4   $-0.01+0.2\sin(0.3(14+r))\cdot \exp(-r)$
  Sine 5   $0.7\sin(0.4(11+r))\cdot \exp(-r)$
  Sine 6   $0.9\sin(0.4(11+r))\cdot \exp(-r)$
  Sine 7   $1.1\sin(0.4(11+r))\cdot \exp(-r)$

  : High-fidelity potential sine modification terms[]{data-label="tbl:sine"}

A final high-fidelity model tested is the Morse potential, defined as the sum of two exponentials: $$\label{eq:Morse}
\phi=D_0(e^{-2\alpha(r-r_0)} -2e^{-\alpha(r-r_0)})$$ We use $D_0=0.161 eV$, $\alpha=2.09$Å${}^{-1}$, and $r_0=2.62$Å to similarly roughly describe copper.

For all potentials a smoothing function is used to ensure stable dynamics near the cutoff. The function is of fourth order to create potential energy and force curves that both smoothly tend to zero: $$\label{eq:smooth}
s(r) = \frac{(\frac{(r - r_c)}{w})^4}{(1+\frac{(r - r_c)}{w})^4}$$ where $r_c$ is the cutoff distance and $w$ is the width of the smoothing. For all potentials the cutoff is 5.79Å ($2.5\sigma$, commonly used for LJ potentials) and smoothing width 1.5Å. Each potential curve is created by summing the base equation and the modification term and subsequently taking the product with the smoothing function. The force curve is then created with product rule differentiation of the potential. These potentials are shown in Figure \[fig:potentials\].

Each system consists of 500 atoms simulated under isothermal, isochoric conditions (canonical ensemble). Three physical states of the system were simulated: one solid at ambient temperature and pressure ($300 K$ with density 