Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy February 15, 2016 We ll correlate the absorbance maximum of a series of dyes with structural changes between them 1. Chemicals absorb light through electronic transitions, and dyes chemicals that absorb light in the visible region of the electromagnetic spectrum often do so through electronic transitions in π-bonding regions of the molecule. A series of polymethine dyes has been chosen such that the only difference is the length of the conjugated carbon chain connecting the two ring structures (See figure 1, left). We ll work with a simple quantum mechanical model that captures the changes in energy spectrum due to changes in a length dimension. N + R N 4 E=E 4 - E 3 The three dyes are: 1,1 -diethyl-2,2 -cyanine 1,1 -diethyl-2,2 -carbocyanine -R= for each dye is: -CH= -CH=CH-CH= E n = n2 h 2 8mL 2 3 2 n = 1 1,1 -diethyl-2,2 -dicarbocyanine -CH=CH-CH=CH-CH= Figure 1. Left: The structure of the cyanine cation dye we re modeling and the list of specific dyes. Right: The particle-in-a-box energy spectrum for the cyanine dye (R=CH, N = 6). The six electrons pair up following the Pauli Exclusion Principle, and the ground state is n = 3. Visible light of energy E can be absorbed through electronic transitions between the n = 3 to 4 states. A free-electron model for π-electrons We can use a simple quantum mechanical model for regions of delocalized π-electrons by applying the following assumptions. First, lets assume that the structure of the dye is determined by the network of σ-bonds. Since σ- bonds don t begin to absorb until far into the UV, we should be able to neglect them for analysis of absorption in the visible. Second, we ll assume that the π-electrons are free to move along the length of the conjugated region. For now, lets consider the conjugated region of interest to be between the two nitrogens, so for the carbocyanine dye, this would be the -:N-C=C-C=C-C=N+- chain. The one-dimensional particle in a box is a very simple quantum mechanical model that describes free motion within a confined region. A particle in a box feels no forces and moves at a constant velocity. Eventually it hits a wall through which it cannot (i.e. encounters a region with infinite potential energy), and it turns around abruptly and sharply to remain in the potential-free region. Think on this: Compare a free particle in a one-dimensional box with an actual delocalized electron moving along
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 2 a chain of positively charged atoms with σ-electrons. How potential-free do you think the electron really is? How sharply and abruptly we expect an actual electron to turn around? From quantum mechanics, the allowed energies of a particle in a box of length L is E n = n2 h 2, n = 1, 2, 3,... (1) 8mL2 where m is the mass of the electron (9.109 10 31 kg), h is Planck s constant (6.626 10 34 J s), and n is the quantum number of the state. The lowest allowed state is found by choosing n = 1, and higher-energy states are found at larger n. To apply this model, we ll populate the energy spectrum predicted by equation 1 with π-electrons following the Pauli Exclusion Principal. For example, the cyanine dye has 6 electrons in the conjugated region 1 from each of the three carbons, 1 from one nitrogen, and 2 from the other nitrogen, and the ground state corresponds to n = 3. This is illustrated in figure 1, right. More generally, the ground state of a conjugated chain with N π-electrons is n = N 2. The first electronic absorption corresponding to the lowest energy electronic transition is from the filled N 2 level to the empty N 2 +1 level. The energy of light absorbed by this transition is E = E N 2 +1 E N 2 ( (N ) 2 = h2 8mL 2 2 + 1 ( ) ) N 2 2 = h2 (N + 1) 8mL 2. (2) Using E = hc λ, the expression for the wavelength of this transitions is λ = 8mcL2 h (N + 1) (3) where c is the speed of light (3.00 10 8 m s ). Lets start to use some of the structural features of our dyes to make equation 3 more useful as a model. Let p be the number of atoms in the nitrogen-carbon-nitrogen chain. The number of π-electrons is then N = p + 1. If we assume that all the C C and C N bonds are the same length d, the distance between the nitrogens would be d (p 1). It s probably not appropriate to assume that the conjugated system ends at the nitrogens, so let s include a factor f allowing for additional bond lengths extending into the rings beyond the nitrogens 2. Using the terms p, d, and f, our length becomes L = d (p 1 + 2f). Note that f is dimensionless; it can be interpreted as the fractional part of a bond (or multiples of bonds) that is added on each end of the chain due to the extent of the π-cloud. This extent should remain constant through our series of dyes which have identical ring structures capping the conjugated
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 3 chain. Substituting these definitions of L and N, equation 3 can be rewritten λ = 8mcd2 (p 1 + 2f) 2. (4) h (p + 2) The best values for the parameters d and f can be found by directly fitting equation 4 to your data, or equation 4 can be rearranged as 8mc λ (p + 2) = d (p 1 + 2f). (5) h A plot of 8mc λ (p + 2) versus p should give a straight line with a slope of h d and an intercept of 8mc h d (2f 1). Procedure 1 mm Methanol solutions of the three dyes have been prepared. Take a moment to appreciate the beautiful colors of the dyes as you set up a UV-vis spectrometer. Accurately measure the peak wavelength in the visible. For some of the dyes you may a smaller peak on the blue side of the major peak. This absorption is due to the presence of a low concentration of dye-dimers, and can be disregarded. In the Schupf Lab, follow the instructions in the appendix to use Gaussian and GaussiView to determine the minimum energy structure, to visualize the HOMO and LUMO densities, and to obtain predicted absorbance maxima using a different quantum mechanical model. What to include in your lab summary due next week We ll generate an R script to work up your data using equations 4 to determine d the approximate C C and C N bond lengths and f the fractional d distance that the π cloud extends beyond the end of the chain that are most consistent with your data. Briefly report the following: Report your values for d and f. Consider how d compares to bond-lengths from literature. Relate your f value to the structure of the dyes. Calculate the peak absorption wavelength for the next dye in this series (quinotricarbocyanine, =CH-CH=CH-CH=CH-CH=CH-) and predict its color. Compare that prediction to the absorbance maximum from literature. Use error propagation d and f to get an error on your predicted wavelength. Report your values for L for the carbocyanine dye as well as the N-N distance predicted by your fit model. Compare this N-N distance to the distance you d predict using bond lengths for C-C bonds and N-C bonds from bond-tables, citing your sources. Consider how well the model is working and how you may have to reinterpret the d parameter to better capture the structure of the dyes. Use error propagation d and f to get an error on the L and N-N distances. Note, too, that f is also simply an empirical fudge parameter that improves the fit of the model to the data.
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 4 Compare your value for d to measurements of the minimum energy configuration from the Gaussian calculations. Use the orbital densities of the HOMO and LUMO to discuss the interpretation of f and the accuracy of this interpretation. Briefly summarize your thoughts on the validity of the approximations made in the development of the PIB model used in this lab. Include either a composite figure or a series of figures that that show 1) all three absorption spectra, 2) a plot including your experimental data and the best fit to your experimental data, and 3) the HOMO and LUMO orbital densities. Include a table comparing the HOMO-LUMO gap predicted by the Gaussian calculations to your experimental absorbance maxima. References 1. Shoemaker, D. P.; Garland, C. W.; Steinfeld, J. I.; Nibler, J. W. Experiments in Physical Chemistry, 4th ed.; McGraw-Hill: New York, 1981; pp 412-417. 2. Suggested in: Hollingsworth, W.; Ferrett, T. Manual for Advanced Lab I: Spectroscopy; Carleton College: Northfield, MN, 2002; ch 2.
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 5 Appendix: Gaussian calculations This lab is a good opportunity to compare our experimental and particle in a box model results to some electronic structure calculations. This appendix will walk you through the steps of running these calculations using Gaussian. Unlike in your previous courses, we ll run Gaussian from the command line following steps you would follow to run a Gaussian calculations on a off-site super computer. You ll be assigned a dye and an initial orientation of the two rings or the ethyl groups. Open terminal, and enter the following commands in in his order hitting. return after each. Log on to the schupflab computer. You ll need to type yes and enter your password. Change your current directory to the directory we ll run in today. Make a directory for your job. Use CH1 if you re running the dye with one carbon in the N-C-N chain, CH3 for the carbocyanine dye, and CH5 for the dicarbocyanine dye. Append the dye name with your own initials. Structure files that can be opened by GaussView can be found in the PIBdyes folder on schupflab. Open GaussView to set up your input file. Use GaussView to open the pdb file for your assigned structure. Play around with your mouse to manipulate the molecule you should be able to zoom and rotate the molecule. Use the Modify Dihedral Tool ( ) to adjust the dihedral angles to match your assigned geometry. Once you have the approximate initial geometry, go to Calculate. Gaussian Calculation. Setup.... Under the General. tab, unclick Write Connectivity and Write PDB Data. Click Submit...., and save the file as gap.com to your folder (e.g. ) on schupflab. HIT CANCEL ON THE NEXT WINDOW! Open your gap.com file using TextWrangler s. File. Open from FTP/SFTP Server.... In server enter schupflab, entering your Colby username and password and checking the box for SFTP. Also open the example.com file in the folder. Edit gap.com using the information from example.com to like this:
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 6 Note: We re using the semi-empirical PM6 method, because it will give us fast results. Generally, you ll want to use a higher-level method for your own work. Save the edited gap.com file. You ve generated a file that Gaussian will read and perform a calculation in two steps. The first step is to find the minimum energy configuration for the molecule, and the second step is to calculate the energies of 6 additional electronic states for the minimum energy configuration. Back in terminal, change your current directory to your directory. Make sure your input file is in there. Look at the contents of the script we ll use to run Gaussian Run Gaussian in the background. Run top to verify your job is running. Hit to exit top. This should take about an hour. During this time we ll generate best fits to equation 4. After the jobs are done running, we need to find the structure of each dye with the lowest energy. We ll use the lowest energy structure to determine the wavelength of the first excited state corresponding
Modeling the UV-Vis Absorption of a Series of Dyes CH342L: Spectroscopy 7 to the absorbance maximum of that dye. Look for the last in in the gap.log output file that contains SCF Done:. The energy is given on this line in units of Hartrees. For the lowest energy structure for each dye, find the line in the log file that contains Excited State 1:. This is the energy from the ground state to the first excited state. Pick a dye and for the lowest-energy structure open the checkpoint file (gap.chk) in GaussView. Click on the MO Editor Tool ( ). Click the Visualize. tab and visualize the HOMO and LUMO with a fine grid using Add Type and the Update. button. Control buttons will appear next to the HOMO and LUMO in the list of orbitals in the top right corner of this window allowing your to toggle back and forth between the HOMO and LUMO densities. You can close the MO Editor window and open the Results. Surfaces/Contours. window to show the HOMO and LUMO in separate visualization windows. Take a screen shot of each cmd. + shift. + 4.. I ll go over another option for visualizing orbitals for a better-looking figures using Visual Molecular Dynamics at the end of lab.