Potential Energy Function
The Morse potential energy function is of the form
Here is the distance between the atoms, is the equilibrium bond distance, is the well depth (defined relative to the dissociated atoms), and controls the 'width' of the potential (the smaller is, the larger the well). The dissociation energy of the bond can be calculated by subtracting the zero point energy from the depth of the well. The force constant of the bond can be found by Taylor expansion of around to the second derivative of the potential energy function, from which it can be shown that the parameter, is
- ,
where is the force constant at the minimum of the well.
Since the zero of potential energy is arbitrary, the equation for the Morse potential can be rewritten any number of ways by adding or subtracting a constant value. When it is used to model the atom-surface interaction, the Morse potential is usually written in the form
where is now the coordinate perpendicular to the surface. This form approaches zero at infinite and equals at its minimum. It clearly shows that the Morse potential is the combination of a short-range repulsion and a longer-range attractive tail.
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