) we introduced the formula used to relate the magnetic moment to the number of unpaired spins in a transition metal complex.

μs.o. = √{4S(S+1)} B.M.

During the laboratory session you will carry out a measurement of the magnetic susceptibility which is a measure of the force exerted by the magnetic field on a unit mass of the sample under investigation. This is related to the number of unpaired electrons per unit weight and hence per mole and in the simplest picture we consider that this is solely dependent on the presence of unpaired electrons.

For a Ti(III) complex with 1 unpaired electron this corresponds to:
μs.o. = 2 √ (1/2 (1/2 + 1)) B.M
μs.o. = √ (3) B.M.
μs.o. = 1.73 Bohr Magneton

We will see later that while the spin-only approximation works in many cases, for a more complete analysis it is necessary to consider the contribution made by the orbital motion of the electron as well.