| 201 |
|
where $K_\mathrm{v}$, $K_\mathrm{\theta}$, and $K_\mathrm{\omega}$ are |
| 202 |
|
the spring constants restraining translational motion and deflection |
| 203 |
|
of and rotation around the principle axis of the molecule |
| 204 |
< |
respectively. It is clear from Fig. \ref{waterSpring} that the values |
| 205 |
< |
of $\theta$ range from $0$ to $\pi$, while $\omega$ ranges from |
| 206 |
< |
$-\pi$ to $\pi$. The partition function for a molecular crystal |
| 204 |
> |
respectively. These spring constants are typically calculated from |
| 205 |
> |
the mean-square displacements of water molecules in an unrestrained |
| 206 |
> |
ice crystal at 200 K. For these studies, $K_\mathrm{r} = 4.29$ kcal |
| 207 |
> |
mol$^{-1}$, $K_\theta\ = 13.88$ kcal mol$^{-1}$, and $K_\omega\ = |
| 208 |
> |
17.75$ kcal mol$^{-1}$. It is clear from Fig. \ref{waterSpring} that |
| 209 |
> |
the values of $\theta$ range from $0$ to $\pi$, while $\omega$ ranges |
| 210 |
> |
from $-\pi$ to $\pi$. The partition function for a molecular crystal |
| 211 |
|
restrained in this fashion can be evaluated analytically, and the |
| 212 |
|
Helmholtz Free Energy ({\it A}) is given by |
| 213 |
|
\begin{eqnarray} |
