Absorption Spectrum of a Conjugated Dye

Abstract:

The highly conjugated system of cyanine dyes makes these compounds good candidates

for labeling of biomacromolecules for diagnostic purposes or for the development of more efficient

solar cells. In this experiment, the suitability of a simplified model of a particle-in-a-box to predict

the wavelength of maximum absorbance is analyzed. The spectrum of six cyanine dyes was

recorded and compared to the predicted wavelength of maximum absorbance. The results

indicated that the model proposed by Kuhn is appropriate for the two dyes with less polarizable

end groups, 1,1’ diethyl-4,4’-carbocyanine iodide and 1,1’-diethyl-4,4’-cyanine iodide, but required

the adjustment of an empirical parameter α to 0.675 to provide more reliable predictions for 3,3’-

diethylthiatricarbocyanine iodide, 3,3’-diethylthiacyanineiodide, 3,3’-diethylthiacarbocyanine iodide

and 3,3’-diethylthiadicarbocyanine iodide. General trends such as lower separation between the

highest occupied molecular orbital and the lowest unoccupied molecular orbital were observed with

increasing conjugation across the two series of dyes, while the series with the more polarizable

end groups absorbed higher wavelength light than the corresponding dyes with less polarizable

end groups indicating the contribution of the end group to extending the one-dimensional box.

Kuhn’s free electron model proved reasonably reliable for this system.

Introduction:

The highly conjugated electron system in polymethine dyes allows these compounds to

absorb light in the visible region of the electromagnetic spectrum. Carbocyanine dyes contain

variable length chains of methine carbons and two heterocycles that can act both as electron

donors and as electron acceptors. Polymethine carbocyanine dyes can have applications ranging

from the development of solar cells and heat absorbers to use as labels for biomacromolecules

such as DNA and protein. 1, 2, 3

This experiment will use a model proposed by Kuhn in which the conjugated π electron

system of the dye is modeled as a particle-in-a-box to predict the wavelengths of maximum

absorbance in a series of conjugated carbocyanine dyes.4 Each conjugated dye molecule is

considered a one-dimensional box of length L with an energy level given by

E = h2n2

8mL2 (1)

where h is Planck’s constant, n is the quantum number and m is the mass of an electron. The Pauli

exclusion principle allows only two electrons to occupy each energy level which means that a

system with N π electrons will have the lower n1=N/2 levels filled and the remaining levels empty.

When the dye molecule absorbs radiation an electron will be promoted to the lowest unoccupied

level n2=N/2+1. The energy change of this transition is

ΔE=h2(n2

2−n12)

8mL2=h2 (N+1 )8mL2

(2)

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with a wavelength

λ= 8mc L2

h(N+1) (3)

where c is the speed of light.

Using the number of π electrons N=p+3 and the length of the one dimensional box L=(p+3)l, where

p is the number of carbon atoms on the methine chain and l is the known bond length of a benzene

molecule equation 3 can be rewritten as

λnm=8mc l2( p+3+α)2

h( p+4)=63.7¿¿ (4)

where l=0.139 nm and α is a constant for a series of dyes. The parameter α is used when dyes

have polarizable end groups, which lengthen the box.

Experimental procedure:

The following polymethine dyes were dissolved in methanol to give dilute solutions: 1,1’-

diethyl-4,4’ carbocyanine iodide, 1,1’-diethyl-4,4’ cyanine iodide, 3,3’-diethylthiatricarbocyanine

iodide, 3,3’-diethylthiacyanine iodide, 3,3’-diethylthiacarbocyanine iodide and 3,3’-

diethylthiadicarbocyanine iodide. The solutions were made dilute enough so that the color could be

perceived and the absorbance spectrum to have a smooth maximum with an absorbance below 1

AU. Absorbances were measured between 300 and 1000 nm using an Ocean Optics HR 4000CG-

UV-NIR High Resolution Spectrometer with 1.0 path length quartz cuvettes and methanol as a

blank.

Results:

Wavelengths were calculated using equation 4 and compared to the experimentally

observed wavelengths. When calculated wavelengths differed drastically from the observed ones,

a nonzero parameter α was used. For 1,1’-diethyl-4,4’-carbocyanine iodide the observed

wavelength was equal to the calculated one 706 nm. For 1,1’-diethyl-4,4’-cyanine iodide the

predicted wavelength, 579 nm was reasonably close to the observed 588 nm with 1.5% error. For

the dyes containing the sulfur and nitrogen heterocycles, the predicted wavelengths included a

parameter α. Equation 4 was used for determining one value for α using each of the known

observed wavelengths and then averaging the four values. After the average α was determined, it

was used in equation 4 to get the theoretical wavelengths. This approach minimized the percent

difference between the calculated and the observed wavelengths to less than 5.0%. The observed

wavelengths for 3,3’-diethylthiatricarbocyanine iodide, 3,3’-diethylthiacyanine iodide, 3,3’-

diethylthiacarbocyanine, 3,3’-diethylthiadicarbocyanine were 757, 423, 556 and 652 nm respectively, while

the wavelengths predicted by the free-electron model were 787, 405, 532 and 660 nm.

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Table 1. Calculated and observed wavelengths for 1,1’-diethyl-4,4’-carbocyanine, 1,1’-diethyl-4,4’-carbocyanine 3,3’-diethylthiatricarbocyanine iodide, 3,3’-diethylthiacyanine iodide, 3,3’- diethylthiacarbocyanine, 3,3’-diethylthiadicarbocyanine.

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Dyeλobserved

(nm)λcalculated

(nm)Percent difference between

λcalculated and λobservedα

1,1’ diethyl-4,4’-carbocyanine iodide

706 706 0 0

1,1’-diethyl-4,4’-cyanine iodide

588 579 1.5 0

3,3’-diethylthiatricarbocyanine iodide

757 787 4.0 0.675

3,3’-diethylthiacyanine iodide

423 405 4.3 0.675

3,3’-diethylthiacarbocyanine iodide

556 532 4.3 0.675

3,3’-diethylthiadicarbocyanine iodide

652 660 1.2 0.675

Figure 1. Absorption spectra of 1,1’ diethyl-4,4’-carbocyanine iodide (blue), 1,1’-diethyl-4,4’-cyanine iodide (red), 3,3’-diethylthiatricarbocyanine (green), 3,3’-diethylthiacyanine iodide (purple), 3,3’diethylthiatricarbocyanine (cyan) and 3,3’diethylthiadicarbocyanine iodide (orange).

Figure 1 shows the absorbance spectra of the six conjugated dyes. There is a general

increase in the wavelength of absorbance with an increase in the number of carbon atoms in the

methine chain with the lowest wavelength of absorbance corresponding to the dye with the

shortest methine chain (p=3), 3,3’-diethylthiacyanine iodide and the longest wavelengths

corresponding to the dyes with the longest methine chains (p=9), 1,1’-diethyl-4,4’-carbocyanine

iodide and 3,3’-diethylthiatricarbocyanine iodide. The first series of dyes, 1,1’ diethyl-4,4’-

carbocyanine iodide and 1,1’-diethyl-4,4’-cyanine iodide had lower wavelengths of absorption, 706

and 588 nm respectively, than the dyes with the same number of methine carbon atoms in the

second series, 3,3’-diethylthiatricarbocyanine iodide and 3,3’-diethylthiadicarbocyanine with 757 and 652

nm, respectively. Some of the dyes, 3,3’diethylthiatricarbocyanine, 3,3’diethylthiadicarbocyanine

iodide and 3,3’-diethylthiatricarbocyanine present a small shoulder at a lower wavelength.

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Figure 2. Wavelength of maximum absorbance (nm) as a function of the number of carbon atoms in the polymethine chain in 1,1’-iethyl-4,4’-carbocyanine iodide and 1,1’-diethyl-4,4’-cyanine iodide.

Figure 2 shows a positive correlation between the number of carbon atoms in the first

series of dyes consisting of 1,1’-diethyl-4,4’-carbocyanine iodide and 1,1’-diethyl-4,4’-cyanine

iodide with the longer wavelength corresponding to the dye with the longer methine chain.

Figure 3. Wavelength of maximum absorbance (nm) as a function of the number of carbon atoms in the methine chain of 3,3’-diethylthiatricarbocyanine, 3,3’-diethylthiacyanine iodide, 3,3’diethylthiatricarbocyanine and 3,3’diethylthiadicarbocyanine iodide.

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Figure 3 shows a positive correlation between the wavelength of maximum absorbance and

the number of carbon atoms in the second series of dyes consisting of 3,3’-

diethylthiatricarbocyanine, 3,3’-diethylthiacyanine iodide, 3,3’diethylthiatricarbocyanine and

3,3’diethylthiadicarbocyanine iodide, with the longest wavelength (757 nm) corresponding to the

longest conjugated system, 3,3’-diethylthiatricarbocyanine iodide.

Discussion:

Analysis of two series of dyes using the free electron model proposed by Kuhn allowed for

observation of a more accurate model than the bond-orbital and molecular-orbital calculations

previously used on these compounds. Assuming that the potential energy along the methine chain

is constant and that it rises drastically at the ends of the box replaced the π electron system with

free electrons moving in a one-dimensional box, which led to a simple formula for a predicted

wavelength.

The first series of dyes, 1,1’-diethyl-4,4’-carbocyanine iodide and 1,1’-diethyl-4,4’-cyanine

iodide had predicted wavelengths in good agreement with the experimental ones even without

adjusting the parameter α. According to the absorbance spectra, Figure 1, and Figure 2 there is a

positive correlation between the number of carbon atoms in the conjugated π system and the

wavelength of absorbance. A longer wavelength, corresponding to a lower energy transition is

correlated with the compound with a longer methine chain, which indicated that the separation

between the highest occupied molecular orbital and the lowest unoccupied molecular orbital is

smaller for the larger conjugated π system of 1,1’ diethyl-4,4’-carbocyanine iodide. The accuracy of

the predicted wavelength without the use of α suggests the end groups on these two dyes are not

as easily polarizable as the ones in the other type of dyes.

The second series of dyes required the use of a correction parameter α because of the

polarizability of the end groups. After an average α of 0.675 was calculated from the observed

wavelengths and then used to obtain theoretical wavelengths, the theoretical and experimental

data differed by less than 5%. The value obtained for α is in close agreement with the value

reported by Farrell for the same series of dyes.5 The longer the conjugated system, the lower the

energy of the light absorbed by the molecule was with 3,3’-diethylthiatricarbocyanine iodide having the

longest wavelength followed by 3,3’-diethylthiadicarbocyanine, 3,3’-diethylthiacarbocyanine and 3,3’-

diethylthiacyanine iodide.

Across series, the dyes containing the sulfur and nitrogen heterocycles had transitions with lower

energies than the dyes with the same number of carbon atoms in the other series, which indicates that the

more polarizable end groups add to the stability of the conjugated system to give lower energy transitions.

The appearance of bands as opposed to sharp peaks is related to the fact that in molecular orbitals a change

in an electronic transition is often accompanied by rotational and vibrational changes, thus leading to the a

wider signal.

The shoulders present in addition to the peak of maximum absorbance for

3,3’diethylthiatricarbocyanine, 3,3’diethylthiadicarbocyanine iodide and 3,3’-

diethylthiatricarbocyanine may be an indicator of some dimerization of the compounds in solution.

The resolution of the spectrometer used is as precise as 0.02 nm, therefore the measured

wavelengths can be considered accurate to the nanometer.

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Conclusion:

Using the Kuhn free-electron model allows for reasonable prediction of the estimated wavelengths of

maximum absorbance in compounds with conjugated π bonds just from the number of carbon atoms in the

methine chain. In this experiment, the visible spectra of six conjugated dyes of two types were recorded and

the wavelength of maximum absorbance was compared to the wavelength predicted by the particle-in-a-box

model. The dyes containing the more polarizable end groups required the use of an empirical parameter α to

account for the lengthening of the box, while the first two dyes had reasonably accurate results without the

use of this parameter. Overall, the free electron model predicted wavelengths are in reasonable agreement

to the experimental ones, which makes this simple model appropriate for conjugated systems such as

cyanine dyes.

Literature Cited:

1. Chamberlain, G.A. Solar Cells 1983, 8, 47-83. Organic solar cells: A review.

2. Southwick, P.L., Ernst, L.A., Tauriello, E.W., Parker, S.R., Mujumdar, R.B., Mujumdar, S.R., Clever, H.A.,

Waggoner, A.S. Cytometry, 1990, 11, 418-430.

3. Mujumdar, R.B.; Ernst, L.A., Mujumdar, S.A., Lewis, C.J., Waggoner, A.S. Bioconjugate chemistry 1993,

4, 105-111. Cyanine dye labeling reagents: Sulfoindocyanine succinimidyl esters.

4. Kuhn, H. J. Chem. Phys. 1949,17, 1198.

5. Farrell, J.J. J. Chem. Educ. 1985, 62, 351-352. The absorption spectra of a series of conjugated dyes.

Determination of the spectroscopic resonance integral.

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