Tuning the Adsorption Interactions of Imidazole Derivatives with

Article pubs.acs.org/JPCA

Tuning the Adsorption Interactions of Imidazole Derivatives with Specific Metal Cations Haining Liu, Jason E. Bara, and C. Heath Turner* Department of Chemical and Biological Engineering, The University of Alabama, Box 870203, Tuscaloosa, Alabama 35487-0203, United States S Supporting Information *

ABSTRACT: In this work, we report a computational study of the interactions between metal cations and imidazole derivatives in the gas phase. We first performed a systematic assessment of various density functionals and basis sets for predicting the binding energies between metal cations and the imidazoles. We find that the M11L functional in combination with the 6-311++G(d,p) basis set provides the best compromise between accuracy and computational cost with our metal···imidazole complexes. We then evaluated the binding of a series of metal cations, including Li+, Na+, K+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+, Ba2+, Hg2+, and Pb2+, with several substituted imidazole derivatives. We find that electrondonating groups increase the metal-binding energy, whereas electron-withdrawing groups decrease the metal-binding energy. Furthermore, the binding energy trends can be rationalized by the hardness of the metal cations and imidazole derivatives, providing a quick way to estimate the metal···imidazole binding strength. This insight can enable efficient screening protocols for identifying effective imidazole-based solvents and membranes for metal adsorption and provide a framework for understanding metal···imidazole interactions in biological systems.

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been previously synthesized,19−23 and the related compounds have shown promising catalytic properties in certain chemical reactions, such as hydrogenations and Grignard cross-coupling reactions.18,22,24 In addition, imidazole derivatives have also been used to extract certain metal cations, such as Co2+, Ni2+, Cu2+, Zn2+, Ag+, and Pb2+, from aqueous solution.25−28 However, there is not a clear framework for predicting the metal adsorption properties of these imidazole compounds. Due to these ongoing and emerging applications, it is important to understand the fundamental interactions between metal cations and imidazoles, so that effective adsorbents and catalysts can be quickly identified from a library of compounds. Here, we report a comprehensive density functional theory (DFT) study of the interactions between a series of metal cations and various imidazole derivatives. Although several computational studies on the properties of metal···imidazole complexes29−34 and other metal···ligand complexes in general35−42 have been reported, we are still lacking a systematic analysis of the effect of exocyclic substituents on the binding of metal cations with imidazoles. In addition, it has been previously noted that more computational guidance is needed to accurately assess metal···imidazole binding energies.34 Hence, a more thorough computational study on metal··· imidazole complexes is still needed. Furthermore, regarding the application of imidazole-based molecules in CO2 capture, we

INTRODUCTION Imidazole-based molecules are found in a broad range of applications. For example, an imidazole group is the key component of histidine, a naturally occurring amino acid, and it is found in many other antifungal drugs.1 An important enzyme, carbonic anhydrase, features Zn2+ coordinated to three imidazole rings.2 Furthermore, imidazoles are used as corrosion inhibitors for certain metals.3 In addition to these well-known applications, imidazoles and imidazolium-based ionic liquids (ILs) have shown potential for absorbing and separating CO2 from combustion sources. An advantage of imidazole-based materials is their highly tunable structural and thermophysical properties. Recently, a number of experimental4−9 and computational studies10−17 have characterized the thermophysical properties (viscosity, vapor pressure, heat capacity, etc.) of imidazole derivatives, and these studies have greatly contributed to our understanding of these compounds. Imidazoles and/or imidazolium salts can also be used as ligands to bind with metal cations via their N(3) lone pair electrons (Figure 1).18 A variety of metal-containing ILs have

Received: March 4, 2014 Revised: April 22, 2014 Published: May 14, 2014

Figure 1. Schematic illustration of the interaction between metal cations (Mn+) and imidazole. © 2014 American Chemical Society

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dx.doi.org/10.1021/jp502222z | J. Phys. Chem. A 2014, 118, 3944−3951

The Journal of Physical Chemistry A

Article

Table 1. Calculated Binding Energies and Basis Set Superposition Errors (kJ mol−1) of Li+···Imidazole, Na+···Imidazole and K+··· Imidazole Complexes Using the B3LYP and M11L Functional in Combination with Various Basis Sets Li

+

Na+

K+

a

B3LYP/6-31G(d,p) B3LYP/6-311G(d,p) B3LYP/6-31+G(d,p) B3LYP/6-31++G(d,p) B3LYP/6-311++G(d,p) B3LYP/6-311++G(3df,3pd) M11L/6-31G(d,p) M11L/6-311G(d,p) M11L/6-31+G(d,p) M11L/6-31++G(d,p) M11L/6-311++G(d,p) M11L/6-311++G(3df,3pd) B3LYP/6-31G(d,p) B3LYP/6-311G(d,p) B3LYP/6-31+G(d,p) B3LYP/6-31++G(d,p) B3LYP/6-311++G(d,p) B3LYP/6-311++G(3df,3pd) M11L/6-31G(d,p) M11L/6-311G(d,p) M11L/6-31+G(d,p) M11L/6-31++G(d,p) M11L/6-311++G(d,p) M11L/6-311++G(3df,3pd) B3LYP/6-31G(d,p) B3LYP/6-311G(d,p) B3LYP/6-31+G(d,p) B3LYP/6-31++G(d,p) B3LYP/6-311++G(d,p) B3LYP/6-311++G(3df,3pd) M11L/6-31G(d,p) M11L/6-311G(d,p) M11L/6-31+G(d,p) M11L/6-31++G(d,p) M11L/6-311++G(d,p) M11L/6-311++G(3df,3pd)

BEa

BSSE

BEb

expt

227.5 224.8 211.3 211.3 214.2 214.1 204.5 206.6 197.5 197.5 199.5 201.0 169.3 164.0 156.1 156.2 154.4 155.1 154.3 148.9 151.0 151.0 142.1 142.6 119.9 119.0 108.2 108.2 111.0 110.0 112.6 112.6 105.3 105.1 106.6 106.4

11.9 8.4 1.6 1.6 1.6 0.9 8.4 6.6 3.0 3.1 2.4 3.3 10.8 8.0 3.8 3.9 2.0 2.1 7.7 6.2 8.9 9.1 2.2 2.2 9.9 6.5 1.3 1.3 0.8 0.6 7.3 5.3 3.1 3.1 1.3 1.3

215.6 216.4 209.7 209.7 212.6 213.2 196.2 200.0 194.5 194.4 197.1 197.7 158.5 156.0 152.3 152.3 152.4 153.0 146.6 142.7 142.1 141.9 139.9 140.4 110.0 112.5 106.9 106.9 110.2 109.4 105.3 107.2 102.2 102.0 105.3 105.1

210.8(9.5)c

139.4(6.4)d, 139.7(5.2)c

109.0(5.6)c

Binding energy without BSSE correction. bBinding energy with BSSE correction. cref 45. dref 34.

have previously shown that the acid/base properties of imidazoles, which affect CO2 absorption in aqueous solutions and transport through imidazole-based polymer membranes, can be tuned with different exocyclic substituents.43 Similarly, the metal cation binding affinity of imidazoles may also be tuned via selection of the exocyclic substituent(s). In order to provide deeper insights into these structure− property relationships, we have considered two substituents, methyl (electron-donating) and trifluoromethyl (electronwithdrawing), at various exocyclic positions. The metal cations considered in this study include Li+, Na+, K+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+, Ba2+, Hg2+, and Pb2+, which are frequently used in experimental studies and industrial applications. In this work, only gas phase calculations are reported. This allows us to directly evaluate the metal···imidazole interaction without the interference of other ligands, such as solvent molecules, which may introduce additional uncertainties into the calculations.44 More importantly, accurate gas phase metal···imidazole binding energies are available from experimental studies,34,45 which makes it possible to benchmark various computational methods for calculating the binding energies of metal···imidazole

complexes. Although it is possible that the gas phase geometries and binding energies may change when solvation is included, the gas phase results serve as a baseline for further studies of solvated systems.46

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COMPUTATIONAL METHODS

All calculations were performed using the Gaussian 09 program.47 Various density functionals, including B3LYP,48−50 M11L,51 N12,52 MN12L,53 N12SX,54 and MN12SX,54 in combination with various basis sets ranging from 6-31G(d,p) to 6-311++G(3df,3pd) were chosen to assess their performance to obtain accurate metal···imidazole binding energies. For the open shell systems (Co2+, Ni2+ and Cu2+), all the possible spin multiplicities were considered, and only the lowest energy structures and energies were reported in this work (quartet for Co2+, triplet for Ni2+, and doublet for Cu2+). Frequency calculations were also performed to confirm that the obtained structures are minima on the potential energy surface and to obtain zero-point vibrational energy (ZPVE) corrections. The basis set superposition error (BSSE) corrections were obtained 3945



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by the counterpoise method.55,56 Both ZPVE and BSSE are included in the reported energies in this study.

with the experimental result. For example, at the B3LYP/631+G(d,p) and B3LYP/6-31++G(d,p) levels, the BSSEcorrected binding energies only differ from the experimentally measured binding energy by −1.1 kJ mol−1. Upon further increase of the basis set to 6-311++G(d,p) and 6-311+ +G(3df,3pd), the difference between the BSSE-corrected binding energies and experimentally measured binding energy are slightly larger at 1.8 and 2.4 kJ mol−1, respectively. The performance of the M11L functional is slightly worse than the B3LYP functional for the Li+···imidazole complex. For example, the M11L/6-311++G(d,p) level underestimates the binding energy in this system by 13.7 kJ mol−1. However, it should be noted that the experimentally measured binding energy is subjected to an error of ∼9.5 kJ mol−1.34 For K+, both B3LYP and M11L are able to provide accurate binding energies, with the difference between the calculated and experimental binding energies within 7.0 kJ mol−1 using the basis sets assessed in this work. The B3LYP/6-311++G(d,p) and B3LYP/6-311++G(3df,3pd) methods have the best performance, with differences between BSSE-corrected binding energies and experimentally measured binding energies of only 1.2 and 0.4 kJ mol−1, respectively. The performance of M11L is slightly worse. For instance, at the M11L/6-311++G(d,p) level, the BSSE-corrected binding energy is smaller than the experimentally measured binding energy by 3.7 kJ mol−1. Although the B3LYP method is able to provide very accurate binding energies for Li+···imidazole and K+···imidazole complexes, it significantly overestimates the Na+···imidazole energies by 12.9−19.1 kJ mol−1, similar to the study by Rodgers and co-workers.34 The most accurate method found in Rodgers’s study34 is CBS-QB3, which differs from the experimental Na+···imidazole binding energy by only 1.2 kJ mol−1. However, CBS-QB3 is a computationally intensive method, which may not be practical for calculating a large set of metal cations, especially when higher molecular weight imidazoles are considered. The M11L method, however, performs much better than B3LYP. The M11L/6-311++G(d,p) level only overestimates the Na+···imidazole binding energy by 0.2−0.5 kJ mol−1. Further increasing the basis set to 6-311+ +G(3df,3pd) slightly increases the difference from the experimentally measured binding energy to 1.0 kJ mol−1. As a result, the M11L/6-311++G(d,p) level appears to be the best method to calculate the metal···imidazole binding energies. Although it underestimates the Li+···imidazole binding energy by 13.7 kJ mol−1, it should be noted that as the smallest metal cation, Li+ is fundamentally different from the metal cations considered in this study because of the lack of core electrons in Li+. Hence, we feel that M11L/6-311++G(d,p) is the best compromise between accuracy and computational cost to calculate the metal···imidazole binding energies. We further assessed the performance of four more recent functionals, N12, MN12L, N12SX, and MN12SX, for calculating the binding energy of the Na+···imidazole complex. Two basis sets, 6-311++G(d,p) and 6-311++G(3df,3pd), were used. The calculated binding energies as well as the BSSE are shown in Table 2. As can be seen, the N12 and N12SX functionals have a similar performance to B3LYP. They overestimate the Na+···imidazole binding energy by 12.8− 13.5 kJ mol−1. In contrast, MN12L and MN12SX are able to provide more accurate binding energies, which only overestimate the Na+···imidazole binding energy by 3.4−7.0 kJ mol−1. However, they are still slightly worse than M11L in describing the Na+···imidazole binding energy. Hence, the

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RESULTS AND DISCUSSION Computational Method Assessment. We first performed an assessment of various computational methods and basis sets for predicting metal cation binding energies with imidazole molecules. In previous studies, Rodgers and co-workers experimentally measured the binding energies of various metal cations with imidazole molecules using the quantitative threshold collision-induced dissociation method,34,35,45 and they evaluated the accuracy of B3LYP, MP2(full) and the complete basis set extrapolations CBS-Q and CBS-QB3 methods in combination with various basis sets to calculate these binding energies.34,35 In general, no single level of theory was able to obtain accurate binding energies for a diverse set of metal cations. In their work, Rodgers and co-workers34 found that the B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G* level of theory significantly overestimates the Na+···imidazole binding energy by 13.8 kJ mol−1 (as compared to experimental results). The MP2(full)/6-311++G(3df,3pd)//B3LYP/6-31G* level, however, is even worse by overestimating the Na+···imidazole binding energy by 24.4 kJ mol−1. The much more expensive methods, CBS-Q and CBS-QB3, have better performance as they only slightly overestimate the Na+···imidazole binding energy by 7.4 and 1.2 kJ mol−1, respectively. However, they overestimate the K+···imidazole binding by 11.2 and 14.1 kJ mol−1, respectively. In contrast, the B3LYP/6-311++G (3df,3pd)//B3LYP/6-31G* level has a much better performance for K+···imidazole, which overestimates its binding energy by only 0.4 kJ mol−1. As a result, it appears that each method demonstrates some limitations when determining the binding energies of certain metal cations. In particular, both B3LYP and MP2(full) significantly overestimate the binding energy of the Na+···imidazole complex, a very common metal cation found in solution and biological systems. In order to obtain an appropriate level that balances the accuracy and computational cost, we first assessed the B3LYP functional and some of the more recently developed Minnesota series of functionals for determining the binding energies of Li+···imidazole, Na+··· imidazole and K+···imidazole complexes. The experimentally determined binding energies of other metal cations are also available from the study by Rodgers and co-workers.34 However, those reported metal cations are in uncommon oxidation states, such as Co+ and Zn+. These +1 charged metal cations are usually not found in solution. Therefore, they may not be relevant for the application of imidazoles to selectively extract metal cations from solution or the use of imidazolebased polymer membrane for CO2 capture. As a result, only the three common metal cations, Li+, Na+, and K+, are included in our assessment. Table 1 lists the calculated binding energies of Li+··· imidazole, Na+···imidazole and K+···imidazole complexes using the B3LYP and M11L functionals in combination with various basis sets. As expected for both methods, as the basis set increases from 6-31G(d,p) to 6-311++G(3df,3pd), the BSSE decreases from ∼10 kJ mol−1 to within 3 kJ mol−1. This suggests that the change of basis set does not have a significant effect on the BSSE-corrected binding energies. For example, the largest difference of the binding energies upon using different basis sets is observed with Li+ at the B3LYP level and with Na+ at the M11L level, both of which vary by only 6.7 kJ mol−1. For Li+, the binding energies obtained using B3LYP agree very well 3946



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withdrawing groups (EWGs). For the alkali metals, the binding energies with 1-methylimidazole are 25.6−34.5 kJ mol−1 higher than those with 1-trifluoromethyl-imidazole. In addition, the distances between the metal and the N(3) site of 1methylimidazole are ∼0.01−0.04 Å shorter than those between the metal and the 1-trifluoromethyl-imidazole (Table 4). For all the other metal cations considered in this study, the binding energy differences with 1-methylimidazole and 1-trifluoromethyl-imidazole are much larger at 68.3−114.5 kJ mol−1. When all three positions are substituted by EDGs, the resulting imidazole derivative (1,2,4-trimethylimidazole) has the largest binding energies with the metal cations. However, when multiple positions are substituted by EWGs, the imidazole derivatives do not always have smaller metal binding energies than those of the 1-trifluoromethyl-imidazoles. This is perhaps due to the electrostatic interaction between the metal cation and the −CF3 group at the 2-position or 4-position. As an example, Figure 2 shows the optimized structures of Na+···1,2-ditrifluoromethylimidazole and Na+···1,2,4-tritrifluoromethylimidazole complexes. In the Na+···1,2-ditrifluoromethylimidazole complex, Na+ interacts with both N3 and the −CF3 group at the 2position with distances of 2.368 and 2.399 Å, respectively. This weak Na+···CF3 interaction perhaps contributes to the small increase of 2.7 kJ mol−1 in the binding energy of Na+···1,2ditrifluoromethyl-imidazole compared to Na+···1-trifluoromethyl-imidazole. As for Na+···1,2,4-tritrifluoromethylimidazole, the interaction between Na+ and 2-CF3 is weakened with the Na+··· 2-CF3 distance significantly increased to 2.932 Å. However, Na+ now interacts with the −CF3 substituent at the 4-position with a Na+···4-CF3 distance of 2.503 Å. This is 0.135 Å longer than the Na+···CF3 interaction in Na+···1,2-ditrifluoromethyl-imidazole. As a result, it may not have a large contribution to the binding energy, which allows 1,2,4-tritrifluoromethyl-imidazole to have the smallest binding energy with Na+, as expected by the general effect of EWGs on the binding energy. Similar interactions with the −CF3 substituent are also observed for other metal cations with the key metal···CF3 interaction distances listed in Table 5. For the experimental applications of imidazoles, such as extracting metal cations from solution or for CO2 capture processes, it is important to predict performance trends, such as the binding energy change with respect to different metal cations and/or imidazoles. It appears that the change of the

Table 2. Calculated Binding Energies and Basis Set Superposition Errors (kJ mol−1) of the Na+···Imidazole Complex Using the N12, MN12L, N12SX, and MN12SX Functionals +

Na

N12/6-311++G(d,p) N12/6-311++G(3df,3pd) MN12L/6-311++G(d,p) MN12L/6-311++G(3df,3pd) N12SX/6-311++G(d,p) N12SX/6-311++G(3df,3pd) MN12SX/6-311++G(d,p) MN12SX/6-311++G(3df,3pd)

BEa

BSSE

BEb

154.2 154.9 144.4 144.7 154.8 155.1 147.7 147.5

2.0 2.0 1.6 1.3 2.3 2.2 1.7 1.1

152.2 152.9 142.8 143.4 152.5 152.9 146.0 146.4

a

Binding energy without BSSE correction. bBinding energy with BSSE correction.

M11L/6-311++G(d,p) level was chosen to calculate the binding energies for all of the main group and first row transition metals in this study. For Cd2+, Hg2+, Pb2+, and Ba2+, for which the 6-311++G(d,p) basis set is not applicable, the LanL2DZ basis set was used, which includes an effective core potential (ECP). We realize that there is still the possibility that a single method may not work well for all the metal cations considered in this study. Ideally, one can perform an assessment to find out the best method for each metal cation. However, this can be extremely costly with respect to computational expense, and the binding energies for certain metal cations may not have been determined experimentally. As a result, it is more practical to use a common method for all the metal cations considered in this study. Metal···Imidazole Binding Energies. As discussed above, several imidazole derivatives with either an electron-donating methyl group(s) or an electron-withdrawing trifluoromethyl group(s) were considered in this work. Because different exocyclic positions can be substituted by these groups, we considered the N(1)-position, N(1) and C(2)-positions, and N(1), C(2), and C(4)-positions in this study. The calculated BSSE-corrected binding energies are listed in Table 3, whereas the key interaction distances between the metal cations and the N(3) position of the imidazole derivatives are listed in Table 4. It can be seen that when the exocyclic position is substituted by an electron-donating group (EDG), the metal binding energies are larger than the imidazoles substituted with the electron-

Table 3. Calculated BSSE-Corrected Binding Energies (kJ mol−1) of the Metal Cations with Imidazole Derivatives (−Im) +

Li Na+ K+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+ Pb2+

1-CH3−Im

1,2-CH3−Im

1,2,4-CH3−Im

1-CF3−Im

1,2-CF3−Im

1,2,4-CF3−Im

205.7 146.9 110.7 1196.7 1188.0 933.1 699.0 552.3 258.3 593.4 493.8

211.4 150.1 114.5 1252.1 1236.2 997.5 734.7 585.2 269.6 636.7 521.3

216.2 153.3 115.5 1298.2 1279.7 1054.9 773.8 622.7 285.5 680.7 551.5

171.2 117.5 85.1 1116.3 1109.4 847.2 626.5 484.0 143.8b 522.3 423.1

176.9 120.2 87.8 1098.9a 1114.2 819.5 653.2 501.8 232.9 515.0 432.6

164.4 113.2 83.2 1084.1 1112.5 785.1 653.1 504.7 241.5 507.2 432.9

a

Binding energy obtained by single-point calculations at the M11L/6-311++G(d,p) level based on the geometry optimized at the M11L/6-31+ +G(d,p) level, due to failed optimization at the M11L/6-311++G(d,p) level. bBinding energy obtained by single-point calculations at the M11L/6311++G(d,p) level based on the geometry optimized at the B3LYP/6-31G level, because frequency calculations confirmed that the optimized geometry at the M11L/6-311++G(d,p) level is not a minimum on the potential energy surface. 3947



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Table 4. Calculated Distances (Å) between Metal Cations and the N3 Site of the Imidazole Derivatives (−Im) of All the Molecules Considered in This Study Li+ Na+ K+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+ Pb2+

1-CH3−Im

1,2-CH3−Im

1,2,4-CH3−Im

1-CF3−Im

1,2-CF3−Im

1,2,4-CF3−Im

1.915 2.299 2.656 1.905 1.875 1.937 1.833 2.128 2.692 2.260 2.235

1.907 2.291 2.645 1.909 1.874 1.914 1.834 2.145 2.670 2.310 2.214

1.906 2.291 2.647 1.928 1.875 1.905 1.853 2.159 2.684 2.367 2.223

1.929 2.327 2.698 1.915 1.881 1.943 1.840 2.128 2.711 2.254 2.270

1.954 2.368 2.756 1.897 1.882 1.953 1.873 2.150 2.801 2.232 2.303

1.976 2.375 2.740 1.874 1.848 1.922 1.864 2.139 2.752 2.211 2.317

explain their binding energy trends. Although the transition metal binding energies can indeed be correlated with the cation size (see Supporting Information), a simple, effective, and broadly applicable approach is to rationalize the binding energy by the Hard−Soft Acid−Base (HSAB) theory. As the metal cations are Lewis acids, their interactions with imidazoles (Lewis bases) may be determined by the hardness of the metal cations. It was proposed that the absolute hardness (η) of a Lewis acid can be estimated by half of the highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap.57

Figure 2. Optimized structures of (a) Na+···1,2-ditrifluoromethylimidazole and (b) Na+···1,2,4-tritrifluoromethyl-imidazole complexes. Key distances are shown in angstroms.

E(LUMO) − E(HOMO) (1) 2 We calculated the hardness values of all of the metal cations and imidazole derivatives, which are listed in Table 6. It should η=

Table 5. Calculated Key Metal···CF3 Distances (Å) in the Metal···1,2-Di-trifluoromethylimidazole and Metal···1,2,4Tri-trifluoromethylimidazole Complexes

Table 6. Calculated Absolute Hardness (kJ mol−1) of Metal Cations and Imidazole Derivatives Considered in This Study hardness

Li+ Na+ K+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+ Pb2+

r

r1

r2

2.002 2.399 2.708 2.117 1.967 2.414 1.989 2.212 2.672 2.453 2.391

2.910 2.932 3.055 2.269 2.235 2.506 2.281 2.421 3.016 2.574 2.649

2.019 2.503 2.969 2.010 1.979 2.322 2.078 2.280 3.033 2.476 2.516

Li+ Na+ K+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+ Pb2+ 1-CH3−Imidazole 1,2-di-CH3−Imidazole 1,2,4-tri-CH3−Imidazole 1-CF3−Imidazole 1,2-di-CF3−Imidazole 1,2,4-tri-CF3−Imidazole

binding energies can be attributed in part to the charge and the radius of the metal cations. For example, the +2 charged metal cations (Co2+, Ni2+, Cu2+, Zn2+, Cd2+, Ba2+, Hg2+, and Pb2+) have larger binding energies than the +1 charged metal cations (Li+, Na+, and K+). In addition, the smaller metal cations tend to have a larger binding energy than the larger metal cations. For example, for Li+, Na+ and K+, the binding energies follow Li+ > Na+ > K+. For the transition metal cations, other factors such as the hybridization of their valence orbitals,34 need to be taken into account, which makes it much more challenging to

2656.3 1402.4 881.6 137.1 272.9 108.3 468.5 624.5 906.5 476.5 657.9 176.9 160.7 150.1 215.5 233.7 251.1

be noted that some of the trends we obtained are not consistent with experimental observations. For example, from our calculations, Cd2+ is much harder than Zn2+. However, Cd2+ is normally considered as a soft acid, whereas Zn2+ is normally considered as a borderline acid. This is due to the fact that experimental observations are usually from aqueous solutions. It was previously found58 that solvation effects may invert the trend observed in the gas phase and in solution, regarding the 3948



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hardness of metal cations. Indeed, if Zn(H2O)62+ and Cd(H2O)62+ are used to represent the solvated cations, the calculated values of the absolute hardness are 345.3 and 328.5 kJ mol−1, respectively, which is consistent with the experimental observation that Zn2+ is harder than Cd2+. To further analyze the correlation between the calculated binding energies and the absolute hardness of the metal cations, we separated the metal cations into two groups based on their formal charge, and the square of the correlation coefficient (r2) of the binding energy versus the absolute hardness was calculated and listed in Table 7. For Li+, Na+, and K+, which

metal···imidazole binding energies can be correlated by simultaneously using the hardness of the metal cations and the imidazoles. For +1 charged metal cations (Li+, Na+, and K+), the following relationship is obtained: BE = 0.05 × η(metal) − 0.44 × η(imidazole) + 145.75 (2) 2+

For +2 charged metal cations (Co , Ni , Cu , Zn , Cd2+, Ba2+, Hg2+ and Pb2+), the following relationship is applicable:

1-CH3−Imidazole 1,2-di-CH3−Imidazole 1,2,4-tri-CH3−Imidazole 1-CF3−Imidazole 1,2-di-CF3−Imidazole 1,2,4-tri-CF3−Imidazole

Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+, and Pb2+

0.991 0.993 0.992 0.992 0.994 0.993

0.844 0.862 0.875 0.849 0.803 0.774

+ 1536.25

2+

(3)

The r2 values for eqs 2 and 3 are 0.979 and 0.835, respectively, which indicate the reliability of using these two empirical equations to predict the metal···imidazole binding energies for new metals and/or new imidazole derivatives. The significant tunability of imidazole derivatives to bind with metal cations further provides insights into the competitive binding of multiple ligands with metal cations. Taking Na+ as an example, the Na+···imidazole binding energy is larger than other azoles, such as 1H-1,2,4-triazole (experimentally measured BE at 123.5 kJ mol−145), but smaller than amino acids, such as glycine (experimentally measured BE at 151.9 kJ mol−159). When the imidazole is substituted by EDGs, the resulting molecule, such as 1,2,4-trimethylimidazole, is found to have a comparable Na+ binding energy (153.3 kJ mol−1) to glycine. In contrast, the EWG-substituted derivative, 1,2-ditrifluoromethyl-imidazole, has a Na+ binding energy (120.2 kJ mol−1) slightly lower than that of 1H-1,2,4triazole. Therefore, one can easily use exocyclic substitutents to tune the metal···imidazole binding energies in the desired range. This can be very useful for selectively extracting metal cation from solution where a large number of competitive ligands usually coexist.

are all alkali metals, a linear relationship is observed, with an r2 value greater than 0.99. When the +2 charged metals are considered, the obtained r2 values are all above 0.8 (except for 1,2,4-tritrifluoromethyl-imidazole with an r2 value of 0.77), which also corroborated the linear relationship between the binding energies and the absolute hardness. Simultaneously, the binding energies can also be correlated with the hardness of the Lewis base (imidazole), and the obtained r2 values are listed in Table 8. Except for Ba2+, all of the r2 values are above 0.8, and Table 8. Square of the Correlation Coefficient (R2) of the Binding Energy versus the Absolute Hardness of Imidazole Derivatives

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CONCLUSION In this study, we investigated the binding energies of various metal cations with imidazoles in the gas phase. On the basis of our assessment, we conclude that the M11L/6-311++G(d,p) level of theory offers the best compromise between accuracy and computational cost, with respect to the metal cation binding energies with imidazoles. By using this method, we found that exocyclic electron-donating groups increase the binding between metal cations and imidazoles. In contrast, exocyclic electron-withdrawing groups decrease the binding between cations and imidazoles. Furthermore, the strength of the binding can be correlated with the hardness of the metal cation or the imidazole derivatives and reliable empirical equations can be obtained to predict the binding energies from these two parameters, which provide a quick approach to estimate the metal’s binding strength. Our gas phase calculations are intended to serve as the foundation for further assessment of the metal···imidazole binding in solution, which will be addressed in future studies.

2

r Li+ Na+ K+ Co2+ Ni2+ Cu2+ Zn2+ Cd2+ Ba2+ Hg2+ Pb2+

2+

BE = −1.12 × η(metal) − 1.53 × η(imidazole)

Table 7. Square of the Correlation Coefficient (r2) of the Binding Energy versus the Absolute Hardness of Metal Cations Li+, Na+, and K+

2+

0.941 0.939 0.925 0.951 0.884 0.967 0.778 0.809 0.285 0.927 0.876

some of them are larger than 0.9. The extremely low r2 value for Ba2+ is due to the existence of the Ba2+···1-trifluoromethylimidazole complex as an outlier, whose binding energy was obtained using a different method (see Table 3). If this outlier is removed, the new r2 value is 0.854. These results indicate that the binding energies of the metal···imidazole complexes can be correlated with either the hardness of the metal cations or the imidazole derivatives. Hence, the two parameters provide a quick way to predict the relative binding strength of metal cations with imidazoles or other relevant ligands, which offers a useful approach for prescreening a large set of ligands to selectively extract specific metal cations. Furthermore, the

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ASSOCIATED CONTENT

S Supporting Information *

The correlation of calculated binding energy versus the radius of the metal cation and the graphs of the correlation of binding energy versus absolute hardness. This material is available free of charge via the Internet at http://pubs.acs.org. 3949



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Article

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: (205) 348-7558. Tel.: (205) 348-1733. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We appreciate the computational resources of the Alabama Supercomputer Authority. Partial financial support was provided by The University of Alabama Research Stimulation Fund and the National Science Foundation (CBET-1159397).

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Tuning the Adsorption Interactions of Imidazole Derivatives with

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