Two dimensional surface, with a projected contour plot. It shows two minima (M) and a reaction path (in red) connecting them. The maximum in the red line represents the TS.
This plot can be used to illustrate a general computational feature. It is possible to calculate the red path from the TS down hill, ending in either of the two minima. This is what the IRC calculation in MOPAC does.
Such a path is also called an MEP, a minimum energy path.
In the TS it is clear that the calculated reaction coordinate should be followed. Outside the TS, there are more negative values in the second derivative matrix (updated after a certain number of steps), and the algorithm has to select one (the largest negative?) to follow downwards.
The opposite action, calculating the path from M to TS, is not possible. A gradual ascent from the minimum on the right would follow the blue line rather than the red one.
('if you are somewhere in the mountains and knock over your bucket of ping pong balls, you can pretty well predict where they will go; but for the people in the valley it is difficult to tell where the balls came from'.)
The MOPAC saddle algorithm (paragraph 2C) uses information from the other side of the hill, the geometry on the other side of the TS, to 'pull' the two geometries together.
Back to paragraph 1A.