Electronic Spectra of Cyanine Dyes
Timothy Pillow
Abstract
Cyanine Dyes are excellent molecules for illustrating applications of the one-dimensional
particle in a box model. In this experiment we used 4 cyanine dyes and measured their
absorbance using Ultraviolet-visible spectroscopy (UV-Vis). We were able to compute the
length of double bonds in our conjugated cyanine dyes, as well as the length of the molecule
(box length). Furthermore, using both the box model and computational software, we could
predict HOMO and LUMO energy levels for each of the molecules. It was found that theoretical
approximations for HOMO and LUMO energy levels were more accurate for the longer
conjugated chain molecules (within 2%) and were less accurate for shorter molecules (37%
error). Theoretical predictions for the conjugated double bonds differed by 25% from
experimental results and by 23% when predicting the length of the box.
Introduction
In this experiment we investigate how 4 conjugated Cyanine Dyes differ in their electronic
spectra, and how well a particle in a box model can model their energies, wavelengths and
length of conjugated pi bonds within the molecule. We will also incorporate computational
basis sets in order to compare our theoretical model with HOMO and LUMO energy levels as
calculated on computers.
The Dyes in question within the experiment are 3,3-Diethylthiacyanine iodide (thiacyanine),
3,3’-Diethylthiacarbocyanine iodide (thiacarbocyanine), 3,3’-Diethylthiadicarbocyanine iodide
(thiadicarbocyanine) and 3,3’-Diethylthiatricarbocyanine iodide (thiatricarbocyanine). The
general structure of the Dyes is shown below in Fig 1. The only difference between the
molecules is the length of their conjugated chain where ‘k’ represents the number of double
bonds in addition to the double bond adjacent to the Nitrogen with a lone pair. The total
length of the conjugated chain is given by 5+2k.
Fig 1. General structure of Cyanine Dye molecules.
Thiacyanine (k=0) ; Thiacarbocyanine (k=1) ;
thiadicarbocyanine (k=2) ; Thiatricarbocyanine (k=3)
To use the particle in a box model we must assume that an electron can move freely within a
box. Our “box” is the conjugated chain between each Nitrogen on the molecule and is said to
have length ‘b’. We will assume that the average length of each bond in the chain has a length
of 144pm and a bond angle of 120°. When we know the length between 2 atoms such as C1
and C2 (j) and the distance between C2 and C3 (k) then we can calculate distance between C1
and C3 using the cosine rule:
j
k
𝑤 = √𝑗 2 + 𝑘 2 − 2(𝑗)(𝑘)cos(120)
Since we are assuming the average length of bonds is 144pm we assume that j=k=144pm.
Incorporating bond angle we can calculate ‘w’, (defined as w = j+k):
√1442 + 1442 − 2(144)(144)cos(120) = 144√3 ≈ 249pm
Therefore 249pm represents the length of each –CH=CH- group (‘a’) in our conjugated chains
and there is a total of (k+1) of these. When you include the length of 2 N-C bonds, and the
additional =C- group that is adjacent to the lone pair Nitrogen we must add an additional length
length ‘b’ of approximately 450 – 600pm to the length of our box.
The total length (L) of our box is therefore:
𝐿 = 𝑎(𝑘 + 1) + 𝑏
(1)
The allowed energies of the Schrodinger Equation and for our particle in a box are:
(2)
Where me = mass of electron, n = quantum number, h = plank’s constant
The wave function that corresponds to these energies is:
(3)
Equation (3) can be easily graphed in a program like Wolfram Mathmatica (Fig 2) where the
wave (red) and it’s corresponding density function (blue) can be seen for varying quantum ‘n’
levels. The graph below is an example of the wave function with a quantum number of 5.
Fig 2.Example of a graphed wave function with the wave function in red
and the density function (squared) in Blue.
The Energies of the HOMO and LUMO energy levels are given in equations (4) and (5)
respectively below:
(4)
(5)
The transition energies between different quantum levels is simply the difference between
equation (5) and (4) and can be simplified to:
(6)
We know that transition energy in equation (6) is also equal to hcv where c is the speed of light
and v is the frequency. Therefore setting equation (6) equal to hcv and solving for frequency we
have:
(7)
Wavelength is simply the inverse of frequency, so our final important result is the inverse of (7):
(8)
One of our main experimental goals is to determine the constants ‘a’ and ‘b’ in (1) from our
data. We will then compare these to our calculated approximations of bond length and box
length. Using the equations shown above we can also compute theoretical HOMO and LUMO
energies and because we know the allowed energies in (2) we can subsequently see which
quantum number is associated with each HOMO and LUMO energy level. Equation (8) will allow
us to compare theoretical wavelengths at λMAX with our experimental λMAX values. Finally, using
Gamess computational software, we were able to run energy calculations for the HOMO and
LUMO states of the 4 molecules in question and then determine the transition energies and
compare to theoretical predictions.
A final calculation we were able to perform is finding the Einstein coefficient which is a
mathematical probability of absorption of emission of light by an atom and is defined below:
(9)
Where ε = molar absorptivity, c = speed of light, v = frequency in transition and NAV = avagadro’s
number.
From beer’s law we know that absorbance = c L ε where c = concentration, L = path length and ε =
molar extinction coefficient. If we integrate Absorbance with respect to v we get the following result:
∫ 𝐴𝑑𝑣 = ∫ 𝐶 𝑙 ε dv
Therefore we can solve for ε dv (the area under our graphs in results):
∫ 𝐴𝑑𝑣 =
∫ ε dv
(10)
𝑐𝑙
Combining the integration of our area under graphs (10) with (9) we can easily calculation the
Einstein coefficient since all the other symbols in (9) are known, except v which is easiely
calculated from (7).
Method
A Biospec-1601 UV-Vis machine using UV Probe 2.21 (Software) was used to collect and analyze
data. Scans were run from 800nm and ended at 300nm. The scanning speed for the machine
was set to fast with a sampling interval of 0.1. The scan mode was set to repeat with 5
repetitions (scans) for each sample. In our data analysis, we took the average of all 5 scans for
each of the 4 dyes to analyze. The slit width in the machine was fixed at 2.0nm and a normal
S/R exchange was used. All samples used had a concentration of approximately 1x10 -5 M. On
average, each scan using the machine took 2mins 35secs.
When performing computational calculations we initially used a Hartree-Fock method with a
3-21G basis set. We then tested a more complex 6-31G(d,p) basis set using a Density Functional
method (B3LYP) to determine transition energies between HOMO and LUMO. Using the more
complex basis sets took 2hrs 10mins on average to run whilst a 3-21G basis calculation took
only 5mins. Allocation of enough memory to the Gamess engine was important in preventing
failed computations for the more complex basis sets. After successful completion of these
calculations we performed another Hartree-Fock calculation using a 6-311++G(2d,p) basis set.
This calculation took just over 23 hours to run but completed successfully for the thiacyanine
molecule. Subsequent calculations using the same method on the other dyes all failed due to a
computer crash. All calculations were performed by Gamess with input files created using the
Gamess extension in Avagadro. The settings for all Avagadro input files were set to single point
energy calculations, in gas, with singlet multiplicity and a cation charge.
Results
Graph 1 – Absorbance v wavelength with Gaussian Fits overlayed
Graph 2 – λmax values plotted against ‘k’ with a fit attempted using using (8) with (1) substituted in to find ‘a’ and ‘b’ lengths
Graph 3 – Gaussian Fits
Fig 2
Gaussian Fitting Parameters
**REST OF RESULTS ARE AT END OF PAPER**
Our results in Graph 1 show that the Gaussian fits mimic the behavior of our absorption graphs
quite well, although shifting the fits to the right slightly would overlay them even better. The
exact Gaussian fitting parameters used can be seen in Fig 2. Graph 2 is the result of plotting
our λmax values for our dyes against their respective k values. From this, we were able to create
a fit using wavelength equation (10) (with equation 1 substituted in for ‘L’). The box within
Graph 2 shows the fitting parameters found calculated using software (Igor Pro). The fitting
parameters of of m, h and c show no indeterminate error ( ±0) because these are known
constants and were held constant during the fitting. The box in Graph 2 shows that ‘a’ is
calculated at 200.83pm and ‘b’ as 677.55pm. Graph 3 shows the Gaussian fits alone to aid in
visual comparison with Graph 1 and allows the reader to see the general shape of each dye’s
absorption. Table 1 and Table 2 show the HOMO and LUMO energy calculations respectively
with their differences shows in Table 3. For the computational HOMO energies the DFT 631G(d,p) basis set consistently gave energies closest to theoretical values. It also matched
theoretical energies best for the LUMO as well, with the except of the thiacyanine molecule,
which the Hartree-Fock 6-311++G(2d,p) predicted closer to the theoretical value. Table 4
shows theoretical wavelengths and frequencies which can be compared to Table 7 showing the
experimentally measured wavelengths and the percent different between experimental
wavelengths and theoretical wavelengths in Table 4. After finding the fitting parameters in
Graph 2 which show the fits predictions for lengths ‘a’ and ‘b’, we were able to plug in these
into (4) and (5) to re-calculate HOMO and LUMO energies respectively and evaluate the
difference between HOMO and LUMO values calculated using our theoretical guesses. The
results can be seen in Table 5 and Table 6. The percent difference between predicted HOMO
and LUMO energies is about the same each molecule. Our Einstein coefficients were calculated
using (9) and (10) whereby we first calculated Einstein coefficients by integrating the space
under our raw UV-Vis graphs. We then calculated the coefficients by integrating the space
under the Gaussian curves for comparison sake. It can be seen in Table 8 that the area under
the Gaussian curves mimics closely the area under the UV-Vis graphs. This is because the
percent difference between the coefficient by the two methods is relatively small (<10%) with
the exception of the thiatricyanine molecule which has a percent difference of almost 20%.
Discussion
The experiment was performed successfully and our data analysis shows results for
determining ‘a’ and ‘b’ lengths were not too different from our theoretical predictions. The
length of the conjugated double bonds ‘a’ were determined as 200.83pm and the length of the
“box” ‘b’ was determined at 677.55pm, these are both within 22-25% of our theoretical values.
Graph 2 shows that although the plots of k vs max absorbance did not give a perfectly linear
line, our line fit using (8) fit the data points well and produced a line of best fit successfully
which makes us confident in our determination of ‘a’ and ‘b’, furthermore the error of
uncertainty for ‘a’ and ‘b’ calculated by Igor Pro shows that uncertainty is within 2-5 x 10-11
meters for both.
Graph 1 shows that Gaussian fits mimic the transition behavior of our HOMO to LUMO energy
levels well, as demonstrated by their close fit to the peak of each molecule’s spectrum.
However, it can also be seen in Graph 1 that each molecule’s spectrum shows another less
defined peak to the left of each λmax peak. These other peaks are suspected to be other
transitions occurring. Likewise, because these less defined transitional peaks occur at slightly
lower wavelengths, they have higher frequencies and thus higher energies. These other
transitional peaks are thus electrons moving to higher energy orbitals above the HOMO and
LUMO.
When determining the Einstein Bmn coefficient we had to integrate the area under our graphs.
Part of the error inherent in this integration is counting the area under the less defined
transitional peaks as well. Since it is not possible to separate our λmax peak from the transitional
peak because they are overlaid on one another, we suspect integration values may be slightly
higher than their correct theoretical value. However, since our Gaussian fits were aligned closer
to our λmax peaks than the transitional peaks, then the area under our Gaussian fits mostly
ignores the area under transitional peaks, and may actually offer more accurate Bmn coefficient
predictions after integrating. Table 8 shows that the percent difference between Bmn calculated
using Gaussian integration vs raw spectra data is actually quite small (2%) for the thiacyanine
dye, but percent difference increase as we increase the length of the conjugated chain. This
makes sense because with a larger molecule there is a bigger margin of error. The error for
thiatricarbocyanine has the largest error in Table 8. We suspect part of this error is from the
data available to analyze; it can be seen to the far right of Graph 1 that the thiatricarbocyanine
spectra stops at 800nm even though it is clear that the spectra continues. This part of spectra is
not shown is the result of a human error when exporting the data from the UV-probe software.
This part of the spectra was also not integrated and may contribute largely to the error in B mn
of thiatricarbocyanine.
Computational estimations of HOMO and LUMO levels were convenient in creating data for
comparing to our theoretical predictions. DFT 6-31G(d,p) calculations gave the closest values to
theoretical (for HOMO and LUMO) with HF 6-311++G(2d,p) calculations giving the second
closest. Despite HF 6-311++G(2d,p) taking the longest to run (23 hours) the results were not
significantly better or closer to theoretical than the density functional theorem calculations
(which took only a few hours). We suspect this is because the Hartree-Fock reaches its
maximum capability for predicting HOMO and LUMO levels using even moderately complex
basis functions. Using the most complex basis set we could rendered results that were not
significantly better and used considerable time and resources, which were arguably
unnecessary.
Using Avagadro we were able to measure the length of ‘a’ and ‘b’ using energy minimizations of
the molecules. Avagadro predicted ‘a’ and ‘b’ values (in picometers) respectively for the
following molecules: thiacyanine: 175.0 & 577.5; thiacarbocyanine: 135.4 & 537.9;
thiadicarbocyanine: 134.3 & 782.1; thiatricarbocyanine: 140.4 & 1184.6. These all match within
100pm of our theoretical predictions for ‘b’ and within 25pm for ‘a’. None of the ‘a’ values
match very closely with the 149ppm as originally predicted by ‘a’. This may be due to
limitations of the computational software or because we originally took an average bond length
when originally predicting ‘a’. Interestingly, our slightly larger theoretical predictions for ‘a’ are
closer to our experimentally determined ‘a’ of 200pm. Since both our theoretical prediction and
experimental result for ‘a’ are larger than what was calculated in Avagadro, we conclude that
Avagadro’s predictions are likely to short for bond lengths.
Our particle in a box model failed to correctly predict wavelengths. It can be seen in Table 7
that wavelength predictions were generally off by 25-35%. However, it can be seen in Table 7
that the error from theoretical predictions got less as the length of the conjugated dye
increased (larger k). If we were to repeat this experiment, it would be interesting to test even
longer conjugated Dyes to see if the box model only works correctly for molecules bigger than a
certain length. For our experiment, the limited data and lack of molecules tested does not allow
us to conclude that the particle in a box model fails for these dyes indefinitely though.
References
George M. Shalhoub , Visible Spectra Conjugated Dyes: Integrating Quantum Chemical
Concepts with Experimental Data , Journal of Chemical Education 1997 74 (11), 1317, DOI:
10.1021/ed074p1317
Hardwick, John. Physical Chemistry Laboratory, University of Oregon, 61-66, 2015. Print.
Willemsen, Connor. Modelling of Cyanine Dyes, University of Oregon, 2015
Acknowledgments
John Hardwick
Kelly Wilson – Giving advice on things to include within this report and explaining the other
transitions occurring within our spectra.
Regina Ciszewski – Explaining equation (10) and answering questions about Einstein Coefficent.