The Morse Potential

The Morse potential has the form: The Morse potential may be written as
\begin{displaymath} V_M = \epsilon\sum_{i<j} e^{\rho_0(1-r_{ij}/r_0)}(e^{\rho_0(1-r_{ij}/r_0)}-2),\end{displaymath} (1)
where $\epsilon$ is the pair well depth and r0 the equilibrium pair separation. In reduced units ($\epsilon=1$ and r0=1) there is a single adjustable parameter, $\rho_0$, which determines the range of the interparticle forces. The Figure shows that decreasing $\rho_0$ increases the range of the attractive part of the potential and softens the repulsive wall, thus widening the potential well. The LJ potential has the same curvature at the bottom of the well as the Morse potential when $\rho_0=6$. Girifalco has obtained an intermolecular potential for $\rm C_{60}$ molecules which is isotropic and short-ranged relative to the equilibrium pair separation, with an effective value of $\rho_0=13.62$. The alkali metals have longer-ranged interactions, for example $\rho_0$=3.15 has been suggested for sodium. Fitting to bulk data gives a value of $\rho_0$=3.96 for nickel.

Figure: The Morse potential for different values of the range parameter $\rho_0$ as indicated.
\begin{figure} \epsfig {figure=figures/m.potential.eps,width=13.6cm} \vspace{3mm}\end{figure}

Reference: P. M. Morse, Phys. Rev.34, 57 (1929).

Jon Doye
11/5/1997