Article pubs.acs.org/JPCA

Cation−Alkane Interaction J. Richard Premkumar and G. Narahari Sastry* Centre for Molecular Modelling, CSIR-Indian Institute of Chemical Technology, Hyderabad 500 007, India S Supporting Information *

ABSTRACT: Ab initio computations, up to CCSD(T)/CBS on model systems, and MP2/cc-pVTZ and DFT calculations are performed on cation−alkane and cation−alkene complexes, cation = Li+, Na+, Be2+, Mg2+, Ca2+, Cu+ and Zn2+; alkane = CnH2n+2 (n = 1−10) and C6H12; and alkene = C2H4 and C6H6. Density functional theory−symmetry adapted perturbation theory (DFT-SAPT) calculations reveal that the cation−alkane interactions are predominantly constituted of induction component. The dramatic modulation of the strength of their interaction and the topological features obtained from atoms in molecules (AIM) analysis are consistent with the characteristics of a typical noncovalent interaction. In contrast to many of the conventional noncovalent interactions, cation−alkane interactions are substantially strong and are comparable in strength to the well studied cation−π interactions.

1. INTRODUCTION Noncovalent interactions, which are traditionally touted as weak interactions, have emerged as a topic of outstanding importance with potential applications in wide ranging fields, spanning chemistry, material science, biology, and medicine.1−6 While hydrogen bonding is most extensively studied,7,8 the importance of other noncovalent interactions such as π−π stacking, CH···π interactions, cation−π, anion−π, and halogen bonding in molecular recognition, catalysis, material design, supramolecular assembly, and in related areas are very well established.1,5,9−17 Cation−π interaction is the strongest among various noncovalent interactions and is shown to have profound importance in controlling the structure and function of macromolecules.1,9,16 The modulation of strength of cation−π interactions by solvation18−20 size of π-system,21−24 and the nature of cation24 have been systematically investigated. An important feature of the noncovalent interactions is their nonadditivity, leading to substantial cooperative or anticooperative effects.25−29 Hydrogen bonding interaction also shows modulation in their strength with respect to the water cluster size as observed in the case of cation−π interaction.30−32 The metal ion interaction with graphene (cation−π) is the topic of high interest in ion-batteries, and the interactions are grouped into two: chemisorbed and physisorbed with respect to the nature of the cation.33,34 Several reports have been investigated using polyaromatic hydrocarbons (PAH) as an example, to mimic the graphene surface.5,35,36 Nevertheless, the saturated analogue of cation−π interaction, i.e., the cation interaction with an alkane plays a major role in seemingly different scientific areas such as CH-activation reactions and cation passage through a lipid bilayer.37−50 CH-activation reactions are important from a fundamental point of view, since it transforms inexpensive alkanes into the reactive or unsaturated compounds, and they are useful in developing new synthetic strategies. Many transition metal ion complexes are now known for the CH-activation reactions. In a recent report,51 © XXXX American Chemical Society

aromatization of n-alkanes has been achieved (up to 89%) using transition metal ion complex as a catalyst. The computational studies on the CH-activation reaction mechanism have shown that the interaction between a cation and an alkane is the cause for such transformation.52,53 About two decades before, Hill et al.54 demonstrated that, in some of the transition metal ion-alkene complexes, the alkene (Cn) has been replaced by an alkane (Cn+1), which clearly points to the competitive binding of alkanes and alkenes with metal ions. A recent computational study has shown evidence of hydrogen bonding between a hydronium ion and an alkane.55 Despite the fact that cation−alkane interactions are known for a long time, the fundamental understanding of it is still imprecise and rather incomplete. Therefore, elucidating the physical origin and nature of cation-alkane interaction is interesting in its own right. In this article, we propose that cation−alkane interaction is an important class of noncovalent interaction, which possesses binding strength comparable to cation−π interaction. First, the study demonstrates that the cation−alkane interactions are fairly strong, and we then show that this strength becomes substantially exalted as the size of the alkane increases for all the metal cations studied. Such dramatic modulation is a feature of noncovalent interactions owing to their nonadditive nature.25−29 Second, we seek to employ Bader’s theory of Atoms in Molecules (AIM) approach to characterize the nature of these interactions and demonstrate the topological features of that of noncovalent interaction. After characterizing the interaction between a cation and an alkane as noncovalent, we carried out DFT-SAPT calculations to reveal the origin of cation−alkane interaction, and these calculations delineate the contrast between cation−alkane and cation−alkene. The Received: July 30, 2014 Revised: November 10, 2014

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Scheme 1. Model Systems Considered

poise approach developed by Boys and Bernardi.57 The BSSE has been corrected with the counterpoise = N option, where N stands for the total number of monomers in the complex. The geometry optimization and the above-mentioned BE calculations were carried out using the Gaussian 09 program package.58 In order to obtain the detailed information on different forces in cation−hydrocarbon interaction, energy decomposition analysis (EDA) calculations have been done on the B3LYP/6-31G* geometries. The DFT-SAPT calculations have been carried out using a combination of symmetry-adapted perturbation theory (SAPT)59 of intermolecular interactions truncated at the second order with a density functional theory description of the monomer at the PBE0/aug-cc-pVDZ level. The HF-SAPT calculations were done at the HF/aug-cc-pVDZ level of theory for the representative cation−hydrocarbon complexes. Both DFT-SAPT and HF-SAPT calculations were carried out using the MOLPRO program.60 These EDA calculations split the overall binding energy (BEsapt) of a cation−hydrocarbon complex into electrostatic (Ees), exchange repulsion (Eex), induction (Eind), exchange-induction (Eex‑ind), dispersion (Edisp), exchange-dispersion (Eex‑disp) and the estimated higher order correction to the Hartree−Fock contribution (δHF). As no higher than second-order terms are currently implemented in SAPT, third- and higher-order induction and exchange-induction contributions were estimated using the supermolecular approach at the Hartree−Fock level61 and added to the sum of first- and second-order DFT-SAPT energy contributions. To obtain reliable results of DFT-SAPT, it requires asymptotically corrected Kohn−Sham calculations. In this study we have used the gradient-regulated asymptotic correction62 by providing the highest occupied molecular orbital (HOMO) values and experimental ionization potential values of the monomers (Supporting Information Table S4). Obtained exchange-induction (Eex‑ind) and exchange-dispersion (Eex‑disp) components are included in Eind and Edisp components, respectively, to simplify the discussion as done by others.43,63,64

various cation−hydrocarbon complexes considered for the current study are depicted in Scheme 1.

2. COMPUTATIONAL DETAILS Geometry optimization of all the structures was carried out at B3LYP/6-31G* level of theory. In addition to that, we have also performed geometry optimization at MP2/cc-pVTZ level of theory for the representative model structures such as M-A2, M-E2, M-cA6, and M-cE6 (Scheme 1). A measure of the strength of cation−hydrocarbon interaction is given by the binding energy (BE), which is defined as the difference between the energy of the complex and those of the interacting fragments in their distorted conformation that they have in complex, as shown in eq 1. BE = (Ecation + E hydrocarbon − distorted) − Ecation − hydrocarbon (1)

The BEs were calculated at the MP2/cc-pVTZ level for both B3LYP/6-31G* and MP2/cc-pVTZ optimized structures. The MP2/cc-pVTZ//B3LYP/6-31G* BEs were found to be very similar to MP2/cc-pVTZ//MP2/cc-pVTZ BEs. The energy differences between those results were found to be less than 0.36 kcal/mol, except for Cu+−hydrocarbon complexes (Table S1). The variation of BEs with respect to different hydrocarbons at the MP2/cc-pVTZ//B3LYP/6-31G* level and at the MP2/cc-pVTZ//MP2/cc-pVTZ level showed a similar trend. Therefore, we feel that B3LYP/6-31G* structures and MP2/cc-pVTZ//B3LYP/6-31G* energies are adequate to delineate the cation−hydrocarbon interaction, and report the same unless otherwise stated. The CCSD(T)/CBS BEs were estimated for the representative model systems (M-A2, M-E2, M-cA6, and M-cE6) on the basis of the extrapolation method proposed by Helgaker et al.56 using the following eqs 2 and 3. BECCSD(T)/CBS = BEMP2/CBS + {BECCSD(T)/aug ‐ cc ‐ pVDZ − BEMP2/aug ‐ cc ‐ pVDZ}

(2)

BEsapt = Ees + Eex + E ind + Edisp + δ HF

BEMP2/CBS = (64BEMP2/aug ‐ cc ‐ pVQZ − 27BEMP2/aug ‐ cc ‐ pVTZ)/37 (3)

(4)

The second-order terms (induction and dispersion) usually require a larger augmented correlation consistent basis set in order to yield reliable results. We employed the aug-cc-pVTZ basis set to verify the convergence of these second-order energy

The BEs obtained from eq 2 and 3 were calculated using the MP2/cc-pVTZ geometries. The reported BEs were corrected for the basis set superposition error (BSSE) by the counterB

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components. The test calculations at PBE0/aug-cc-pVTZ have been carried out for specific systems such as Li+···A2, Li+···A6, Li+···cA6, Li+···E2, and Li+···cE6. We found that, for the present purposes, the use of smaller aug-cc-pVDZ basis set appears to be adequate. In the test calculations on the model systems, a comparison with aug-cc-pVTZ results has shown that the deviations are less than half a kcal/mol (Table S6). Thus, we feel that the reported results at PBE0/aug-cc-pVDZ are able to provide reasonable numbers. In addition to the SAPT-based EDA calculations, the “reduced variational space”65,66 (RVS) formalism as implemented in the GAMESS program package was also carried out.67 The RVS formalism splits the overall binding energy (BErvs) of a cation− hydrocarbon complex into electrostatic (Ees), exchangerepulsion (Eex), polarization (POL), and charge transfer interactions (CT) as shown in eq 5. BErvs = Ees + Eex + POL + CT

(5)

POL and CT terms were associated with the intramolecular and intermolecular orbital relaxation energies of the two fragments. Each POL and CT term was further divided into two individual components viz., POLA, POLM, CTA‑M, and CTM‑A; here M = cation and A = hydrocarbon. HF-SAPT and RVS calculations were done only for representative cation− hydrocarbon complexes (M-A2, M-cA6, M-E2, and M-cE6). In this work, we reversed the sign for the energy components in the EDA, and thus the positive and negative values correspond to attractive and repulsive terms, respectively. The wave function files were generated at the MP2/cc-pVTZ level of theory to characterize the nature of the cation−hydrocarbon interaction. The electron density (ρ) and the Laplacian of the electron density (∇ 2 ρ) values were obtained at the intermolecular bond critical point (BCP). In cases where more than a number of intermolecular BCPs were observed in the cation−hydrocarbon complex, the BCP with the larger ρ value was considered for the discussion.

Figure 1. Various binding modes for Li+-A1 and Li+-A2 complexes.

energy difference of 0.01 kcal/mol. Other binding modes such as, η1 (C3v) and η2 (C2v) were saddle point structures with the imaginary frequencies of 234i and 182i, respectively. The geometry optimizations of η1 and η2 structures without any symmetry constraints were also collapsed into the η3 mode of binding. It has been reported that the negative charge density will be higher on the C3 axis of methane,68 and thus the cation prefers to bind above the tetrahedral plane at the C3 axis of methane molecule. Based on this conformational analysis of Li+-A1, the structures such as Li+ contacts with each CH and CH2 bonds of alkane were avoided for the higher alkane conformational search. Thus, the conformations of the Li+-A2 complex have been limited to five as shown in Figure 1. In general, n-alkanes are stable in their extended conformation,69 and it is clear from earlier reports that n-alkanes or alkyl chains prefer to be in the folded conformation (gauche) upon cation binding.70−72 So the eclipsed conformation of ethane has also been considered to find out the possibility of such structures in metal complexes (Figure 1). Out of five Li+-A2 complexes, only two of them were minima on the potential energy surface (PES), viz., η3 (C3v) and η3 (Cs), where ethane exists in staggered conformation. The rest of the three Li+-A2 complexes were not minima on the PES, where ethane exists in eclipsed conformation. In the Li+-A1 complex, the lower energy structure is found in which Li+ is in contact with the maximum number of σ-bonds. In line with that, the minimum energy structure of Li+-A2 (η3, Cs), the cation found to have maximum number of σ-bonds contact. Based on the conformational analysis of Li+-A1 and Li+-A2 complexes, we made a few decisions before analyzing the conformations of Li+ with higher alkanes. They are (i) models where cation contact with CH and CH2 bonds can be avoided and (ii) models where eclipsed conformation of an alkane in a complex can be avoided. However, the gauche conformations of an n-alkane in a cation− alkane complex need to be investigated, as shown by Lammertsma et al.70 (iii) The gauche conformations of a branched alkane binding to a cation need not be investigated,

3. RESULTS AND DISCUSSION In this section we first deal with the structural features of cation−hydrocarbon complexes followed by the discussion of modulation of cation−alkane interaction in terms of alkane size and the nature of the cation. AIM results of the representative model systems (M-A2, M-E2, M-cA6, and M-cE6) will be discussed next, in Section 3.3. The various components of BE of cation−hydrocarbon complexes obtained from EDA calculations and the experimental relevance of this study are discussed at the end of this section. 3.1. Conformational Analysis of Cation−Hydrocarbon Complexes. The initial conformational search was done with the prototypical metal cation Li+ binding to alkanes (A1−A10). Four possible binding modes were investigated (Figure 1) for Li+-A1 considering the minimum to maximum number of CH bond interactions to the Li+ cation. If Li+-A1 has four possible binding modes, apparently, there will be a number of possible binding modes for Li+ binding to larger alkanes. Moreover, each alkane (excluding methane, ethane, and propane) has several skeletal isomers; for example, decane has 75 skeletal isomers. Keeping this in mind, we have looked at the structures and energetics of various Li+-A1 and Li+-A2 complexes. Out of four binding modes of Li+ with A1 complex, three distinct stationary points were obtained. Upon geometry optimization, the η2 (Cs) structure of Li+-A1 is collapsed into η3 structure. The η2 (Cs) and η3 (C3v) structures were closer in energy, with the relative C

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Figure 2. Lower energy conformations of Li+−alkane complexes obtained at the B3LYP/6-31G* level of theory.

since they do not provide maximum σ-bond contacts to the cation as an n-alkane does. These considerations helped us limit the conformational search with a particular number (Figure S1−S6). The obtained lower energy structures of Li+−alkane (alkane = A1 to A10) complexes are shown in Figure 2, and those structures were taken as a reference starting point for the geometry optimization of other cation−alkane complexes (cation = Na+, Be2+, Mg2+, Ca2+, Cu+, and Zn2+). The complexes thus generated were subjected to the geometry optimization at the B3LYP/6-31G* level of theory, and all the cation−alkane (M-An) complexes were considered for further studies. The η3 structure of Cu+-A1 (C3v) was not a minimum on the PES. To find out the minimum energy structure of Cu+A1, we particularly looked at the other possible conformations for Cu+-A1 as shown for Li+-A1 (Figure 1). We observed that the η2 structure of Cu+-A1 (C2v) as a minimum energy structure on the PES, which is 6.34 kcal/mol lower in energy as compared to the C3v structure. So only for Cu+-A1 has the C2v structure been taken into the study. The cationic complexes of ethylene (M-E2) and benzene (M-cE6) were taken as cation−π analogues to compare with the cation−alkane complexes of M-A2 and M-cA6, respectively (Scheme 1). The initial structures of M-E2, M-cA6, and M-cE6 complexes were modeled as the cation binding at the principal axis of ethylene (C2), cyclohexane (C3) and benzene (C6) respectively. All the cation−π complexes and the M-cA6 complexes were found to be minima on the PES except Be2+E2. In the minimum energy structure of Be2+-E2, Be2+ binds near one of the carbons in ethylene. However, the structure where the cation binds at the top of the π-cloud was of interest. Such a structure was obtained through constrained geometry

optimization with the C2v point group.73 The structural differences of Cu+-A1 and Be2+-E2 complexes might be due to a certain degree of covalency between a cation and the hydrocarbon. Certainly, in most noncovalent interactions, including a hydrogen bond, there is a degree of covalency that is clearly documented.96 However, it is known that the perturbation methods fail to describe the short-range interactions. The advancement in density functional theory (DFT) calculations is useful to predict the transition metal ion complexes accurately. Thus, we have analyzed the differences of BEs of cation−hydrocarbon complexes obtained at the M062X/cc-pVTZ and MP2/cc-pVTZ methods. In general, it is found that the M06-2X/cc-pVTZ BEs are larger as compared to the MP2/cc-pVTZ BEs (Tables S7 and S8). However, in the cases of Cu+-A1, Cu+-E2, and Cu+-cE6, M06-2X/cc-pVTZ BEs are lower compared to the MP2/cc-pVTZ BEs. The overbinding of Cu+−hydrocarbon interaction by the MP2/cc-pVTZ level might be due to a certain degree of covalency in Cu+ complexes. It is worth noting that Cu+ complexes show a higher degree of covalency compared to the rest. 3.2. Nature of Cation and Size of Alkane in Cation− Alkane Interaction. The BEs of cation−alkane complexes were plotted against the number of carbon atoms in the cation−alkane complex as shown in Figure 3. The BEs of cation−alkane complexes as a function of cation follow the order of Na+ < Li+ < Cu+ < Ca2+ < Mg2+ < Zn2+ < Be2+. While the nature of the cation significantly modulates the strength of cation−alkane interaction, alkane size is an important factor that substantially modulates the strength of cation−alkane interaction. The range of BEs of cation−alkane complexes is observed as 5.95 kcal/mol (Na+-A1) to 273.20 kcal/mol (Be2+D

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the sign of the ∇2ρ are the indicators used to characterize the intermolecular interactions. It has been used to analyze even the weakest alkane−alkane interaction76 in addition to the wellknown hydrogen bonding interaction.77 The ρ and ∇2ρ values at the (3,−1) intermolecular BCP are given in Figure 4. It shows that the ρ values range between 0.01 and 0.11 a.u. for various cation−hydrocarbon complexes. Here, the ρ values of cation−alkane complexes are found to be very close with that of cation−π, and interestingly, for Be2+-A2, the ρ value is slightly higher than the ρ value of Be2+-E2. The obtained electron density values are smaller than those found for typical covalent bonds (0.200−0.400 a.u.). Moreover, the positive values of ∇2ρ (Figure 4 and Table S3) indicate that the intermolecular interaction between the closed shells.79 Therefore, AIM analysis clearly illustrates that the interaction between a cation and an alkane is noncovalent in nature. 3.4. Energy Decomposition Analysis (EDA). In this section, we first discuss the DFT-SAPT results of cation− alkane complexes (Li+-An and Mg2+-An where n = 1−8). This is followed by a comparison of the DFT-SAPT results of cation−alkane (M-A2 and M-cA6) and cation−π (M-E2 and M-cE6) complexes (where M=Li+, Na+, Be2+, Mg2+, Ca2+, Cu+ and Zn2+). Furthermore, brief discussions on HF-SAPT and RVS results have been provided. The DFT-SAPT results of Li+−alkane and Mg2+−alkane complexes are shown in Figure 5. The attractive Ees interaction can be almost offset by the repulsive Eex component. Except Eind component no other components followed the trend of BEdft‑sapt as a function of alkane size (Figure 5). Thus, the variation in cation−alkane strength by alkane size and by cationic nature is largely governed by the change of induction (Eind) interaction. The above results point out that the force holding maximum contribution to the cation−alkane interaction is Eind, and thus the origin of cation−alkane interactions is induction. After understanding that the modulation of cation-alkane strength is due to an induction component, we have analyzed the differences of DFT-SAPT results of cation−alkane (M-A2 and M-cA6) and cation−π (M-E2 and M-cE6) complexes as shown in the bar graph analysis (Figure 6). In Figure 6a,b, the bar on the positive side indicates that the particular component is larger for cation−π complexes compared to their cation− alkane analogues. The bar on the negative side indicates that

Figure 3. MP2/cc-pVTZ binding energies (kcal/mol) of cation− alkane complexes.

A10). The modulation in the strength of cation−π interactions due to the size of the π-system and the nature of the cation have already been demonstrated by our group.22,24 The present study shows that the larger the alkane size, the stronger the cation−alkane interaction, and thus provides an explanation for the decrease of cation mobility in liquid alkanes as the alkane size increases.74 The BE of Li+-A10 (34.51 kcal/mol) is competitive with the BE of Li+-H2O (experimental value = 34.02 kcal/mol75 and computed value = 32.69 kcal/mol95). The BE results emphasize that cation−alkane interactions can be extremely strong, and in their limit they compete with the weak covalent bonds. In general, the charge on a cation in a cation−alkane complex has been well correlated with its BE, i.e., the lower the charge on the cation, the higher the BE. The lower BE of Be2+-A9 as compared to Be2+-A8 is due to the lower charge transfer of the Be2+-A9 complex (Table S2). 3.3. Signature of a Noncovalent Interaction. Topological analysis of the electron density (ρ) and the Laplacian of the electron density (∇2ρ) at the intermolecular bond critical point (BCP) can be analyzed using Bader’s AIM approach. It is a useful tool to characterize whether the intermolecular interaction is covalent or noncovalent.76−78 The ρ values and

Figure 4. MP2/cc-pVTZ electron density (ρ, in a.u.) and the Laplacian of the electron density (∇2ρ, in a.u.) obtained at (3,−1) intermolecular bond critical bond (LHS) and obtained in between the CC bond of the cation−hydrocarbon complexes (RHS). For Cu+ and Zn2+ complexes, MP2/6311++G** level wave functions have been used. E

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Figure 6. Difference in the BE components (ΔE) of cation−π and cation−alkane complexes: (a) ΔE = EM‑A2 − EM‑E2, (b) ΔE = EM‑cA6 − EM‑cE6. ΔBE were obtained from the CCSD(T)/CBS BEs (except Ca2+ complexes). For Ca2+ complexes MP2/cc-pVTZ BEs were taken. All the results are given in kcal/mol units.

Figure 5. EDA results of Li+−alkane and Mg2+−alkane complexes. The values are expressed in kcal/mol.

the particular component is larger for cation−alkane complexes as compared to their cation−π analogues. The bars of ΔEes exist on the positive side (Figure 6); this indicates that the Ees of cation−π interactions is stronger compared to the Ees of the cation−alkane analogues. The ΔEex of all cationic complexes does not exist on one particular side, as shown by ΔEes. The ΔEex bars of Na+, Cu+, Be2+, and Mg2+ retains the same side for both in M-A2 as well as in M-cA6 complexes. The Eind component is found to be higher for cation−alkane complexes as compared to the cation−π complexes except Cu+−alkane complexes. So, the induction interaction is not only the predominant force in cation−alkane interactions, but it is also significantly larger for cation−alkane complexes as compared to their cation−π analogues. The induction (Eind) or polarizability term is a measure of change in a molecule’s electron distribution in response to an approaching electric field.80 The reported molecular polarizability of benzene, cyclohexane, and n-hexane are 10 Å3, 11 Å3, and 12 Å3, respectively.80 It signifies that the saturated hydrocarbons are inherently more polarizable than their unsaturated analogues, and thus the induction interaction is found to be larger for cation−alkane complexes as compared to their cation−π analogues. Moreover, the π-bonds (CC) are not rotatable, and thus the rotatable C−C bonds become largely polarized as compared to the CC bond by a cation. The contribution of

the dispersion component of cation−hydrocarbon interaction is less than 5% of the total BE, except in transition metal ion complexes (Table S5). Edisp is the predominant force of π−π complexes, which is found to be the least contributing force of cation−hydrocarbon complexes. However, it significantly contributes to the transition metal ion hydrocarbon complexes (up to 14%). The two attractive components, viz., Ees and Eind, were found to be prominent for the cation−hydrocarbon interaction. The electrostatic interaction is always higher for cation−π systems and induction interaction is mostly higher for cation−alkane systems. However, cation−π interactions are significantly stronger (except Be2+-E2) as compared to their cation−alkane analogues. This might be due to the larger contribution of electrostatic interaction in cases of cation−π complexes. The Ees component is observed as a dominating binding force for monocation−π complexes, and the Eind component is observed as a dominating binding force for dication−π and cation− alkane complexes (Table 1). Hence it can be stated that the cation−π interactions are electrostatic in nature in the presence of monocation; however, in the presence of dication, the electrostatic interaction will be dominated by the induction F

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Table 1. Binding Energy Components of Obtained from HF-SAPT and DFT-SAPT Calculations As Compared to RVS Calculations, the Numbers Are Expressed in kcal/mol RVS Li −Ees −Eex −POLH −POLM −CTH‑M −CTM‑H −(POL+CT) −BErvs −Ees −Eex −POLH −POLM −CTH‑M −CTM‑H −(POL+CT) −BErvs

−Ees −Eex −Eind −Edisp −δHF −(Eind+δHF) −BEhf‑sapt −Ees −Eex −Eind −Edisp −δHF −(Eind+δHF) −BEhf‑sapt

−Ees −Eex −Eind −Edisp −δHF −(Eind+δHF) −BEdft‑sapt −Ees −Eex −Eind −Edisp −δHF −(Eind+δHF) −BEdft‑sapt

A2 4.48 −6.80 11.64 0.00 4.01 0.00 15.65 13.34 cA6 4.88 −13.27 23.34 0.00 5.07 0.00 28.41 20.04

+

+

Na E2 15.94 −6.77 7.36 0.01 6.43 0.00 13.8 22.97 cE6 21.77 −10.65 17.50 0.00 11.07 0.00 28.57 39.71

A2 2.98 −4.14 6.46 0.01 1.58 0.02 8.07 6.93 cA6 1.82 −5.47 12.16 0.01 1.73 0.04 13.94 10.31

Be E2 11.87 −5.15 4.31 0.02 4.56 0.02 8.91 15.65 cE6 18.24 −7.74 9.56 0.02 6.32 0.05 15.95 26.49

A2 12.79 −44.18 102.11 0.04 69.85 0.01 172.01 140.67 cA6 13.40 −61.25 200.51 0.05 83.38 0.02 283.96 209.36

2+

Mg2+

E2 48.85 −24.60 56.13 0.03 64.41 0.01 120.58 165.96 cE6 36.94 −42.82 132.03 0.02 107.27 0.01 239.33 233.53

A2 16.76 −20.93 45.92 0.01 17.08 0.00 63.01 58.92 cA6 21.65 −35.44 88.75 0.03 22.65 −0.01 111.42 97.80 HF-SAPT

E2 34.17 −15.30 27.77 0.02 31.33 0.00 59.12 78.09 cE6 46.46 −27.40 62.60 0.02 38.15 −0.01 100.76 119.99

Ca2+ A2 9.26 −14.00 24.12 0.03 9.38 0.01 33.54 29.42 cA6 12.65 −23.54 47.61 0.05 12.51 0.03 60.2 49.70

Cu+

E2 21.88 −10.30 14.21 0.10 15.35 0.01 29.67 41.58 cE6 36.40 −21.52 34.49 0.10 26.96 0.01 61.56 77.10

A2 47.95 −81.79 13.73 11.56 4.25 14.75 44.29 15.10 cA6 44.31 −81.45 23.57 8.09 5.45 17.85 54.96 24.28

Zn2+

E2 107.01 −137.60 12.15 14.31 6.54 27.19 60.19 35.95 cE6 78.24 −119.30 21.18 13.20 10.28 28.41 73.07 43.81

A2 41.45 −54.12 57.53 1.93 20.73 3.20 83.39 73.65 cA6 45.05 −63.40 93.83 1.45 33.07 4.07 132.42 118.47

E2 63.28 −48.57 38.33 1.57 42.77 2.87 85.54 103.46 cE6 72.80 −70.53 76.93 2.17 47.89 5.46 132.45 140.66

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

3.75 −6.74 17.28 0.33 0.98 18.26 15.61 cA6 4.49 −13.48 30.17 0.83 1.78 31.95 23.79

17.22 −10.25 15.10 0.16 −0.22 14.88 22.01 cE6 19.74 −12.46 28.86 0.58 2.58 31.44 39.31

2.89 −4.45 9.61 0.23 −0.40 9.21 7.89 cA6 2.27 −6.45 15.48 0.36 −0.61 14.87 11.06

14.32 −8.52 9.99 0.16 −1.56 8.43 14.39 cE6 18.25 −9.86 16.79 0.45 −1.00 15.79 24.63

10.38 −42.13 159.57 0.49 16.75 176.32 145.05 cA6 −15.56 −57.40 259.92 1.09 26.56 286.48 214.61

49.23 −29.50 119.31 0.13 4.34 123.65 143.51 cE6 28.28 −43.56 214.17 0.67 31.53 245.70 231.09

15.00 −20.22 70.53 0.36 −1.59 68.94 64.08 cA6 20.56 −34.79 121.33 0.79 −2.36 118.97 105.53 DFT-SAPT

37.72 −21.13 64.46 0.20 −3.85 60.61 77.41 cE6 42.02 −29.33 107.33 0.57 −0.90 106.43 119.68

8.85 −14.49 35.71 2.23 3.75 39.46 36.05 cA6 14.19 −26.02 62.86 3.85 4.24 67.10 59.10

26.74 −16.94 32.47 1.49 −0.56 31.91 43.19 cE6 36.95 −26.39 58.38 3.76 8.46 66.84 81.16

58.40 −93.02 39.86 13.04 −5.47 34.39 12.81 cA6 57.30 −96.23 47.41 16.92 −2.63 44.78 22.77

130.65 −159.04 78.47 13.86 −35.07 43.40 28.88 cE6 96.70 −139.50 55.03 20.55 3.48 58.51 36.26

39.76 −53.97 100.81 7.92 −6.46 94.35 88.07 cA6 47.71 −66.54 150.78 10.72 −6.04 144.74 136.63

72.20 −59.05 112.47 6.61 −21.54 90.93 110.69 cE6 70.42 −74.38 148.48 11.80 −4.18 144.30 152.14

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

A2

E2

4.35 −7.34 17.79 0.33 0.96 18.75 16.09 cA6 5.90 −14.45 30.88 0.87 1.78 32.66 24.97

14.82 −8.72 14.58 0.16 −0.25 14.33 20.59 cE6 17.47 −11.95 28.01 0.58 2.59 30.60 36.70

3.27 −5.11 9.96 0.24 −0.41 9.55 7.96 cA6 2.75 −7.37 16.10 0.40 −0.61 15.49 11.28

12.36 −7.70 9.71 0.16 −1.57 8.14 12.96 cE6 16.11 −9.35 16.27 0.48 −1.00 15.27 22.50

13.31 −43.19 162.97 0.50 16.77 179.74 150.35 cA6 −5.01 −61.87 266.23 1.12 26.56 292.79 227.04

42.27 −25.29 113.65 0.13 4.03 117.68 134.79 cE6 26.85 −42.15 210.84 0.67 31.53 242.37 227.74

16.75 −21.79 72.83 0.36 −1.67 71.16 66.48 cA6 23.40 −36.77 125.16 0.84 −2.36 122.80 110.27

32.22 −18.56 61.78 0.20 −3.99 57.79 71.64 cE6 37.73 −27.73 104.71 0.60 −0.90 103.81 114.41

9.67 −15.33 37.10 2.27 3.75 40.85 37.46 cA6 15.29 −27.03 65.43 3.91 4.24 69.67 61.83

23.02 −14.63 31.83 1.44 −0.56 31.27 41.10 cE6 34.55 −32.45 57.67 4.33 4.24 61.91 68.33

63.65 −98.83 43.42 14.52 −5.47 37.95 17.28 cA6 64.67 −105.03 52.29 18.89 −2.63 49.66 28.19

120.17 −148.10 72.53 14.66 −35.07 37.46 24.19 cE6 99.24 −143.58 56.57 22.18 3.48 60.05 37.89

43.79 −56.86 106.95 8.79 −6.46 100.49 96.22 cA6 50.24 −69.66 159.38 11.91 −6.04 153.34 145.83

62.68 −51.62 106.11 6.88 −21.54 84.57 102.50 cE6 66.31 −72.08 147.93 12.60 −4.18 143.75 150.57

RVS calculations. Both HF-SAPT and DFT-SAPT schemes yield the same energy terms (eq 4) for the intermolecular interaction. It is worth noting that the energy components of HF-SAPT deviate within ±2.50 kcal/mol from the DFT-SAPT results (Table 1) for Li+ and Na+ complexes. However, for alkaline earth and the transition metal ion complexes, the

interaction. These observations are in agreement with the earlier reports.81,82 However, we also found that for cation− alkane interaction, whether the cation is mono or divalent, the dominating force is always found to be induction interaction (except Cu+−alkane complexes). Further, we have provided a brief discussion on the results obtained from HF-SAPT and G

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results is significant for transition metal ion complexes. The use of perturbation theory to treat the transition metal ion is somewhat worrisome due to the higher D1 diagnostic values of transition metal ions complexes (Table S9). According to CCSD(T)/CBS computations, the BE of Cu+-cE6 is 52.66 kcal/mol (BEMP2/cc‑pVTZ of Cu+-cE6 is 53.84 kcal/mol), which is very close to the experimental binding energy of 50.00 ± 2.00 kcal/mol.87,88 It has been reported that DFT-SAPT predicts close results with the CCSD(T) method.84−86 However, the BEdft‑sapt of the Cu+-cE6 complex is 37.89 kcal/mol. The DFTSAPT results are largely deviated from the experimental prediction and CCSD(T)/CBS results of BEs, and this might be due to the artifact in the DFT-SAPT calculations considering transition metal ions. Even though DFT-SAPT results of Cu+ and Zn2+ complexes showed larger deviation compared with the ab initio results, the trends of BEs between cation−alkane and cation−π complexes are very consistent and not mismatched as shown by ab initio results. And thus for qualitative comparison of cation−alkane and cation−π interactions, the DFT-SAPT results of Cu+ and Zn2+ are also included in this work. 3. 5. Experimental Relevance. Cation binding to benzene and cyclohexane can be logically related with cation adsorption with graphene and graphane because it has been reported that the Li/C ratio in single-layer graphene was close to 1/6, and it demonstrates that a minimum of 6 carbons were required for cationic binding at the graphene surface.89 Graphene-based materials were used as a cathode in the rechargeable ionbatteries. The developments of graphene electrodes in ionbatteries are highly desired for the long-life service.90−92 During the charge and discharge process of ion-batteries, the adsorption and desorption of metal ions occur at the electrode. One of the disadvantages of graphene-based electrodes in ionbatteries is instability of completing the charge/discharge cycle for a long run;93 this may be due to the adsorbed cations that are retained in the graphene electrodes because of the strong cation−π interactions. So we expect that the charge/discharge process in ion-batteries might be made easier by the use of graphane (saturated) (or) partially reduced graphene-based materials compared to the graphene electrodes. Thus, our study may stimulate the new experimental investigation to use graphane or partially reduced graphene as an electrode in ionbatteries. Interestingly, graphane sheets in crystal form under pressure have been recently achieved.94

deviation of HF-SAPT resulting from DFT-SAPT values is found to be higher (±11.00 kcal/mol). It is known that the Hartree−Fock method overestimates the strength of dipoles,83 and thus we expected that the Ees component of HF-SAPT will be larger than the DFT-SAPT values. However, for Cu+-cE6 and cation−alkane complexes, the Ees values of DFT-SAPT were found to be larger than the HF-SAPT values (Table 1). We summed up the absolute values of POL and CT terms of RVS and compared with the HF-SAPT and DFT-SAPT results. Interestingly, for Li+ and Na+ complexes, the sum of POL and CT is closer to the Eind term of HF-SAPT or DFT-SAPT. Otherwise, it can be stated that the Eind component of HFSAPT or DFT-SAPT results can be separated into POL and CT with the help of RVS (within the limit of ±2.50 kcal/mol) for the Li+− and Na+−hydrocarbon complexes. Interestingly, for Be2+-E2, Mg2+-A2, Mg2+-E2, Mg2+-cA6, Ca2+-E2, Cu+-E2, Zn2+-A2, Zn2+-E2, Zn2+-cA6, and Zn2+-cE6, the Eind of DFTSAPT results can be separated into POL and CT within 3% error with the help of RVS (Table S5). However, the sum of Eind and δHF was found to be closer to POL+CT values, since the δHF term is due to the third and higher order induction contributions calculated at the Hartree−Fock level (Table 1). The RVS results of Cu+ complexes behave quite differently from all the other cations. The cation itself polarizes, and it transfers charge to the hydrocarbon. Moreover, this is significant in the cases of ethylene and benzene (π-acids) complexes. The contrast of Cu+ complexes might be due to the π-bonding (also called back bonding) interactions with the hydrocarbons. The behavior of Zn2+ is different from the alkali and alkaline earth metals, but not remarkably so (Table 1). However, HF-SAPT and RVS calculations were carried out at the HF level using double-ζ quality of basis sets, which are computationally inexpensive, and especially HF-SAPT results are found to be closer to DFT-SAPT results for the alkali metal ion complexes. The BEs obtained from RVS, HF-SAPT, DFT-SAPT, and MP2/cc-pVTZ calculations were benchmarked with high-level CCSD(T)/CBS results, as shown in Figure 7. The deviation of BEs obtained from EDA methods from the CCSD(T)/CBS

4. CONCLUSIONS In summary, the current study comprehensively demonstrates that cation−alkane interactions are strong noncovalent interactions. The remarkable modulations that these interactions undergo as a function of alkane size and the nature of the cation show their similarity with cation−π interactions. The study also accounts for the reduced mobility of cations in liquid alkanes as their size increases and offers an idea in improving the charge/discharge cycle of ion-batteries. A deeper understanding of the nature and tunability of the cation−alkane interaction may prove to be of fundamental importance in effecting supramolecular assembly, material design, crystal engineering, and catalyst design.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 7. Comparison of HF/6-31G* (RVS), HF/aug-cc-pVDZ (HFSAPT), PBEO/aug-cc-pVDZ (DFT-SAPT), and MP2/cc-pVTZ BEs (kcal/mol) with CCSD(T)/CBS results.

NBO charges and ρ and ∇2ρ values obtained from AIM calculations of cation−alkane systems are given. The B3LYP/6H

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31G* structures of cation-hydrocarbon complexes are given. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +91 40 27193016. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Council of Scientific and Industrial Research (CSIR), New Delhi, India, 12th five year plan projects INTELCOAT (CSC-0114) and GENESIS (BSC-0121). J.R.P. thanks CSIR for SRF.

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