When hydrogen bonding overcomes Coulomb repulsion: from kinetic to thermodynamic stability of cationic dimers

T. Niemann a, P. Stange a, A. Strate a and R. Ludwig *abc
aUniversität Rostock, Institut für Chemie, Abteilung für Physikalische Chemie, Dr.-Lorenz-Weg 2, 18059, Rostock, Germany. E-mail: ralf.ludwig@uni-rostock.de
bDepartment LL&M, University of Rostock, Albert-Einstein-Str. 25, 18059, Rostock, Germany
cLeibniz-Institut für Katalyse an der Universität Rostock e.V., Albert-Einstein-Str. 29a, 18059 Rostock, Germany

Received 15th October 2018 , Accepted 14th January 2019

First published on 15th January 2019

Quantum chemical calculations have been employed to study the kinetic and thermodynamic stability of hydroxy-functionalized 1-(3-hydroxyalkyl)pyridinium cationic dimers. For [Py–(CH2)n–OH+]2 structures with n = 2–17 we have calculated the robust local minima with clear dissociation barriers preventing their “Coulomb explosion” into separated cations. For n = 15 hydrogen bonding and dispersion forces fully compensate for the repulsive Coulomb forces between the cations allowing for the quantification of the pure hydrogen bond in the order of 20 kJ mol−1. The increasing kinetic stability even turns to thermodynamic stability with further elongated hydroxyalkyl chains. Now, quantum-type short-range attraction wins over classical long-range electrostatic repulsion resulting in negative binding energies and providing the first thermodynamically stable cationic dimers. The electronic, structural and spectroscopic signatures of the cationic dimers could be correlated to NBO parameters, supporting the existence of anti-electrostatic hydrogen bonds (AEHB) as recently suggested by Weinhold. In principle, these pure cationic dimers should be detectable in gas-phase experiments at low temperatures without the need of mediating molecules or counteranions.

Weinhold and Klein recently predicted the existence of dimers of like-charged ions. Such cationic and anionic dimers are kinetically stabilized by hydrogen bonding, opposing their “Coulomb explosion” into separated ions.1–3 These findings strongly challenged the claim of Braga and co-workers that anionic dimers would fall apart if the countercations are removed.4 And indeed, experimental evidence for cationic or anionic dimers is only provided for systems wherein the repulsive Coulomb forces are mediated by molecules or counterions.5–14 Most similar to pure cationic dimers are isolated ion clusters in the gas phase consisting of two cations and one anion, as recently reported by Menges et al.15 For ternary (HEMIm+)2NTf2 complexes consisting of two 1-(2-hydroxyethyl)-3-methylimidazolium cations and one weakly interacting bis(trifluoromethylsulfonyl)imide anion, two isomers could be isolated by cryogenic ion vibrational predissociation spectroscopy combined with double resonance techniques.15,16 One (2,1) complex was identified to exhibit direct contact between the cations. Therein, the OH group of one cation binds to the OH group of the other, which then attaches to the basic nitrogen atom of the NTf2 anion.15 That was the first experimental evidence for cation–cation hydrogen bonds in small isolated clusters of ionic liquids (ILs). Still, we cannot ignore the mediation role of the counteranion so far. Nevertheless, for the doubly hydrogen bonded hydrogen sulfate dimer (HSO4)2, Weinhold calculated a potential energy curve with a remarkably deep potential well of about ΔE* = 13.5 kJ mol−1.3 However, these anionic dimers still exhibit positive energies lying at approximately ΔE = 164.84 kJ mol−1 above the asymptotic limit of infinitely separated ions (ΔE = 0). The meta-stable dimers are still far away from thermodynamic stability. Recently, we could show that dimers of hydroxy-functionalized cations also exhibit robust kinetic stability.17 Ammonium-, imidazolium- and pyridinium-based cations with hydrogen bonding hydroxyethyl groups are well-known constituents of ionic liquids. In such cationic dimers, hydrogen bonding opposes the repulsive Coulomb forces between the positive charges.18–23 In principle, the Coulomb repulsion can be further attenuated by elongation of the hydroxyalkyl chain, thus increasing the distance between the positively charged centres of the cations.24 This way, robust kinetically stable complexes should exist without altering the dielectric environment. An ultimate goal would be the prediction of a cationic dimer exhibiting negative binding energies that should be observable in sophisticated gas phase experiments.

It is the aim of this work to show that the interplay between attractive short-range hydrogen bonds and repulsive long-range Coulomb forces provides kinetic well-depths and barrier widths for simple cationic dimers with net charge Q = +2e. We demonstrate that hydrogen-bonded dimers of hydroxy-functionalized 1-(3-hydroxyalkyl)pyridinium cations exhibit substantial kinetic stability without being embedded in a dielectric medium by adding molecules or counterions.17 We show that with increasing length of the hydroxyalkyl chain tether even absolute thermodynamic stability is achieved. In these cationic species, hydrogen bonding does not only attenuate, but also overcomes the repulsive Coulomb forces. Then, the hydrogen bond strength and geometry in the cationic dimer approach those of familiar molecular species such as water and alcohols. Thus, there is a good chance for finding these like-charged dimers in gas phase experiments at low temperatures.

Kinetically stabilized dimers [Py–(CH2)n–OH+]2 with n = 2–6

For that purpose we calculated the potential energy curves for dimers of the hydroxy-functionalized cations 1-(3-hydroxyalkyl)pyridinium [Py–(CH2)n–OH+]2 with n = 2–6 at the unrestricted second-order Møller–Plesset perturbation theory (UMP2) by using the well-balanced but small 6-31+G* basis set as implemented in the Gaussian 09 program (Scheme 1).25 The methylene (CH2) groups in the alkyl chains of the cations are all kept in trans position to the hydroxy functional group –OH. Analytical positive frequencies were obtained for all species n = 2–6 to verify the local stability of each optimized structure. The optimized geometries and frequencies for the dimers n = 2–6 are given in the ESI.
image file: c8cp06417b-s1.tif
Scheme 1 1-(3-Hydroxyalkyl)pyridinium dimer [Py–(CH2)n–OH+]2.

For the cationic dimers [Py–(CH2)n–OH+]2 with n = 2–6 we calculated relaxed potential energy curves by varying the HO intermolecular distance and optimizing all other geometrical variables at each step of the scan. The resulting potential energy curves for each dimers [Py–(CH2)n–OH+]2 with n = 2–6 are shown in Fig. 1a. For each curve, we show the net energy release ΔE and the activation barrier height ΔE* for the dissociation potentials of the cationic dimers. Additionally, we indicated the optimized equilibrium H-bond distances R(HO). Table 1 lists all these energetic and geometric parameters. As shown in Fig. 1a, robust kinetic stabilities with clear dissociation barriers are achieved for the UMP2 treatment. As an example we first discuss the potential energy curve for the smallest cationic dimer [Py–(CH2)2–OH+]2 dissociated along the R(HO) H-bond stretching coordinate with respect to the energy of the isolated cations at ΔE = 0. In Fig. 1c the vertical arrow at R(HO) = 1.9994 Å shows the calculated ΔE = 136.4 kJ mol−1 equilibrium well depth at this level of theory. The effective well depth is measured with respect to the transition state (near R(HO) = 3.0 Å) that signals descent toward separated cations, corresponding to an activation barrier height of ΔE* = 4.52 kJ mol−1. In the following section we discuss the energetic and geometric parameters for the larger dimers with hydroxyalkyl tethers n = 3–6. The ΔE values drop from 136.4 kJ mol−1 for n = 2 down to 39.3 kJ mol−1 for n = 6 as shown in Fig. 1a. Thus, the equilibrium energy for the cationic dimer [Py–(CH2)6–OH+]2 is only moderately above that of the isolated cations. The stronger attractive interaction with increasing tether length is also reflected in shortened hydrogen bond distances R(HO), changing from 1.9994 Å for n = 2 down to 1.891 Å for n = 6, as indicated by the dots at the potential minima in Fig. 1a. Similarly, the deep potential wells ΔE* increase from 4.5 to 20 kJ mol−1, exceeding significantly the values reported for other cationic and anionic dimers.1–3Fig. 1 also displays the extreme breadth of the potential barrier through which the dimeric species must tunnel to reach the lower energy of long-range dissociation. This barrier breadth already increases from R(HO) = 2.0 Å to R(HO) = 4.5 Å by adding only one methylene group to the hydroxyalkyl chain tether of the cationic dimer [Py–(CH2)2–OH+]2, resulting in [Py–(CH2)3–OH+]2. The full potential barrier for the dimer [Py–(CH2)n–OH+]2 with n = 6 could not be calculated at the demanding UMP2 level of theory in reasonable time. At this point we conclude that elongation of the hydroxyalkyl chain tether up to n = 6 leads to cationic dimer energies of only 40 kJ mol−1 above those of the dissociated cations, and to energetic barriers of about 20 kJ mol−1.

image file: c8cp06417b-f1.tif
Fig. 1 (a) The potential energy curves for the cationic dimers [Py–(CH2)n–OH+]2 with n = 2–6 were calculated at the UMP2/6-31+G* basis level of theory relaxing the structures for each bond length RH⋯O. The dissociative energy profiles show pronounced binding wells with respect to the dissociated cations and effective equilibrium well depths with respect to the transition state. (b) The bond lengths R(H⋯O) at the minima shift to shorter distances due to increasing hydrogen bonding. (c) The potential energy curve for the [Py–(CH2)2–OH+]2 dimer shows a pronounced binding well at 136.4 kJ mol−1 with respect to the dissociated cations, an effective equilibrium well depth of 3.6 kJ mol−1 with respect to the transition state, and an energy barrier width of about 2 Å, respectively.
Table 1 Calculated intermolecular distances R(H⋯O) and R(O⋯O) along with the energies relative to the asymptotic dissociated ions, ΔE, and the binding energies, ΔE* of the optimized dimer structures [Py–(CH2)nOH+]2 with n = 2–17 calculated at the UMP2/6-31+G* level of theory
n R (H⋯O) R (O⋯O) ΔE/kJ mol−1 ΔE*/kJ mol−1
2 1.9994 2.8807 136.43 4.52
3 1.9174 2.8808 82.51 12.54
4 1.9015 2.8661 62.62 17.59
5 1.8949 2.8670 50.28 19.33
6 1.8906 2.8638 39.31 21.27
7 1.8892 2.8642 31.46
8 1.8871 2.8624 24.42
9 1.8859 2.8617 19.31
10 1.8850 2.8608 14.83
11 1.8874 2.8603 10.76
12 1.8835 2.8599 7.50
13 1.8824 2.8592 4.64
14 1.8820 2.8592 2.71
15 1.8814 2.8584 0.0
16 1.8818 2.8588 −1.89
17 1.8826 2.8595 −3.61

Kinetically and thermodynamically stabilized dimers [Py–(CH2)n–OH+]2 with n = 7–17

The cationic dimers [Py–(CH2)n–OH+]2 including longer hydroxyalkyl chain tethers n = 7–16 were fully optimized at the MP2/6-31+G*. Unfortunately, frequencies and potential energy curves could not be obtained at this demanding level of theory. For these cationic dimers we calculated the net energy release relative to the dissociated cations, ΔE, the potential energy and the R(H⋯O) distances that are shown along with the properties of [Py–(CH2)n–OH+]2 with n = 2–6 in Fig. 2 and 3. In Fig. 2 we show the calculated energies ΔE for all dimers [Py–(CH2)n–OH+]2 which decrease from 136.4 kJ mol−1 for n = 2 via 39.3 kJ mol−1 for n = 6 down to −3.6 kJ mol−1 for n = 17, respectively. With increasing hydroxyalkyl chain length, a robust kinetic stability switches to weak thermodynamic stability. For [Py–(CH2)n–OH+]2 with n = 16, 17 the binding energies are slightly negative. The hydrogen bond overcomes the repulsive Coulomb forces that are attenuated by the elongated alkyl chains. The quantum chemical calculations tell us that about ninety percent of the positive charge is located on the pyridinium rings (see ESI). Putting +0.9e charges at the centres of both rings and using the calculated ring–ring distances, we can estimate the Coulomb energies for all dimers. They are shown in comparison to the calculated MP2/6-31+G* energies in Fig. 2. For the cationic dimers [Py–(CH2)15–OH+]2 the energy release is zero (ΔE = 0). At a ring–ring distance of about 42 Å, the energy of the cationic dimer is exactly the same as that of the isolated cations. In this case, the repulsive Coulomb forces are fully counter-balanced by the attractive HO hydrogen bond and dispersion forces that are both described reasonably well by the MP2 method. For dissecting the amount of stabilizing energy of about 26.8 kJ mol−1 into hydrogen bonding and dispersion contributions, we performed additional B3LYP/6-31+G* calculations on the MP2/6-31+G* optimized geometries with and without including dispersion forces. This is realized by using Grimme's D3-method26–28 The B3LYP-D3/6-31+G* calculated energy on the UMP2/6-31+G* optimized geometries ΔE = 1.42 kJ mol−1 is only slightly above ΔE = 0 kJ mol−1, justifying the applied approach. Overall, the calculated dispersion energy stabilizes the cation–cation interaction by 6.7 kJ mol−1. Now we are able to dissect the overall attractive interaction energy of about 26.8 kJ mol−1. The energy difference of about 20.1 kJ mol−1 can be referred to the pure HO hydrogen bond in the cationic dimer. Such a H-bond energy is typical for hydrogen-bonded dimers of water and alcohols.29–34
image file: c8cp06417b-f2.tif
Fig. 2 (a) The binding energies for all cationic dimers [Py–(CH2)n–OH+]2 with n = 2–17 were calculated at the UMP2/6-31+G* basis level of theory (circles). They are compared to the long-range e2/R behavior of idealized Coulomb electrostatic repulsion assuming positive charges q = +0.9e on the pyridinium ring (squares). (b) For the [Py–(CH2)15–OH+]2 dimer the Coulomb repulsion is perfectly counter-balanced by the attractive hydrogen bond and dispersion forces resulting in ΔE = 0 (filled symbols). The energy difference represents the sum of the H-bond and dispersion energy as indicated by the brown and grey bars, respectively.

image file: c8cp06417b-f3.tif
Fig. 3 The intermolecular hydrogen bond distances, R(H⋯O) for the equilibrium structures of [Py–(CH2)n–OH+]2 with n = 2–17 decrease with increasing hydroxyalkyl chain length. Each additional (CH2) group attenuates the Coulomb repulsion and results in enhanced hydrogen bonding as indicated by shorter H-bond lengths. If hydrogen bonding is maximized at about n = 15, no further shortening of R(H⋯O) is observed. Then the R(H⋯O) distances agree with those obtained for calculated n-alcohol dimers with n = 2–6 (red squares).

Remarkably, the energies of the cationic dimers [Py–(CH2)n–OH+]2 with n > 15 dip below the asymptotic limit of cationic dissociation, thereby achieving thermodynamic as well as kinetic stability (see Fig. 3). Such surprising thermodynamic stability suggests that [Py–(CH2)17–OH+]2, once formed, should be observable in gas phase experiments already at moderate temperatures. The energies become negative because attractive hydrogen bonding overcomes the Coulomb repulsion. Following Coulomb's law, the repulsive interaction is getting weaker with 1/r, whereas the attractive forces seem to maximize. This is best observed for the optimized H-bond distances R(HO) with increasing hydroxyalkyl chain length in Fig. 3. From n = 2 to n = 17 the equilibrium distances are shortened due to enhanced hydrogen bonding while the Coulomb repulsion is constantly weakened. It seems that hydrogen bonding is maximized in [Py–(CH2)16–OH+]2 indicated by constant H-bond distances R(HO). The hydrogen bond is fully relaxed and no longer competes with stronger repulsive Coulomb forces. For the largest cationic dimer the H-bond length is 1.882 Å, in good agreement with values calculated for methanol and ethanol dimers at the same level of theory.29–34

NBO parameter versus energy, H-bond distances and NMR proton chemical shifts

The H-bonded cationic dimers demonstrate that the short-range donor–acceptor covalent forces compete with the powerful long-range electrostatic repulsions.1–3,17 Characteristic covalency features of HO hydrogen bonds can be readily recognized in the framework of the natural bond orbital (NBO) analysis as distinctive nO → σOH* donor–acceptor interactions expressed by the second order stabilization energies image file: c8cp06417b-t1.tif and estimated total charge transfers qCT for the enhanced OHOH hydrogen bonds, respectively.35,36 Charge from the oxygen lone pair orbital of a first cation is donated into the OH anti-bond orbital of second cation. This way the short-range donor–acceptor covalent forces overcome the strong long-range electrostatic repulsive forces as expected for ions of like charge. In Fig. 4 the NBO energy descriptors are plotted versus binding energies ΔE, H-bond distances R(H⋯O) and proton chemical shifts differences between the H-bonded and free OH of the dimers, Δ(δ1H). As shown in Fig. 4, the second order stabilization energies image file: c8cp06417b-t2.tif and the total charge transfers, qCT are strongly correlated to the enhanced H-bond strength in the order from n = 2 to n = 6. This behavior is reflected as lower energies ΔE, shorter H-bond distances R(H⋯O) and larger proton chemical shift differences Δ(δ1H). The NBO parameters strongly indicate the covalent and anti-electrostatic character of hydrogen bonding also in dimers of like-charged ions.
image file: c8cp06417b-f4.tif
Fig. 4 NBO calculated second order stabilization energies image file: c8cp06417b-t3.tif (open circles) and estimated total charge transfers qCT (closed squares) for cationic dimers with n = 2–6 plotted versus calculated (a) energies ΔE, (b) intermolecular hydrogen bond distances, R(H⋯O) and (c) proton chemical shifts differences between the H-bonded and free OH of the dimers, Δ(δ1H). The linear dependence indicates the strong relation between NBO stabilization energies and charge transfers with energetic, geometric and spectroscopic properties of the cationic dimers.


In this work we employed quantum chemistry for calculating the kinetic and thermodynamic stability of hydroxy-functionalized 1-(3-hydroxyalkyl)pyridinium cationic dimers. The meta-stable dimers [Py–(CH2)n–OH+]2 with n = 2–6 provide net energy releases from 136 down to 39 kJ mol−1, and activation barrier heights from 6 up to 20 kJ mol−1, respectively. Quantum chemical calculations at the MP2 level of theory suggest that short-range and directional hydrogen bonds attenuate the long-range repulsive Coulomb forces preventing the dimers from dissociation and providing robust kinetic stability. For the cationic dimer [Py–(CH2)15–OH+]2 the energy release is zero and the repulsive Coulomb forces are fully counter-balanced by attractive hydrogen bonding and dispersion forces. B3LYP calculations with and without considering dispersion forces allow dissecting the pure hydrogen bond energy in the cationic dimer. The H-bond energy is 20 kJ mol−1 and thus comparable to those known for water and methanol dimers. The attenuation of the repulsive Coulomb forces with elongation of the hydroxyalkyl chain tethers leads to enhanced hydrogen bonding as expressed by substantial shortening of the H-bond length of about 0.1 Å. Further lengthening of the hydroxyalkyl chain length changes the cationic dimers from intrinsically meta-stable to thermodynamically stable complexes. These cationic dimers should be observable in gas phase experiments at lower temperatures.

Conflicts of interest

There are no conflicts to declare.


This work has been supported by the DFG Research Grant LU-506/14-1.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cp06417b

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