Alexandre A. Shvartsburg

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

Abstract 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 geometrics with grossly concave surfaces.

Structures of medium-sized silicon clusters

Silicon is the most important semiconducting material in the microelectronics industry. If current miniaturization trends continue, minimum device features will soon approach the size of atomic clusters. In this size regime, the structure and properties of materials often differ dramatically from those of the bulk. An enormous effort has been devoted to determining the structures of free silicon clusters. Although progress has been made for Sin with n < 8, theoretical predictions for larger clusters are contradictory and none enjoy any compelling experimental support. Here we report geometries calculated for medium-sized silicon clusters using an unbiased global search with a genetic algorithm. Ion mobilities determined for these geometries by trajectory calculations are in excellent agreement with the values that we measure experimentally. The cluster geometries that we obtain do not correspond to fragments of the bulk. For n = 12–18 they are built on a structural motif consisting of a stack of Si9 tricapped trigonal prisms. For n ⩾ 19, our calculations predict that near-spherical cage structures become the most stable. The transition to these more spherical geometries occurs in the measured mobilities for slightly larger clusters than in the calculations, possibly because of entropic effects.

Fundamentals of Traveling Wave Ion Mobility Spectrometry

Traveling wave ion mobility spectrometry (TW IMS) is a new IMS method implemented in the Synapt IMS/mass spectrometry system (Waters). Despite its wide adoption, the foundations of TW IMS were only qualitatively understood and factors governing the ion transit time (the separation parameter) and resolution remained murky. Here we develop the theory of TW IMS using derivations and ion dynamics simulations. The key parameter is the ratio (c) of ion drift velocity at the steepest wave slope to wave speed. At low c, the ion transit velocity is proportional to the squares of mobility (K) and electric field intensity (E), as opposed to linear scaling in drift tube (DT) IMS and differential mobility analyzers. At higher c, the scaling deviates from quadratic in a way controlled by the waveform profile, becoming more gradual with the ideal triangular profile but first steeper and then more gradual for realistic profiles with variable E. At highest c, the transit velocity asymptotically approaches the wave speed. Unlike with DT IMS, the resolving power of TW IMS depends on mobility, scaling as K(1/2) in the low-c limit and less at higher c. A nonlinear dependence of the transit time on mobility means that the true resolving power of TW IMS differs from that indicated by the spectrum. A near-optimum resolution is achievable over an approximately 300-400% range of mobilities. The major predicted trends are in agreement with TW IMS measurements for peptide ions as a function of mobility, wave amplitude, and gas pressure. The issues of proper TW IMS calibration and ion distortion by field heating are also discussed. The new quantitative understanding of TW IMS separations allows rational optimization of instrument design and operation and improved spectral calibration.

Ionization of medium-sized silicon clusters and the geometries of the cations

We have performed a systematic ground state geometry search for the singly charged Sin cations in the medium-size range (n⩽20) using density functional theory in the local density approximation (LDA) and generalized gradient approximation (GGA). The structures resulting for n⩽18 generally follow the prolate “stacked Si9 tricapped trigonal prism” pattern recently established for the lowest energy geometries of neutral silicon clusters in this size range. However, the global minima of Sin and Sin+ for n=6, 8, 11, 12, and 13 differ significantly in their details. For Si19 and Si20 neutrals and cations, GGA renders the prolate stacks practically isoenergetic with the near-spherical structures that are global minima in LDA. The mobilities in He gas evaluated for all lowest energy Sin+ geometries using the trajectory method agree with the experiment, except for n=18 where the second lowest isomer fits the measurements. The effect of gradient corrections for either the neutral or cationic clusters is subtle, but...

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 fo...

Mobilities of carbon cluster ions: Critical importance of the molecular attractive potential

Mobilities in helium gas for isomers belonging to the major structural families of carbon clusters identified in drift tube studies (chains, monocyclic and bicyclic rings, graphite sheets, and fullerenes and their dimers) have been evaluated by trajectory calculations employing a realistic ion-He interaction potential. For all the species considered, the agreement between the measured and calculated mobilities at room temperature improves by at least a factor of 3 over that obtained with the widely used hard-sphere projection approximation. Furthermore, for a large representative sample of clusters belonging to all the above families, the results of trajectory calculations as a function of temperature over the range of 78–360 K are in a good agreement with the measured mobilities. This shows that the C–He pairwise potential is only weakly dependent on the structure and chemical bonding of a carbon cluster. Thus this study demonstrates the universal suitability of trajectory calculations for the accurate p...

High-Resolution Differential Ion Mobility Separations Using Helium-Rich Gases

Analyses of complex mixtures and characterization of ions increasingly involve gas-phase separations by ion mobility spectrometry (IMS) and particularly differential or field asymmetric waveform IMS (FAIMS) based on the difference of ion mobility in strong and weak electric fields. The key advantage of FAIMS is substantial orthogonality to mass spectrometry (MS), which makes FAIMS/MS hybrid a powerful analytical platform of broad utility. However, the potential of FAIMS has been constrained by limited resolution. Here, we report that the use of gas mixtures comprising up to 75% He dramatically increases the FAIMS separation capability, with the resolving power for peptides and peak capacity for protein digests reaching and exceeding 100. The resolution gains extend to small molecules, where previously unresolved isomers can now be separated. These performance levels open major new applications of FAIMS in proteomic and other biomolecular analyses.

Structural information from ion mobility measurements: applications to semiconductor clusters

Ion mobility measurements are one of the few methods presently available that can directly probe the structures of relatively large molecules in the gas phase. Here we review the application of ion mobility methods to the elucidation of the structures of semiconductor clusters (Sin, Gen, and Snn). We describe the new high-resolution implementation of the technique and the advanced methods of mobility calculations that are crucial for the correct analysis of the experimental data.

Separation and Classification of Lipids Using Differential Ion Mobility Spectrometry

Correlations between the dimensions of a 2-D separation create trend lines that depend on structural or chemical characteristics of the compound class and thus facilitate classification of unknowns. This broadly applies to conventional ion mobility spectrometry (IMS)/mass spectrometry (MS), where the major biomolecular classes (e.g., lipids, peptides, nucleotides) occupy different trend line domains. However, strong correlation between the IMS and MS separations for ions of same charge has impeded finer distinctions. Differential IMS (or FAIMS) is generally less correlated to MS and thus could separate those domains better. We report the first observation of chemical class separation by trend lines using FAIMS, here for lipids. For lipids, FAIMS is indeed more independent of MS than conventional IMS, and subclasses (such as phospho-, glycero-, or sphingolipids) form distinct, often non-overlapping domains. Even finer categories with different functional groups or degrees of unsaturation are often separated. As expected, resolution improves in He-rich gases: at 70% He, glycerolipid isomers with different fatty acid positions can be resolved. These results open the door for application of FAIMS to lipids, particularly in shotgun lipidomics and targeted analyses of bioactive lipids.

Separation of Peptide Isomers with Variant Modified Sites by High-Resolution Differential Ion Mobility Spectrometry

Many proteins and proteolytic peptides incorporate the same post-translational modification (PTM) at different sites, creating multiple localization variants with different functions or activities that may coexist in cells. Current analytical methods based on liquid chromatography (LC) followed by tandem mass spectrometry (MS/MS) are challenged by such isomers that often coelute in LC and/or produce nonunique fragment ions. The application of ion mobility spectrometry (IMS) was explored, but success has been limited by insufficient resolution. We show that high-resolution differential ion mobility spectrometry (FAIMS) employing helium-rich gases can readily separate phosphopeptides with variant modification sites. Use of He/N(2) mixtures containing up to 74% He has allowed separating to >95% three monophosphorylated peptides of identical sequence. Similar separation was achieved at 50% He, using an elevated electric field. Bisphosphorylated isomers that differ in only one modification site were separated to the same extent. We anticipate FAIMS capabilities for such separations to extend to other PTMs.