Diphenylpolyene Dye Spectra

Transcription

1 Diphenylpolyene Dye Spectra The purpose of this lab is to interpret uv-visible spectra of three diphenyl polyenes. The uv-visible transitions are compared to a particle-in-a-box model and to transitions calculated using timedependent density functional theory. A molecular vibration frequency is extracted from vibrational structure. Introduction Phenyl-substituted polyenes include stilbene, which has a single Figure 1: diphenyl polyenes C=C linking two phenyl rings; the butadiene, hexatriene and octatetraene polyenes that are the subject of this lab; and longer-chain polyenes. The diphenylpolyenes absorb uv-visible light strongly and fluoresce significantly. In the photo-excited state, they may undergo cis-trans isomerization about the linking polyene, so they have been used to study the fundamentals of isomerization kinetics and to model visual pigments. Absorption and fluorescence spectra of diphenylbutadiene 1 are shown at right. Spectra of the larger polyenes are similar but red-shifted. The evident vibronic structure has been attributed 2,3 to a carbon-carbon stretching vibration that has ag symmetry in the molecule s C 2h point group. We will record diphenylpolyene absorption spectra and then analyze them with two models, the particle-in-a-box model 4,5,6 and the time-dependent density functional (tddft) quantum-chemical method. Figure 2: Wallace-Williams, et al., J. Phys. Chem. 1994, 98, dyespec_tddft.odt 1

2 Theory A simple approximation for an electronic transition is that it arises from transfer of an electron from the highest occupied molecular orbital (HOMO) of the molecule to the lowest unoccupied molecular orbital (LUMO). One theory with which the electronic transitions in diphenyl polyenes have been treated is the particle-in-a-box model 4-6. The electron is the particle and the polyene is the box. The energy difference between states ni and nf is Δ E = (n f 2 ni 2 ) h 2 8m e L 2 (1) Figure 3: box levels where h is Planck's constant ( J s) and m e is the mass of an electron ( kg). If ni is the quantum number of the HOMO, and nf the LUMO, then the energy gap is related to the spectral wavelength by ΔE = h c λ (2) where c is the speed of light, m/s. The simple particle-in-a-box model correctly predicts the most striking feature of diphenylpolyene spectra: they are displaced to longer wavelengths as the length of the polyene increases. The HOMO-LUMO energy gap could also be calculated from semi-empirical or ab initio quantumchemical theories. 7 Equation 2 would still apply. However, considering only the HOMO and the LUMO gives poor results. Excitation wavelengths obtained from many-electron calculations will be poor unless electron-electron correlation is considered. Consequently, we will use the timedependent density functional method (tddft) when calculating wavelengths quantum mechanically. The tddft method 8 is a popular quantum-mechanical method for calculating excitation energies. dyespec_tddft.odt 2

3 During the electronic excitation vibrations may also be excited. If primarily one vibrational mode is excited then the electronic spectrum will consist of several peaks separated by a constant energy difference. The longest-wavelength peak corresponds to no vibrational excitation and is referred to as the 0-0 transition. The energy difference between successive peaks equals the vibrational energy (literally hc ~ ν ) of the excited mode. ~ ν vib = ( 1 λ 01 1 λ 00 ). (3) Figure 4: absorption peaks The vibration frequency obtained from equation 3 actually applies to the first excited state of the diphenylpolyene molecule, S 1 as indicated in the sketch of potential energy surfaces at right. 3 For this particular carboncarbon vibration, the frequency in the S 1 excited state approximately equals the frequency in the S 0 ground state. Figure 5: energy surfaces Reagents and Supplies 5 ml M 1,4-diphenyl-1,3-butadiene in cyclohexane 5 ml M 1,6-diphenyl-1,3,5-hexatriene in cyclohexane 5 ml M 1,8-diphenyl-1,3,5,7-octatetraene in cyclohexane a few ml cyclohexane to rinse cells NOTE: cyclohexane is highly volatile, flammable, and irritating to breathe. Keep solutions and cuvettes covered! Dispose of samples and waste solutions in the proper waste bottle. You will need a transfer pipet to transfer samples from the bottles to the cuvette. A glass disposable pipet will do. You will need one or two clean glass or quartz (not plastic) cuvettes. There may be cuvettes near the spectrometer. dyespec_tddft.odt 3

4 Procedure Retrieve the dye solutions from the refrigerator or the hood. If they are frozen allow them to thaw on the bench top or in warm water. (Cyclohexane solutions thaw quickly.) Spectra may be recorded using the Cary 50 uv-visible spectrophotometer. Instructions for taking spectra with the Cary 50 spectrophotometer If it is not already running, open the Cary WinUV software. Open the Scan program. The program will turn on the Cary 50 uv-visible spectrophotometer. After a minute or two, commands can be given. On the Setup menu, choose the following. On the Cary tab X mode nm range Y mode in Abs from to 0.25 Beam mode double Cycle mode should be unselected Scan speed 200 nm/min On the Baseline tab Baseline correction On the main screen, click the zero button should then be displayed in the upper-left corner. Figure 6: Cary 50 spectrophotometer Place a cuvette (glass or quartz, not plastic) containing solvent (cyclohexane) in the cell holder. Click the Baseline button to record the solvent's spectrum as a baseline. The Cary software will subtract this baseline absorbance from all subsequent spectra. Fill the cuvette with diphenylbutadiene dissolved in cyclohexane. Place it in the sample holder. Click Start to record the spectrum. Use the vertical double-arrow icon to autoscale the y axis. Use Peak labels, with All peaks selected, to label peaks. You may need to label some peaks by hand. To do that, choose the cursor tool by clicking on the diagonal-left green-arrow icon. Move the cursor to a peak. Then use the right mouse button to add a label. You may save a spectrum as a spreadsheet-compatible csv file, as follows. On the File menu, choose Save data as.... Then choose the file type Spreadsheet Ascii (*.csv) and check the Save only focused trace box. Take spectra of the other two dyes in the same way. Include the spectra in your report. dyespec_tddft.odt 4

5 (in Experiment-Based Calculations Make a table that contains the wavelengths of the peaks in your spectra. Record the two longest-wavelength peaks (i.e., λ 00 and λ 01 ) in each compound's spectrum. Also convert their wavelengths to wavenumbers (cm -1 ) and record those. Either include your spectra in your report or attach them to your report. The dyes can degrade or be contaminated during the semester, so watch out for spurious peaks. The spacing between λ 00 and λ 01 is due to excitation of a carbon-carbon vibration. From ν your spectral data, calculate the vibration frequency wavenumbers) for each compound. Particle-in-Box-Based Calculations Interpret the 0-0 transitions as those of polyene π electrons in one-dimensional boxes. The average carbon-carbon bond length in a chain of alternating single and double bounds is 139 pm. The length of the carbon chain between the phenyl rings is L=(2j+1) 139pm, where j is the number of double bonds in the polyene chain (e.g., j=2 for diphenylbutadiene). Calculate L for each of the three dye molecules. Note that 1 pm = meters. Each double bond contributes two π electrons. For diphenylbutadiene, the HOMO corresponds to n i =2 and the LUMO to n f =3. Calculate the HOMO-LUMO ΔE for each of the diphenylpolyenes, using equation 1. From each ΔE calculate λ, using equation 2. Compare the calculated particle-in-a-box λ values to the spectral λ 00 values. Time-Dependent Density-Functional Calculations Following the procedure below, use WebMO and GAMESS to calculate the dye molecules' equilibrium geometry, and then the excitation energy of each molecule. The excitation energy can be converted to wavelength (using λ = hc/δe), and that wavelength can be compared to your observed λ 00 values. Step-by-step instructions follow. 1. Draw the diphenylbutadiene molecule. 2. Prepare a GAMESS input file to optimize geometry using the semiempirical method, AM1. The AM1 method is approximate but fast. It will optimize hydrocarbon bond lengths and angles to near-correct values. Key input-file lines, other than coordinates, follow. Figure 7: diphenylbutadiene OPTTOL= is a loose geometry-optimization criterion, making convergence more dyespec_tddft.odt 5

6 likely than with the default $CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE $END $BASIS GBASIS=AM1 $END $STATPT OPTTOL= NSTEP=500 $END There sometimes is trouble getting the geometry optimization to converge. An error message about being unable to calculate the Hessian, and suggesting changing coordinates, is troublesome. These solutions have sometimes have given some success: (1) re-orient the molecule along the x, y or z axis, (2) flatten the molecule, and (3) specify the rational function optimization method by inserting METHOD=RFO in the STATPT command line. 3. Run a TDDFT calculation to determine the energy required to excite the molecule from its ground state. Use density functional theory, the B3LYP functional and the 6-31G(d) basis set. TDDFT is used for this step because it is one of the few methods able to calculate energies of excited states. It is slow, however. One may expect this step to require one-half hour per molecule. (Note: choosing RUNTYP=OPTIMIZE rather than ENERGY will greatly extend the calculation time and is not recommended.) WebMO does not offer TDDFT as a menu option, so choose a "Molecular Energy" calculation with DFT theory and the B3LYP functional. You can add TDDFT=EXCITE and MAXIT=50 to the input on the Preview screen. Here are key input lines. $CONTRL SCFTYP=RHF RUNTYP=ENERGY DFTTYP=B3LYP TDDFT=EXCITE MAXIT=50 $END $BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 $END $SYSTEM MWORDS=64 $END The CONTRL line above specifies a TDDFT calculation using the B3LYP functional. The basis-set line is routine. The $SYSTEM line allocates 64 megawords of memory. Allocate that much or more. The DATA section is not shown. It contains the AM1-optimized coordinates of the molecule. When the calculation is done, look for SINGLET EXCITATIONS near the end of the output file. Both state energies and ΔE will be in the file. Either use the ΔE that is given or calculate ΔE from ground- and excited-state energies. 1 ev = 1.602X10-19 Joules. 4. Calculate λ from hc/δe. Compare λ to your experimental λ Repeat the above steps for diphenylhexatriene and diphenyloctatetraene. Calculating excitation energy is difficult with any routine theory, including tddft, so wavelength errors of 20 to 40 nm are not unusual. However, tddft (or almost any theory) should reproduce the trend of increasing excitation wavelength with increasing molecular size. dyespec_tddft.odt 6

7 References 1. Wallace-Williams, S.E.; Schwartz, B.J.; Moller, S.; Goldbeck, R.A.; Yee, W.A.; El-Bayoumi, M.A.; Kliger, D.S. Excited state spectra and dynamics of phenyl-substituted butadienes. Journal of Physical Chemistry 1994, 98, Zerbetto, F.; Zgierski, M.Z. On the 1A g 1B u absorption spectrum of four butadiene isotopomers. Chemical Physics Letters 1989, 157, Mustroph, H.; Reiner, K.; Mistol, J.; Ernst, S.; Dietmar, K.; Hennig, L. Relationship between the molecular structure of cyanine dyes and the vibrational fine structure of their electronic absorption spectra. ChemPhysChem 2009, 10, Anderson, B. D. Alternative compounds for the particle in a box experiment. Journal of Chemical Education 1997, 74, Engel, T.; Reid, P.; Hehre, W. Physical Chemistry, Third Edition, Person Education: Boston, The particle-in-a-box model is applied to uv-visible transitions of pi electrons in Section Vibrational transitions that accompany electronic transitions are discussed in Sections 25.4 and Autschbach, Jochen Why the particle-in-a-box model works well for cyanine dyes but not for conjugated polyenes. Journal of Chemical Education 2007, 84(11), Cao, J.; Wu, T.; Hu, C.; Tao, L.; Sun, W.; Fan, J.; Peng, X. The nature of the different environmental sensitivity of symmetrical and unsymmetrical cyanine dyes: an experimental and theoretical study. Physical Chemistry Chemical Physics, 2012, 14, Cramer, C. J. Essentials of Computational Chemistry: Theories and Models; John Wiley & Sons: New York, 2002; page 136. dyespec_tddft.odt 7