An exact hard-spheres scattering model for the mobilities of polyatomic ions

We describe an exact hard-spheres scattering model for calculating the gas phase mobilities of polyatomic ions. Ion mobility measurements have recently been used to deduce structural information for clusters and biomolecules in the gas phase. In virtually all of the previous ion mobility studies, mobilities were evaluated for comparison with the experimental data using a projection approximation. Comparison of the collision integrals calculated using the exact hard-spheres scattering model with those estimated using the projection approximation shows that large deviations, over 20%, occur for some geometries with grossly concave surfaces. The mobility of a polyatomic ion depends on its structure [1-3]. Ion mobility measurements can resolve structural isomers and provide information about their geometries. This technique has been particularly valuable in the study of medium-sized clusters where spectroscopic information is difficult to obtain [4-10]. For example, chains, a variety of ring isomers, graphite sheets, and fullerenes have been observed for carbon clusters [7-10]. Recently, this approach has also been used to examine the conformations of peptides [11] and proteins [12] in the gas phase. Furthermore, instrumental advances now make it possible to perform high-resolution ion mobility measurements where isomers with very similar geometries can be resolved, as demonstrated by some recent studies of (NaCI),C1clusters [13]. Information about the geometries is obtained by comparing measured mobilities with mobilities calculated for an assumed geometry. The zero-field mobility can be obtained from [14] K ( 1 8 r r ) ' / 2 [ 1 1 ] ./2 ze 1 1 16 m b ( k B T ) ' / 2 a ( ~ l ) N "