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sc::TorsSimpleCo Class Reference

The TorsSimpleCo class describes an torsion internal coordinate of a molecule. More...

#include <simple.h>

Inheritance diagram for sc::TorsSimpleCo:

sc::SimpleCo sc::IntCoor sc::SavableState sc::DescribedClass sc::RefCount sc::Identity List of all members.

Detailed Description

The TorsSimpleCo class describes an torsion internal coordinate of a molecule.

The input is described in the documentation of its parent class SimpleCo.

Designating the four atoms as $a$, $b$, $c$, and $d$ and their cartesian positions as $\bar{r}_a$, $\bar{r}_b$, $\bar{r}_c$, and $\bar{r}_d$, the value of the coordinate, $\tau$, is given by

\[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\]

\[ \bar{u}_{cb} = \frac{\bar{r}_c - \bar{r}_b}{\| \bar{r}_c - \bar{r}_b \|}\]

\[ \bar{u}_{cd} = \frac{\bar{r}_c - \bar{r}_d}{\| \bar{r}_c - \bar{r}_b \|}\]

\[ \bar{n}_{abc}= \frac{\bar{u}_{ab} \times \bar{u}_{cb}} {\| \bar{u}_{ab} \times \bar{u}_{cb} \|} \]

\[ \bar{n}_{bcd}= \frac{\bar{u}_{cd} \times \bar{u}_{bc}} {\| \bar{u}_{cd} \times \bar{u}_{bc} \|} \]

\[ s = \left\{ \begin{array}{ll} 1 & \mbox{if $(\bar{n}_{abc}\times\bar{n}_{bcd}) \cdot \bar{u}_{cb} > 0;$} \\ -1 & \mbox{otherwise} \end{array} \right. \]

\[ \tau = s \arccos ( - \bar{n}_{abc} \cdot \bar{n}_{bcd} ) \]


The documentation for this class was generated from the following file:
Generated at Fri Mar 19 10:48:43 2004 for MPQC 2.2.1 using the documentation package Doxygen 1.3.5.