A generalized Newton iteration for computing the solution of the inverse Henderson problem
This work provides a more efficient algorithm for the inverse Henderson problem, which is relevant for computational physics and materials science.
The authors develop a generalized Newton iteration (IHNC) for constructing effective pair potentials that reproduce a given radial distribution function. The method requires only one molecular dynamics computation per iteration, achieving efficiency comparable to Inverse Monte Carlo while allowing thermodynamic constraints.
We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made 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.