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The microsolvated state of a molecule, represented by its interactions with only a small number of solvent molecules, can play a key role in determining the observable bulk properties of the molecule. This is especially true in cases where strong local hydrogen bonding exists between the molecule and the solvent. One method that can probe the microsolvated states of charged molecules is differential mobility spectrometry (DMS), which rapidly interrogates an ion’s transitions between a solvated and desolvated state in the gas phase (i.e., few solvent molecules present). However, can the results of DMS analyses of a class of molecules reveal information about the bulk physicochemical properties of those species? Our findings presented here show that DMS behaviors correlate strongly with the measured solution phase pKa and pKb values, and cell permeabilities of a set of structurally related drug molecules, even yielding high-resolution discrimination between isomeric forms of these drugs. This is due to DMS’s ability to separate species based upon only subtle (yet predictable) changes in structure: the same subtle changes that can influence isomers’ different bulk properties. Using 2-methylquinolin-8-ol as the core structure, we demonstrate how DMS shows promise for rapidly and sensitively probing the physicochemical properties of molecules, with particular attention paid to drug candidates at the early stage of drug development. This study serves as a foundation upon which future drug molecules of different structural classes could be examined.
Differential mobility spectrometry can be used to probe the microsolvated forms of molecules, providing insights into their bulk physicochemical properties, including passive cell permeability.
Many studies involving microsolvated species—isolated ions or molecules bound noncovalently to a small, defined number of solvent molecules—usually reflect on whether the knowledge gained provides valuable insights into their analogous bulk-solvated states.1 That is, do the properties of microsolvated species teach us anything about the same molecules’ behavior as observed in liquid solution? Ultimately, it is the presence of any strong correlations observed between the properties of microsolvated molecules and their bulk-solvated forms and a reasonably argued theory explaining these relationships that lend the best support to such comparisons.
Among the many analytical tools employed to study the microsolvated states of molecules is differential mobility spectrometry (DMS).2−4 While DMS is a technology known more for its ability to separate analytical ions from chemical noise,5 we have recently employed DMS to examine how the microsolvation properties of ions are affected by their specific structural attributes. For example, we have observed the influence of electronic/resonance effects,6 the steric hindrance of charge sites,7−9 and the influence of intramolecular hydrogen bonding on DMS behavior.10 Based upon these recent discoveries, we focused efforts on determining whether any links could be made between the DMS-probed microsolvation of molecules and their bulk physicochemical properties.
Medicinal chemistry, more specifically drug design, might benefit from a technology such as DMS that could help predict molecular physicochemical properties with sensitivity and speed. Presently, during the early stages of small molecule drug discovery, medicinal chemists try to relate a drug candidate’s chemical structure and physicochemical properties to its cellular availability.11,12 Many of these properties can be experimentally measured using cell-based permeability assays (e.g., MDCK, RRCK, Caco-2),13 and physicochemical examination (e.g., pKa, shake-flask log D, PAMPA, turbidometry).14 These benchtop in vitro studies serve as preliminary appraisals of a molecule’s fitness to navigate biological barriers in vivo. Unfortunately, existing methodologies lack the resolution to discriminate between closely related structural analogues or motifs.15,16 Moreover, while progress has been made in streamlining these assays,17−19 they still require considerable resources and experience suboptimal reproducibility.20,21
With this as our focus, we report on the use of DMS as a probe of the microsolvated forms of drug molecules, and relate the measured DMS behavior to those drug molecules’ condensed phase physicochemical properties. Here, we demonstrate that the DMS properties of drug molecules, which measure the molecule’s binding interactions with a protic solvent vapor, correlate strongly with experimentally determined pKa, pKb, and cell permeability measurements. Moreover, these measurements require only a fraction of the time, sample, and resources of current state-of-the-art techniques (vide infra). These correlations derive from the ability of the DMS instrument to probe the ion–solvent interactions of gas-phase forms of drug molecules, which relates to both a drug molecule’s inherent acidity/basicity (pKa/pKb) and its ability to desolvate such that it might transit a hydrophobic lipid bilayer (cell permeability). Our findings demonstrate that, in addition to being able to distinguish isomeric drug molecules easily, the DMS behaviors of drug molecules can be predicted based upon subtle changes in structure related back to specific Hammett parameters (σ+) and van der Waals radii of the functional groups.
In this study, we employed DMS–MS to examine drug molecules that shared a common core: 2-methylquinolin-8-ol (Scheme 1). This drug and its analogues have been employed for years in a variety of pharmaceutical applications and physicochemical studies.22−32 In total, we examined 22 drug molecules: 7 triplets of isomers (each bearing one of 7 functional groups in either the 5-, 6-, or 7-position of the quinoline ring) as well as 2-methylquinolin-8-ol itself. One of the reasons for choosing this model drug chemistry was that several types of structural motifs are present that could impact the microsolvation, as well as the bulk physicochemical properties of these molecules; the different functional groups provide opportunities for varied steric and electronic effects to be present, as well as the presence of intramolecular hydrogen bonds (IMHBs), that could also impact the behavior of these molecules. Overall, our aim was to relate the DMS-based ion–solvent interaction measurements to in vitro diagnostics of interest to medicinal chemists, including the passive cell permeability using the Ralph-Russ Canine Kidney (RRCK) method33 and experimentally determined pKa/pKb measurements.19,34 These conventional methodologies are described in more detail in the Supporting Information.
The critical DMS output that relates directly to a specific molecule’s solvent binding energy is the relationship between the applied separation voltage (SV) and the measured optimum compensation voltage (CV) for transmission of the ionized drugs through the DMS cell (see Supporting Information for further detail).9 For example, Figure Figure11 depicts the results of the DMS CV-ramping experiments conducted with three isomers of methoxy-2-methylquinolin-8-ol and fluoro-2-methylquinolin-8-ol where SV was stepped from 0 to 4000 V. There are clear trends for each drug as the site of substitution is varied from the 5-, to 6-, to 7-positions (see Scheme 1).
The more negative the CV shift experienced by the protonated drug molecule, the stronger the interaction with the solvent vapor that molecule exhibits.7,9 Thus, for both the methoxy- and fluoro-substituted drugs, the 7-substituted isomer displayed the weakest ion–solvent interaction, followed by the 5- and then the 6-substituted isomers. Moreover, the overall magnitude of the negative CV shifts was greater for the fluoro-substituted drugs than for the methoxy-substituted species, revealing the greater ion–solvent interactions of the fluoro-substituted molecules (vide infra). Similar DMS-based examinations were conducted for all 22 drug molecules. Ultimately, we have found that the SV value at which at ion’s CV reaches a minimum value (SV@CVmin) represents a measure for the ion’s desolvated/solvated equilibrium,2,3,7,35 and overall, its ion–solvent binding (i.e., microsolvation) energy.9
Our comparison of the DMS data with the experimental physicochemical data yielded strong and promising correlations. Figure Figure22 plots cell permeability values and SV@CVmin measurements for three sets of structural isomers: methoxy-, chloro-, and cyano-2-methylquinolin-8-ol derivatives. It is clear that SV@CVmin measurements track with the relative cell permeability for each isomer of a given substituent. The subtle structural differences between these drug isomers can affect their respective solvent binding energies, resulting in the drugs’ distinct relative cell permeabilities. For example, the more strongly microsolvated 6-substituted 2-quinolin-8-ol derivatives (i.e., those with larger SV@CVmin values) display lower cellular permeability than the 5- and 7-substituted species. This result supports our hypothesis that stronger ion–solvent interactions correlate with slower desolvation and transport kinetics at the cell membrane, thereby lowering the rate of passive diffusion. Similar comparisons for all seven substituent groups are presented in Figure S1. The relationship between the observed DMS ion–solvent interaction and relative passive cell permeability is in accord with the general thinking behind the mechanism of passive transport of drug molecules across cell membranes.36−39 As a drug molecule exhibits a greater tendency to shed solvent molecules from its immediate environment, it can then begin to interact with a cell’s outer wall and proceed to transit this barrier.
In general, cell permeability is significantly higher for all 7-substituted isomers compared with their 5- and 6-substituted analogues. While this trend was consistent across the 2-methylquinolin-8-ol isomers for a particular substituent (Figure Figure22), the ion–solvent interactions of the different substituted derivatives (e.g., methoxy versus cyano) were not directly correlated with apparent cell permeability. For example, 7-methoxy-2-methylquinolin-8-ol and 7-cyano-2-methylquinolin-8-ol both exhibited a cell permeability of ~3 × 10–6 cm s–1, but the SV@CVmin value for the 7-cyano derivative was significantly larger than that for the 7-methoxy analogue. Based on our hypothesis, we would expect greater cell permeability for the 7-methoxy analogue than for the 7-cyano species due to the weaker microsolvation of the methoxy species (i.e., lower values of SV@CVmin). These differences are presently under investigation.
The experimentally measured pKa and pKb values for the 2-methylquinolin-8-ol derivatives also correlate strongly with the DMS results. We observe that species with lower pKa and pKb values exhibit greater ion–solvent interactions (see Figures Figures33A and and3B);3B); the 5- and 6-substituted 2-methylquinolin-8-ol derivatives show strong correlations, but the 7-substituted isomers exhibit greater variability in this relationship (Figure Figure33, blue squares). We attribute this variability in the pKa/pKb–DMS correlation plots for the 7-substituted species to the variability in chemical and physical interactions between 7-position substituents and solvent molecules (afforded by the closer proximity to the solvent binding site). Indeed, we find that the data points which are furthest from the pKa/pKb–DMS correlation trend line are all associated with 7-substituted species that exhibit NH–solvent binding, rather than the more common OH solvent binding motif (hollow blue squares in Figure Figure33). In other words, the variability in the physicochemical properties of the 7-substituted derivatives arises due to steric effects, which in turn influence the solvent binding motif. The strong correlations that we observe for the 5- and 6-substituted species, on the other hand, demonstrate that DMS ion–solvent clustering measurements are sensitive to steric and electronic effects (vide infra).
The ability for the DMS to measure SV@CVmin values for a large collection of drug molecules both rapidly (~2 min per analysis) and with great sensitivity (only picograms of material are required) makes the observed correlations between the DMS data and the physicochemical parameters very compelling. But what is the nature of the underlying mechanisms that link these gas-phase measurements with the mated in vitro experiments?
First, we must examine the other parameters with which DMS displays strong correlations: calculated ion–solvent binding energies (i.e., microsolvation energies) and functional group-specific linear free energy parameters (e.g., σ+ values). The correlation between the DMS results and the calculated solvent binding energies for the twenty two 2-methylquinolin-8-ol species support a hypothesis that steric and electronic effects account for the observed variations in CVs. In addition, the fact that the binding energy for a single solvent molecule correlates best with the DMS data also supports a mechanism wherein a strong local hydrogen bond is playing a key role.40
Figures Figures44A and and4B4B plot the calculated methanol binding energies against measured DMS SV@CVmin for the 5- and 6-substituted 2-methylquinolin-8-ol species, respectively. Clearly, species which bind solvent molecules more strongly exhibit greater SV@CVmin values as measured by DMS. Figure Figure44C displays the correlation between binding energy and measured CV for the 7-substituted species. In this case, the voltages required to correct the ion trajectories encompass a much broader range and the correlation with calculated binding energies is poorer. As was the case with the pKa/pKb correlations (vide supra), the relatively poor correlation between calculated solvent binding energy and DMS ion trajectory for the 7-substituted species arises due to steric effects, which ultimately influence whether the solvent molecule is bound to the OH group or to the NH group. The data points for the 7-substituted species that favor the NH–solvent binding motif are plotted as hollow squares in Figure Figure44C. In general, the NH-bound solvent clusters exhibit weaker calculated binding energies and DMS-measured microsolvation energies than the species which favor the OH–solvent binding motif. Given the fact that across the series of 7-substituted derivatives we are probing two different ion–solvent binding motifs, each of which will exhibit inherently different clustering/declustering dynamics, it is not unreasonable to expect a higher degree of variability in the correlation plot.
Also plotted in Figure Figure44 are the substituent-specific DMS behaviors of the electron-donating (ED) and electron-withdrawing (EW) groups, which are apparent for the 5-subsituted species through strong correlations with Brown and Okamoto’s σP+ constants (i.e., Hammett parameters; Table S1).41,42 Similarly, the DMS behavior of the 6-substituted species trends consistently with the meta-position electrophilic substituent constants (σM+, Table S1). However, as was the case with calculated solvent binding energies, the 7-substituted species exhibit a comparatively weaker correlation when plotting σp+ versus measured SV@CVmin. Again, we attribute this to the convolution of resonance and steric effects for substituents at the 7-position,23,24 a conclusion that we base on the fact that the species which exhibit NH–solvent binding (Figure Figure44C, hollow blue squares) seem to follow a slightly different trend than those which exhibit OH–solvent binding (Figure Figure44C, filled blue squares). Note also that substituents in the 7-position can potentially influence the microsolvation process via formation of an intramolecular hydrogen bond (IMHB) with the proton of the 8-hydroxy group (e.g., 7-nitro; see Supporting Information).43 This notion is supported by the fact that, when the data for the 7-nitro substituted drugs are removed from the linear regression model of the DMS data comparison with cell permeability, pKa, or pKb (Figure S2, Table S3), the correlation improves. Further support for this conclusion comes from the calculated lowest-energy cluster geometries; many of the 7-substituted 2-methylquinolin-8-ol derivatives exhibit structures that suggest the possibility of intramolecular hydrogen bonding (see Supporting Information).9 Moreover, our findings here are supported by past studies where the effects of electron-donating and electron-withdrawing substituents (and their respective σ or σ+ constants) on pKa23,24,26,29 and solubility30,32 have been examined for quinoline-8-ol derivatives. Ultimately, this apparent influence of electronic effects on DMS separation suggests a connection to linear free energy relationship and possibly to quantitative structure–activity relationships (QSAR).44,45
The behavior of the 7-substituted 2-methylquinolin-8-ol derivatives is similar to that of the 5-substituted isomers by virtue of the analogous electronic effects (i.e., charge delocalization) present (Scheme 2). However, the 7-substituted species induce a weaker ion–solvent binding interaction due to steric hindrance arising from the proximity of the functional group to the site of solvent binding. For all 5- and 6-substituted derivatives, solvent molecules were calculated to bind to the 8-hydroxy group in the lowest energy structures (see Supporting Information). However, as mentioned above, in some cases the global minima for the 7-substituted ion–solvent clusters exhibited NH-bound solvent molecules. Interestingly, this apparent trend in microsolvation of 7-substituted species tracks well with the van der Waals radii of the substituents (Table S3, Figures S7–S9). Derivatives in which the substituent in the 7-position was smaller than the methyl group in the 2-position exhibited OH–solvent binding (as was observed for the 5- and 6-substituted species). However, when the substituent in the 7-position was larger than the methyl group in the 2-position, NH–solvent binding was favored. These steric effects are visualized in Figures S7 and S8, which plot substituent van der Waals radii as a function of the relative isomer energies (i.e., OH-bound versus NH-bound). Given this clear steric effect, we postulate that 7-substituted derivatives are more easily desolvated owing to the fact that substituents in the 7-position can disrupt the extended hydrogen bonding network near the site of solvent nucleation. Further to this, nitro and methoxy groups in the 7-position are also capable of changing the microsolvation environment by forming intramolecular hydrogen bonds with the 8-hydroxy group. Thus, these species contain an intramolecular “switch”, which (when engaged) enhances molecular lipophilicity.46 Taken as a whole, these interactions weaken the ion–solvent binding energy of 7-substituted species, and this is reflected in their lower SV@CVmin values and enhanced cell permeabilities.
These relationships (as well as other previously identified DMS parameters,7Figure S2) reveal the impact of molecular structure on the DMS results (Figures Figures22, ,3).3). Based upon the relative CV shifts observed, we conclude that the positioning of the substituents on the quinoline moiety affected microsolvation by providing (1) different degrees of electron donation/withdrawal from the quinoline system and (2) different levels of steric hindrance for the formation of stable ionized solute/solvent clusters. We have previously demonstrated the influence of steric hindrance in DMS, specifically in a set of quinoline molecules structurally similar to those studied here.9 Based upon those results, we initially hypothesized that the closer the substituent on the quinoline ring to the site of charging, the weaker the microsolvation energy should be (i.e., ion–solvent binding energy for 5- < 6- < 7-substituted species). However, if the substituents are able to donate electron density to, or withdraw electron density from, the quinoline ring conjugated π-system, they would influence the molecular charge densities via resonance. As a result, ion–solvent interactions should be determined by substituent inductive resonance effects, which in turn influence ion–solvent electrostatic interactions (e.g., charge-dipole, hydrogen-bonding). For example, species with electron-withdrawing groups (e.g., −CN) should display stronger microsolvation energies because the positive partial charges at the ring NH and OH groups, the sites of solvent nucleation, will be enhanced.
From the DMS data (Figure S3, Table S1), we observe that the microsolvation energies of these species are not determined solely by the geometric distance of the substituent from the site of solvent binding (i.e., the protonated ring nitrogen and 8-hydroxyl group);9 the electron-donating/withdrawing characteristics of the substituents in the 5-, 6-, and 7-positions are also found to play a major role in ionized solute–solvent interactions. Upon protonation of the ring nitrogen atom, resonant charge delocalization results in relatively high partial charges at the 1-, 2-, 4-, 5-, 7-, and 10-positions of the quinoline moiety. This increased positive charge of the ring system enhances the polarization of the hydroxyl group in the 8-position. When we consider the putative resonance structures of the 2-methylquinolin-8-ol derivatives (Scheme 2) and their possible roles in the observed DMS behavior, we note that substituents in the 6-position do not influence charge density of the ring system at the aforementioned positions via resonance. In this case, charge is delocalized through the π-system to a lesser extent and solvent clustering is generally strongest due to the more localized, stable charge site, compared with substitutions at 5- and 7-positions. While all 6-position substituents cluster strongly, the electron-donating substituents (e.g., methyl and methoxy) form weaker solvent clusters compared with electron-withdrawing congeners. For example, the SV@CVmin value and calculated ion–solvent binding energy for protonated 6-methoxy-2-methylquinolin-8-ol reveal a more weakly microsolvated species than the 6-cyano analogue (see Table S1), as expected based on electron-donating/withdrawing arguments. These differences in microsolvation energy as a function of substituent correlate strongly with the electron-donating/withdrawing properties of the functional groups (see Table S1).
We also find that the 7-substituted isomers exhibit weaker clustering interactions than do the 5-substituted isomers. Note that 7-position methoxy, methyl, and bromo substituents have >10-, 3-, and 4-fold weaker solvent binding, respectively, compared with their 5-position isomers. This difference in ion–solvent interaction strength likely arises from a moderate steric effect due to the location of the 7-substituted group proximal to the protonated ring nitrogen and 8-hydroxy group (viz., the site of solvent binding).7,9 These structural changes may serve to destabilize the solvent shell that forms during the low-field portion of the DMS cycle. Ultimately, the 7-substituted molecules exhibit weaker microsolvation energies that may be reflective of their ability to easily desolvate/solvate as biological barriers are traversed (vide infra).
To study drug candidates using mass spectrometry, it is necessary to probe the ionized forms (e.g., protonated 2-methylquinolin-8-ol derivatives). Nevertheless, while we are examining the solvent binding properties of the protonated species, we can extend the results obtained here to the neutral drug molecule counterparts. It is also important to note that the protonated forms of many drugs (such as these quinoline-8-ol derivatives) may play a key role in absorption given the pH of the gut environment in vivo (from pH ~1.7 in the stomach to ~6.5 in the intestines).47 For the quinoline-8-ol derivatives studied here, the ring nitrogen, which is the locus of greatest electron density, is also the site of protonation (e.g., see Figure Figure55).9,48,49 This and the adjacent OH group of the quinolin-8-ol derivatives are the principal sites of interaction for solvent molecules in both the protonated and neutral molecules. Thus, the protonated analogue is a useful example of the hydrogen bonding experienced by these drug molecules in bulk aqueous (protic) solution; intermolecular hydrogen bonding is the first step in protonation of a molecule, and these motifs have been characterized as resembling the initial stages of the proton-transfer process.40,50,51
We also find that the binding energy of the first solvent molecule exhibits the strongest correlation to the DMS data.9 This accords with the hypothesis that we are probing the initial instances of the prompt solvation mechanism52 that includes a strong local hydrogen bond formed between the drug molecule and the first solvating molecule.53 When considering the computational accuracy of pKa prediction, Kelly and co-workers recognized that their calculations only tracked with experimental observations when a single explicit solvent molecule was included.53,54 While the DMS studies described herein differ from the more traditional “ion solvation” type studies conducted with mass spectrometry (i.e., where specific numbers of solvent molecules bound to an ion have been detected explicitly), some of these studies have revealed the importance of the initial ion–solvent molecule interaction.55−57
The work that we present here evaluates the microsolvation properties of 2-methylquinolin-8-ol derivatives with water and methanol. In future work we will investigate the effects of other volatile solvents in the DMS environment to assess the specific roles of other polar and nonpolar solvents.58 Lastly, given the demonstrated ability of DMS to separate isomeric drug species based upon simple substitution patterns of EW and ED groups, one could envision using DMS–MS as a high-throughput platform (e.g., requiring a few minutes, not hours or days)59 for assessing Hammett parameters experimentally, with very high degrees of both sensitivity and selectivity. While relationships between specific σ+ constants and solvation energies have previously been postulated,60,61 to our knowledge, this is the first time the correlation has been demonstrated experimentally.
In this study, we demonstrate that DMS can be used to assess the physicochemical properties of drug molecules by probing the behavior of their microsolvated forms in a robust and precise manner. These results are supported by a number of orthogonal methods, including empirically parametrized Hammett parameters and extensive computational modeling. The parallel study of DMS-determined solvent binding properties and calculated geometric and electronic structure allows us to relate the structural properties of a drug to its experimentally determined pKa and pKb values, and its relative cell permeability.
Overall, the correlation of DMS measurements and cell permeabilities of isomeric drugs can complement the cell-based measurements by presenting additional ways for medicinal chemists to rationalize the impact of steric and electronic effects within a chemical series. Furthermore, the SV@CVmin end points are very precise (<2%) and consistent across day-to-day replicate experiments, a far greater reproducibility than cell-based assays can typically achieve.10 Hence, the combination of cell- and DMS-based methodologies could yield finer distinction between structural motifs to guide drug design. Consequently, DMS is a very promising new tool for rational drug design, where identifying and describing subtle steric and electronic interactions for a given drug structural motif facilitates the testing of structure–activity relationship hypotheses.
Substituted 2-methylquinolin-8-ol derivatives (Scheme 1) were purchased from ACES Pharma (Princeton, NJ) and were used without further purification. HPLC grade acetonitrile and methanol were bought from Caledon Laboratory Chemicals (Georgetown, ON, Canada), and formic acid was purchased from Sigma-Aldrich (Oakville, ON, Canada). Distilled deionized water (18 MΩ) was produced in-house using a Millipore (Billerica, MA, USA) Integral 10 water purification system.
A DMS system (SCIEX, Concord, ON) was mounted on a hybrid quadrupole linear ion trap mass spectrometer (SCIEX) system in the atmospheric region between the sampling orifice and its electrospray ionization (ESI) source.5,35 The ESI probe was maintained at a voltage of 5500 V. A constant gas flow in the DMS cell was achieved by the curtain gas flow (N2; 30 psi, 7.1 L/min) and the primary stage vacuum pumping of the MS system. The temperature of the transport gas in the DMS cell was maintained at ~100 °C (DMS heater setting of 150 °C). Methanol or water could be added to the curtain gas at 1.5% by a PerkinElmer 200 LC pump (Waltham, MA). In each experiment, analytes were dissolved in solution (50/50 acetonitrile/water with 0.1% formic acid) to a concentration of 100 ng/mL. Each solution was infused into the ESI source (5500 V spray voltage) at a rate of 7 μL/min.
The fundamental behavior of the DMS has been described elsewhere.2−4,62 These experiments begin by subjecting a solution of drug molecules to ESI, producing gas-phase ions for these species. These ions are then sampled by the DMS cell: two parallel plates across which an asymmetric rf waveform (the separation voltage or SV) is applied (Figure S5). The ion’s transit through the DMS cell will depend upon the amplitude of the SV (generally held at a constant value) and an additional dc voltage (compensation voltage or CV) used to stabilize the ion’s trajectory. When we purposefully add solvent vapor (e.g., water, methanol) to the DMS cell, the ions undergo dynamic clustering/declustering cycles as their trajectory and kinetic energies oscillate with the rf waveform (see Supporting Information for more detail). Consequently, the probed species undergo incipient solvation several thousand times as they transit the DMS cell. Since the collision and clustering properties of an ion also relate directly to the structural features of the ion itself, the SV/CV settings required for optimal transmission encode the statistically sampled geometries and interaction potentials of the ions with the solvent vapor molecules.35
To identify the most stable ion–solvent cluster structures, cluster potential energy landscapes were mapped with a custom written basin-hopping (BH) algorithm.63 Details of our implementation of the BH algorithm are reported elsewhere where we have demonstrated this methodology as an accurate means of assessing ion–solvent binding.7,9,64,65 Convergence criteria were set to the default criteria of the Gaussian 09 suite of programs.66 Cluster systems were modeled using the AMBER force field, with atomic partial charges calculated for the monomers with the CHelpG partition scheme67 at the B3LYP/6-31+G(d,p) level of theory.68,69 For each BH step, a random rotation of −20° ≤ θ ≤ 20° was applied about the body-fixed x, y, and z axes for each solvent molecule, and each solvent molecule was also randomly translated by −0.7 Å ≤ η ≤ 0.7 Å in the x, y, and z directions. BH searches explored ~20,000 structures for clusters containing one solvent molecule. Unique isomers identified by the BH routine were optimized at the B3LYP/6-311++G(d,p) level of theory68,69 employing the GD3 empirical dispersion correction.70 Normal mode analyses were conducted for each isomer to ensure that it corresponded to a local minimum on the potential energy surface. In all cases, we determined that protonation occurred on the ring nitrogen. All cluster structures and XYZ coordinates are available in the Supporting Information. To account for basis-set superposition error in solvent binding energy calculations, counterpoise correction was employed.71
We gratefully acknowledge high performance computing support from the SHARCNET consortium of Compute Canada. We are also grateful to Professor Terry McMahon (University of Waterloo), Dr. Tom Covey (SCIEX), and Drs. Michael Shapiro, Christopher Keefer, and George Chang (Pfizer) for helpful conversations. We thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support through an ENGAGE grant (EGP No. 449354-13), an ENGAGE Plus grant (EGP No. 463974-14), and a Collaborative Research and Development grant (490885). We thank the Ontario Centres of Excellence (OCE) for financial support through a Voucher for Innovation and Productivity II grant (25050).
The authors declare no competing financial interest.