Improved First-Principles Model of Differential Mobility Using Higher Order Two-Temperature Theory

Ion mobility calculations of flexible all-atom systems at arbitrary fields using two-temperature theory

Ion mobility spectrometry (IMS) separates and analyzes ions based on their mobility in a gas under an electric field. When the field is increased, the mobility varies in a complex way that depends on the relative velocity between gas and ion, their electrostatic potential interactions, and the effects from direct impingement. Recently, the two-temperature theory, primarily developed for monoatomic ions in monoatomic gases, has been extended to study mobilities at arbitrary fields using polyatomic ions in polyatomic gases, with some success. However, this extension poses challenges, such as inelastic collisions between gas and ion and structural modifications of ions as they heat up. These challenges become significant when working with diatomic gases and flexible molecules. In a previous study, experimental mobilities of tetraalkylammonium salts were obtained using a FAIMS instrument, showing satisfactory agreement with numerical two-temperature theory predictions. However, deviations occurred at fields greater than 100 Td. To address this issue, this paper introduces a modified high-field calculation method that accounts for the structural changes in ions due to field heating. The study focuses on tetraheptylammonium (THA+), tetradecylammonium (TDA+), and tetradodecylammonium (TDDA+) salts. Molecular structures were generated at various temperatures using MM2 forcefield. The mobility was calculated using IMoS 1.13 with two-temperature trajectory method calculations up to the fourth approximation. Multiple effective temperatures were considered, and a linear weighing system was used to create mobility vs. reduced field strength plots. The results suggest that the structural enlargement due to ion heating plays a significant role in mobility at high fields, aligning better with experimental data. FAIMS' dispersion plots also show improved agreement with experimental results. However, the contribution of inelastic collisions and energy transfer to rotational degrees of freedom in gas molecules remains a complex and challenging aspect.

Bridging the Gap between Differential Mobility, Log S, and Log P Using Machine Learning and SHAP Analysis

Aqueous solubility, log S, and the water-octanol partition coefficient, log P, are physicochemical properties that are used to screen the viability of drug candidates and to estimate mass transport in the environment. In this work, differential mobility spectrometry (DMS) experiments performed in microsolvating environments are used to train machine learning (ML) frameworks that predict the log S and log P of various molecule classes. In lieu of a consistent source of experimentally measured log S and log P values, the OPERA package was used to evaluate the aqueous solubility and hydrophobicity of 333 analytes. With ion mobility/DMS data (e.g., CCS, dispersion curves) as input, we used ML regressors and ensemble stacking to derive relationships with a high degree of explainability, as assessed via SHapley Additive exPlanations (SHAP) analysis. The DMS-based regression models returned scores of R² = 0.67 and RMSE = 1.03 ± 0.10 for log S predictions and R² = 0.67 and RMSE = 1.20 ± 0.10 for log P after 5-fold random cross-validation. SHAP analysis reveals that the regressors strongly weighted gas-phase clustering in log P correlations. The addition of structural descriptors (e.g., # of aromatic carbons) improved log S predictions to yield RMSE = 0.84 ± 0.07 and R² = 0.78. Similarly, log P predictions using the same data resulted in an RMSE of 0.83 ± 0.04 and R² = 0.84. The SHAP analysis of log P models highlights the need for additional experimental parameters describing hydrophobic interactions. These results were achieved with a smaller dataset (333 instances) and minimal structural correlation compared to purely structure-based models, underscoring the value of employing DMS data in predictive models.

MobCal-MPI 2.0: an accurate and parallelized package for calculating field-dependent collision cross sections and ion mobilities

Ion mobility spectrometry (IMS), which can be employed as either a stand-alone instrument or coupled to mass spectrometry, has become an important tool for analytical chemistry. Because of the direct relation between an ion's mobility and its structure, which is intrinsically related to its collision cross section (CCS), IMS techniques can be used in tandem with computational tools to elucidate ion geometric structure. Here, we present MobCal-MPI 2.0, a software package that demonstrates excellent accuracy (RMSE 2.16%) and efficiency in calculating low-field CCSs via the trajectory method (≤30 minutes on 8 cores for ions with ≤70 atoms). MobCal-MPI 2.0 expands on its predecessor by enabling the calculation of high-field mobilities through the implementation of the 2^nd order approximation to two-temperature theory (2TT). By further introducing an empirical correction to account for deviations between 2TT and experiment, MobCal-MPI 2.0 can compute accurate high-field mobilities that exhibit a mean deviation of <4% from experimentally measured values. Moreover, the velocities used to sample ion-neutral collisions were updated from a weighted to a linear grid, enabling the near-instantaneous evaluation of mobility/CCS at any effective temperature from a single set of N₂ scattering trajectories. Several enhancements made to the code are also discussed, including updates to the statistical analysis of collision event sampling and benchmarking of overall performance.

Chemical Transformations Can Occur during DMS Separations: Lessons Learned from Beer's Bittering Compounds

While developing a DMS-based separation method for beer's bittering compounds, we observed that the argentinated forms of humulone tautomers (i.e., [Hum + Ag]⁺) were partially resolvable in a N₂ environment seeded with 1.5 mol % of isopropyl alcohol (IPA). Attempting to improve the separation by introducing resolving gas unexpectedly caused the peaks for the cis-keto and trans-keto tautomers of [Hum + Ag]⁺ to coalesce. To understand why resolution loss occurred, we first confirmed that each of the tautomeric forms (i.e., dienol, cis-keto, and trans-keto) responsible for the three peaks in the [Hum + Ag]⁺ ionogram were assigned to the correct species by employing collision-induced dissociation, UV photodissociation spectroscopy, and hydrogen-deuterium exchange (HDX). The observation of HDX indicated that proton transfer was stimulated by dynamic clustering processes between IPA and [Hum + Ag]⁺ during DMS transit. Because IPA accretion preferentially occurs at Ag⁺, which can form pseudocovalent bonds with a suitable electron donor, solvent clustering also facilitated the formation of exceptionally stable microsolvated ions. The exceptional stability of these microsolvated configurations disproportionately impacted the compensation voltage (CV) required to elute each tautomer when the temperature within the DMS cell was varied. The disparity in CV response caused the peaks for the cis- and trans-keto species to merge when a temperature gradient was induced by the resolving gas. Moreover, simulations showed that microsolvation with IPA mediates dienol to trans-keto tautomerization during DMS transit, which, to the best of our knowledge, is the first observation of keto/enol tautomerization occurring within an ion-mobility device.

Validation of Field-Dependent Ion-Solvent Cluster Modeling via Direct Measurement of Cluster Size Distributions

Ion mobility spectrometry is widely used in analytical chemistry, either as a stand-alone technique or coupled to mass spectrometry. Ions in the gas phase tend to form loosely bound clusters with surrounding solvent vapors, artificially increasing the collisional cross section and the mass of the ion. This, in turn, affects ion mobility and influences separation. Further, ion-solvent clusters play an important role in most ionization mechanisms occurring in the gas phase. Consequently, a deeper understanding of ion-solvent cluster association and dissociation processes is desirable to guide experimental design and interpretation. A few computational models exist, which aim to describe the amount of clustering as a function of the reduced electric field strength, bath gas pressure and temperature, and the chemical species probed. It is especially challenging to model ion mobility under high reduced electrical field strengths due to the nonthermal conditions created by the field. In this work, we aim to validate a recently proposed first-principles model by comparing its predictions with direct measurements of cluster size distributions over a range of 20-120 Td as observed using a High Kinetic Energy Ion Mobility Spectrometer coupled to a mass spectrometer (HiKE-IMS-MS). By studying H⁺(H₂O)_n, [MeOH + H + n(H₂O)]⁺, [ACE + H + n(H₂O)]⁺, and [PhNH₂ + H + n(H₂O)]⁺ as test systems, we find very good agreement between model and experiment, supporting the validity of the computational workflow. Further, the detailed information gained from the modeling yields important insights into the cluster dynamics within the HiKE-IMS, allowing for better interpretation of the measured ion mobility spectra.

First-Principles Modeling of Preferential Solvation in Mixed-Modifier Differential Mobility Spectrometry

Differential mobility spectrometry (DMS) separates ions based on mobility differences between high and low electric field conditions. To enhance resolution, solvents such as water and acetonitrile are often used to modify the collision environment and take advantage of differing dynamic clustering behavior between analytes that coelute in hard-sphere environments (e.g., N₂). When binary solvent mixtures are used to modify the DMS environment, one solvent can have a dominant influence over the other with respect to ion trajectories. For example, for quinoline derivatives, a 9:1 water:acetonitrile solvent mixture exhibited identical behavior to an environment containing only acetonitrile as a modifier. It was hypothesized that this effect arises due to the significantly different binding strengths of the two solvents. Here, we utilize a first-principles model of DMS to study analytes in single and binary solvent mixtures and explore the effects governing the dominance of one solvent over the other. Computed DMS dispersion curves of quinoline derivatives are in excellent agreement with those measured experimentally. For mixed-modifier environments, the predicted cluster populations show a clear preferential solvation of ions with the stronger binding solvent. The influence of ion-solvent binding energies, solvent concentration, and solvent molecule size is discussed in the context of the observed DMS behavior. This work can guide the usage of binary solvent mixtures for improving ion separations in cases where compounds coelute in pure N₂ and in single-solvent modifier environments. Moreover, our results indicate that binary solvent mixtures can be used to create a relative scale for solvent binding energies.

Argentination: A Silver Bullet for Cannabinoid Separation by Differential Mobility Spectrometry

As the legality of cannabis continues to evolve globally, there is a growing demand for methods that can accurately quantitate cannabinoids found in commercial products. However, the isobaric nature of many cannabinoids, along with variations in extraction methods and product formulations, makes cannabinoid quantitation by mass spectrometry (MS) challenging. Here, we demonstrate that differential mobility spectrometry (DMS) and tandem-MS can distinguish a set of seven cannabinoids, five of which are isobaric: Δ⁹-tetrahydrocannabinol (Δ⁹-THC), Δ⁸-THC, exo-THC, cannabidiol, cannabichromene, cannabinol, and cannabigerol. Analytes were detected as argentinated species ([M + Ag]⁺), which, when subjected to collision-induced dissociation, led to the unexpected discovery that argentination promotes distinct fragmentation patterns for each cannabinoid. The unique fragment ions formed were rationalized by discerning fragmentation mechanisms that follow each cannabinoid's MS³ behavior. The differing fragmentation behaviors between species suggest that argentination can distinguish cannabinoids by tandem-MS, although not quantitatively as some cannabinoids produce small amounts of a fragment ion that is isobaric with the major fragment generated by another cannabinoid. By adding DMS to the tandem-MS workflow, it becomes possible to resolve each cannabinoid in a pure N₂ environment by deconvoluting the contribution of each cannabinoid to a specific fragmentation channel. To this end, we used DMS in conjunction with a multiple reaction monitoring workflow to assess cannabinoid levels in two cannabis extracts. Our methodology exhibited excellent accuracy, limits of detection (10-20 ppb depending on the cannabinoid), and linearity during quantitation by standard addition (R² > 0.99).

Investigation of Zero-/High-Field Ion Mobility Orthogonal Separation Using a Hyphenated DMA-FAIMS System and Validation of the Two-Temperature Theory at Arbitrary Field for Tetraalkylammonium Salts in Nitrogen

Toward greater separation techniques for ions, a differential mobility analyzer (DMA) has been coupled with field asymmetric waveform ion mobility spectrometry (FAIMS) to take advantage of two mobility-related but different methods of separation. The filtering effect of the DMA allows ions to be selected individually based on low-field mobility and studied in FAIMS at variable electric field, yielding mobility separations in two dimensions. Because spectra fully describe ion mobility at variable field strength, results are then compared with a two-temperature theory-predicted mobility up to the fourth-order approximation. The comparison yields excellent results up to at least 100 Td, beyond which the theory deviates from experiments. This is attributed to two effects, the enlargement of the structure due to ion heating and the inelasticity of the collisions with the nitrogen bath gas. The corrected mobility can then be used to predict the dispersion plot through a newly developed implicit equation that circumvents the possible issues related to the more elaborate Buryakov equation. Our results simultaneously show that the DMA-FAIMS coupling yields complete information on ion mobility versus the field-strength to gas-density ratio and works toward predicting such spectra from ion structures and gas properties.

Kinetics in DMS: Modeling Clustering and Declustering Reactions

Differential mobility spectrometry (DMS) uses high-frequency oscillating electrical fields to harness the differential mobility of ions for separating complex sample mixtures prior to detection. To increase the resolving power, a dynamic microsolvation environment is often created by introducing solvent vapors. Here, relatively large clusters are formed at low-field conditions which then evaporate to form smaller clusters at high-field conditions. The kinetics of these processes as the electrical field strength oscillates are not well studied. Here, we develop a computational framework to investigate how the different reactions (cluster association, cluster dissociation, and fast conformational changes) behave at different field strengths. We aim to better understand these processes, their effect on experimental outcomes, and whether DMS model accuracy is improved via incorporating their description. We find that cluster association and dissociation reactions for typical ion-solvent pairs are fast compared to the time scale of the varying separation fields usually used. However, low solvent concentration, small dipole moments, and strong ion-solvent binding can result in reaction rates small enough that a lag is observed in the ion's DMS response. This can yield differences of several volts in the compensation voltages required to correct ion trajectories for optimal transmission. We also find that the proposed kinetic approach yields generally better agreement with experiment than using a modified Boltzmann weighting scheme. Thus, this work provides insights into the chemical dynamics occurring within the DMS cell while also increasing the accuracy of dispersion plot predictions.

The hitchhiker's guide to dynamic ion-solvent clustering: applications in differential ion mobility spectrometry

This article highlights the fundamentals of ion-solvent clustering processes that are pertinent to understanding an ion's behaviour during differential mobility spectrometry (DMS) experiments. We contrast DMS with static-field ion mobility, where separation is affected by mobility differences under the high-field and low-field conditions of an asymmetric oscillating electric field. Although commonly used in mass spectrometric (MS) workflows to enhance signal-to-noise ratios and remove isobaric contaminants, the chemistry and physics that underpins the phenomenon of differential mobility has yet to be fully fleshed out. Moreover, we are just now making progress towards understanding how the DMS separation waveform creates a dynamic clustering environment when the carrier gas is seeded with the vapour of a volatile solvent molecule (e.g., methanol). Interestingly, one can correlate the dynamic clustering behaviour observed in DMS experiments with gas-phase and solution-phase molecular properties such as hydrophobicity, acidity, and solubility. However, to create a generalized, global model for property determination using DMS data one must employ machine learning. In this article, we provide a first-principles description of differential ion mobility in a dynamic clustering environment. We then discuss the correlation between dynamic clustering propensity and analyte physicochemical properties and demonstrate that analytes exhibiting similar ion-solvent interactions (e.g., charge-dipole) follow well-defined trends with respect to DMS clustering behaviour. Finally, we describe how supervised machine learning can be used to create predictive models of molecular properties using DMS data. We additionally highlight open questions in the field and provide our perspective on future directions that can be explored.