Model approximation

Note that these potential functions only approximately represent molecular structures.

For example, bond vibrations are commonly represented as a simple harmonic with a force constant and bond equilibrium length that represent the characteristics of the bond. Such a representation is not realistic because it renders the bond as unbreakable, as shown in the diagram below.

Note that the harmonic function is only a close fit around the equilibrium distance \(b_0\). This approximation is usually applicable close to room temperature (298 K) and might not be appropriate for higher temperatures.

Alternatively, a Morse function, which provides a better fit to reality, can be used. It is a better approximation for the vibrational structure of the molecule that accounts for the anharmonicity of a real bond.

The Morse function would need fitting to three parameters:

• \(D_e\), the well depth, which measures the bond strength
• \(\alpha\), which is associated with the width of the potential
• \(b_0\), the equilibrium bond length

The quantity \(\alpha\) is related to the (harmonic) force constant, \(k_b\), at the minimum well depth:

\[\alpha = \sqrt{\frac{k_b}{2 D_e}}\]

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