A generalized Newton iteration for computing the solution of the inverse Henderson problem

We develop a generalized Newton scheme called IHNC (inverse hypernetted-chain iteration) for the construction of effective pair potentials for systems of interacting point-like particles. The construction is realized in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step and no further expensive cross-correlations. Numerical experiments are shown to demonstrate that the method is as efficient as the IMC scheme, and that it easily allows to incorporate thermodynamical constraints.