Monte Carlo simulation of ion trajectories of reacting chemical systems: mobility of small water clusters in ion mobility spectrometry

Molecular Dynamics-Based Modeling of Ion-Neutral Collisions in an Open Ion Trajectory Simulation Framework

Ion mobility spectrometry (IMS) and ion mobility mass spectrometry (IMS-MS) methods have become increasingly popular and are important analytical techniques to determine information about the structural parameters of gas-phase analytes. The accurate description of the interaction between molecular ions and neutral background gas particles is an essential part of high-quality simulations of such modern mass- and ion-mobility-spectrometric systems. Established ion-neutral collision models (Hard-sphere collision modeling and statistical diffusion simulations) in common ion-trajectory simulation systems like SIMION use strongly simplified assumptions and are thus limited in their predictive ability. In contrast, collision cross-section (CCS) modeling programs (e.g., MOBCAL, IMoS, and Colloidoscope) allow high-quality ion mobility predictions for low-field equilibrium conditions using explicit scattering processes with a molecular dynamics-based trajectory method but cannot be used for nonequilibrium collision modeling in an ion trajectory simulation. This work presents an extension to the open-source Ion Dynamics Simulation Framework (IDSimF), which allows the simulation of ion dynamics under arbitrary and even nonequilibrium conditions. It was extended by an advanced collision model employing the molecular dynamics trajectory method for a detailed microscopic description of ion-neutral collisions within ion-trajectory simulations. We used drift tube ion mobility spectrometry (DT-IMS) to validate the predictive abilities of the model and to estimate the runtime requirements for productive simulations. Simulated high-field ion mobilities for small ion systems in a drift tube IMS are compared to experimental values from the literature and an implementation of a hard-sphere model in IDSimF for helium and argon as background gas particles. Significant improvements in ion mobility predictions using the molecular dynamics trajectory approach are obtained with deviations of only a few percent from experimental values. Therefore, the established and publicly available MD collision model will serve as foundation for nonequilibrium ion dynamics simulations and the development of improved ion dynamics modeling methods.

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.

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.

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

Differential mobility spectrometry is a separation technique that may be applied to a variety of analytes ranging from small molecule drugs to peptides and proteins. Although rudimentary theoretical models of differential mobility exist, these models are often only applied to small molecules and atomic ions without considering the effects of dynamic microsolvation. Here, we advance our theoretical description of differential ion mobility in pure N₂ and microsolvating environments by incorporating higher order corrections to two-temperature theory (2TT) and a pseudoequilibrium approach to describe ion-neutral interactions. When comparing theoretical predictions to experimentally measured dispersion plots of over 300 different compounds, we find that higher order corrections to 2TT reduce errors by roughly a factor of 2 when compared to first order. Model predictions are accurate especially for pure N₂ environments (mean absolute error of 4 V at SV = 4000 V). For strongly clustering environments, accurate thermochemical corrections for ion-solvent clustering are likely required to reliably predict differential ion mobility behavior. Within our model, general trends associated with clustering strength, solvent vapor concentration, and background gas temperature are well reproduced, and fine structure visible in some dispersion plots is captured. These results provide insight into the dynamic ion-solvent clustering process that underpins the phenomenon of differential ion mobility.

Simulation of Cluster Dynamics of Proton-Bound Water Clusters in a High Kinetic Energy Ion-Mobility Spectrometer

Ions are separated in ion mobility spectrometry (IMS) by their characteristic motion through a gas-filled drift tube with a static electric field present. Chemical dynamics, such as clustering and declustering of chemically reactive systems, and physical parameters, as, for example, the electric field strength or background gas temperature, impact on the observed ion mobility. In high kinetic energy IMS (HiKE-IMS), the reduced electric field strength is up to 120 Td in both the reaction region and drift region of the instrument. The ion generation in a corona discharge driven chemical ionization source leads generally to formation of proton-bound water clusters. However, the reduced electric field strength and therefore the effective ion temperature has a significant influence on the chemical equilibria of this reaction system. In order to characterize the effects occurring in IMS systems in general, numerical simulations can support and potentially explain experimental observations. The comparison of the simulation of a well characterized chemical reaction system (i.e., the proton-bound water cluster system) with experimental results allows us to validate the numerical model applied in this work. Numerical simulations of the proton-bound water cluster system were performed with the custom particle-based ion dynamics simulation framework (IDSimF). The ion-transport calculation in the model is based on a Verlet integration of the equations of motion and uses a customized Barnes-Hut method to calculate space charge interactions. The chemical kinetics is modeled stochastically with a Monte Carlo method. The experimental and simulated drift spectra are in good qualitative and quantitative agreement, and experimentally observed individual transitions of cluster ions are clearly reproduced and identified by the numerical model.

Influence of Reduced Field Strength on Product Ion Formation in High Kinetic Energy Ion Mobility Spectrometry (HiKE-IMS)

Classical ion mobility spectrometers (IMS) operated at ambient pressure, often use atmospheric pressure chemical ionization (APCI) sources to ionize organic compounds. In APCI, reactant ions ionize neutral analyte molecules via gas-phase ion-molecule reactions. The positively charged reactant ions in purified, dry air are H₃O⁺, NO⁺, and O₂^+•. However, the hydration of reactant ions in classical IMS operated at ambient pressure renders ionization of certain analytes difficult. In contrast to classical IMS operated at ambient pressure, High Kinetic Energy Ion Mobility Spectrometers (HiKE-IMS) are operated at a decreased pressure of 10-40 mbar, allowing operation at high reduced electric field strengths of up to 120 Td. At such high reduced field strengths, ions reach high effective temperatures causing collision-induced cluster dissociation of the hydrated gas-phase ions, allowing ionization of nonpolar and low proton affinity analytes. The reactant ion population, consisting of H₃O⁺(H₂O)_n, NO⁺(H₂O)_m, and O₂^+•(H₂O)_p with an individual abundance that strongly depends on the reduced field strength, differs from the reactant ion population in IMS operated at ambient pressure, which affects the ionization of analyte molecules. In this work, we investigate the influence of reduced field strength on the product ion formation of aromatic hydrocarbons used as model substances. A HiKE-IMS-MS coupling was used to identify the detected ion species. The results show that the analytes form parent cations via charge transfer with NO⁺(H₂O)_m and O₂^+•(H₂O)_p depending on ionization energy and protonated parent molecules via proton transfer and ligand switching with H₃O⁺(H₂O)_n mainly depending on proton affinity.

Field-Dependent Reduced Ion Mobilities of Positive and Negative Ions in Air and Nitrogen in High Kinetic Energy Ion Mobility Spectrometry (HiKE-IMS)

In High Kinetic Energy Ion Mobility Spectrometry (HiKE-IMS), ions are formed in a reaction region and separated in a drift region, which is similar to classical drift tube ion mobility spectrometers (IMS) operated at ambient pressure. However, in contrast to the latter, the HiKE-IMS is operated at a decreased background pressure of 10-40 mbar and achieves high reduced electric field strengths of up to 120 Td in both the reaction and the drift region. Thus, the HiKE-IMS allows insights into the chemical kinetics of ion-bound water cluster systems at effective ion temperatures exceeding 1000 K, although it is operated at the low absolute temperature of 45 °C. In this work, a HiKE-IMS with a high resolving power of R_P = 140 is used to study the dependence of reduced ion mobilities on the drift gas humidity and the effective ion temperature for the positive reactant ions H₃O⁺(H₂O)_n, O₂⁺(H₂O)_n, NO⁺(H₂O)_n, NO₂⁺(H₂O)_n, and NH₄⁺(H₂O)_n, as well as the negative reactant ions O₂^-(H₂O)_n, O₃^-(H₂O)_n, CO₃^-(H₂O)_n, HCO₃^-(H₂O)_n, and NO₂^-(H₂O)_n. By varying the reduced electric field strength in the drift region, cluster transitions are observed in the ion mobility spectra. This is demonstrated for the cluster systems H₃O⁺(H₂O)_n and NO⁺(H₂O)_n.

Computational analysis of the proton-bound acetonitrile dimer, (ACN)2 H. RAPID COMMUNICATIONS IN MASS SPECTROMETRY : RCM 2020;34:e8767. [PMID: 32115782 DOI: 10.1002/rcm.8767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

RATIONALE

In atmospheric pressure ionization mass spectrometry the theoretical thermodynamic treatment of proton-bound cluster stabilities helps us to understand the prevailing chemical processes. However, such calculations are rather challenging because low-barrier internal rotations and strong anharmonicity of the hydrogen bonds cause the breakdown of the usually applied harmonic approximation. Even the implemented anharmonic treatment in standard ab initio software failed in the case of (ACN)₂ H⁺ .

METHODS

For a case study of the proton-bound acetonitrile dimer, (ACN)₂ H⁺ , we scan the potential energy surface (PES) for the internal rotation and the proton movement in all three spatial directions. We correct the partition functions by treating the internal rotation as a free rotor and by solving the nuclear Schrödinger equation explicitly for the proton movement. An additional PES scan for the dissociation surface further improves the understanding of the cluster behavior.

RESULTS

The internal rotation is essentially barrier free (V₀  = 2.6 × 10^-6 eV) and the proton's movement between the two nitrogen atoms follows a quartic rather than quadratic potential. As a figure of merit we calculate the free dissociation enthalpy of the dimer. Our description significantly improves the standard results from about 118.3 kJ/mol to 99.6 kJ/mol, compared with the experimentally determined value of 92.2 kJ/mol. The dissociation surface reveals strong crosstalk between modes and is essentially responsible for the observed errors.

CONCLUSIONS

The presented corrections to the partition functions significantly improve their accuracy and are rather easy to implement. In addition, this work stresses the importance of alternative theoretical methods for proton-bound cluster systems besides the standard harmonic approximations.

Analyzing Positive Reactant Ions in High Kinetic Energy Ion Mobility Spectrometry (HiKE-IMS) by HiKE-IMS-MS

In contrast to classical ion mobility spectrometers (IMS) operating at ambient pressure, the high kinetic energy ion mobility spectrometer (HiKE-IMS) is operated at reduced pressures between 10-40 mbar. In HiKE-IMS, ions are generated in a reaction region before they are separated in a drift region. Due to the operation at reduced pressure, it is possible to reach high reduced electric field strengths up to 120 Td in both the reaction as well as drift region, resulting in a pronounced decrease in chemical cross sensitivities and a significant enhancement of the dynamic range. Until now though, only limited knowledge about the ionization pathways in HiKE-IMS is available. Typically, proton bound water clusters, H⁺(H₂O)_n, are the most abundant positive reactant ion species in classical IMS with atmospheric chemical ionization sources. However, at reduced pressure and increased effective ion temperature, the reactant ion population significantly changes. As the ionization efficiency of analyte molecules in HiKE-IMS strongly depends on the reactant ion population, a detailed knowledge of the reactant ion population generated in HiKE-IMS is essential. Here, we present a coupling stage of the HiKE-IMS to a mass spectrometer enabling the identification of ion species and the investigation of ion molecule reactions prevailing in HiKE-IMS. In the present study, the HiKE-IMS-MS is used to identify positive reactant ion populations in both, purified air and nitrogen, respectively. The experimental data suggest the generation of systems of clustered primary ions (H⁺(H₂O)_n, NO⁺(H₂O)_m, and O₂⁺(H₂O)_p), which most probably serve as reactant ions. Their relative abundances highly depend on the reduced electric field strength in the reaction region. Furthermore, their effective mobilities are studied as a function of the reduced electric field strength in the drift region.

A First Principle Model of Differential Ion Mobility: the Effect of Ion-Solvent Clustering

The use of differential mobility spectrometry (DMS) as a separation tool prior to mass analysis has increased in popularity over the years. However, the fundamental principles behind the difference between high- and low-field mobility is still a matter of debate-especially regarding the strong impact of solvent molecules added to the gas phase in chemically modified DMS environments. In this contribution, we aim to present a thorough model for the determination of the ion mobility over a wide range of field strengths and subsequent calculation of DMS dispersion plots. Our model relies on first principle calculations only, incorporating the modeling of the "hard-sphere" mobility, the change in CCS with field strength, and the degree of clustering of solvent molecules to the ion. We show that all three factors have to be taken into account to qualitatively predict dispersion plots. In particular, type A behavior (i.e., strong clustering) in DMS can only be explained by a significant change of the mean cluster size with field strengths. The fact that our model correctly predicts trends between differently strong binding solvents, as well as the solvent concentration and the background gas temperature, highlights the importance of clustering for differential mobility.

Systematic Ion Source Parameter Assessment by Automated Determination of the Distribution of Ion Acceptance (DIA) Using APLI

The determination of the spatially resolved ion signal with atmospheric pressure laser ionization (APLI), which was introduced as distribution of ion acceptance (DIA), serves as a valuable tool for the understanding of complex and highly dynamical conditions in modern atmospheric pressure (AP) ion sources. DIA provides information about fluid dynamics, ion transport, and ion transformation processes in such sources and is an ideal basis for the validation of numerical models of the dynamics in the ion source enclosure.We present a fully automated setup for DIA measurements, which enabled us to acquire a comprehensive dataset of over 700 individual DIA measurements in a commercial AP ion source (Bruker Multi Purpose Ion Source, MPIS). Ion source parameters as voltages, gas heater temperatures and gas flows, were varied, and the effect of those parameters on the DIA of a chemically inert analyte, pyrene, was systematically investigated. It is shown that the response of the DIA is nonlinear and that gas dynamics largely dominates the ion transport in the ion source. Particularly, the position of the heated nebulizer, which is used to introduce one of two gas flows and the analyte into the ion source chamber, had a profound effect on the DIA. This suggests that the gas dynamics in the source switches between different states. The now available comprehensive DIA dataset reveals such critical effects and will guide further numerical modeling efforts to understand the details of the dynamics of ions in the source chamber. Graphical Abstract.

Correlation between experimental data of protonation of aromatic compounds at (+) atmospheric pressure photoionization and theoretically calculated enthalpies

RATIONALE

The theoretical enthalpy calculated from the overall protonation reaction (electron transfer plus hydrogen transfer) in positive-mode (+) atmospheric-pressure photoionization (APPI) was compared with experimental results for 49 aromatic compounds. A linear relationship was observed between the calculated ΔH and the relative abundance of the protonated peak. The parameter gives reasonable predictions for all the aromatic hydrocarbon compounds used in this study.

METHODS

A parameter is devised by combining experimental MS data and high-level theoretical calculations. A (+) APPI Q Exactive Orbitrap mass spectrometer was used to obtain MS data for each solution. B3LYP exchange-correlation functions with the standard 6-311+G(df,2p) basis set was used to perform density functional theory (DFT) calculations.

RESULTS

All the molecules with ΔH <0 kcal/mol for the overall protonation reaction with toluene clusters produced protonated ions, regardless of the desolvation temperature. For molecules with ΔH >0, molecular ions were more abundant at typical APPI desolvation temperatures (300°C), while the protonated ions became comparable or dominant at higher temperatures (400°C). The toluene cluster size was an important factor when predicting the ionization behavior of aromatic hydrocarbon ions in (+) APPI.

CONCLUSIONS

The data used in this study clearly show that the theoretically calculated reaction enthalpy (ΔH) of protonation with toluene dimers can be used to predict the protonation behavior of aromatic compounds. When compounds have a negative ΔH value, the types of ions generated for aromatic compounds could be very well predicted based on the ΔH value. The ΔH can explain overall protonation behavior of compounds with ΔH values >0. Copyright © 2017 John Wiley & Sons, Ltd.

Comparison of Experimental and Calculated Ion Mobilities of Small Molecules in Air

Ion mobility spectrometry is a well-known technique for analyzing gases. Examples are military applications, but also safety related applications, for example, for protection of employees in industries working with hazardous gases. In the last 15 years, this technique has been further developed as a tool for structural analysis, for example, in pharmaceutical applications. In particular, the collision cross section, which is related to the mobility, is of interest here. With help of theoretic principles, it is possible to develop molecular models that can be verified by the comparison of their calculated cross sections with experimental data. In this paper, it is analyzed how well the ion trajectory method is suitable to reproduce the measured ion mobility of small organic molecules such as the water clusters forming the positively charged reactant ions, simple aromatic substances, and n-alkanes.

Review on ion mobility spectrometry. Part 1: current instrumentation

Ion Mobility Spectrometry (IMS) is a widely used and 'well-known' technique of ion separation in the gaseous phase based on the differences in ion mobilities under an electric field. All IMS instruments operate with an electric field that provides space separation, but some IMS instruments also operate with a drift gas flow that provides also a temporal separation. In this review we will summarize the current IMS instrumentation. IMS techniques have received an increased interest as new instrumentation and have become available to be coupled with mass spectrometry (MS). For each of the eight types of IMS instruments reviewed it is mentioned whether they can be hyphenated with MS and whether they are commercially available. Finally, out of the described devices, the six most-consolidated ones are compared. The current review article is followed by a companion review article which details the IMS hyphenated techniques (mainly gas chromatography and mass spectrometry) and the factors that make the data from an IMS device change as a function of device parameters and sampling conditions. These reviews will provide the reader with an insightful view of the main characteristics and aspects of the IMS technique.

Development of an ion activation stage for atmospheric pressure ionization sources

RATIONALE

The ion-molecule chemistry in typical atmospheric pressure ion sources is essentially thermodynamically controlled. Methods relying on gas-phase protonation reactions, e.g. atmospheric pressure chemical ionization (APCI), thus suffer from the low reactivity of the equilibrated reagent ion population, which is mostly [H + (H2O)n](+). Reagent ion activation to yield reactive species such as H3O(+) is largely uncontrolled in commercial API mass spectrometers.

METHODS

The ion activation stage (IAS) is realized as an ion 'tunnel' device. The 30-electrode geometry has an octagonal cross section and an inner diameter of 10 mm. The tunnel is mounted in a vacuum chamber, which directly attaches to the first pumping stage of API mass spectrometers. The effluent from a typical inlet capillary is expanding into the IAS. Reagent ions are generated at atmospheric pressure. Mass spectrometric analysis is performed with quadrupole and time-of-flight instruments.

RESULTS

The performance of the IAS is demonstrated by the controlled activation of the initially equilibrated proton-bound water cluster system. It is shown that a gradual increase in the RF voltage amplitude applied to the electrode structure leads to a reproducible shift of the cluster distribution along with clearly discernible protonation thresholds of selected analytes. Increasing the radiofrequency (RF) voltage from zero to maximum values does not change the average ion residence time within the IAS.

CONCLUSIONS

We have developed an IAS for operation in the intermediate (1-10 mbar) regime in the ion transfer region of API mass spectrometers. This stage is fully compatible with the recently introduced cAPCI method, which relies on the operation of a liquid point electrode generating very clean and stable thermal distributions of [H + (H2O)n] clusters. The IAS allows controlled ion activation by increasing the ion temperature, which is demonstrated by selective analyte protonation.

Capillary atmospheric pressure chemical ionization using liquid point electrodes

RATIONALE

Atmospheric pressure chemical ionization (APCI) sources operated with point to plane DC discharges ('Coronas') frequently suffer from point electrode degradation and potentially lead to oxidation and/or fragmentation of the generated analyte ions. It is postulated that these adverse effects are caused by the interaction of these ions with the discharge chemistry as well as en route to the mass analyzer region.

METHODS

The corona discharge metal point electrode is replaced by the conically shaped liquid effluent evolving from a fused-silica capillary, which is analogous but not identical to the Taylor cone formation in electrospray ionization. The liquid consisting of either pure water or water containing 0.1 %V formic acid is fed via a nano-flow delivery stage at typical flow rates between 1-800 μL/h. The liquid flow is continuously replenishing the surface of the point electrode. The source is directly coupled to the inlet capillary of appropriate mass spectrometers, e.g., the Bruker Daltonics and Agilent varieties.

RESULTS

The actively pumped liquid flow is supplying a constant amount of the reagent gas (H2O) to the corona region in the 20 ppmV to 30 %V range, leading to controlled, very stable operation of the source. The typical light emission observed for corona discharges is in very close proximity to the aqueous surface. Analyte protonation is the dominating ionization pathway. The degree of primary analyte fragmentation is extremely low.

CONCLUSIONS

We have developed a novel atmospheric pressure chemical ionization source designed for the hyphenation of nano-flow liquid chromatography and gas chromatography with atmospheric pressure ionization mass spectrometry. The proposed reaction mechanism including the electrochemistry occurring in the source along with formation of protonated analyte molecules via collision-induced dissociation (CID) is in full accord with the experimental results. The system exhibits an extremely stable performance over prolonged operation times, sole generation of protonated molecules, and low degree of analyte ion fragmentation.

Atmospheric pressure ion source development: experimental validation of simulated ion trajectories within complex flow and electrical fields

Three-dimensionally (3D) resolved ion trajectory calculations within the complex viscous flow field of an atmospheric pressure ion source are presented. The model calculations are validated with spatially resolved measurements of the relative sensitivity distribution within the source enclosure, referred to as the distribution of ion acceptance (DIA) of the mass analyzer. In previous work, we have shown that the DIA shapes as well as the maximum signal strengths strongly depend on ion source operational parameters such as gas flows and temperatures, as well as electrical field gradients established by various source electrode potentials (e.g., capillary inlet port potential and spray shield potential). In all cases studied, distinct, reproducible, and, to some extent, surprising DIA patterns were observed. We have thus attempted to model selected experimental operational source modes (called operational points) using a validated computational flow dynamics derived 3D-velocity field as an input parameter set for SIMION/SDS, along with a suite of custom software for data analysis and parameter set processing. Despite the complexity of the system, the modeling results reproduce the experimentally derived DIA unexpectedly well. It is concluded that SIMION/SDS in combination with accurate computational fluid dynamics (CFD) input data and adequate analysis software is capable of successfully modeling operational points of an atmospheric pressure ion (API) source. This approach should be very useful in the computer-aided design of future API sources.