Modeling ionic mobilities by scattering on electronic density isosurfaces: Application to silicon cluster anions

We have developed a new formalism to evaluate the gas-phase mobility of an ion based on elastic scattering on an electronic density isosurface (SEDI). In this method, the ion is represented by a surface of arbitrary shape defined as a set of points in space where the total electron density assumes a certain value. This value is the only adjustable parameter in the model. Conceptually, this treatment emulates the interaction between a drifting ion and the buffer gas atoms closer than the previously described methods, the exact hard spheres scattering (EHSS) model and trajectory calculations, where the scattering occurs in potentials centered on the nuclei. We have employed EHSS, trajectory calculations, and SEDI to compute the room temperature mobilities for low-energy isomers of Sin (n⩽20) cations and anions optimized by density functional theory (DFT) in the local density approximation and generalized gradient approximation. The results produced by SEDI are in excellent agreement with the measurements for both charge states, while other methods can fit the mobilities for cations only. Using SEDI, we have confirmed the structural differences between Sin+ and Sin− predicted by DFT calculations, including the major rearrangements for n=9, 15, 16, and 18. We have also assigned the multiple isomers observed in recent high-resolution mobility measurements for Sin+ with n=17–19, some of them to near-spherical cage-like geometries.