where the label on the integration bounds, I m k ℓ m k , is the integration bounds of interval ℓ m k of mode m k . The ADGA integral is in general a multidimensional integral over all dimensions included in a MC. T mn I mn ℓ mn is obtained from the PES fitted to the calculated SPs in the MC in the current iteration, V mn (q), and the multi-dimensional wave function density of the MC obtained by using the potential in the current iteration, ρ mn ave (q). The ADGA integral is used by the ADGA to determine whether an integration box is converged and the size of the integral can also be interpreted as how "important" an area of the PES is, which will be discussed further below.