and
Absorption bands in the visible region of the spectrum correspond to transitions from ground state of a molecule to an excited state which is 40 - 80 kcal/mole above the ground state. In many substances the lowest electronic state is more than 80 kcal/mole above the ground state and therefore they do not absorb light in the visible range of spectrum. Such substances are not colored. Compounds that absorb in the visible region of the spectrum (these compounds have color ) generally have some weakly bound or delocalized electrons. In these systems, the energy difference between the lowest unfilled orbital (LUO) and the highest filled orbital (HFO) corresponds to the energies of quanta in the visible region. In this experiment, the visible spectra of a class of compounds known as polymethine dyes will be measured. Since the electrons involved in the transition exhibit similar conditions to those of a particle confined in a one dimensional box, a simple quantum mechanical model can be used to interpret the data.
The visible bands for polyemethine dyes arise from electronic transitions involving the p electrons along the polyemethine chain. The wavelength of these bands depends on the spacing of the electronic energy levels.
The arrangement of alternating single-double bonds in an organic molecule usually implies that the p electrons are delocalized over the framework of the "conjugated" system. Since these p electrons are mobile throughout the carbon atom skeleton containing the alternating double bonds, a very simple theoretical model can be applied to such a system in order to account for the energy of these electrons in the molecule. If one makes the seemingly drastic assumption that the several p electrons which comprise the system are non-interacting (presumably, if the p electrons are delocalized over the -C=C-C=C-C=C- framework, they spread out, minimizing repulsion between them), then one can view the energetics of this system as arising from the simple quantum mechanical assembly of one electron energy levels appropriate to the particle in the box model. In this case, one considers the potential energy of the electron as being constant throughout the length of the molecular box and then rising to infinity at each end of the conjugated portion of the molecule.
The application of the Schroedinger equation to this problem results in the well known expressions for the wavefunctions and energies, namely:
and
n is the quantum number (n= 1, 2, 3,…), L is the 'length' of the (one dimensional) molecular box, m is the mass of the particle (electron), and h is Planck's constant. The spatial variable x is a displacement along the -C=C-C=C- molecular backbone.
Each wavefunction can be referred to as a molecular orbital, and its respective energy is the orbital energy. If the spin properties of the electron are (by necessity) taken into account along with the ad hoc invocation of Pauli's exclusion principle, the model is then refined to include spin quantum numbers for the electron (1/2) along with the restriction that (1) no more than two electrons can occupy a given wavefunction or level, and (2) the spin quantum numbers of the two electrons occupying a given energy level are opposite (spin up and spin down).
This allows the electronic structure for the p electrons in a conjugated dye molecule to be constructed according to the 'aufbau' principle. For example, if the conjugated molecule shown below is considered, the orbital energy diagram becomes:
Note that there are, in this case, 6 p electrons since each carbon is sp2 hybridized and thus contributes a p orbital and one p electron to the system. The lowest energy configuration, called the electronic ground state, corresponds to the 6 electrons being in the lowest three orbitals. Higher energy configurations are constructed by promoting an electron from (for example) the highest filled orbital (HFO) to a higher, vacant orbital. This higher energy arrangement is called an electronically excited state. The lowest or first electronically excited state, of course, is achieved by promotion of an electron from the HFO to the lowest unfilled orbital (LUO). The energy difference between these two states is simply given by the following expression:
The energy required for this electronic transition can be supplied by a photon of the appropriate frequency, given by the Planck relation:
E = hn = hc/l
where h is Planck's constant, n is frequency, c is the speed of light and l is the wavelength.
Thus, the ground state of a molecule with N p
electrons will have N/2 lowest levels filled (if N is even) and all higher
levels empty. Thus nLUO =N/2 and nHFO=N/2+1
or
Let us denote the number of carbon atoms in a
polymethine chain as p; then N=p+3. Kuhn assumed that L was the length of
the chain between nitrogen atoms plus one bond distance on each side (in order
to take into account that box boundary is not vertical). Thus L=(p+3)*l where
l is the bond length between atoms along the chin. Therefore
l can be estimated from the bond length in benzene
l=1.39 Å or 0.139 nm.
In order to adjust better experiment and theory the
special fitting parameter a
sometimes used:
where a
is constant for a series of dyes of a given type.
The dyes you will be using in this experiment are toxic. You should be careful in working with them, and avoid getting the solutions on your skin. In addition, these dyes will slowly degrade in the presence of light, so you should keep the solutions in the dark when they are not in use.
We will make use of four dyes with the structures shown in Fig. 1
Figure 1.Structures of the four thiacyanine dyes.
DTC (n=0):[2197-01-5] 3,3'-diethylthiacyanine iodide
DTCC (n=1):[905-97-5] 3,3'-diethylthiacarbocyanine iodide
DTDC (n=2):[514-73-8] 3,3'-diethylthiadicarbocyanine iodide
DTTC (n=3):[3071-70-3] 3,3'-diethylthiatricarbocyanine iodide
1. Measure the absorption spectra of molecules from fig.1 using Ocean optics spectrophotometer. In order to do it correctly you need to choose correct exposition time and the solution concentration. It allow you to avoid saturation and reach a good sensitivity. You will receive in the beginning of the work the dye solutions of known concentration which are usually higher than optimal. Dilute it until the optimal concentration will be obtained. Write down number and extent of dilution in order to be able to determine the final working concentration of dyes.
2. Using Origin software determine the wavelengths of the absorption maxima of the all dyes, convert the absorption spectra in the units exctinction coefficient versus wavenumbers, deconvolute different peaks in each spectrum and find the integral absorption coefficient (IAC) and oscillator strength for each transition. You can read how to do it here.
3. Learn HeperChem program using the five lesson tutorial. Draw and "build" the studied molecule, optimize their structure and determine bond lengths, which you need for calculations using particle-in-box model. Image of molecule, you have to receive, must be similar to that shown in Fig. 2
Fig.2 HyperChem structure of 3,3'-diethylthiacarbocyanine (DTCC)
4. Calculate wavelengths of the transitions using Hyperchem semi-empirical methods and compare it with experimental data.
5. Hyperchem program allows to calculate electronic spectra and oscillator strength of the transitions. Calculate them and compare with your experimental values.
6. Compare your experimental values with the literature data. You can find useful information in Aldrich
1. Estimate L for DTDC dye according to the Kuhn model
2. Find the wavelength of the absorption of DTTC dye according to the particle in box model
11-May-04