The pdf file shows Lennard-Jones  (LJ) potentials in 2 dimensions

Plot 1: There is a fixed particle located at (x=0,y=0), another particle moves in the xy-plane,
           both particles interact with a (totally arbitrary) LJ potential,
           The energy (plotted as the z-coordinate) are very high at short distances
           (not so nicely plotted). Then, at a certain distance, ther is a 'ring' of lowest energies
           (the minimum is thus a ring,not a point like in 1D), t larger distance the energy increades
            and approaches zero

Plot 2: I have now put a second fixed particle at (x=0.85,y=0)m the moving particles interacts
           with both fixed particles with the same LJ-potential
           (I have neglected the (LJ) energy between the two fixed particles, since they are fixed,
           this energy is constant and would just change my z-axis)
           Now there are two such minimum energy rings, one around each fixed particle,
          but the do not touch each other.
          There is an interesting region where the two minimum energy rings 'almost' meet.

Plots 3-5 explore this region (Note the different length and energy scales)
        We see that there is a ridge (and thus a 'transition state' TS) when the moving particle
        goes from one minimum (ring) to the other.

If now I added a third fixed particle things would become even more complicated