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Calculating Simple Force Constants with Computational Quantum Chemistry

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

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Experiment Overview

This experiment allows the student to calculate the force constant by quantum mechanical calculations for the three diatomic molecules, F2, O2 and N2. 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.

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