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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