#### Including spectators

Collinear triatomic calculations can be used to approximate reaction dynamics of
larger molecules. The three bodies are treated as the major factors while other
atoms are treated as spectators. In the nucleophilic substitution reaction seen
below, the green, grey, and red atoms are the only ones of concern in ab initio
calculation. The other orange and white three are the spectators.
They become harmonically constrained to the precalculated motion of the
collinaer triatomic system.

It is also important to know that as the system approaches dynamical
equilibrium, the arrows begin to balance out. This is seen macroscopically
when a reaction comes to an end.

Below is a real 3 body calculation in the green atom's rest frame. The
reaction dynamics are calculated semi-classically for the reaction BG+R->B+GR.
The quantum vibrational transition probabilities for the reactants
the products are calculated algebraically and continually through the transition
state.The BG and GR molecules are bound anharmonically. The yellow atom is
then harmonically constrained to the precalculated motion of the blue atom. The
yellow atom is a spectator in this "larger" reaction and can be valid if the
mass of the yellow atom is much smaller than the other three. Therefore,
we have approximated the classical motion for the collinear reaction
YBG+R->YB+GR.

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