α , where the sum runs over the Cartesian degrees of freedom with corresponding masses m α and the dot indicates derivative with respect to u. The cyclic boundary conditions require the two paths to connect to each other such that x e (0) = x g (β ) and x e (βτ ) = x g (βτ ). Typically, the stationary condition ensures that these two points, at which the instanton changes from one electronic state to the other, will be found at the same geometry called the "hopping point". It is always located on the crossing seam, where the two diabatic potentials V e and V g are equal, but is not in general identical to the MECP geometry.