#### Title

Using a Spreadsheet to Solve the Schrödinger Equations for H2 in the Ground and Excited States

#### Document Type

Oral Presentation

#### Campus where you would like to present

SURC Room 140

#### Start Date

15-5-2014

#### End Date

15-5-2014

#### Keywords

Chemical Education, Spreadsheet Calculation, Molecular Orbital

#### Abstract

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 S0 ground electronic state and the S1 and T1 excited states of H2. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S0, S1, and T1 states of H2 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 S0, S1, and T1 electronic states of H2. 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.

#### Recommended Citation

Buchanan, Jacob, "Using a Spreadsheet to Solve the Schrödinger Equations for H2 in the Ground and Excited States" (2014). *Symposium Of University Research and Creative Expression (SOURCE)*. 139.

https://digitalcommons.cwu.edu/source/2014/oralpresentations/139

#### Additional Mentoring Department

Chemistry

Using a Spreadsheet to Solve the Schrödinger Equations for H2 in the Ground and Excited States

SURC Room 140

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 S0 ground electronic state and the S1 and T1 excited states of H2. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S0, S1, and T1 states of H2 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 S0, S1, and T1 electronic states of H2. 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.

## Faculty Mentor(s)

Ge, Yingbin