Reaction Coordinate

Very often our intuition tells us what the nature of the reaction coordinate is. We associate it with a changing bond length, or a torsion angle.

The theoretical reaction coordinate, obtained from a FORCE calculation on a particular geometry, is more complicated. This normal coordinate (see paragraph 1B) will be a combination of several cartesian or internal coordinates (see 1C), for atoms that are displaced during the reaction.
This can be seen from the numerical output, or visualized in MOLDEN (Gamess output) or Sybyl (MOPAC).

For example: for an SN2 reaction, obviously the two bonds formed and broken are involved, but also the other substituents attached to the central atom, which move perpendicular to their bonds ('inversion' of geometry).
See below part of the MOPAC output, in which the TS is characterized for the SN2 reaction Cl...CH(CH3)2...Br (isopropyl halide plus anion):

          DESCRIPTION OF VIBRATIONS


 VIBRATION   1  1A'       ATOM PAIR      ENERGY CONTRIBUTION     RADIAL
 FREQ.     -506.27       C 2 --  H 3          -56.8% (-50.7%)     0.4%
 T-DIPOLE   7.4523       C 2 -- Cl 6          -52.1%             97.4%
 TRAVEL     0.1172      Br 1 --  C 2          -44.6%             98.0%
 RED. MASS  7.2931       C 2 --  C 4          -37.4%              0.0%
                         C 2 --  C 5          -37.4%              0.0%
                         C 5 --  H 7          -26.9%              8.4%
                         C 4 --  H12          -26.8%              8.2%
                         C 4 --  H10          -25.7%             14.7%
                         C 5 --  H 9          -25.7%             14.5%
                         C 5 --  H 8          -11.6%              0.1%

 VIBRATION   2  1A"       ATOM PAIR      ENERGY CONTRIBUTION     RADIAL
 FREQ.       92.10       C 4 --  H11           16.9% (482.3%)     0.0%
 T-DIPOLE   0.0598       C 5 --  H 8  ....
 
(In paragraph 2A the procedure to obtain such a file is explained)
There is one negative eigenvalue, with frequency -506.27 cm-1. This vibration represents the reaction coordinate.
C2-Cl and C2-Br take part, almost 100% radial, i.e. in the direction of the bond.
H3, C4 and C5 are the other substituents at C2, which move 0% radial, so perpendicular to their bond direction.
In a visualization of this frequency, one will see C2 moving inside the 'cage' of its five substituents. The amplitudes are written in another part of the output file. See also paragraph 2A on how to perform such a visualization in SYBYL.


Back to Chapter 1, part A.