# Calculating Simple Force Constants with Computational Quantum Chemistry

Posted on Apr 14 2006
by Brian J. Salter-Duke, Vinutha Ramakrishna, David Chalmers

## Experiment Overview

This experiment allows the student to calculate the force constant by quantum mechanical calculations for the three diatomic molecules, F_{2}, O_{2} and N_{2}. It uses the Gaussian and Mopac quantum chemistry codes running on a server and accessed by forms through a web browser. A selection of Hartree-Fock and Density Functional Theory methods are available, along with the semi-empirical AM1 and PM3 methods. Rather than using the "black box" calculation of the force constants from a calculation of the frequencies, here the student calculates the energy at the optimum bond length and with the bond length increased and decreased by 0.01 A. They then fit a parabola through these points to calculate the second derivative and hence the force constant. For some more advanced calculations the appropriate energies are provided rather then calculated.

This experiment is a suitable introduction to quantum mechanical calculations. It provides insight into the principles of vibrational spectroscopy and particularly a deeper appreciation of the concept of force constants.

- It reinforces students understanding of bond strengths in single, double and triple bonds.
- It shows that bond-stretching energy curve is not harmonic, so they can appreciate that anharmonic terms may sometimes be needed.
- It allows the student to learn how to do simple quantum chemistry calculations and recognise that that this is no longer a complex and hard to learn activity.
- It can support the teaching of Molecular Mechanics methods in Computational Chemistry courses.

Feedback supports the view that this experiment is relevant to students who are studying molecular modelling and/or spectroscopy and that it helps to appreciate the link between bond length and bond strength.