Quantum and Spectroscopy:
(a) Huckel Theory: Using Huckel theory, write a program which solves for the molecular orbitals and energy levels in a conjugated or aromatic hydrocarbon (that is, ethylene, butadiene, or benzene, cyclobutadiene, and so on.). The program must accept as input, in a GUI text window, a description of the molecule (that is, if linear, how many carbons, if aromatic, how many carbons). The algorithm will use matrix-based methods to solve simultaneous linear equations as illustrated in any p-chem book. Output will comprise of the values of the energies and molecular orbitals. Plot, in subplots, the molecular orbitals as the linear combination of 2p atomic orbitals (define your coordinate system and pick your favorite one).
(b) Vibronic Spectroscopy: In the harmonic oscillator approximation, simulate the So-S1 absorption spectrum of a diatomic. The simulation must convey both the energies of the transitions, and the relative intensities (think about Franck-Condon factors). Input must comprise the force constants in the ground and excited states (remember this determines the steepness of the wells, and the vibrational energy separation in each state) and re, the internuclear bond distance, in each state. The shift in relative re will determine the Franck-Condon factors of each transition (think about how to calculate constructive interference of two vibrational wavefunctions that may be shifted with respect to on another).
Output the simulated absorption spectrum on the GUI.
(c) Particle in a Box 1 (from Dr. Liebman): You will remember that the energy of a particle in a 3 (and 2) dimensional box is defined by 3 (or 2) quantum numbers. This brings up the concept of degeneracy: a particle with quantum numbers nx, ny, and nz = 3, 3, and 3 has the same energy as a particle with quantum numbers nx, ny, and nz = 1, 1, and 5, and so on. The question comes up whether or not there are any patterns to the degeneracy (Does this only happen with odd numbers? Are there certain patterns of odd numbers that give rise to degeneracy, and so on) Computers can, of course, calculate a set of energy levels very rapidly. Can you create a pattern-recognition algorithm to identify degeneracy patterns? It would also be nice to display, on a GUI, the pattern and show the user (that is, a p-chem student) what this degeneracy pattern is. (N.B. – Dr. Liebman has indicated that identifying such patterns in degeneracy might be a publishable piece of work).