Below we provide training materials to face the 52nd International Chemistry Olympiad (IChO) of 2020 which will be held in Istanbul Turkey.
Problem 1. A frog in a well
The energy levels of an electron in a one-dimensional box are given by:
in which h is the Planck’s constant, m is the mass of the electron, and L is the length of the box.
1) The π electrons in a linear conjugated neutral molecule are treated as individual particles in a one-dimensional box. Assume that the π electrons are delocalized in the molecular length with the total number of N π electrons and their arrangement is governed by the principles of quantum mechanics.
a. Derive the general expression for ∆ELUMO–HOMO when an electron is excited from the HOMO to the LUMO.
b. Determine the wavelength λ of the absorption from the HOMO to the LUMO.
2) Apply the model of π electrons in a one-dimensional box for three dye molecules with the following structures (see the structural formula). Assume that the π electrons are delocalized in the space between the two phenyl groups with the length L is approximately equal to (2k+1)(0.140) nm, in which k is the number of the double bonds
a. Calculate the box length L (Å) for each of the dyes.
b. Determine the wavelength λ (nm) of the absorption for the molecules of the investigated dyes.
3) Recalculate the box length L (Å) for the three dye molecules, assuming that the π electrons are delocalized over the linear conjugated chain which is presented as a line plotted between the two phenyl groups (see the structural formula). The bond angle C–C–C is 120o and the average length of C–C bond is 0.140 nm.
4) Give the following experimental data on the wavelength λ of absorption.
a. Determine the box length L (Å) of the linear conjugated chain for each of the three investigated dyes.
b. Tabulate the values of the box length L for the dyes calculated above by the three different methods, denoted as 1, 2, and 3. Choose the method which is the most fit to the experimental data.