Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator. An Undergraduate Vibrational Spectroscopy Laboratory Exercise

Abstract

An undergraduate exercise in vibrational spectroscopy is described, involving the prediction of wavenumber positions for absorptions associated with stretching vibrational modes of common organic molecules. This is done by modeling the portion of the molecule undergoing the bulk of the normal mode motion with a pseudodiatomic molecule, for which the known solution to the quantum-mechanical harmonic oscillator is approximately valid. Student-generated stretching vibrational mode data are used to determine an effective single-bond force constant for stretching modes of any typical covalently bound molecule composed of C, H, O, and N. Double- and triple-bond stretching modes are treated as having a force constant equal to twice or three times the single-bond value. The effective single-bond force constant is then refined to obtain the best possible value for stretching modes of organic molecules, 556 N m-1 for our data set. The exercise demonstrates that, for a well-behaved class of molecules, the major caus...