Ion mobility spectrometry (IMS) is increasingly employed to probe the structures of gas-phase ions, particularly those of proteins and other biological macromolecules. This process involves comparing measured mobilities to those computed for potential geometries, which requires evaluation of orientationally averaged cross sections using some approximate treatment of ion-buffer gas collisions. Two common models are the projection approximation (PA) and exact hard-spheres scattering (EHSS) that represent ions as collections of hard spheres. Though calculations for large ions and/or conformer ensembles take significant time, no algorithmic optimization had been explored. Previous EHSS programs were dominated by ion rotation operations that allow orientational averaging. We have developed two new algorithms for PA and EHSS calculations: one simplifies those operations and greatly reduces their number, and the other disposes of them altogether by propagating trajectories from a random origin. The new algorithms were tested for a representative set of seven ion geometries including diverse sizes and shapes. While the best choice depends on the geometry in a nonobvious way, the difference between the two codes is generally modest. Both are much more efficient than the existing software, for example faster than the widely used Mobcal (implementing EHSS) approximately 10-30-fold.

Technologies for separating and characterizing ions based on their transport properties in gases have been around for three decades. The early method of ion mobility spectrometry (IMS) distinguished ions by absolute mobility that depends on the collision cross section with buffer gas atoms. The more recent technique of field asymmetric waveform IMS (FAIMS) measures the difference between mobilities at high and low electric fields. Coupling IMS and FAIMS to soft ionization sources and mass spectrometry (MS) has greatly expanded their utility, enabling new applications in biomedical and nanomaterials research. Here, we show that time-dependent electric fields comprising more than two intensity levels could, in principle, effect an infinite number of distinct differential separations based on the higher-order terms of expression for ion mobility. These analyses could employ the hardware and operational procedures similar to those utilized in FAIMS. Methods up to the 4 th or 5 th order (where conventional IMS is 1 st order and FAIMS is 2 nd order) should be practical at field intensities accessible in ambient air, with still higher orders potentially achievable in insulating gases. Available experimental data suggest that higher-order separations should be largely orthogonal to each other and to FAIMS, IMS, and MS.Approaches to separation of ion mixtures and characterization of ions in the gas phase based on ion mobility are becoming commonplace in analytical chemistry. The key advantage of gas-phase separations over condensed phase methods is the exceptional speed enabled by rapid molecular motion in gases. This inherent benefit is made increasingly topical by the growing focus of analytical technology on higher throughput. Since their first demonstration a decade ago, 1-3 instrumental platforms combining electrospray ionization (ESI) or matrixassisted laser desorption ionization (MALDI) sources with ion mobility separations and mass-spectrometry (MS) have undergone a sustained development that has improved their resolution and sensitivity to the levels demanded by practical applications. 4-10 Recent commercial introduction of such systems 11-14 is expanding interest in ion mobility/MS, particularly for analyses of complex biological samples such as proteolytic digests and lipids, nucleotides, and metabolites. [15][16][17][18][19][20][21][22][23][24] Single-stage ion mobility spectrometry (IMS) was investigated since the 1970s, 25-27 with a noteworthy development of ESI/IMS in 1980s. 28 In IMS, ions drift through a non-reactive buffer gas under the influence of a modest electric field. The drift velocity (v) in the field of intensity E is determined by ion mobility (K):(1)For consistency, measured mobilities are normally converted to reduced values K 0 by adjusting the buffer gas temperature (T, Kelvin) and pressure (P, Torr) to standard (STP) conditions:NIH Public Access