| 16 |
|
|
| 17 |
|
Integration schemes for the rotational motion of the rigid molecules |
| 18 |
|
in the microcanonical ensemble have been extensively studied over |
| 19 |
< |
the last two decades. Matubayasi\cite{Matubayasi1999} developed a |
| 19 |
> |
the last two decades. Matubayasi developed a |
| 20 |
|
time-reversible integrator for rigid bodies in quaternion |
| 21 |
< |
representation. Although it is not symplectic, this integrator still |
| 21 |
> |
representation\cite{Matubayasi1999}. Although it is not symplectic, this integrator still |
| 22 |
|
demonstrates a better long-time energy conservation than Euler angle |
| 23 |
|
methods because of the time-reversible nature. Extending the |
| 24 |
|
Trotter-Suzuki factorization to general system with a flat phase |
| 74 |
|
/ 2) \cdot \mathsf{G}_x(a_x /2), |
| 75 |
|
\end{equation} |
| 76 |
|
where each rotational propagator, $\mathsf{G}_\alpha(\theta)$, |
| 77 |
< |
rotates both the rotation matrix ($\mathsf{Q}$) and the body-fixed |
| 78 |
< |
angular momentum (${\bf j}$) by an angle $\theta$ around body-fixed |
| 77 |
> |
rotates both the rotation matrix $\mathsf{Q}$ and the body-fixed |
| 78 |
> |
angular momentum ${\bf j}$ by an angle $\theta$ around body-fixed |
| 79 |
|
axis $\alpha$, |
| 80 |
|
\begin{equation} |
| 81 |
|
\mathsf{G}_\alpha( \theta ) = \left\{ |
