Many proteins contain metalporphyrin molecules that can be modeled as a planar square with an edge length of10Å. The π system can be described as electrons in a box
1. Write down the Schroedinger equation for the square and find the eigen values and eigen functionsof the system.
2. Use the electron masskgand Jsecand the length of the edge of the square to determine theenergy levels in cm-1as a function of the two indices nxand nyfor the particle in a square). You mayuse any book with a table for conversion of energyunits. It is recommended to work first with a single system(meter/kilogram/second?) and then convert the result tocm-1.
3. Electrons enter the wave functions as pairs. I.e. to every wave function wecan put two electrons and we start with the lowest energy states and go up. The heme has 18 electrons. What is the lowest energy absorption (moving electron from occupied to empty orbital) that we can have in the mode? (experimentally the excitation is of 17,000cm-1).