Reaction paths


MOPAC has the capability to model the effects of changing an internal coordinate. In the data-set, the relevant internal coordinate is flagged with a `-1' rather than a '1' or '0'. Two options then exist to allow the values of the changing coordinate to be defined.

First, the various values of the coordinate can be supplied after the geometry and any symmetry data have been entered. An example for the SN2 reaction Cl- + CH3F $\rightarrow$ CH3Cl + F- is given in Figure 1.

  
Figure 1: Example of an SN2 reaction path calculation 
 CHARGE=-1
 SN2 reaction, Cl(-) + CH3F = CH3Cl + F(-)
   C
   F   1.4  1
   H   1.1  1   109.5 1     0    0    1 2
   H   1.1  1   109.5 1   120.0  0    1 2 3
   H   1.1  1   109.5 1   120.0  0    1 2 3
   Cl 20.0 -1   127.3 1   180.0  0    1 2 3
   0   0.00 0     0.0 0     0.0  0    0 0 0
  10.0 5.0 4.0 3.0 2.9 2.8 2.7 2.6 2.5
   2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6
 
A useful alternative to using atom numbers when defining the connectivity is to use atom labels.

Second, if the step-size is a constant, then the step-size and number of steps can be defined on the keyword line. An example of such a "reaction" would be the rotation of a methyl group in, e.g., ethane, Figure 2. Here, symmetry is used to maintain D3 symmetry as the rotation takes place. Note that SYMMETRY can be used to relate coordinates to the reaction coordinate. The path calculations work by optimizing the geometry while the reaction coordinate is fixed at the starting value. Once the geometry is optimized, the reaction coordinate is changed, and the geometry re-optimized. This is done for all points on the reaction path.

  
Figure 2: Example of a rotation barrier calculation 
step=5 points=13  SYMMETRY
Ethane, Barrier to Rotation
C
C  1.5 1    0 0    0  0   1 0 0
H  1.0 1  111 1    0  0   2 1 0
H  1.0 0  111 0  120  0   2 1 3
H  1.0 0  111 0 -120  0   2 1 3
H  1.0 0  111 0   60 -1   1 2 3
H  1.0 0  111 0  180  0   1 2 3
H  1.0 0  111 0  -60  0   1 2 3
0  0.0 0    0 0    0  0   0 0 0
3 1 4 5 6 7 8
3 2 4 5 6 7 8
6 7 7
6 11 8
 

      Reaction paths can be used for calculating mechanical properties. For example, to calculate Hook's force constant for stretching polyethylene, the translation vector could be steadily increased, Figure 3.


  
Figure 3: Data set to stretch a polymer 
step=0.05 points=20
Trans-polyparaphenylene benzobisthiazole
Stretching the polymer
  C    0.0  0      0  0      0  0    0  0  0
  N    1.3  1      0  0      0  0    1  0  0
  S    1.7  1    115  1      0  0    1  2  0
  C    1.6  1     92  1      0  1    3  1  2
  C    1.4  1    109  1     -0  1    2  1  3
  C    1.4  1    124  1   -180  1    5  2  1
  C    1.4  1    116  1    180  1    6  5  2
  C    1.4  1    121  1      0  1    7  6  5
  C    1.4  1    129  1    180  1    4  3  1
  S    1.6  1    129  1    180  1    7  6  5
  C    1.7  1     92  1    180  1   10  7  6
  N    1.4  1    113  1   -180  1    8  7  6
  C    1.4  1    121  1   -180  1   11 10  7
  C    1.4  1    120  1    -90  1   13 11 10
  C    1.4  1    120  1    180  1   14 13 11
  C    1.4  1    120  1      0  1   15 14 13
  C    1.4  1    118  1     -0  1   16 15 14
  C    1.4  1    120  1      0  1   17 16 15
  H    1.0  1    121  1     -0  1    6  5  2
  H    1.0  1    121  1      0  1    9  4  3
  H    1.0  1    120  1     -0  1   14 13 11
  H    1.0  1    119  1   -180  1   15 14 13
  H    1.0  1    120  1   -180  1   17 16 15
  H    1.0  1    119  1    180  1   18 17 16
 xx    1.4  1    120  1    180  1   16 15 14
 Tv   12.6 -1      0  0      0  0    1 25 24