An analytical expression for interatomic surfaces in the theory of atoms in molecules

Summary According to the theory of Atoms in Molecules as developed by Bader and coworkers a molecule is partitioned into atoms separated by surfaces of zero flux in the gradient of the charge density. For the first time an accurate and explicit analytical expression is given for these interatomic surfaces. They are generated by a system of differential equations which can in principle be solved by using a series expansion. Unfortunately, this expansion has a small radius of convergence and can therefore not be applied in practice. However, by a combined Chebyshev-Fourier fit to a numerically obtained surface, the interatomic surface is globally described to any given accuracy. Finally, the algorithm is tested on a set of simple molecules and on the amide interatomic surfaces of the glycyl residue |HNCH₂CO|.