2A: Path or line searches in MOPAC

MOPAC allows the systematic variation of one or two parameters from the z-matrix in the input file.
For a parameter marked with a '-1' a series of values will be entered, in a way that is also specified in the input file.
In the one-dimensional case we call this searching a reaction path or, for short, a line search. When two parameters are marked with a '-1', a grid search is performed.

The values to be entered into the calculation are either For a grid search only the keyword input can be used.

Example of line search:

The SN1 reaction of CH3Br can be described by one coordinate, the C-Br distance. Starting from a crude methyl bromide geometry the following two input files could be used to scan this distance for a maximum in the Heat of Formation.
 AM1 SYMMETRY T=3600 NOINTER NOXYZ
  reaction coordinate values at bottom of file
  c - br distance
 C              0.000000  0    0.000000  0    0.000000  0    0    0    0
 H              0.999600  1    0.000000  0    0.000000  0    1    0    0
 H              1.004440  0  108.958790  1    0.000000  0    1    2    0
 H              1.000000  0  109.885165  0 -120.322005  1    1    2    3
 Br             1.900000 -1  108.958790  1  119.355990  1    1    2    3
 0              0.000000  0    0.000000  0    0.000000  0    0    0    0
 2, 1, 3, 4
 3, 2, 4

 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.5 4.0
The same using keywords: 
 AM1 SYMMETRY STEP=0.1 POINT=12 T=3600 NOINTER NOXYZ
  reaction coordinate specified by keywords STEP and POINT
  c - br distance
 C              0.000000  0    0.000000  0    0.000000  0    0    0    0
 H              0.999600  1    0.000000  0    0.000000  0    1    0    0
 H              1.004440  0  108.958790  1    0.000000  0    1    2    0
 H              1.000000  0  109.885165  0 -120.322005  1    1    2    3
 Br             1.900000 -1  108.958790  1  119.355990  1    1    2    3
 0              0.000000  0    0.000000  0    0.000000  0    0    0    0
 2, 1, 3, 4
 3, 2, 4
Note how the first method allows for an increase in step size towards the end of the range.
If no maximum is found, either the range should be extended, or a different coordinate selected, or the question should be reconsidered! E.g. in the example above, one can tell beforehand (talking about intuition) that without a solvation contribution, a maximum is not likely to appear!
These days a lot of effort is put into methods that incorporate solvent effects (see also part 3C.

SN2 reactions (X - - C-Y) can often be described by one parameter as well, e.g. the distance X - C, nucleophile-central carbon. The incoming nucleophile will push the leaving group Y out, i.e. calculate the optimal distance C-Y at each point. 

 AM1 CHARGE=-1 T=600 NOINTER NOXYZ
 sn2 reaction
 cl-  2-bromopropane
Br	0.0  
 C	1.9	1	  0.0   0     0.0 0  1  0  0
 H	1.12	1   	110.0	1     0.0 0  2  1  0
 C	1.42	1	110.0	1   120.0 1  2  1  3
 C	1.42	1	110.0	1   240.0 1  2  1  3
Cl	3.5    -1	154.0   1     0.0 0  2  1  3
 H	1.1     1       110.0   1    60.0 1  5  2  4
 H	1.1     1  	110.0   1   180.0 1  5  2  4
 H	1.1     1  	110.0   1   300.0 1  5  2  4
 H	1.1     1  	110.0   1    60.0 1  4  2  5
 H	1.1     1  	110.0   1   180.0 1  4  2  5
 H	1.1     1  	110.0   1   300.0 1  4  2  5
 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
Result, visualization of MOPAC output (.arc file, renamed to .moo file).
In Molden, switch to solid display to show the unconnected chlorine atom.
Check the Cl-C-Br angle at the TS.
Care has to be taken to keep the attacking agent on the right track, i.e. in the direction of the central atom. Sometimes elimination (E2 mechanism) rather than substitution is observed, if the negative Cl is attracted by a positive hydrogen.
The use of symmetry can be helpful here. Do you see what the zero (and constant) torsion angle in the definition for Cl implies?
Check your answer!

The maximum of this curve is used as the starting point for the next step, the exact location and characterization of the TS. The C-Cl and C-Br distances are measured (2.20 and 2.33 respectively), and entered in the input file as constants, flag 0. This structure is minimized in the normal way. From the resulting .arc file a new input file is extracted, which is then fully optimized (all flags 1) using the keyword TS.
This gives the proper TS geometry, which in turn can be checked by a calculation in which the keyword TS is replaced by FORCE.
In Chapter 1, part A, the one negative eigenvalue was shown (figure of 1D plot, under 'reaction coordinate').
Sybyl can show an animation of the calculated vibrations, also the one with the negative frequency. A description of the procedure is given separately.

In paragraph 1E we prepared an input file for a Diels-Alder reaction. Because of the symmetry in the unsubstituted skeleton, we could assume a symmetric TS, and therefore change only one bond in a path search, the second bond made equivalent through a symmetry relation.
The result of this calculation (the .arc file, renamed to .moo) can be viewed using MOLDEN: a maximum appears between 2.0 and 2.2 angstrom.
In case of substituted compounds we can use this TS as a starting point for a grid search, in which we change both bonds independently. See paragraph 2B: grid search in MOPAC.

New, experimental service! You may submit short MOPAC jobs and view the result. Copy one of the input files written above and paste it in the window on the MOPAC submit page. Or edit it, or type your own input!
Dr. Jeffrey Gosper, Brunel University, computed and animated a large number of substitution reactions, which can be accessed from his web page.
The remaining parts of chapter 2 are:
2C: The MOPAC Saddle algorithm
2D: From MOPAC to Gamess
Back to Contents page of Chapter 2.
This is the second chapter: How to locate a Transition State
Previous chapter: Types of coordinates, z-matrices, input files
Next chapter: More theory
Back to Main Contents page.