Effect of Basicity and Structure on the Hydration of Protonated Molecules, Proton-Bound Dimer and Cluster Formation: An Ion Mobility-Time of Flight Mass Spectrometry and Theoretical Study


Protonation, hydration, and cluster formation of ammonia, formaldehyde, formic acid, acetone, butanone, 2-ocatanone, 2-nonanone, acetophenone, ethanol, pyridine, and its derivatives were studied by IMS-TOFMS technique equipped with a corona discharge ion source. It was found that tendency of the protonated molecules, MH+, to participate in hydration or cluster formation depends on the basicity of M. The molecules with higher basicity were hydrated less than those with lower basicity. The mass spectra of the low basic molecules such as formaldehyde exhibited larger clusters of MnH+(H2O)n, while for compounds with high basicity such as pyridine, only MH+ and MH+M peaks were observed. The results of DFT calculations show that enthalpies of hydrations and cluster formation decrease as basicities of the molecules increases. Using comparison of mass spectra of formic acid, formaldehyde, and ethanol, effect of structure on the cluster formation was also investigated. Formation of symmetric (MH+M) and asymmetric proton-bound dimers (MH+N) was studied by ion mobility and mass spectrometry techniques. Both theoretical and experimental results show that asymmetric dimers are formed more easily between molecules (M and N) with comparable basicity. As the basicity difference between M and N increases, the enthalpy of MH+N formation decreases.


Ion molecule reactions play crucial roles in many phenomena occurring in atmosphere and living systems [1,2,3,4]. Among these reactions, proton transfer has been the subject of intensive investigations [5,6,7,8] because of its importance and applications in biology, environmental sciences, and chemistry.

Theoretical and experimental studies show that proton can be hydrated to form hydronium clusters (H2O)nH3O+, with different numbers of water molecules [9,10,11]. Konig and Fales [9] studied hydronium ions with up to 222 water molecule using quadrupole mass spectrometry. They showed that for medium-sized clusters, those with 21 and 28 water molecules have more stability. A theoretical study on the hydronium ions with 21 H2O molecule revealed that the H3O+ ion tends to be located on the surface of the clusters [11]. Protonated molecules, MH+, are also hydrated in the presence of water, or can form ionic clusters with other neutral molecules [12, 13]. It has been shown that in the Mn(H2O)mH+ clusters with large numbers of water molecules, the proton tends to remain on the H3O+, even if M has high basicity [8, 14,15,16]. In the MH+(H2O)n clusters with 1 or 2 water molecules, instead, the proton usually remains on the M [17, 18]. Hydration of protonated molecules influences their stability, and structural and thermodynamic properties [19, 20]. Hydration of alkyl diammonium cations influences their structures so that the linear alkyl chain is folded to form a bent structure [19, 21].

In mass spectrometers equipped with electrospray or corona discharge (CD) atmospheric pressure chemical ionization (APCI) sources, the protonated molecules are often hydrated and they are observed as MH+(H2O)n [22,23,24]. The number of water molecules in MH+(H2O)n depends on the temperature and water concentration of the systems; so that at lower temperatures and higher water concentrations the amount of hydration is more [25]. Also, the amount of hydration of MH+ is influenced by structural and chemical properties of M.

Protonated molecules, MH+, also form proton-bound dimers in the presence of excess amount of the neutral molecule, M [26, 27],

$$ {\mathrm{MH}}^{+}+\mathrm{M}\to {\mathrm{MH}\mathrm{M}}^{+} $$

The ions are usually hydrated; however, they are shown without hydration for convenience. In the presence of extra amount of M, reaction (1) may proceed to form proton-bound trimmers [28], even though, it is reported that the proton-bound trimers are not stable and have short lifetime so that they are observed at lower temperatures in the presence of higher vapor concentration of the sample [29]. Many researchers have reported that the proton-bound dimers are rarely hydrated or hydration destroys these dimers [8, 25, 30]. Asymmetric proton–bound dimers are also observed in ion mobility (IMS) and mass spectrometry (MS) studies [28].

$$ {\mathrm{MH}}^{+}+\mathrm{N}\to {\mathrm{MH}\mathrm{N}}^{+} $$

However, formation of asymmetric proton–bound dimers, MHN+, is not as easy as that of symmetric proton–bound dimers, MHM+ [31,32,33], so that the former are formed with only some special M and N molecules.

In this work, hydration of different protonated molecules is studied using IMS and MS techniques and DFT methods. The amount of hydration of the protonated molecules, MH+, is discussed based on the basicity and structure of the neutral molecule M. In addition, the required criteria for successful formation of symmetric and asymmetric proton–bound dimers are determined and discussed.


The experiments were performed with an IMS-TOFMS equipped with a corona discharge (CD) ionization source operating in positive mode. In the CD ion source, hydronium ions, H+(H2O)n, are produced as the main reactant ions (RI). The mechanism of ionization in CD is based on proton transfer from hydronium ion to the molecule, M, and formation of MH+(H2O)m as product ions. The IMS-TOFMS was a homemade instrument constructed in the Department of Experimental Physics of Comenius University in Slovakia. A detailed description of the instrument can be found elsewhere [34]. The IMS operated at sub-ambient pressure (0.75 bar) so that the sample could be sucked into the ionization region with adjustable flow rate of 20 ml/min. Because of suction of the ambient air into the ionization region, the ionization region and drift tube of IMS always have some moisture. The humidity of the exited drift gas was measured by a dew point meter (Xentaur, USA) as 20–50 ppm. A stream of dry air was used as the drift gas. The flow rate of the drift gas was 500 ml/min. The drift tube temperature was set to 110 °C. A voltage of 8 kV was applied to the whole cell of IMS (12.5 cm) to provide a drift field of 640 V/cm. The CD was supplied by potential difference of 3 kV between the electrodes. The length of the linear time-of-flight mass spectrometer (TOF-MS) was 54.7 cm with internal pressure of 10−5 mbar. A multichannel plate (MCP) was used as a detector for TOF-MS.

Materials and Method

Pyridine, 2,6-dimethyl pyridine, 2,6-di-tert-butyl pyridine (DTBP), and ammonium carbonate were Sigma-Aldrich products and acetone, formic acid, formaldehyde, ethanol, 2-butanone, 2-octanone, 2-nonanoe, and acetophenone were purchased from Fluka. The head space vapor of each sample (1 ml) at ambient temperature (~ 20 °C) was injected to the ionization region by a syringe. The vapor pressure of the molecules is summarized in Table S1 (Supplementary Materials). The head space vapor of ammonium carbonate, (NH4)2CO3, was injected to the ionization region to study ionization and hydration of NH3. The experiments were carried out at a drift tube temperature of 110 °C.

Computational Details

The structures of all molecules and clusters including neutral and protonated molecules and their hydrated forms were optimized by density functional theory (DFT) and B3LYP functional. The 6-311++G(d,p) basis which includes both polarization and diffuse functions for hydrogen and heavy atoms was used for the calculations. Several isomers were possible for some of the MnH+(H2O)m clusters; hence, preliminary calculations with a small basis set, 6-31G(d), were performed and only the most stable isomers were selected to be included in the final calculations. Also, some of the isomers were converged to one structure after optimization. The DFT methods have been employed for calculation of thermodynamic and structural properties of neutral and ionic systems. Comparison of the DFT results with those obtained experimentally or computed by high-level methods has confirmed their accuracy [35,36,37,38]. These studies showed that the DFT methods with large basis sets can predict the isomerization energies, ionization potentials, and interaction of hydration energies, accurately [35,36,37,38]. Also, comparison of performance of different DFT methods determined that although the M06L functional gives more accurate results for neutral systems, the B3LY functional is more accurate method for calculation of hydration energies of ions [36]. Hence, the B3LYP functional was used in this study. Frequency calculations were performed at the same level of theory to obtain the thermodynamic quantities including proton affinities (PA), enthalpy (∆H), and Gibbs free energy (∆G) of hydration or cluster formation in gas phase at 298 K. Although the experiments were carried out at 110 °C (383 K), and H depends on temperature, however, the enthalpy difference (∆H = Hproduct – Hreactant) at 298 and 383 K is not so different, because the H383H298 for both the reactants and products are approximately the same [39]. The charge distributions were computed using natural bond orbital (NBO) method. The calculations were carried out at 298.15 K and in gas phase using Gaussian 09 software [40].

Results and Discussion

Effect of Basicity on the Hydration and Proton-Bound Dimer Formation

Mechanism of ionization of a molecule, M, in the CD ion source can be considered as hydronium attachment to the molecule and formation of an unstable intermediate followed by partial dehydration [18, 41,42,43].

$$ {\mathrm{H}}^{+}{\left({\mathrm{H}}_2\mathrm{O}\right)}_{\mathrm{n}}+\mathrm{M}\to {\left[{\mathrm{MH}}^{+}{\left({\mathrm{H}}_2\mathrm{O}\right)}_{\mathrm{n}}\right]}^{\ast}\to {\mathrm{MH}}^{+}{\left({\mathrm{H}}_2\mathrm{O}\right)}_{\mathrm{x}}+\left(n-x\right){\mathrm{H}}_2\mathrm{O} $$

where x depends on the basicity of M, temperature, and concentration of water content. The rate constant, ka, of the hydronium attachment process and formation of intermediate [MH+(H2O)n]* is in the order of 10−9 cm3 s−1 [18, 41] depending on the temperature, polarization of M, and reduced mass of M and H+(H2O)n. The dehydration rate constants, kd, can be calculated as ka/Keq, where Keq is the equilibrium constant of hydration/dehydration reaction. Therefore, the kd values are different for different reactions and depend on the basicity of M, ∆H and ∆G of hydration and temperature [18, 41]. Figure 1 compares typical IMS and MS spectra for acetophenone recorded with an IMS-MS equipped with CD ion source. In the IMS spectrum, only one peak for hydronium ion and one peak for MH+(H2O)n are observed while MS spectrum shows that H+(H2O)n is a mixture of H+(H2O)3 and H+(H2O)4 and MH+(H2O)n is a combination of MH+ and MH+(H2O). Because the hydration and dehydration processes occur very fast during the traveling of ions through the drift tube, the MH+ and MH+(H2O) reach the detector, concurrently, and one peak is observed in IMS spectrum for them as monomer. The same discussion is true for the hydronium ion. Hence, IMS cannot determine the amount of hydration. In the flight tube of TOF-MS, because of lack of humidity, there is no hydration-dehydration equilibrium and the ions with different number of water molecule are separated and individual peaks are observed for MH+(H2O)n ions.

Figure 1

Comparison of (a) IMS and (b) MS spectra of 10 μL of head space of acetophenone in an IMS-MS with drift tube temperature and pressure of 110 °C and 0.75 bar, respectively

Figure 2 shows the mass spectra of formaldehyde, acetone, 2-butanone, 2-octanone, 2-nonanoe, acetophenone, pyridine, 2,6-dimethyl pyridine (DMP), and 2,6-di-tert-butyl pyridine (DTBP). The amount of hydration and cluster formation decreases from formaldehyde to DTBP. Formaldehyde and acetone form clusters with up to three H2O molecules; the protonated butanone is di-hydrated; other larger ketones and pyridine and DMP are only mono-hydrated while DTBP is not hydrated. Also, we observed a proton-bound trimer (M3H+) peak for formaldehyde and a proton-bound dimer (MH+M) for ketones, while DMP and DTBP do not form any dimer or trimer. Since the water concentration and drift cell temperature were the same for the all experiments, the difference in the amount of hydration is attributed to the basicity of the molecules. The calculated values of proton affinities (PA) and gas phase basicities (GB) are summarized in Table 1. The calculated enthalpies (∆H) and Gibbs free energies (∆G) of mono-hydration and proton-bound dimer formation are also included in Table 1. The ∆H and ∆G values for di-, tri-, and tetra-hydration as well as trimer formation are provided in Tables S2 and S3 (Supplementary Materials). The data in Table 1 show that the basicity increases from formaldehyde to DTBP while ∆H and ∆G values of hydration and dimer formation decrease. In other words, the protonated forms (MH+) of molecules with higher basicity are less hydrated.

Figure 2

The MS spectra of 10 μL of head space of (a) formaldehyde, (b) acetone, (c) 2-butanone, (d) 2-octanone, (e) 2-nonanone, (f) acetophenone, (g) pyridine, (h) 2,6-dimetyl pyridine, and (i) 2,6-di-tert-butyl pyridine. The basicity increases from (a) to (i)

Table 1 The Calculated Values of Proton Affinities (PA), Gas Phase Basicities (GB), Enthalpies (∆H), and Gibbs Free Energies (∆G) of Mono-hydration and Proton-Bound Dimer Formation at 298 K. The Energies Are in kJ/mol

Figure 3 shows linear relationships between PA and GB of M and ∆H and ∆G values of hydration of MH+, respectively. Hydration of MH+ can be considered as a competition between M and H2O to interact with H+ in the M–H+–H2O cluster [18]. When the M–H+ interaction is strong (for M with higher PA and GB), the most part of positive charge of H+ is transferred on the M and H2O–H+ becomes weaker. For the molecule with low basicity, the main part of the positive charge remains on H+ and a strong H2O–H+ (dipole–charge) interaction is established. Figure S1 also shows the relationship between PA and GB of M and ∆H and ∆G values for dimer (M2H+) formation. As the basicity of M increases, the ∆H and ∆G values of dimer formation decrease; however, these correlations are not completely linear (Figure 3c, d).

Figure 3

Relationship between (a) ∆H of hydration of MH+ and PA of M, (b) ∆G of hydration of MH+ and GB of M, (c) ∆H of proton-bound dimer formation from M and MH+ and PA of M, and (d) ∆G of proton-bound dimer formation from M and MH+ and GB of M

Figure 4 shows the optimized structures of the clusters observed in the MS spectra of Figure 2. Comparison of the MH+…OH2 bond lengths reveals that this distance is shorter for molecules (M) with lower basicity and longer for molecules with higher basicity which is in agreement with hydration enthalpies. The same trend is observed for the bond lengths in the proton-bound dimers, MH+…M. The relationship between basicity of M and MH+…M distance has been recently predicted theoretically [46]. Figure S1 (Supplementary Materials) shows the variations of MH+…OH2 and MH+…M distances versus PA of M. These plots show that there is a linear relationship between these hydrogen bond distances and PA so that as PA increases the hydrogen bonds are lengthened. The more basic molecules have more ability to delocalize the positive charge of the entering proton; therefore, it is expected that the partial charge on the proton in MH+ is smaller for more basic molecules. Figure S2 (Supplementary Materials) shows the NBO charge distributions for the protonated molecules studied in this work. As PA of M increases, the main part of the positive charge of H+ is transferred to M so that the partial charge (q) on the H atom of MH+ decreases. Hence, the MH+/H2O or MH+/M interactions become weaker and the ∆H values of hydration or dimer formation decrease.

Figure 4

The optimized structures of the clusters observed in the MS spectra of Figure 2. The bond lengths are in Å. Ac: Acetone; But: 2-Butanone; Oct: 2-Octanone; Non: 2-Nonanone, AcPh: acetophenone; Pyr: pyridine; DMP: 2,6-dimethyl pyridine; DTBP: di-tertbutyl pyridine

Some part of low tendency of DTBPH+ to hydration or dimer formation is due to steric hindrance of bulky butyl groups adjacent to the proton acceptor site, N. To investigate this effect, hydration enthalpy of a molecule with strong basicity (PA = 1020 kJ/mol) [47] without any steric hindrance was calculated (Figure S3 in Supplementary Materials). The calculated hydration enthalpy for this molecule is – 50 kJ/mol which is smaller than those for all molecules studied in this work except DTBP. Therefore, although steric hindrance may influence the hydration enthalpy, basicity has a determinant effect on the hydration.

It has been reported that moisture can destroy the proton-bound dimers or proton-bound dimers are rarely hydrated [8, 25, 30]. Comparison of the enthalpies of hydration and dimer formation (Table 1) shows that formation of proton-bound dimers from MH+ and M is thermodynamically more favorable than the hydration of MH+. However, in the presence of high amount of water vapor, according to the Le Chatelier’s principle, the reaction M2H+ + H2O → MH+(H2O) + M may be occurred resulting in dimer destruction. Hydration of proton-bound dimers depends on the structures of M and MH+ which is discussed in the next section.

Effect of Size and Structure on the Hydration and Proton-Bound Dimer Formation

Other than basicity, size and structure of a molecule affect its hydration and cluster formation enthalpies. Figure 5a, b compares the MS spectra of NH3 and H2O. PA of NH3 is comparable with those of octanone, nonanone, and acetophenone (~ 850). However, in Figure 2, we observed that octanone-H+, nonanone-H+, and acetophenone-H+ are mono-hydrated while Figure 5 b shows that hydration of NH4+ proceeds to tri-hydration, NH4+(H2O)3. Therefore, PA is not the only factor influencing the hydration, and a large amount of hydration of small ions such as H3O+ and NH4+ can be attributed to their large surface density of the positive charge leading in strong interactions with water molecules. However, comparison of the hydration enthalpies of H3O+ and NH4+ (Table S2) shows that hydration enthalpies of NH4+ are noticeably smaller than those of H3O+. Another factor influencing the hydration of NH4+ is four identical hydrogen atoms which can participate in hydrogen bonding interactions with water molecules (Figure S4 in Supplementary Materials).

Figure 5

MS spectra for (a) water clusters, (b) hydrated ammonium, (c) ethanol, and (d) formic acid

To investigate effect of structure in more details, hydration and clustering of ethanol, C2H5OH, and formic acid, HCOOH, with the same molecular weights, comparable PAs, and different structures were studied. Figure 5 c and d compare the MS spectra of ethanol and formic acid. Both (C2H5OH)H+ and (HCOOH)H+, the protonated forms of ethanol and formic acid, have two hydrogen atoms which can participate in hydration or cluster formation. However, Figure 5 shows two different patterns of hydration and clustering for ethanol and formic acid. (C2H5OH)H+ mainly participates in hydration processes while (HCOOH)H+ tends to be both hydrated and clustered. The optimized structures of different clusters of ethanol and formic acid are provided in Supplementary Materials (Figures S5, S6, and S7). Neutral formic acid, HCOOH, has a carbonyl group, C=O, whose oxygen atom acts as a hydrogen bond acceptor without any steric hindrance while, at the same time, the OH group is involved in another hydrogen bonding interaction. Therefore, each formic acid molecule plays the role of a ring of a chain in a hydrogen bonding network (Figure S7). On the other hand, ethanol, C2H5OH, cannot act as both a hydrogen bond donor and a hydrogen bond acceptor, simultaneously; instead, it forms only one hydrogen bond via its H or O atom. It should be mentioned that the higher tendency of formic acid to be clustered compared to ethanol is not due to higher concentration of formic acid in the ionization region because we injected the head space vapor of the compounds and vapor pressure of ethanol is more than that of formic acid.

Figure 2 shows that, similar to formic acid, aldehyde also forms a proton-bound trimer, (H2CO)3H+. Because of the small size of formaldehyde and the high charge density of its protonated form, (H2CO)H+, the hydrogen of CH group also participates in cluster formation (Figure 4). Another reason for formation of formaldehyde trimer is its higher concentration in the ionization region due to its high vapor pressure (Table S1). However, enthalpy of trimer formation, M2H+ + M → M3H+, for formaldehyde is about 34 kJ/mol smaller than that for formic acid (Table S3 in Supplementary Materials). H2O molecules can act as bridges between the formaldehyde molecules and form more stable cluster of (H2CO)3H+(H2O)3 whose peak is more intense than the (H2CO)3H+ peak (Figure 2a). Formaldehyde, CH2O, may react with H2O to produce methanediol, CH2(OH)2; however, our calculations showed that this reaction is not thermodynamically possible (∆G = + 23.5 kJ mol−1). In the case of formic acid, the (HCOOH)3H+ peak is more intense compared to the (HCOOH)3H+(H2O)3 peak. Comparison of the formation enthalpies in Tables S3 and S4 shows that although (HCOOH)3H+ is more stable than (H2CO)3H+, the stability for the tri-hydrated clusters is reverse so that (H2CO)3H+(H2O)3 is more stable than (HCOOH)3H+(H2O)3. This observation reveals that the structure of formic acid with both hydrogen bond donor and acceptor sites compared to formaldehyde with only one proton bond acceptor site is more capable for clustering so that the formic acid forms more stable trimers without any water bridge. The structures of (H2CO)3H+(H2O)3 and (HCOOH)3H+(H2O)3 are shown in Figures 4 and S7, respectively. (H2CO)3H+(H2O)3 has only one stable structure, while different isomers were predicted for (HCOOH)3H+(H2O)3.

Clustering of formic acid proceeds up to tetramer with three water molecules, (HCOOH)4H+(H2O)3. The eight possible structures for the (HCOOH)4H+(H2O)3 are shown in Figure 6. Comparison of the relative stabilities of the (HCOOH)3H+(H2O)3 (Figure S7) and (HCOOH)4H+(H2O)3 isomers (Figure 6) shows that the structures in which the proton remains on the water and H3O+ is the core center of the cluster are more stable. These results are in accordance with those previously reported [14,15,16]. The isomers a and b of (HCOOH)4H+(H2O)3, in which the water and formic acid molecules have been positioned alternatively, are the less stable structures. The isomers c and f with a water cluster of H3O+(H2O)2 are the most stable structures; however, the isomer c in which the H3O+(H2O)2 group is located in the center of the (HCOOH)4H+(H2O)3 is more stable.

Figure 6

The optimized structures of different isomers of (HCOOH)4H+(H2O)3 cluster. The relative energies and bond lengths are in kJ/mol and Å, respectively

Effect of Basicity on the Asymmetric Proton–Bound Dimer Formation

The MS spectra of Figures 2 and 5 show that although the chance of formation of the symmetric proton–bound dimers (MH+M) decreases with an increase in the basicity of the molecule M, these symmetric dimers are readily formed. Figure 7a compares the IMS spectra of 2-octanone, acetophenone, and their mixtures. The IMS spectra of 2-octanone and acetophenone show only the monomer (MH+) and dimer (MH+M) peaks of these molecules. In the IMS spectrum of their mixture, a new peak with high intensity appears between the symmetric dimers. The MS spectrum of this mixture (Figure 7b) confirms that the new peak is due to formation of the asymmetric dimer of octanone–H+–acetophenone. Also, the IMS spectra show only one peak for the protonated molecules because of hydration/dehydration equilibrium in the drift tube while the MS spectra show that the monomers are a mixture of MH+ and MH+(H2O) species. When a mixture of pyridine and 2-octanone was injected into IMS, a small peak was hardly observed between the dimer peaks of pyridine and 2-octanone (Figure 7c). The experiment was repeated with several mixtures with different ratios of 2-octanone/pyridine. The MS spectrum of the octanone/pyridine mixture shows that the new peak is due to the asymmetric dimer of octanone–H+–pyridine (Figure 7d).

Figure 7

(a) IMS spectra for 2-octanone, acetophenone, and their mixture; (b) MS spectrum for 2-ocatnone/acetophenone mixture; (c) IMS spectra for 2-octanone, pyridine, and their mixture; and (d) MS spectrum of the 2-octanone/pyridine mixture. The peaks of the asymmetric proton–bound dimers have been shown by purple color. The spectra of the pure compounds were recorded after injection of 1 ml of the head space vapor of the compounds. To observe the asymmetric dimers, 2 ml of the binary mixture (1 ml of the head space vapor of each component) was injected. Oct, 2-octanone; AcPh, acetophenone; Pyr. pyridine

The calculated values of ∆H and ∆G for formation of the symmetric (MH+M) and asymmetric dimers (MH+N) are tabulated in Table 2. Furthermore, PA differences (∆PA) of the molecules participating in the dimer formation are also included in Table 2. For the symmetric dimer, the ∆PA values are zero and the enthalpies of dimer formation are about − 102 to – 117 kJ/mol. For the asymmetric dimer octanone–H+–acetophenone, the basicities of octanone and acetophenone are not so different (∆PA = 28 kJ/mol); therefore, this asymmetric dimer is easily formed with enthalpy of – 106 kJ/mol. The difference of basicity between octanone and pyridine is considerable (∆PA = 94 kJ/mol) resulting in lower enthalpy of asymmetric dimer formation (∆H = − 85 kJ/mol). In summary, the asymmetric dimers are formed more easily between the molecules with comparable basicity.

Table 2 The Calculated Values of ∆H and ∆G for the Symmetric and Asymmetric Dimer Formations. The Energies Are in kJ/mol

The optimized structures of the studied symmetric and asymmetric proton–bound dimers are compared in Figure 8. The M…H…M and M…H…N hydrogen bond lengths are also shown in Å. In the symmetric dimer of acetophenone, with the highest enthalpy of formation, the bond lengths are 1.353 and 1.091 Å and their difference is 0.262 Å. On the other hand, for the asymmetric dimer of octanone–H+–pyridine, with the lowest enthalpy of formation, the difference in the bond lengths is 0.601 Å. It seems there is a direct relationship between the enthalpy of dimer formation and the structure. The plot of variations of enthalpy of dimer formation versus the difference in the hydrogen bond lengths in the dimer structures is shown in Figure S8 (Supplementary Materials). Observation of this relationship is expectable because the difference in the hydrogen bond lengths is due to the difference in the basicities of the molecules participating in proton-bound formation which, as mentioned above, determines the enthalpy of dimer formation.

Figure 8

The optimized structures of the studied symmetric and asymmetric proton–bound dimers. The bond lengths are in Å


The thermodynamic and structural criteria for cluster formation and hydration of protonated molecules (MH+) were investigated both experimentally and theoretically. Comparison of the MS spectra of a class of compounds with a wide range of basicity (PA = 690–990 kJ/mol) showed that amount of hydration of MH+ decreases as the PA of M increases so that more basic compounds form smaller MH+(H2O)n clusters. The same trend was observed for formation of proton-bound dimers (M2H+), trimers (M3H+), and tetramers (M4H+) so that the more basic molecules showed lower tendency for dimer, trimer, or tetramer formation. Generally, the protonated form of a more basic molecule tends to form smaller clusters. The structures of M and MH+ also influence the amount of hydration or clustering. Although NH3 has high basicity, its MS spectrum shows that the cluster NH4+(H2O)3 is easily formed because of four identical hydrogen atoms of NH4+ acting as hydrogen bond donors. Also, formic acid due to its C=O and OH groups can interact with two hydrogen bond donor and acceptor atoms simultaneously forming a network or chain cluster. Therefore, despite of its higher basicity compared to H2O and formaldehyde, it can form a larger cluster such as M4H+(H2O)3 in the same condition. Effect of basicity of M and N on the formation of their asymmetric dimer (MH+N) was investigated. It was found that the enthalpy of MH+N formation depends on the difference in the basicities of M and N. The asymmetric dimer of 2-ocatanone and acetophenone with comparable PA is formed easily with ∆H of − 106 kJ/mol while the ∆H for formation of asymmetric dimer of 2-ocatanone and pyridine with ∆PA of 94 kJ/mol is – 85 kJ/mol.


  1. 1.

    Jacquemin, D., Zuniga, J., Requena, A., Ceron-Carrasco, J.P.: Assessing the importance of proton transfer reactions in DNA. Acc. Chem. Res. 47, 2467–2474 (2014)

    Article  CAS  PubMed  Google Scholar 

  2. 2.

    Lepine, F., Milot, S., Deziel, E., He, J., Rahme, L.G.: Electrospray/mass spectrometric identification and analysis of 4-hydroxy-2-alkylquinolines (HAQs) produced by Pseudomonas aeruginosa. J. Am. Soc. Mass Spectrom. 15, 862–869 (2004)

    Article  CAS  PubMed  Google Scholar 

  3. 3.

    Wyttenbach, T., Bowers, M.T.: Hydration of biomolecules. Chem. Phys. Lett. 480, 1–16 (2009)

    Article  CAS  Google Scholar 

  4. 4.

    Elm, J., Passananti, M., Kurtén, T., Vehkamäki, H.: Diamines can initiate new particle formation in the atmosphere. J. Phys. Chem. A. 121, 6155–6164 (2017)

    Article  CAS  PubMed  Google Scholar 

  5. 5.

    Blake, R.S., Monks, P.S., Ellis, A.M.: Proton-transfer reaction mass spectrometry. Chem. Rev. 19, 861–896 (2009)

    Article  CAS  Google Scholar 

  6. 6.

    Valadbeigi, Y., Farrokhpour, H., Rouholahnejad, F., Tabrizchi, M.: Experimental and theoretical study of the kinetic of proton transfer reaction by ion mobility spectrometry. Int. J. Mass Spectrom. 369, 105–111 (2014)

    Article  CAS  Google Scholar 

  7. 7.

    Zhang, Q., Zou, X., Liang, Q., Wang, H., Huang, C., Shen, C., Chu, Y.: Ammonia-assisted proton transfer reaction mass spectrometry for detecting triacetone triperoxide (TATP) explosive. J. Am. Soc. Mass Spectrom. (2018). https://doi.org/10.1007/s13361-018-2108-6

  8. 8.

    Meot-Ner (Mautner), M., Scheiner, S., Yu, W.O.: Ionic hydrogen bonds in bioenergetics. 3. Proton transport in membranes, modeled by ketone/water clusters. J. Am. Chem. Soc. 120, 6980–6990 (1998)

    Article  Google Scholar 

  9. 9.

    Konig, S., Fales, H.M.: Formation and decomposition of water clusters as observed in triple quadrupole mass spectrometer. J. Am. Soc. Mass Spectrom. 9, 814–822 (1998)

    Article  CAS  Google Scholar 

  10. 10.

    Huang, C., Kresin, V.V., Pysanenko, A., Farnik, M.: Water cluster fragmentation probed by pickup experiments. J. Chem. Phys. 145, 104304 (2016)

    Article  CAS  PubMed  Google Scholar 

  11. 11.

    Iyengar, S.S., Petersen, M.K., Day, T.J.F., Burnham, C.J., Teige, V.E., Voth, G.A.: J. Chem. Phys. 123, 084309 (2005)

    Article  CAS  PubMed  Google Scholar 

  12. 12.

    Sunner, J., Beech, I.B., Hiroka, K.: On the distribution of ion/neutral clusters in electrospray and laser spray-a cluster division model for the electrospray processes. J. Am. Chem. Mass Spectrom. 17, 151–162 (2006)

    Article  CAS  Google Scholar 

  13. 13.

    Postulka, J., Slavicek, P., Domaracka, A., Pysanenko, A., Farnik, M., Kocisek, J.: Proton transfer from pinene stabilizes water clusters. Phys. Chem. Chem. Phys. (2019). https://doi.org/10.1039/C8CP05959D

  14. 14.

    Keesee, R.G., Castleman, A.W.: Thermochemical data on gas-phase ion-molecule association and clustering reactions. J. Phys. Chem. Ref. Data. 15, 1011 (1986)

    Article  CAS  Google Scholar 

  15. 15.

    Kebarle, P.: Ion thermochemistry and solvation from gas phase ion equilibria. Annu. Rev. Phys. Chem. 28, 445–476 (1977)

    Article  CAS  Google Scholar 

  16. 16.

    Meot-Ner (Mautner), M.: The ionic hydrogen bond and ion solvation. 1. NH+…O, NH+…N, and OH+…O bonds. Correlations with proton affinity. Deviation due to structural effects. J. Am. Chem. Soc. 106, 1257–1264 (1984)

    Article  Google Scholar 

  17. 17.

    Valadbeigi, Y.: Proton affinities of hydrated molecules. Chem. Phys. Lett. 660, 301–306 (2016)

    Article  CAS  Google Scholar 

  18. 18.

    Valadbeigi, Y., Ilbeigi, V., Michalczuk, B., Sabo, M., Matejcik, S.: Study of atmospheric pressure chemical ionization mechanism in corona discharge ion source with and without NH3 dopant by ion mobility spectrometry combined with mass spectrometry: a theoretical and experimental study. J. Phys. Chem. A. 123, 313–322 (2019)

    Article  CAS  PubMed  Google Scholar 

  19. 19.

    Demireva, M., O’Brien, J.T., Williams, E.R.: Water-induced folding of 1,7-diammoniumheptane. J. Am. Chem. Soc. 134, 11216–11224 (2012)

    Article  CAS  PubMed  Google Scholar 

  20. 20.

    Noh, D.H., Lee, S.J.C., Lee, J.W., Kim, H.I.: Host-guest chemistry in the gas phase: complex formation of cucurbit[6]urcil with proton-bound water dimer. J. Am. Chem. Soc. Mass Spectrom. 25, 410–421 (2014)

    Article  CAS  Google Scholar 

  21. 21.

    Li, X., Wang, X., dell’ Arco Passaro, M., Spinell, N., Apicella, B.: Insights on clusters formation mechanism by time of flight mass spectrometry. 1. The case of ethanol-water clusters. J. Am. Chem. Mass Spectrom. 26, 1665–1675 (2015)

    Article  CAS  Google Scholar 

  22. 22.

    Gao, B., Wyttenbach, T., Bowers, M.T.: Hydration of protonated aromatic amino acids: phenylalanine, tryptophan, and tyrosine. J. Am. Chem. Soc. 131, 4695–4701 (2009)

    Article  CAS  PubMed  Google Scholar 

  23. 23.

    Kebarle, P.: A brief overview of the present status of the mechanisms involved in electrospray mass spectrometry. J. Mass Spectrom. 35, 804–817 (2000)

    Article  CAS  PubMed  Google Scholar 

  24. 24.

    Li, J., Wei, W., Nye, L.C., Schulz, P.S., Wasserscheid, P., Ivanovic-Burmazovic, I., Drewello, T.: Zwitterionic clusters with dianion core produced by electrospray ionisation of Brønsted acidic ionic liquids. Phys. Chem. Chem. Phys. 14, 5115–5121 (2012)

    Article  CAS  PubMed  Google Scholar 

  25. 25.

    Valadbeigi, Y., Farrokhpour, H., Tabrizchi, M.: Effect of hydration on the kinetics of proton-bound dimer formation: experimental and theoretical study. J. Phys. Chem. A. 118, 7663–7671 (2014)

    Article  CAS  PubMed  Google Scholar 

  26. 26.

    Jacobs, A.D., Jose, K.V.J., Horness, R., Raghavachari, K., Thielges, M.C., Clemmer, D.E.: Cooperative formation of icosahedral proline clusters from dimers. J. Am. Chem. Soc. Mass Spectrom. 29, 95–102 (2018)

    Article  CAS  Google Scholar 

  27. 27.

    Wu, R., Marta, R.A., Martnes, J.K., Eldridge, K.R., McMahon, T.B.: Experimental and theoretical investigation of the proton-bound dimers of lysine. J. Am. Chem. Mass Spectrom. 22, 1651–1659 (2011)

    Article  CAS  Google Scholar 

  28. 28.

    Ewing, R.G., Eiceman, G.A., Stone, J.A.: Proton-bound cluster ions in ion mobility spectrometry. Int. J. Mass Spectrom. 193, 57–68 (1999)

    Article  CAS  Google Scholar 

  29. 29.

    Eiceman, G.A., Karpas, Z., Hill Jr., H.H.: Ion Mobility Spectrometry, 3th edn. CRC Press, Boca Raton (2014)

    Google Scholar 

  30. 30.

    Makinen, M., Sillanpaa, M., Viitanen, A.K., Knap, A., Makela, J.M., Puton, J.: The effect of humidity on sensitivity of amine detection in ion mobility spectrometry. Talanta. 84, 116–121 (2011)

    Article  CAS  PubMed  Google Scholar 

  31. 31.

    Roscioli, J.R., McCunn, L.R., Johnson, M.A.: Quantum structure of the intermolecular proton bond. Science. 316, 249–254 (2007)

    Article  CAS  PubMed  Google Scholar 

  32. 32.

    Witt, M., Grutzmacher, H.F.: Proton bound homodimers and heterodimers of amides and amines in the gas phase. Equilibrium studies by Fourier transformation ion cyclotron resonance spectrometry. J. Am. Chem. Soc. Mass Spectrom. 13, 1273–1281 (2002)

    Article  CAS  Google Scholar 

  33. 33.

    Tan, J.A., Kuo, J.L.: A closer examination of the coupling between ionic hydrogen bond (IHB) stretching and flanking group motions in (CH3OH)2H+: the strong isotope effects. Phys. Chem. Chem. Phys. 18, 14531–14542 (2016)

    Article  CAS  PubMed  Google Scholar 

  34. 34.

    Sabo, M., Matejcik, S.: Corona discharge ion mobility spectrometry with orthogonal acceleration time of flight mass spectrometry for monitoring of volatile organic compounds. Anal. Chem. 84, 5327–5334 (2012)

    Article  CAS  PubMed  Google Scholar 

  35. 35.

    Tirado-Rives, J., Jorgensen, W.L.: Performance of B3LYP density functional methods for a large set of organic molecules. J. Chem. Theory Comput. 4, 297–306 (2008)

    Article  CAS  PubMed  Google Scholar 

  36. 36.

    Bryantsev, V.S., Diallo, M.S., van Duin, A.C.T., Goddard III, W.A.: Evaluation of B3LYP, X3LYP, and M06-class density functionals for predicting the binding energies of neutral, protonated, and deprotonated water clusters. J. Chem. Theory Comput. 5, 1016–1026 (2009)

    Article  CAS  PubMed  Google Scholar 

  37. 37.

    McKechnie, S., Booth, G.H., Cohen, A.J., Cole, J.M.: On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies. J. Chem. Phys. 142, 194114 (2015)

    Article  CAS  PubMed  Google Scholar 

  38. 38.

    Mardirossian, N., Head-Gordon, M.: Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals. Mol. Phys. 115, 2315–2372 (2017)

    Article  CAS  Google Scholar 

  39. 39.

    Valadbeigi, Y., Farrokhpour, H., Tabrizchi, M.: Theoretical study on the mechanism and kinetics of atmospheric reactions NH2OH+OOH and NH2CH3+OOH. Phys. Lett. A. 378, 777–784 (2014)

    Article  CAS  Google Scholar 

  40. 40.

    Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G.A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H.P., Izmaylov, A.F., Bloino, J., Zheng, G., Sonnenberg, J.L., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery Jr., J.A., Peralta, J.E., Ogliaro, F., Bearpark, M., Heyd, J.J., Brothers, E., Kudin, K.N., Staroverov, V.N., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A., Burant, J.C., Iyengar, S.S., Tomasi, J., Cossi, M., Rega, N., Millam, J.M., Klene, M., Knox, J.E., Cross, J.B., Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R.E., Yazyev, O., Austin, A.J., Cammi, R., Pomelli, C., Ochterski, J.W., Martin, R.L., Morokuma, K., Zakrzewski, V.G., Voth, G.A., Salvador, P., Dannenberg, J.J., Dapprich, S., Daniels, A.D., Farkas, O., Foresman, J.B., Ortiz, J.V., Cioslowski, J., Fox, D.J.: Gaussian 09, Revision A.1. Gaussian, Inc, Wallingford (2009)

    Google Scholar 

  41. 41.

    Sunner, J., Gordon, N., Kebarle, P.: Factors determining relative sensitivity of analytes in positive mode atmospheric pressure ionization mass spectrometry. Anal. Chem. 60, 1300–1307 (1988)

    Article  CAS  Google Scholar 

  42. 42.

    Meot-Ner (Mautner), M.: The ionic hydrogen bond. Chem. Rev. 105, 213–284 (2005)

    Article  CAS  Google Scholar 

  43. 43.

    Bohme, D.K., Mackay, G.I., Tanner, S.D.: An experimental study of the gas-phase kinetics of reactions with hydrated H3O+ ions (n=1-3) at 298 K. J. Am. Chem. Soc. 101, 3724–3730 (1979)

    Article  CAS  Google Scholar 

  44. 44.

    Hunter, E.P.L., Lias, S.G.: Evaluated gas phase basicities and proton affinities of molecules: an update. J. Phys. Chem. Ref. Data. 27, 413–656 (1998)

    Article  CAS  Google Scholar 

  45. 45.

    Valadbeigi, Y., Farrokhpour, H.: DFT, CBS-Q, W1BD and G4MP2 calculation of the proton and electron affinities, gas phase basicities and ionization energies of saturated and unsaturated carboxylic acids (C1–C4). Int. J. Quantum Chem. 113, 1717–1721 (2013)

    Article  CAS  Google Scholar 

  46. 46.

    Valadbeigi, Y.: Relationship between proton affinities and structures of proton-bound dimers. Eur. J. Mass Spectrom. 23, 55–63 (2017)

    Article  CAS  Google Scholar 

  47. 47.

    Valadbeigi, Y.: Superbasicity of 1,3,5-cycloheptatriene derivatives and their proton sponges in gas phase. Chem. Phys. Lett. 689, 1–7 (2017)

    Article  CAS  Google Scholar 

Download references


This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement no. 692335 and Marie skłodowska-Curie grant agreement no. 674911. This work was supported by the Slovak Research and Development Agency (contract nos. APVV-0259-12 and APVV-15-0580) and the Slovak Grant Agency for Science (contract no. VEGA 1/0787/18). YV thanks HPC Computing Facility of IKIU, Iran, for computational resources.

Author information



Corresponding authors

Correspondence to Younes Valadbeigi or Stefan Matejcik.

Electronic Supplementary Material


(PDF 981 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Valadbeigi, Y., Ilbeigi, V., Michalczuk, B. et al. Effect of Basicity and Structure on the Hydration of Protonated Molecules, Proton-Bound Dimer and Cluster Formation: An Ion Mobility-Time of Flight Mass Spectrometry and Theoretical Study. J. Am. Soc. Mass Spectrom. 30, 1242–1253 (2019). https://doi.org/10.1007/s13361-019-02180-z

Download citation


  • Proton affinity
  • Clustering
  • Hydration
  • Proton-bound dimer
  • Mass spectrometry