Quantum Chemistry of Dyes
Copyright (c) Lant, Montgomery, and Mazziotti 2023 This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Learning Goals:
Indigo vs Tyrian Purple
References
By the end of this lesson, students will be able to:
Use quantum chemistry calculations to predict the absorption frequencies of the indigo and tyrian purple dyes
Relate the differences in absorbed frequencies to the differences in colors
We have found that if we want to calculate where a particular compound will absorb, we must be able to calculate the energy levels. In the previous section, we found that the Particle in a Box model works remarkably well for cyanine dyes. In this section, we want to show that it does not work well for ALL systems. That is, there is a limit to the ability of a model to capture the key physics in a system.
Consider two related dyes: indigo and tyrian purple:
Figure 1: Structures of indigo (left) and tyrian purple (right).
The only difference between the two structures is that tyrian purple has bromines at the 6 and 6' positions. This does not affect the number of π-electrons or the length of the conjugated chain, so the particle in a box model would treat these two dyes as being identical!
For more complex compounds, one must use more sophisticated methods to calculate the energy levels. Here we use the QuantumChemistry toolbox to calculate the ground and excited states of each of these dyes.
restart:Digits≔15:withQuantumChemistry:
We enter the geometry of the indigo dye
indigo≔C,−2.82265000,0.73898000,0.00005000,C,−3.96802000,1.53537000,0.,C,−5.20393000,0.88612000,−0.00005000,C,−5.31138000,−0.51504000,−0.00005000,C,−4.16296000,−1.30350000,−0.00001000,C,−2.91836000,−0.67319000,0.00003000,H,−6.29247000,−0.97833000,−0.00009000,H,−4.21764000,−2.38780000,−0.00001000,H,−3.90356000,2.61878000,0.00001000,H,−6.10933000,1.48632000,−0.00009000,C,−1.55139000,−1.21054000,0.00005000,C,−0.68036000,0.00041000,0.00006000,N,−1.48727000,1.11979000,0.00017000,O,−1.14282000,−2.37426000,0.00004000,H,−1.10083000,2.05448000,−0.00008000,C,0.68036000,−0.00040000,−0.00006000,N,1.48727000,−1.11979000,−0.00017000,C,2.82264000,−0.73898000,−0.00005000,C,2.91836000,0.67319000,−0.00003000,C,1.55140000,1.21054000,−0.00004000,H,1.10081000,−2.05448000,0.00011000,O,1.14282000,2.37426000,−0.00004000,C,3.96802000,−1.53537000,−0.,C,4.16297000,1.30350000,−0.,C,5.31138000,0.51504000,0.00004000,C,5.20393000,−0.88612000,0.00005000,H,6.10932000,−1.48633000,0.00009000,H,3.90355000,−2.61878000,0.,H,4.21765000,2.38780000,0.,H,6.29247000,0.97832000,0.00007000;
indigo≔C,−2.82265000,0.73898000,0.00005000,C,−3.96802000,1.53537000,0.,C,−5.20393000,0.88612000,−0.00005000,C,−5.31138000,−0.51504000,−0.00005000,C,−4.16296000,−1.30350000,−0.00001000,C,−2.91836000,−0.67319000,0.00003000,H,−6.29247000,−0.97833000,−0.00009000,H,−4.21764000,−2.38780000,−0.00001000,H,−3.90356000,2.61878000,0.00001000,H,−6.10933000,1.48632000,−0.00009000,C,−1.55139000,−1.21054000,0.00005000,C,−0.68036000,0.00041000,0.00006000,N,−1.48727000,1.11979000,0.00017000,O,−1.14282000,−2.37426000,0.00004000,H,−1.10083000,2.05448000,−0.00008000,C,0.68036000,−0.00040000,−0.00006000,N,1.48727000,−1.11979000,−0.00017000,C,2.82264000,−0.73898000,−0.00005000,C,2.91836000,0.67319000,−0.00003000,C,1.55140000,1.21054000,−0.00004000,H,1.10081000,−2.05448000,0.00011000,O,1.14282000,2.37426000,−0.00004000,C,3.96802000,−1.53537000,−0.,C,4.16297000,1.30350000,−0.,C,5.31138000,0.51504000,0.00004000,C,5.20393000,−0.88612000,0.00005000,H,6.10932000,−1.48633000,0.00009000,H,3.90355000,−2.61878000,0.,H,4.21765000,2.38780000,0.,H,6.29247000,0.97832000,0.00007000
Let's plot the molecule
PlotMoleculeindigo;
We can compute the electronic energy and properties of indigo using computational chemistry (namely, density functional theory (DFT)) (Note that the calculation may take a minute).
indigo_DFT≔DensityFunctionalindigo, basis=6-31g;
The energies of the molecular orbitals can be plotted with the blue levels corresponding to occupied orbitals and the red levels corresponding to unoccupied orbitals
MODiagramindigo,method=DensityFunctional,basis=6-31g
We can plot the highest occupied molecular orbital (HOMO) (left) and the lowest unoccupied molecular orbital (LUMO) (right)
HOMO ≔ roundaddindigo_DFTmo_occ2; LUMO ≔ HOMO+1; pHOMO ≔ DensityPlot3Dindigo,indigo_DFT,orbitalindex=HOMO,basis=6-31g,densitycutoff=0.001: pLUMO ≔ DensityPlot3Dindigo,indigo_DFT,orbitalindex=LUMO,basis=6-31g,densitycutoff=0.001: plots:-displayVectorrowpHOMO,pLUMO;
HOMO≔68
LUMO≔69
Finally, we can also compute the excitation spectra (Note that this calculation may take some time to reproduce).
spectra_indigo_b3lyp ≔ ExcitationSpectraindigo,method=DensityFunctional,basis=6-31g, nstates=3,3,showtable:
State
Energy
Wavelength
Spin
Oscillator
1
1.03972808eV
1192.46753221nm
Triplet
0.44895520
2
2.32548387eV
533.15440626nm
Singlet
0.28403090
3
2.35743686eV
525.92796749nm
0.08185276
4
2.42658941eV
510.94015624nm
4.81491290×10−10
5
2.79208571eV
444.05584358nm
2.51377265×10−10
6
3.46710287eV
357.60172717nm
0.00641236
We observe that there is a transition from the ground singlet state to an excited singlet state around 526 nm. (a) Approximately what color is absorbed by the indigo dye? (Hint: To answer this question, you can use the Maple applet below)
Exploreplots:-displayplottools:-disk1, 1, 1, color=ColorTools:-WavelengthToColor'lambda',method=linear, axes=none, 'lambda'=390..750, size=300,300;
λ
Now consider tyrian purple, a compound that is very similar to indigo blue, except for the addition of two bromine atoms:
tyrianpurple≔C,−7.53629000,2.44628000,0.02964000,C,−6.37087000,3.18191000,0.04692000,C,−5.15824000,2.48164000,0.00715000,C,−5.11665000,1.07281000,−0.02689000,C,−6.29914000,0.33034000,−0.01590000,C,−7.48107000,1.04288000,0.02018000,H,−4.16101000,0.55333000,−0.05401000,H,−6.29526000,−0.75397000,−0.03064000,H,−6.39556000,4.26515000,0.09313000,Br,−3.53176000,3.45097000,0.01113000,C,−8.87511000,0.56228000,0.04867000,C,−9.70911000,1.82064000,0.05880000,N,−8.84729000,2.89698000,0.13866000,O,−9.25455000,−0.59150000,0.06050000,H,−9.17649000,3.82873000,−0.08865000,C,−11.03865000,1.75648000,−0.03735000,N,−11.90080000,0.68029000,−0.11662000,C,−13.21148000,1.13137000,−0.00440000,C,−13.26634000,2.53479000,0.00535000,C,−11.87231000,3.01505000,−0.02598000,H,−11.57160000,−0.25121000,0.11179000,O,−11.49263000,4.16874000,−0.03827000,C,−14.37716000,0.39607000,−0.01880000,C,−14.44796000,3.24766000,0.04478000,C,−15.63061000,2.50553000,0.05891000,C,−15.58949000,1.09670000,0.02446000,Br,−17.21626000,0.12784000,0.02504000,H,−14.35292000,−0.68716000,−0.06523000,H,−14.45146000,4.33197000,0.05995000,H,−16.58602000,3.02527000,0.08893000;
tyrianpurple≔C,−7.53629000,2.44628000,0.02964000,C,−6.37087000,3.18191000,0.04692000,C,−5.15824000,2.48164000,0.00715000,C,−5.11665000,1.07281000,−0.02689000,C,−6.29914000,0.33034000,−0.01590000,C,−7.48107000,1.04288000,0.02018000,H,−4.16101000,0.55333000,−0.05401000,H,−6.29526000,−0.75397000,−0.03064000,H,−6.39556000,4.26515000,0.09313000,Br,−3.53176000,3.45097000,0.01113000,C,−8.87511000,0.56228000,0.04867000,C,−9.70911000,1.82064000,0.05880000,N,−8.84729000,2.89698000,0.13866000,O,−9.25455000,−0.59150000,0.06050000,H,−9.17649000,3.82873000,−0.08865000,C,−11.03865000,1.75648000,−0.03735000,N,−11.90080000,0.68029000,−0.11662000,C,−13.21148000,1.13137000,−0.00440000,C,−13.26634000,2.53479000,0.00535000,C,−11.87231000,3.01505000,−0.02598000,H,−11.57160000,−0.25121000,0.11179000,O,−11.49263000,4.16874000,−0.03827000,C,−14.37716000,0.39607000,−0.01880000,C,−14.44796000,3.24766000,0.04478000,C,−15.63061000,2.50553000,0.05891000,C,−15.58949000,1.09670000,0.02446000,Br,−17.21626000,0.12784000,0.02504000,H,−14.35292000,−0.68716000,−0.06523000,H,−14.45146000,4.33197000,0.05995000,H,−16.58602000,3.02527000,0.08893000
As above, we can plot the molecular dye tyrian purple
PlotMoleculetyrianpurple ;
We can compute the electronic energy and properties of tyrian purple using computational chemistry (namely, density functional theory (DFT)) (Note that this calculation may take a minute).
GBasis ≔ C:6-31g;H:6-31g;N:6-31g;O:6-31g;Br:sto-6g:tyrianpurple_DFT≔DensityFunctionaltyrianpurple, basis=GBasis;
MODiagramtyrianpurple,method=DensityFunctional,basis=GBasis
HOMO ≔ roundaddtyrianpurple_DFTmo_occ2; LUMO ≔ HOMO+1; pHOMO ≔ DensityPlot3Dtyrianpurple,tyrianpurple_DFT,orbitalindex=HOMO,basis=GBasis,densitycutoff=0.001: pLUMO ≔ DensityPlot3Dtyrianpurple,tyrianpurple_DFT,orbitalindex=LUMO,basis=GBasis,densitycutoff=0.001: plots:-displayVectorrowpHOMO,pLUMO;
HOMO≔102
LUMO≔103
(b) Compare the HOMO and LUMO orbitals of tyrian purple with those of indigo. Are they similar in pattern?
spectra_tyrianpurple_b3lyp ≔ ExcitationSpectratyrianpurple,method=DensityFunctional,basis=GBasis, nstates=3,3,showtable:
1.18482603eV
1046.43377112nm
0.01063373
1.46300077eV
847.46501988nm
0.42879167
2.46467321eV
503.04517781nm
5.64622357×10−7
2.59177389eV
478.37582495nm
0.30183798
2.93685950eV
422.16591357nm
1.77823855
2.94297131eV
421.28918132nm
0.00001806
(c) Has the transition between the ground singlet state and an excited singlet state (State 4) changed from indigo? Approximately what color is absorbed by the dye? (Hint: Use the Maple applet below)
The calculations reveal how a change in structure translates into a change in the excitation spectra and hence, a change in the color of the dye.
1. Christie, R. The Physical and Chemical Basis of Colour. In Colour Chemistry. 2nd Ed. Royal Chemical Society: Cambridge. 2001. pp. 12-21. 2. Stockman, A., MacLeod, D. I., & Johnson, N. E. (1993). Spectral sensitivities of the human cones. Journal of the Optical Society of America, A, Optics, Image & Science, 10(12), 2491–2521.
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