Article pubs.acs.org/JPCB
Quantum Chemistry Study of Proton Transport in Imidazole Chains Milan Kumar*,† and Arun Venkatnathan*,‡ †
Department of Chemical Engineering, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli 229316, Uttar Pradesh, India Department of Chemistry, Indian Institute of Science Education and Research, Pune 411008, Maharashtra, India
‡
S Supporting Information *
ABSTRACT: Hydrogen bonding in imidazole plays a key role in proton conduction and rotation of an imidazole molecule in the process results in the cleavage of hydrogen bonds between molecules. In the present work, we characterize proton transport and rotation energy barriers in imidazole chains by density functional theory. Our calculations show that propagation of an excess proton along the chain requires crossing of energy barriers, lower than 1 kcal/mol. The presence of the proton has stronger effect on the immediate neighboring imidazole molecules, and the effect is negligible after two molecules. The subsequent rotation of all imidazole molecules after the transfer of first proton is essential to allow the transfer the second proton. The presence of an excess proton in the chain leads to cleavage of hydrogen bonds and the rotation of neighboring imidazole molecule. Further, rotation of one imidazole molecule results in rotation of all molecules in the chain. The calculated rotational energy barriers in two-, three-, and four-imidazolemolecule chains are 8.0, 17.1, and 20.0 kcal, respectively, and are equivalent to the number of hydrogen bonds broken in the process. The rotational barrier is higher than the proton transport barrier along the hydrogen bond and, thus, is the ratedetermining step of proton conduction.
1. INTRODUCTION Imidazole and its derivatives are known to serve as biological building blocks,1 in drugs2,3 and natural products.4 A very high boiling point (256 °C) of imidazole (compared to water) also makes them promising materials as proton carriers in high temperature fuel cells. For example, polymer electrolyte membrane (PEM) fuel cells which deploy perfluorosulfonic acid membranes, such as Nafion, are extensively studied5−10 and are recommended for lower temperature (100 °C) provides many benefits such as increased tolerance of Pt catalyst on electrodes toward CO poisoning, enhanced conductivity of electrolytes, and higher available heat for utilization. Apart from imidazole,14−20 materials with higher boiling point, such as phosphoric acid,15,21−25 and ionic liquids,26−32 have also been investigated. However, imidazole and its derivatives are considered to be attractive choices as an imidazole group attached to an alkyl backbone of a polymer electrolyte membrane shows the lowest rotational barrier with higher hydrophobicity.33 Imidazole exists in a solid form at room temperature with a melting point of ∼90 °C.34 A solid imidazole is an anisotropic monoclinic crystal with four molecules in a unit cell.34,35 Its conductivity along the c crystallographic direction (the hydrogen bond direction) is 3 orders of magnitude higher than the a crystallographic direction.34 Daycock et al.36 argued © XXXX American Chemical Society
that proton conduction in solid imidazole in a direction of external applied electrical field occurs via an intermolecular transfer of proton in a hydrogen bonded chain of imidazole molecules, and after each proton transfer, it requires rotation of all imidazole molecules in the chain to facilitate further proton transfer. This type of intermolecular proton transport is called as “structural diffusion” or more commonly as the “Grotthuss mechanism”.37 As imidazole molecules in the chain are hydrogen bonded, rotation of imidazole molecules results in breaking and re-forming of hydrogen bonds and, hence, is considered the limiting step of proton conduction.36 While solid imidazole has very low proton conductivity (∼10−5 S/cm at 70 °C), the conductivity increases to ∼10−3 S/cm at 90 °C (melting point).14 Similar to water, imidazole can be doped by acids, which results in excess protons in the form of solvated ImiH+ (protonated imidazole) where proton transfers via structural diffusion and reorientation events. For example, Kreuer et al.14 estimated proton diffusion coefficient using conductivity data (using the Nernst−Einstein relation) and experimentally measured the self-diffusion coefficient of proton (pulsed magnetic field gradient NMR spectroscopy) for three imidazole doped systems: sulfonated polyether ketone/ imidazole, sulfonic acid/imidazole, and H2SO4/imidazoleall in liquid state. The authors concluded that proton conduction occurs via creation of proton defect and its mobility (similar to Received: September 5, 2014 Revised: January 27, 2015
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DOI: 10.1021/jp508994c J. Phys. Chem. B XXXX, XXX, XXX−XXX
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a multistate empirical valence bond (MS-EVB) method. Their results showed that, at higher N−N separation distances (≥2.74 Å), proton transfer from an imidazolium cation to imidazole cannot occur even at temperature ∼ 400 K. However, at lower separation distances, proton transfer can occur by mere thermal fluctuations with a low energy barrier (∼1.1 kcal/mol). The authors found that primary and secondary solvation shells of an imidazolium cation are surrounded by imidazole molecules in liquid imidazole, the primary shell being highly ordered via hydrogen bonding, and a substantially disordered secondary shell. The authors also concluded that transfer of proton is a local phenomenon, and rotation of imidazole molecules in the secondary solvation shell is the rate limiting step for proton transport. Mangiatordi et al.19,20 employed density functional theory (DFT) and molecular dynamics (MD) simulations to investigate the effect of backbone of four-tethered and twotethered polyvinylimidazoles on proton conduction. The authors concluded that the proton transfer could be less favorable due to the geometric constraints arising from the backbone of the four-tethered polyvinylimidazole membrane. The energetically favorable pathway of proton transfer requires the rotation of the imidazolium cation, which, consequently, can donate a proton to the neighboring imidazole pendant.19 The authors also reported a rotation energy barrier of 10.7 kcal/mol for the imidazole pendant, which is equal to the energy of cleavage of one hydrogen bond formed between two imidazole molecules. In two-tethered polyvinylimidazole, the proton conduction mechanism involves rotation of all hydrogen bonded imidazole pendants in the series after transferring the first proton,20 as in imidazole chains. The external electric field applied opposite to the system dipole favorably affects the proton conduction in the water and imidazole system by reducing the activation energy barrier.49 Most of the preceding studies have supported proton transport via Grotthuss mechanism and vehicular diffusion in neat liquid imidazole and via Grotthuss mechanism in solid imidazole and its derivatives, and also suggest the rotation of imidazole in an imidazole chain as a rate limiting step. The reported activation energy of direct current (dc) conductivity in imidazole crystal is 40 kcal/mol,34 which is the activation energy of rotation of imidazole in the crystal. This energy is much higher than the calculated activation energy, 3.7 kcal/ mol, at imidazole rotation rates of 1 Hz, using NMR pulse techniques,36 and is also higher than the activation energy barrier of rotation, 19.3 kcal/mol, in adamantane and hexamethylenetetramine.55 Kawada et al.34 argued that the deformation of the crystal lattice before leading to imidazole rotation may cause a higher value of activation energy, i.e., 40 kcal/mol. The calculated rotation barrier of imidazole pendant, using DFT, in polyvinylimidazole is 10.7 kcal/mol;19 the value was associated with the cleavage of one hydrogen bond. However, so far there has been no study to characterize hydrogen bonding (with and without an excess proton) and rotational energy barrier in various imidazole chains. In the present study, a systematic study of hydrogen bonding in twoto seven-imidazole-molecule chains, with and without an excess proton, is studied using DFT calculations. The flipping (180° rotation) energy barrier of imidazole in the chains, consisting of two to four imidazole molecules, is also characterized, and breaking and formation of a hydrogen bond are investigated. This work is organized in the following manner: the details of calculations are presented in Computational Details; a characterization of proton transport and flipping of imidazole
water containing systems), where the higher value of proton diffusion coefficient is due to structural diffusion of protons. Proton transport properties of imidazole derivatives and its mixtures with other materials have also been studied experimentally. For example, Schechter and Savinell15 found that H3PO4 solutions doped with increasing amount of imidazole and 1-methylimidazole shows a decrease in conductivity. The authors concluded that decreasing conductivity is due to acid−base reaction between H3PO4 and imidazole which shows a reduced number of proton charge carriers. Goward et al.38 demonstrated reorientation of imidazolium cation ring about its C2 axis in imidazolium methylsulfonate by employing solid-state NMR. Subsequently, the same group also observed rotation of anions and cations of imidazole methylphosphonate at higher temperatures using 31P center-band-only detection of exchange (CODEX) and variable temperature magic angle spinning NMR spectra. The authors concluded that the proton conduction occurs via a cooperative mechanism between ions.39 Pogorzelec-Glaser et al.40 observed that a new type of proton conducting material, imidazolium selenate dihydrate, shows conductivity of 0.1 S/m at 333 K. The authors concluded that water molecules which form a bridge between selenate anions and imidazolium cations via hydrogen bonding network leads to high proton conductivity. Pu and Wang24 observed that addition of imidazole in H3PO4 doped polyimide membrane not only increases its conductivity but also improves the chemical oxidation stability. The preceding experimental investigations have supported proton transport via the Grotthuss mechanism in imidazole and its derivatives. In contrast, Hickman et al.41 used solid-state 15 NMR and concluded that proton tunneling is responsible for conduction in solid crystalline imidazole. In another study, Jarumaneeroj et al.16 suggested that proton conduction in alkyl urocanates, an imidazole derivative, occurs via molecular mobility in the molten state and via Grotthuss mechanism in the solid state. Proton conduction in imidazole and its derivatives via intermolecular proton transfer and imidazole reorientation have also been studied by computational methods19,20,42−49 and simulations.50−54 Scheiner and Yi42 employed ab initio calculations on a system containing ammonium ion, an imidazole molecule, and a neutral ammonia molecule leading to a formation of a H3NH+···imidazole···NH3 complex. The authors observed that imidazole acts as a proton shuttle from NH4+ to NH3, and the energy required for motion of imidazole between NH4+ and NH3 is higher than for proton transfer between NH4+ and imidazole. Kreuer and co-workers50 performed Car−Parrinello molecular dynamics (CPMD) simulations on a system of imidazole chains with an excess proton. The authors found that the presence of an excess proton results in local disorder in the system, and proton transfer along the hydrogen bonding in imidazole is 2 orders of magnitude faster than the reorientation of imidazole. Their results emphasize that the reorientation of imidazole is a limiting step of proton conduction. Other CPMD studies of proton doped imidazole and imidazole-2-ethylene oxide crystals show that an excess proton is easily accommodated in the flexible crystals through charge and structural defects.51,52 The separation between these defects is favored by fast proton transport via Grotthuss mechanism and thus reduces internal strain by re-distribution of the additional energy resulting from the presence of an excess proton in the system. Voth and coworkers53 simulated proton transport in liquid imidazole using B
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chain are referred to as the internal molecules, and those away from the center are referred to as external molecules. For example, in a chain of six imidazole molecules (a schematic shown in Figure 1), the molecules with nitrogen atoms N4 and N5, and N6 and N7, are referred to as internal molecules and the remaining as external molecules. A. Imidazole Chains. Structures 1−5, shown in Figure 2, represent imidazole chains containing two to six molecules, respectively, where blue, dark gray, and light gray spheres denote nitrogen, carbon, and hydrogen atoms, respectively. An optimized structure of an imidazole chain with an excess proton, added to the first imidazole molecule, is also shown in the figure with a corresponding number with an apostrophe; for example, a proton added to the left of structure 1 results in structure 1′ after optimization. As the proton travels along the hydrogen bond, the structure changes; these structures are distinguished by notations, “a” and “b”. The location of the excess proton in a chain is indicated by a rectangle around the resultant imidazolium cation. The distances between nitrogen atoms of imidazole molecules in these chains, with and without an excess proton, are listed in Table 1. The table shows that the addition of an imidazole molecule to the chain decreases the intermolecular distance of imidazole molecules. This distance converges to ∼2.87 Å, the distance between two consecutive, internal imidazole molecules in structures 4 and 5, and is very close to the experimental value, i.e., 2.86 Å, obtained for imidazole crystal at −150 °C.62 This shows that the internal imidazole molecules in the obtained structures closely represent the bulk imidazole molecules in the crystal. B. Effect of an Excess Proton on Intermolecular Distances and Proton Transport Barrier. Addition of a proton to the first imidazole in the chain, as shown in Figure 2, results in the nonbonded hydrogen atom(s) in the chain and in decrease in the intermolecular distances. In structure 1′, the nonbonded hydrogen atom shuttles between two imidazole molecules. The calculated (see Figure S1 of the Supporting Information) activation energy barrier of proton shuttling is 0.72 kcal/mol (without ZPE corrections) and −1.31 kcal/mol (with ZPE corrections). Similar results were found earlier in the case of proton shuttling between triflic acid and triflate anion.29 A proton, added on the first imidazole in a three-imidazolemolecule chain, results in dissociation of proton from nitrogen atom, N1, and the optimized structure 2′ is shown in Figure 2. The dissociated proton in the structure is closer to N2 and is in a nonbonded state. The structure also shows another nonbonded proton closer to N3. Structure 2′ is an extension of structure 1′ with an excess imidazole molecule. Thus, from these two structures, it can be concluded, conversely, that the third imidazole molecule results in sliding of proton from N1 to N2 without any activation energy barrier. There is no proton shuttling in this case. Rather, both dissociated protons are near the imidazole molecule at the center. In all other chains also, the excess proton resides near the second imidazole, as shown in structures 3′−5′. Further transport of this proton along the hydrogen bonded network in imidazole requires crossing of the activation energy barrier for each proton transfer step. The barrier decreases with increasing number of imidazole molecules in the chain. For example, the barriers, calculated for proton transport from the second to the third imidazole molecule, are 0.88, 0.33, and 0.11 kcal for four-, five-, and siximidazole-molecule chains, respectively, and are reported in Figures S2, S3, and S4, respectively (see the Supporting Information). For a six-imidazole-molecule chain, the calculated
in various imidazole chains is presented in Results and Discussion; and a summary of key results concludes this work.
2. COMPUTATIONAL DETAILS The DFT calculations were performed using the Gaussian 0956 suite of programs. The B3LYP functional57−60 and 6-311+ +G(d,p) basis set were used for all calculations. The optimizations were performed without any symmetry constraints; if otherwise, it is mentioned explicitly. This follows frequency calculations on the optimized geometry. The energy of a chain of molecules was taken as the energy of its formation: the total energy of the chain minus the sum of the energy of an individual molecule and ion in the chain. This energy is the interaction energy between the molecules or between the molecules and cation, and of which a major contribution comes from hydrogen bonding. Zero-point energy (ZPE) correction was also included in the energy calculations except activation energy. The transition-state (TS) structure of proton transfer in a chain was obtained by employing an Opt=TS keyword and using closely representing geometry as the initial guess. This keyword employs the Berny algorithm by using GEDIIS61 to optimize to a transition state. The TS structure was determined by confirming one imaginary frequency of vibration. The flipping energy barrier of a molecule in the chain was determined by employing a potential energy scan (PES). The scanning of energy was performed by changing the dihedral angle of an atom in the molecule with respect to an atom of the immediate neighbor. The optimization of structure was also subsequently performed on each step of the scan. During the scan, the translational movement of a molecule was restrained, and only the rotational movement was allowed by freezing the coordinates of two atoms in the molecule. The steps of rotation were selected such that a flip (180° rotation) of the molecule from its original orientation in the chain was achieved. 3. RESULTS AND DISCUSSION A study of proton conduction in imidazole requires investigation of the molecular structure of imidazole with and without an excess proton. A proton travels from anode to cathode through the electrolyte inside the fuel cell either via vehicular motion of imidazolium cation and/or through hydrogen bonded chains of imidazole molecules. A simplified schematic representation of a chain of six imidazole molecules is shown in Figure 1. This illustration is used here for the
Figure 1. Representation of an imidazole chain. Ellipse represents an imidazole molecule, and two “N” symbols, with or without a number, represent two nitrogen atoms. Dotted lines show hydrogen bonding.
discussion. An ellipse in the figure represents an imidazole molecule in the chain. The two nitrogen atoms of an imidazole molecule are denoted by a symbol, “N”: “N” without a number represents the first and last nitrogen atom in the chain, while with numbers represents all other nitrogen atoms. The figure shows that N and N1 represent two nitrogen atoms of the first imidazole molecule, N2 and N3 of the second imidazole, and so on. A dotted line between two ellipses, i.e., between the two imidazole molecules, represents a connection between two nitrogen atoms of neighboring imidazole molecules, such as N1 and N2, N3 and N4, and so on, that are linked by a hydrogen atom between them. Imidazole molecules near the center of a C
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Figure 2. Structures of imidazole chains with and without a proton. Structures 1, 2, 3, 4, and 5 are imidazole chains, having two, three, four, five, and six imidazole molecules, respectively, and the corresponding structures with a proton are 1′, 2′, 3′, 4′, and 5′, respectively. Structures a and b represent chains with different locations of the excess proton, indicated by a rectangle around the resultant imidazolium cation. Light gray, dark gray, and blue spheres represent hydrogen, carbon, and nitrogen atoms, respectively.
transition-state structure is nearly 2.57 Å. The chain of two imidazole molecules with an excess proton resembles a Zundel ion in water,63,64 where an excess proton is shared by two water molecules. In bigger imidazole chains, an Eigen-like structure, in which excess proton is located on a water molecule, forming a hydronium ion, surrounded by three other water molecules, is more stable. Chen et al.53 used the MS-EVB model on liquid imidazole and observed that an excess charge on the imidazolium cation is highly localized and, as a result, the first solvation shell is highly organized via the formation of hydrogen bonds with its neighbors (Eigen-like structure). The authors also observed a low effect of the excess charge on the imidazole molecules in the second solvation shell. A close examination of atomic distances in structures 4′a and 4′b and structures 5′a and 5′b, as shown in Table 1, illustrate that the proton transport along the chain causes a decrease in intermolecular distances between the two leading imidazole molecules and an increase between two trailing ones. A similar trend was also observed in a chain of seven imidazole molecules as seen in Figure S5 (see the Supporting Information). This indicates that the effect of an imidazolium cation, resulting from the presence of an excess proton in the imidazole chain, on the intermolecular distances with its immediate neighbors, i.e., the first neighboring imidazole molecules, is strongest, and is negligible beyond the third imidazole molecules. Our results support the findings of Chen et al.53
Table 1. Intermolecular Distances in Structures Mentioned in Figure 2a distance (Å) structure
N1···N2
1 1′ 2 2′ 3 3′ 4 4′a 4′b 5 5′a 5′b
2.99 2.67 2.95 2.75 2.93 2.77 2.93 2.78 2.86 2.93 2.79 2.87
N3···N4
2.94 2.75 2.90 2.68 2.88 2.65 2.71 2.88 2.64 2.72
N5···N6
2.93 2.85 2.88 2.80 2.71 2.87 2.78 2.68
N7···N8
2.92 2.89 2.86 2.88 2.84 2.81
N9···N10
N···N
2.92 2.90 2.89
7.23 6.90 11.59 11.46 14.85 15.69 17.74 19.51 19.47 17.74 23.05 23.07
a
The numbering of nitrogen atoms in a chain is followed as indicated in Figure 1.
energy barrier of proton transfer from the third to the fourth imidazole molecule is 0.94 kcal/mol, which is higher by 0.83 kcal/mol than the barrier of proton transfer from the second to the third imidazole molecule. This shows an easy transfer of proton between two external imidazole molecules in a longer chain but requires higher energy for proton transfer between relatively two internal neighboring molecules. In all these cases, the distance between the two imidazole molecules in the D
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Figure 3. Interaction energy of imidazole molecules with increasing number of hydrogen bonds in the chain.
Figure 4. Optimization of a two-imidazole-molecule chain with an excess proton, showing flipping of imidazole, resulting from N−H bond repulsion.
C. Flipping of an Imidazole Molecule in a Chain. Because the primary interaction between molecules in imidazole crystal and liquid is due to hydrogen bonding,34,52,53 the approximate interaction energy was estimated by the energy of formation of the chain from the corresponding number of imidazole molecules. For example, the total hydrogen bonding interaction energy in a chain of four imidazole molecules = energy of the chain − 4 × energy of an
imidazole molecule. This energy was averaged over the total number of hydrogen bonds in the chain to obtain the average hydrogen bond energy. The average energy of a hydrogen bond in different imidazole chains is shown in Figure 3. Because an increase in the number of imidazole molecules in a chain results in a decrease of the intermolecular distances, as shown in Table 1, this, consequently, results in stronger hydrogen bonding interaction between molecules and, thus, in higher interaction E
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Figure 5. PES of a two-imidazole-molecule chain. The first molecule in structure a was rotated in the marked direction in a step of 10°. Structure b shows that, up to eight rotations, i.e., 80° rotation, there is no significant effect on the orientation of the second imidazole. Structure c has the maximum energy, and the imidazole molecules are almost parallel. Structure d shows flipping of both molecules.
energy. The flipping mechanism and energy of barrier for rotation (which is correlated to the energy of hydrogen bonding) is discussed in later text. a. Flipping Induced by an Excess Proton via Hydrogen Bond Repulsion. The optimization steps and corresponding changes in the relative energy of the system, of a chain of two imidazole molecules with an excess proton, placed near N10 of the right imidazole, is shown in Figure 4. The system is fully optimized without freezing any atom. N8−N10 atomic distance and N10−H6−C1−N8 dihedral angle in the structure at optimization steps 1, 6, 15, 21, 25, and 64 are shown in the inset table. Structures are also shown in the figure at steps 1, 15, and 64, which correspond to initial, intermediate, and final stages of optimization. The figure shows that the addition of an excess proton in the chain causes a disorder due to cleavage of the hydrogen bond, N8−H9···N10, and repulsion between the N8−H9 bond and a newly formed N10−H19 bond. The increasing dihedral angle and N8−N10 atomic distance during optimization shows flipping of the left imidazole molecule, induced by the presence of an excess proton on the right imidazole molecule. A similar result was obtained with a chain of three imidazole molecules, an excess proton added to the second proton. A schematic diagram of flipping of an imidazole in the chain is shown in Figure S6 (Supporting Information). Our observations are in accordance with previously reported results.50−52 Münch et al.50 have demonstrated using CPMD simulations that a proton defect, resulting from an excess proton, in imidazole chain causes local disorder and breaking of hydrogen bridges between molecules. Iannuzzi and Parrinello,51 and Iannuzzi52 observed (using CPMD simulations) breaking of hydrogen bonds and flipping of molecule in imidazole-based crystals doped with an excess proton.
b. Flipping Induced by Rotation of the First Imidazole. To understand the flipping of imidazole and to calculate the corresponding energy barrier, three systems were considered: chains consisting of two, three, and four imidazole molecules. The flipping of an imidazole, and its effect on other imidazole molecules and their bonding, was characterized by the PES. For this, an imidazole molecule in the chain was rotated about the C2 axis (C2 axis here, and onward in this work, represents the axis of the corresponding imidazolium cation) by changing the dihedral angle and subsequent optimization was performed on the system. The apical carbon (AC), the one between nitrogen atoms, and the hydrogen atom bonded to it in each imidazole molecule in a chain were kept at a fixed position. This restricts any lateral movement of the molecule during optimization. It was observed that optimization of the structure, without this constraint, at each scan point resulted in the same final structure. The interatomic distances, angles, and dihedral angles in the imidazole molecule, on which rotation was imposed, were represented by internal coordinates in the input file and were kept fixed. This ensures that the geometry of this imidazole does not change during the scan and subsequent optimization. Figure 5 shows the potential energy scan of a chain of two imidazole molecules. Structure a is the initial structure on which the scan was performed. Atoms, numbered from 1 to 4, were kept fixed, and the dihedral angle,
