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19.5A: Color

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  • 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.

    d1 orbital case
    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
    Vis spec of Ti(III)
    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.

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