Adaptive integration grids in instanton theory improve the numerical accuracy at low temperature.

The instanton method allows to accurately calculate tunneling rates down to very low temperature. However, with lowering the temperature, the computational effort steeply increases as many more discretization points are required. This is caused in practical applications by the majority of the discretization points accumulating at a very small region in configuration space. Here, we describe a method to flexibly discretize the instanton path adapted to the temperature. Chosen appropriately, the discretization leads to a much more uniform distribution of the images (control points) along the path which reduces the number of required images by about a factor of two. Combined with a modified Newton-Raphson optimizer and successive updates of the Hessians, the proposed method provides converged reaction rates at computational costs reduced by more than an order of magnitude. We show the success of the method on analytic test potentials and on molecules with energies directly obtained from density functional theory calculations.