Using a Spreadsheet to Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H2

We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the So ground electronic state and the S-1 and T-1 excited states of H-2. The spreadsheet calculations circumvent the construction and diagonalization of the Pock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the So, S,, and T, states of H-2 are constructed from the symmetry-adapted bonding and antibonding molecular orbitals (MO). All quantum mechanical integrals are estimated using the Monte Carlo integration method. Due to the stochastic nature of the spreadsheet calculations, 25 runs were carried out to obtain the mean energy of the So, S,, and T, electronic states of H-2. The accuracy of the spreadsheet calculations is comparable to that of the HF/STO-3G calculations. The atomic and molecular orbitals and the energy components can be easily calculated and plotted for better visualization and understanding of essential quantum chemical concepts. This spreadsheet can also be adapted to tackle a wider range of quantum chemistry problems with different levels of complexity.