This results in a small continuum of configurations that satisfy the energy condition. Scanning the configuration space for all possible solutions to the energy condition is analogous to the 0-1 knapsack problem in mathematics , and is therefore an NP-complete problem, meaning that no solution exists that is both exact and computationally reasonable. However, Shaw and co-workers propose three possible treatments: a brute force scan, stochastic sampling, and expand the configurations linearly. Importantly, linear expansion allows for compartmentalisation of each configuration based on its respective magnitude (index), and shifts the scaling from exponential to polynomial. This redefines the full configuration space from some N-dimensional surface to a two dimensional skewed-Gaussian (Figure ). A Lagrangian provides the maximum index, corresponding to the Gaussian peak, and provides the dominant configurations to the rate constant. Without the expansion, much of the configuration space is left out, and in many cases the rate of internal conversion can often be underestimated significantly . A good analogy for this is approximating the integral of a Gaussian-like structure as a delta function; the approximation holds if the set of configurations that satisfy the energy condition have indices that are all similar in value, but fails in its description if the indices vary.