19.5A: Color
- Page ID
- 34348
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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 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
| 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 |
A = ε c l
where A is the Absorbanceε 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.
Contributors and Attributions
Prof. Robert J. Lancashire (The Department of Chemistry, University of the West Indies)