Role of the Multipolar Electrostatic Interaction Energy Componentsin Strong and Weak Cation−π InteractionsPawel Kadlubanski,† Katherine Calderon-Mojica,‡,⊥ Weyshla A. Rodriguez,§,⊥ D. Majumdar,*,∥

Szczepan Roszak,*,† and Jerzy Leszczynski*,∥

†Institute of Physical and Theoretical Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw,Poland‡Universidad de Puerto Rico en Humacao, Estacidn Postal CUH 100 Carr.908, Humacao PR00791-4300, Puerto Rico§Universidad Metropolitans, P.O. Box 21150, San Juan 00928-21150, Puerto Rico∥Department of Chemistry and Biochemistry, Jackson State University, Jackson, Mississippi 39217, United States

*S Supporting Information

ABSTRACT: Density functional and Møller−Plesset second-order perturbation (MP2) calculations have been carried outon various model cation−π complexes formed through theinteractions of Mg2+, Ca2+, and NH4

+ cations with benzene, p-methylphenol, and 3-methylindole. Partial hydration of themetal cations was also considered in these model studies tomonitor the effect of hydration of cations in cation−πinteractions. The binding energies of these complexes werecomputed from the fully optimized structures using coupledcluster calculations including triple excitations (CCSD(T)) and Gaussian-G4-MP2 (G4MP2) techniques. An analysis of thecharge sharing between the donor (the π-systems) and the acceptors (the cations) together with the partitioning of totalinteraction energies revealed that the strong and weak cation−π interactions have similar electrostatic interaction properties.Further decomposition of such electrostatic terms into their multipolar components showed the importance of the charge−dipole, charge−quadrupole, and charge−octopole terms in shaping the electrostatic forces in such interactions. The computedvibrational spectra of the complexes were analyzed for the specific cation−π interaction modes and have been shown to containthe signature of higher order electrostatic interaction energy components (quadrupole and octopole) in such interactions.

I. INTRODUCTION

Cation−π interactions are noncovalent in nature and were firstpredicted by Kier and coworkers1,2 to be of ion-induced dipolecharacter (from theoretical modeling of acetylcholinesteraseinhibition reactions). These interactions were later establishedas cation−π type by Dougherty and coworkers,3,4 and sincethen it has emerged as a very common binding force tointerpret interactions between cations and aromatics inbiomolecular systems such as protein, receptor−ligandcomplexes, molecular recognition, drug action, and proteinfolding.3−9 The cation−π interactions are strong enough tocompete with the solvation of hydrophilic charged moieties andallow ligand−receptor binding in a hydrophobic pocketconstituted of aromatic residues within the core of thereceptor.8

Cation−π interactions could be classified into weak andrelatively stronger categories. The weak interactions of this classin biological systems usually involve a charged amino/OH2

+

group and the localized π-electron cloud of the aromatic aminoacids (viz. Phe, Trp, or Tyr).4 Several theoretical calculations aswell as experiments have shown that such interactions aremostly on the order of 14−20 kcal/mol (depending on thenature of the cationic part), and although further weaker in

aqueous medium these interactions could still be on the orderof 5 to 10 kcal/mol depending on the nature of hydration.5,10

The stronger cation−π interactions involve metal ions insteadof charged amino/OH2

+ groups, and for monovalent alkalimetals these interactions could be as strong as 45 kcal/mol.4,11

In recent times the interactions between H2B2 (3Σg

−) and metalions have been interpreted as cation−π type, and bindingenergies in such cases have been computed to be several ordersof magnitude higher than regular cation−π interactions of metalcations and aromatic systems.12 The cation−π interactionsinvolving metal dications (e.g., Ca2+, Mg2+, Zn2+, Cu2+, Fe2+,Mn2+, etc.) are more recent developments and have been foundto be important in the structure-modulation, reactivity, andfunctions of the metal binding sites of metalloproteins.13,14

Several divalent cations (e.g., Ca2+, Mg2+) have also been foundto stabilize the unstacked conformations of DNA and RNAthrough cation−π interactions with the bases.15

Cation−π interactions are mostly biological events occurringin proteins or nucleic acid systems and are assumed to occur

Received: April 29, 2013Revised: July 25, 2013Published: July 29, 2013

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due to attraction of the quadrupole created by π-electronclouds of the conjugated ring systems and the cations.4,5,16

Various models are available to interpret the nature ofelectrostatics in cation−π interactions.4 Kim and coworkers16

made a significant contribution in this direction through term-by-term computation of the multipolar electrostatic interactionenergy components in benzene···ammonium (and its methylderivatives) systems (up to charge-quadrupolar term) andfound that these interaction energy components are importantin cation−π interactions. This was also supported through

subsequent studies, although nonelectrostatic energy compo-nents are also important.4,5 The total electrostatic interactionscould be partitioned as the contribution of charge−charge,charge-dipole, charge−quadrupole, charge−octopole (consid-ering the cationic part to be composed of point chargesystems), and higher order terms.17 Although it has been shownthat the quadrupole term of the π-systems is responsible forsuch interactions,4,16 the role of the other electrostatic termsare not properly analyzed. Furthermore, if these electrostaticterms have significant contribution in such interactions, do they

Table 1. Calculated Interacting Distances (r, Å), Binding Energy (ΔEB), Enthalpy (ΔHB298), and Gibbs Free Energy (ΔGB

298) ofBinding (all in kcal/mol) of Various Cation−π Complexes at the DFT/B3LYP, MP2, CCSD(T), and G4MP2 Levels ofTheorya,b

cation−π complex methods rc,d ΔEBd ΔHB298d,e ΔGB

298d,e

benzene-Mg2+ DFT/B3LYP 1.95 −117.76 −118.36 −110.32(1.94) (−117.81) (−118.40) (−108.90)

MP2 1.96 −108.75 −109.71 −100.60(1.98) (−109.66) (−110.32) (−100.72)

CCSD(T) 1.96 −109.00G4MP2 1.92 −117.97 −118.56 −109.40

p-methylphenol-Mg2+ DFT/B3LYP 1.94 −129.68 −130.45 −121.22MP2 1.95 −119.51 −120.63 −110.88CCSD(T) 1.95 −119.51G4MP2 1.91 −129.14 −129.74 −119.44

3-methylindole-Mg2+ DFT/B3LYP 1.90 −145.67 −146.82 −137.81MP2 1.91 −140.18 −136.72 −126.83CCSD(T) 1.91 −135.26G4MP2 1.87 −145.30 −145.89 −137.26

benzene-Ca2+ DFT/B3LYP 2.46 −82.90 −81.44 −73.39(2.36) (−81.59) (−82.26) (−73.06)

MP2 2.47 −68.60 −69.37 −59.55(2.46) (−69.43) (−69.93) (−60.71)

CCSD(T) 2.47 −68.53G4MP2 2.35 −80.20 −80.80 −71.99

p-methylphenol-Ca2+ DFT/B3LYP 2.45 −94.41 −90.98 −82.28MP2 2.45 −74.81 −75.61 −66.52CCSD(T) 2.45 −74.20G4MP2 2.32 −89.07 −89.66 −79.84

3-methylindole-Ca2+ DFT/B3LYP 2.40 −103.96 −104.39 −96.23MP2 2.40 −90.15 −91.12 −81.73CCSD(T) 2.40 −89.53G4MP2 2.27 −103.79 −104.38 −96.07

benzene-NH4+ DFT/B3LYP 3.02 −14.95 −15.71 −5.40

(3.00) (−15.05) (−14.78) (7.47)MP2 2.99 −16.95 −16.97 −8.91

(2.89) (−17.46) (−17.32) (−11.04)CCSD(T) 2.99 −16.06G4MP2 2.92 −17.16 −17.76 −10.29

p-methylphenol-NH4+ DFT/B3LYP 3.09 −16.84 −18.28 −5.63

MP2 2.99 −18.95 −19.03 −9.98CCSD(T) 2.99 −17.95G4MP2 2.90 −19.26 −19.28 −9.71

3-methylindole-NH4+ DFT/B3LYP 2.99 −21.30 −21.16 −12.72

MP2 2.90 −23.70 −23.90 −14.60CCSD(T) 2.90 −22.50G4MP2 2.87 −23.91 −24.50 −15.51

aCalculated energies (i.e., ΔEB, ΔHB298, and ΔGB

298) are after BSSE and zero-point energy (ZPE) corrections. bEnergy values at the DFT/B3LYP,MP2, and CCSD(T) levels are computed using aug-cc-pvdz basis set of atoms (see the text for details). cDistance r is defined as the distance betweenthe cation/cation center and the center of mass of hexagonal carbon ring system (excluding hydrogen or any substituent, see Figure 1). dValues forfully optimized structures (using aug-cc-pvdz basis set) are presented within parentheses. eSuperscript 298 indicates the temperature (K) of ΔHB

298

and ΔGB298 calculations.

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behave similarly in both the strong and weak interaction cases?Could the electrostatic behavior of such cation−π complexes beconnected to any observable properties (molecular/spectro-scopic)? The aim of the present manuscript is to seek answersto these questions using several model cation−π complexes(both strong and weak types). The estimation of electrostaticcontribution in our investigation would require reliablecomputation of binding energies and vibrational frequenciesof the various cation−π complexes.In the present work, we have designed our model π-electron

systems as benzene, p-methylphenol, and 3-methylindole.Benzene is the reference molecule because several cation−πinteraction calculations have been carried out on this standardπ-system and the last two molecules are the standard modelaromatic systems for tyrosine and tryptophan.5,18,19 Thesubstituent effect on the π-cloud and its consequence oncation−π interactions could also be visualized through suchmodel molecules. The interactions of these aromatic systemswere investigated against NH4

+, Mg2+, and Ca2+ ions usingdensity functional (DFT)20 and Møller−Plesset second orderperturbation (MP2)21 theories. The strong cation−π inter-actions were further investigated using the hydrated forms ofthe metal cations. We have computed the structure, vibrationalcharacteristics, binding energies, and related thermodynamicquantities of binding (viz., Gibbs free energy and enthalpy) atthese levels of theory and have further validated the resultsusing G4MP2 and coupled cluster computations. Theinteractions (both gas-phase and hydrated forms) are primarilyanalyzed through a hybrid variational-perturbational interactionenergy decomposition scheme at the Hartree−Fock level.17,22

The electrostatic interaction energy terms of the gas-phasestructures are further analyzed to generate the contribution ofthe multipolar electrostatic energy terms. In the final part of themanuscript, the vibrational spectra of the cation−π complexesare analyzed, and it would be shown that the modesrepresenting cation−π interactions could be correlated withthe nature of electrostatic forces operating to stabilize suchcomplexes.

II. METHODS OF COMPUTATION

Structures of the gas-phase cation−π complexes were initiallyinvestigated at the DFT and MP2 levels of theory using 6-31+g(d) basis sets. The B3LYP functional23−25 was used in theDFT calculations. The hydrated metal cation (Mg2+ andCa2+)−π complexes were investigated at the DFT/B3LYP levelusing 6-31++g(d,p) basis sets for such studies. The extra diffuseand polarization functions properly take care of the waterinteractions in such cases. The geometry of the complexes wasfully optimized and the minimum energy structures in therespective cases were confirmed through frequency calculations.The results were used to compute the binding energies (ΔEB),enthalpy (ΔHB

298), and Gibbs free energy (ΔGB298) of binding

(at 298 K) of the respective complexes with counterpoise (CP)and zero-point energy (ZPE) corrections. The raw bindingenergies (before CP and ZPE corrections) were calculated fromthe difference between the total energy of the complexes andthe sum of total energies of the corresponding isolated cationsand the aromatic moieties. All of the species were considered intheir respective equilibrium geometries, and in the case ofcations Mg2+ and Ca2+ it was made sure that they were in theirrespective ground electronic states (1S0). The calculations ofthermodynamic properties have been carried out by applying

the ideal gas, rigid rotator, and harmonic oscillator approx-imations.26

The computed energy values of the gas-phase clusters werefurther refined using single-point energy calculations on theoptimized structures at the DFT/B3LYP and MP2 levels usingthe aug-cc-pvdz basis set of atoms. The respective ΔHB

298 andΔGB

298 values were approximated from the computed values atthe DFT/B3LYP/6-31+g(d) and MP2/6-31+g(d) levels usingthe following relation 1.

Δ = Δ ‐ + + Δ ‐ ‐

− Δ ‐ + =

X X E

E X H G

(6 31 g(d)) [ (aug cc pvdz)

(6 31 g(d))] ( , )298B

298B B

B(1)

The second term in eq 1 reduces the basis set incompletenesserror of smaller 6-31+g(d) basis (due to the use of morecomplete aug-cc-pvdz basis sets) and hence improves thecomputed ΔX298

B. We have previously used this technique tomodify the binding energies quite satisfactorily.27 The resultsderived from eq 1 in the present manuscript have been furthercalibrated against the fully optimized data of the benzene···Mg2+, benzene···Ca2+, and benzene···NH4

+ complexes using thesame aug-cc-pvdz basis sets (see Section III.a, Table 1). Thebinding energies of the hydrated complexes were modifiedusing similar approximation of eq 1 from the results of DFT/B3LYP/6-31++g(d,p) calculations. A single-point coupled-cluster calculation with triple excitations (CCSD(T))28 usingaug-cc-pvdz basis sets was carried out on the MP2-optimizedgeometries of the complexes (the DFT/B3LYP geometry in thecase of hydrated complexes) to improve accuracy of thecomputed binding energies (ΔEB). These ΔEB values are bothZPE- and BSSE-corrected. The ZPE corrections of ΔEB at theCCSD(T) level were carried out using the ZPE values fromMP2 (DFT/B3LYP values in the case of hydrated complexes)results. The reliability of the computed energies was furthergauged against the results from G4MP229 technique.A hybrid variational−perturbational interaction energy

decomposition scheme21 was used to compute the contribu-tions of various energy terms in such interactions. The SCFinteraction energy is partitioned into first-order electrostatic(εel

(10)), Heitler−London exchange (εex(HL)), and higher order

delocalization (ΔEdelHF) energy terms.

ε εΔ = + + ΔE EHFel(10)

exHL

delHF

(2)

The electron correlation effects are taken into account bymeans of the MP2 theory. The εMP

(2) interaction energy term,which includes the dispersion and correlation contributions tothe Hartree−Fock components, is calculated in the super-molecular approach as the difference of MP2 energy correctionsof the supermolecule and the monomers (eq 3).

ε = − −E E EMP(2)

AB(2)

A(2)

B(2)

(3)

The energy terms on the right-hand side of eq 3 represent thedifference between the MP2 and Hartree−Fock energies of thesupermolecule (AB) and the monomers (A and B).All of the interaction energy terms are calculated consistently

in the dimer-centered basis set and are therefore free from thebasis-set superposition error due to the full CP correction. Thecontribution of the multipolar electrostatic interactions in thecation−π complexes has been carried out using the distributedatomic multipolar expansion of the charge distributions ofmonomers.22 The multipolar expansion technique is based onthe numerically equivalent spherical harmonic formulations of

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Stone et al.30,31 The optimized structures at the MP2 level(optimized DFT/B3LYP structures in the case of hydratedmetal ion clusters) were used to generate the electrostaticinteraction energy surfaces (using aug-cc-pvdz basis sets). It isto be noted in this connection that the results of energydecomposition calculations, which would be presented here, arenot rigorous because there is an element of arbitrariness in anyof such decomposition schemes.The geometry optimization and frequency calculations at the

DFT/B3LYP and MP2 levels were carried out using Gaussian09 code.32 The interaction energy decomposition schemeimplemented in the GAMESS code33 was used for energypartitioning analyses and computation of the multipolarcomponents of the total electrostatic interaction energies.34

The molecular graphics have been generated using GaussView05 software.35

III. RESULTS AND DISCUSSIONIII.a. Structures and Energetics of the Cation−π

Complexes. The results of geometry optimization of variousgas-phase cation−π complexes are shown in Table 1 togetherwith their respective binding energy values (ΔEB, ΔHB

298, andΔGB

298) and optimal distances (r) between the cation centerand the aromatic nucleus. The distance is measured betweenthe cation center and the center of mass (CM) of the aromaticnucleus of the various π-systems. Only the carbon centers ofthe aromatic part are considered for CM calculations, and thestrategy is shown schematically in Figure 1. The optimized

structures are shown in Figure S1 of the SupportingInformation. The results show that the Mg2+ and Ca2+ ionsform very strong cation−π complexes and Mg2+ ion−complexesare more strongly bound than their Ca2+ ion counterparts. Theinteractions are also dependent on the effect of substitution onthe aromatic moieties. The cation−π interactions are thestrongest with 3-methylindole, and they follow the order 3-methylindole > p-methylphenol > benzene in both the classes

(strong and weak) of interactions studied here (Tables 1 and2).The computed binding energies are dependent on the levels

of theory used. The DFT/B3LYP and G4MP2 results agreequite well as the basic geometry optimization procedures aresimilar (use B3LYP functional). The MP2 and CCSD(T)results generate a lower estimate of binding energies, and theyagree in most of the cases (Table 1). We have tested thereliability of the computed ΔEB at different levels against theexperimental results of the benzene···Na+ complex. Theexperimental ΔEB of benzene···Na+ complex is available fromtwo different sources. They are −92.6 ± 5.8 kJ/mol (−22.2 ±1.4 kcal/mol)36 and −88.3 ± 4.3 kJ/mol (−21.1 ± 1.03 kcal/mol),37 respectively. We have carried out DFT/B3LYP, MP2,and G4MP2 calculations on this complex at the same basis-setlevels of the corresponding Mg2+ and Ca2+ complexes (Table1), and the results revealed that the respective ΔEB values at thethree levels are −23.5, −20.0, and −25.14 kcal/mol. The resultsshow that B3LYP and G4MP2 generate the upper limit, whileMP2 computations generate the lower limit of ΔEB(considering the error bar of the experiment). The computedΔGB

298 values (DFT/B3LYP: −14.3 kcal/mol; MP2: −12.3kcal/mol; G4MP2: −17.1 kcal/mol) also show a similar trendwith respect to the estimated ΔGB

298 (−15.3 ± 1.96 kcal/mol)from the experimental data.36 The previously computed38 ΔEBvalues of benzene···Mg2+ (CCSD(T): −109.2 kcal/mol, MP2:−114.4 kcal/mol) and benzene···Ca2+ (CCSD(T): −71.5 kcal/mol, MP2: −80.6 kcal/mol) complexes were used for furthercalibration. These computed ΔEB values are comparable to ourpresent results at the CCSD(T) level (Table 1), while ourresults at the MP2 level are underestimated (Table 1). Thecomputed ΔEB values at the G4MP2 level (Table 1) are againcomparable to the previously computed38 MP2 results.The interactions of NH4

+ ion with all three of aromatics havebeen previously studied (both experimentally and theoret-ically).4,5,10,16 The structure calculations in the present caseshave been carried out using the bidentate orientation of NH4

+

ion over the aromatic moieties (Figure S1 of the SupportingInformation) because the previous studies showed thisorientation to be the most favorable one for such cases.5,10,18

In the case of benzene···NH4+ complex, the results at different

levels show that MP2 (−17.5 kcal/mol), CCSD(T) (−16.1kcal/mol), and G4MP2 (−17.2 kcal/mol) computationsproduce similar ΔEB values (Table1) comparable to previoustheoretical results.16,39,40 The computed ΔHB values are alsosimilar (MP2: −17.32 kcal/mol; G4MP2: −17.8 kcal/mol) andcomparable to the experiment (ΔHB

298: −19.3).41 The DFT/B3LYP generates a somewhat lower estimate of both ΔEB andΔHB (−15.1 and −15.7 kcal/mol, respectively, Table 1) values.It was also previously observed that higher basis setsystematically underestimates the computed binding energyvalues of benzene···NH4

+ complex at the DFT/B3LYP andCPMD computation levels, and the results of CPMDcomputations with 100 Ry cutoff match with our presentDFT/B3LYP results (r: 3.05; Å; ΔEB: −15.4 kcal/mol).42

The interaction of NH4+ ion with p-methylphenol and 3-

methylindole is stronger than benzene. The computed bindingenergies at the MP2 and CCSD(T) levels are similar to theprevious results.5 The G4MP2 technique predicts somewhatstronger binding. In all of these computations, the NH4

+ ionprefers an orthogonal orientation above the aromatic nucleus.Such orientation of the cation with respect to the aromatic ringleads to the overlap of the π and σ*N−H orbitals. In a geometric

Figure 1. Schematic representation of the cation−π complexes for (a)benzene, (b) p-methylphenol, and (c) 3-methylindole. The greensphere represents the position of the cations (Mg2+, Ca2+, NH4

+,Mg(H2O)2

+2, and Ca(H2O)2+2) and the red sphere represents the

position of the center of mass (CM). The CM is computed using thecarbon atoms of the six-member aromatic π-system (as indicated bythe gray spheres). The distance r is measured between the CM and thecation center. The optimized structures of the individual complexes areavailable in Figures S1 and S2 of the Supporting Information.

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sense this would lead to dissimilar N−H bond lengths and H−N−H angles. These are depicted in Figure S3 (SupportingInformation) for the geometries computed at the DFT/B3LYPand G4MP2 levels. The slight elongation of the N−H lengthalong the direction of the π-system and distortion of thecorresponding H−N−H angle (with respect to the other H−N−H angle − not pointing to the π-system) show the overlapof the aromatic π and N−H antibonding orbitals. In all of theseNH4

+···π interactions, the nitrogen center remains negativelycharged. The positively charged hydrogen atoms of NH4

+

interact with the π-cloud of the aromatic counterpart. This isconsidered to be a general characteristic of the electrostaticmodel of cation−π interactions.43

The hydration of the cationic part influences the bindingstrength as well as the geometric pattern of the cation−πcomplexes. The data analysis from protein data bank hasrevealed that the cation−π interactions are usually stabilizedthrough stacked interactions.13,14 In the present paper ourinterest is, of course, different. The focus here is to investigatethe influence of cation hydration on the gas-phase bindingenergies of the model cation−π complexes, and we intend tomodel it using the complexes involving Ca2+ and Mg2+ cations.Previously, similar cases of weak complexes involving NH4

+ andN(CH3)4

+ cations were investigated,10,18,19 and substantialreduction in the strength of cation−π interactions was observeddue to hydration of the cations.The Mg2+ and Ca2+ ions are known to form octahedral

Mg(H2O)62+, and Ca(H2O)6

2+ complexes in their fullyhydrated (first hydration shell) forms.44 Although hydratedmetal ion clusters are known to stabilize the cation−πinteractions through stacking effects, the individual bindingenergies in such cases are found to be quite low in comparisonwith the gas-phase complexes.14 Because our present goal is toinvestigate the effect of hydration on the gas-phase structures ofstrong cation−π complexes (as discussed here), we restrict ourhydrated model systems to Mg(H2O)2

2+ and Ca(H2O)22+

interacting with the π-aromatic systems. The results ofgeometry optimization of such complexes are shown in Table2 together with their computed binding energies and optimizeddistances (r, as defined in Figure 1). The optimized structuresare shown in Figure S2 (Supporting Information). The resultsshow that the hydration of the metal ions substantially reducesthe strength of the cation−π interactions. Moreover, thehydrated p-methylphenol···M(H2O)2

2+ (M: Mg, Ca) complexesshow the formation of weak hydrogen bonds between phenolic-oxygen and one of the hydrogen atoms of the water ofhydration (Figure S2 of the Supporting Information). Thus theinteractions are not fully cation−π-type in these two cases. Thecomputed binding energy (ΔEB, ΔHB

298, and ΔGB298) trend

shows that the CCSD(T) computations slightly improve themover the DFT/B3LYP results. This is understandable, as theCCSD(T) results are obtained using the optimized structuresfrom the DFT/B3LYP analysis. The binding energy improve-ment is due to the higher correlation effect of CCSD(T)technique. The G4MP2 computations, on the other hand,estimate these values on the higher side, as the calculated rvalues in various complexes are shorter than those computed atthe DFT/B3LYP level.The distance (r) between the metal cation and the aromatic

systems is presented in the Tables 1 and 2 and is much shorterand stronger with respect to those in proteins and nucleic acidsystem because in such cases the metal ions are furthercoordinated to the other ligands.13,45,46 For example, in the caseof 3-methylindole···Ca2+, the computed distance between themetal ion and the aromatic moiety is ∼2.40 Å in the optimizedstructure (Table 1), while it is 3.37 Å in the metalloproteinSBA,46 with tilted orientation of the metal ions due tocoordination with other moieties. In the case of NH4

+

complexes (Tables 1 and 2), although the computed distancesand interaction energies are similar to the previous stud-ies,5,10,16,18 they are not pure cation−π types in the realbiological systems. For example, our previous investigations on

Table 2. Calculated Interacting Distances (r, Å), Binding Energy (ΔEB), Enthalpy (ΔHB298), and Gibbs Free Energy (ΔGB

298) ofBinding (all in kcal/mol) of Various Dihydrated Cation−π Complexes at the DFT/B3LYP, CCSD(T), and G4MP2 Levelsa,b

dihydrated complexc method rd ΔEB ΔHB298e ΔGB

298e

benzene-Mg2+ DFT/B3LYP 2.09 −65.97 −65.80 −56.82G4MP2 2.07 −71.68 −72.27 −62.39CCSD(T) 2.09 −66.87

p-methylphenol-Mg2+ DFT/B3LYP 2.07 −73.75 −73.88 −61.25G4MP2 2.04 −80.59 −81.19 −68.54CCSD(T) 2.07 −74.85

3-methylindole-Mg2+ DFT/B3LYP 2.05 −85.83 −85.76 −74.04G4MP2 2.02 −92.66 −93.25 −81.53CCSD(T) 2.05 −87.16

benzene-Ca2+ DFT/B3LYP 2.55 −56.30 −53.31 −45.02G4MP2 2.46 −55.98 −56.57 −47.63CCSD(T) 2.55 −60.10

p-methylphenol-Ca2+ DFT/B3LYP 2.55 −60.55 −60.75 −47.45G4MP2 2.44 −64.86 −65.45 −51.76CCSD(T) 2.55 −65.20

3-methylindole-Ca2+ DFT/B3LYP 2.48 −70.93 −70.57 −59.76G4MP2 2.38 −73.62 −74.21 −63.74CCSD(T) 2.48 −78.60

aCalculated energies (i.e., ΔEB, ΔHB298, and ΔGB

298) are after BSSE and zero-point energy (ZPE) corrections. bCalculated energy values at theDFT/B3LYP and CCSD(T) levels are using aug-cc-pvdz basis set of atoms. (See the text for details.) cRefer to Figure S2 in the SupportingInformationfor the structures of the dihydrated cation−π complexes. dSee Table 1 and the text for the definition of r. eSuperscript 298 indicates thetemperature (in K) of ΔHB

298 and ΔGB298 calculations.

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the nature of interactions of acetylcholine (Ach) within theacetylcholinesterase (AchE) active cavity showed that thequaternary ammonium interactions of Ach to the Tyr-121residue of the AchE cavity are of cation−π-type, albeit otherinteractions are also involved there (due to the surroundingamino acid residues).47 Thus the further interaction energyanalyses of the present model systems (which are continued inthe next section) should generally be valid in ideal cases, butthe results could be extended for the basic understanding ofcation−π interactions.III.b. Nature of Cation−π Interactions in Strong and

Weak Complexes. Table 3 presents the interaction energycomponents of the strong (involving Mg2+ and Ca2+) and weak(NH4

+) cation−π interactions at the HF level. Similar analysesfor the dihydrated metal ion complexes are shown in Table 4.The Tables also contain the contribution of the εMP

(2) term, asrepresented in eq 2. It could be seen that in both gas-phase andhydrated metal ion complexes the contribution of εMP

(2) term isnot important for too-strong cation−π interactions becausethey have repulsive contribution in such cases. For the relativelyweaker interactions, this term has some contribution to thetotal interactions (indicated by the computed negative value ofεMP

(2)) (Tables 3 and 4). In the case of NH4+ complexes (Table

3), of course, this term contributes significantly to the totalinteraction energies. The main attractive contributors to thetotal interaction energies are electrostatic (εel

(10)) anddelocalization (ΔEdel

HF) energies. Some part of these attractiveinteraction energies is offset by the exchange-repulsion term(εex

HL), but still the electrostatic contribution plays a significantrole in the stabilization of the cation−π complexes. Moreover,the optimized structures of the cation−π complexes of Mg2+

and Ca2+ show substantial charge sharing (Δq) from the

aromatic systems to the cation (Table 5). This Δq is much lessin the NH4

+ complexes but not insignificant. A plot of Δqagainst ΔEB (Figure 2) shows that they are linearly correlatedand ΔEB increases with higher charge sharing. Such correlationsshow that forces involving strong and weak cation−πcomplexes have similar electrostatic origin, hence the need toanalyze the importance of various electrostatic interactioncomponents in such complexes.The contribution of the multipolar components of electro-

static terms in cation−π interactions was investigated in somedetail in previous studies.6 The strong electron sharing in thecomplexes shows that they might have considerable influence inshaping the contribution of total electrostatic interactionsbetween the donors and the acceptors. Figures 3 and 4represent the natures of various multipolar components of theelectrostatic interaction energies in Mg2+, Ca2+, and NH4

+

complexes as a function of r (defined in Figure 1). The totalelectrostatic interaction energies (T-El) together with charge−charge (C−C), dipole-charge (D−C), quadrupole-charge (Q−C), and octopole−charge (O−C) components were found tobe important and are presented in the Figures. The influencesof the other multipolar components were found to benegligible. The results show that the total interaction energycurves, with few exceptions, are either repulsive or dispersive innature. The T-El curve of Mg2+ complexes is bound (i.e., havinga minimum), while the similar curves for the Ca2+ complexesare dispersive for benzene and 3-methylindole (Figure 3a,c). Inthis respect, the interactions of p-methylphenol···Ca2+ show aweak minimum (Figure 3c). The nature of the curvesrepresenting the Q−C and O−C components of both thecomplexes as represented in Figure 3b,d shows that they haveeither repulsive or attractive contributions to the total

Table 3. Two-Body Interaction Energy Decomposition Components (aug-cc-pvdz, kcal/mol) of Various Gas-Phase Cation−πComplexes in Their Equilibrium Geometry

interaction energy componentsa

cation−π complexesb εel(10) εex

HL ΔEdelHF ΔEHF εMP

(2)c

benzene-Mg2+ −41.99 28.44 −105.87 −119.42 6.63p-methylphenol-Mg2+ −48.46 30.87 −113.92 −131.50 4.603-methylindole-Mg2+ −54.07 33.40 −124.51 −145.18 3.49benzene-Ca2+ −36.66 26.75 −67.76 −77.66 −0.36p-methylphenol-Ca2+ −40.99 28.44 −73.68 −86.23 −2.123-methylindole-Ca2+ −47.85 32.03 −82.43 −98.26 −3.51benzene-NH4

+ −14.82 12.85 −11.61 −13.58 −4.44p-methylphenol-NH4

+ −15.86 14.70 −14.07 −15.24 −5.293-methylindole-NH4

+ −19.11 14.99 −13.85 −17.97 −6.13aSee the text for the definition of the energy components. bSee Table 1 and Figure S1 in the Supporting Information for the definition of thecomplexes. cDispersion and correlation contribution as defined in eq 3 of the text.

Table 4. Two-Body Interaction Energy Decomposition Components (aug-cc-pvdz, kcal/mol) of Various Dihydrated Cation−πComplexes in Their Equilibrium Geometry

interaction energy componentsa

cation−π complexesb εel(10) εex

HL ΔEdelHF ΔEHF εMP

(2)c

benzene-Mg2+ −32.82 23.26 −67.53 −77.09 1.39p-methylphenol-Mg2+ −39.95 26.97 −71.84 −84.83 −0.773-methylindole-Mg2+ −44.77 28.15 −79.12 −95.74 −1.50benzene-Ca2+ −29.49 20.36 −46.28 −55.41 −2.02p-methylphenol-Ca2+ −38.61 26.22 −50.32 −62.71 −4.933-methylindole-Ca2+ −42.63 25.48 −52.52 −69.66 −3.34

aSee the text for the definition of the energy components. bSee Table 2 and Figure S2 in the Supporting Inforamtion for the definition of thecomplexes. cDispersion and correlation contribution as defined in eq 3 of the text.

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electrostatic interactions in a significant way around theequilibrium r values, thus revealing the importance of suchinteractions in strong cation−π complexes. The D−C and (C−C) components of these metal complexes also behave similarly

(Figure 3a−d) to mostly offset the attractive components togenerate overall shape of the T-El curves.The curves representing the electrostatic components of the

cation−π complexes of NH4+ ion show an altogether different

nature (Figure 4). The D−C components are bound aroundthe equilibrium r for all of the three complexes. The rest of thecomponents around the equilibrium r behave in such a way thatthe T-El are dispersive (contributing attractive T-El around theequilibrium position, Table 3), although such componentssometimes show bound character at larger r (not of muchsignificance here). The curves representing the electrostaticinteraction energy components of the dihydrated metal ions(Mg2+ and Ca2+) with various aromatic systems (studied here)are more or less similar to the nonhydrated cases (shown inFigure 3). These curves are shown in Figure S4 of theSupporting Information. Only the C−C electrostatic inter-action energy component of the complexes of dihydrated metalions (both Mg2+ and Ca2+) and p-methylphenol showsomewhat deeper potential minima with respect to thecorresponding nonhydrated complexes. This is probably duethe possibility of hydrogen bond formation in such structures(Figure S2 of the Supporting Information). The differences ofthe nature of the curves of NH4

+···aromatic complexes (Figure4) with respect to those of the metal ion complexes (Figure 3)could be due to the anisotropic potential expansion of theNH4

+ ion. Although dihydrated metal ions are expected to havesome anisotropic character in this respect, the curves show theyare not strong enough to make too much difference withrespect to nonhydrated cases (where the metal ions are strictlyisotropic).Thus it is evident from these curves that the multipolar

components of electrostatic interactions play a major role in theformation of the cation−π complexes and the nature ofinteractions in such complexes (as is evident from the shape ofthe curves in Figures 3 and 4 and Figure S4 of the SupportingInformation) depends on the substituents of the aromaticmoiety. These substituents are responsible for the chargesharing (or electron flux) from the aromatic moiety to thecation, thus contributing to the stabilizing forces of thecation−π complexes.

III.c. Computed Cation−π Vibrational Modes andTheir Relation to Electrostatic Interaction Components.The nature of the stabilizing forces in cation−π complexes, asanalyzed in the previous section, does not have any directexperimental evidence. The signature of such electrostaticeffects could, of course, be predicted from analyses of theproper cation−π vibrational modes. Two different modes couldbe identified to contain the signature of cation−π interactionsin lower frequency range, viz. intramolecular stretchingfrequency (Sz: up and down motion of the cation combinedwith the out-of-plane twist of the aromatic moiety) and the out-of-plane CH bend (νopCHb) of the π-system.

47 The latter one iscalculated to be highly infrared (IR)-active and exhibitscharacteristic blue shift (ΔνopCHb) with respect to the similarmode of the bare π-system. The calculated frequenciesinvolving these two modes (together with their respective IRintensities) for the various cation−π systems are presented inTable 5. A plot of the ΔEB of these complexes against theirrespective Sz modes (Table 5) show that they are linearlycorrelated (Figure 5a). The ΔνopCHb does not have such ageneral correlation with ΔEB values (Figure 5b). The linearcorrelation of ΔνopCHb with the ΔEB is dependent on the π-systems (but independent of the cations), although it clearly

Table 5. Calculated Charge Shift to the Cation (Δq),Intermolecular Stretching Frequency (Sz, cm

−1), and BlueShift of the Out-of-Plane CH Bend (ΔνopCHb, cm−1) at theG4MP2 Levela,b

cation−π complex Δqc Sz ΔνopCHbd

benzene···Mg2+ 1.02 364 (68.0) 99.0 (76.1)p-methylphenol···Mg2+ 1.09 379 (69.0) 75.6 (68.0)3-methylindole···Mg2+ 1.13 390 (72.2) 85.3 (52.0)benzene···Ca2+ 0.63 267 (47.3) 49.0 (81.3)p-methylphenol···Ca2+ 0.70 286 (45.6) 68.0 (49.9)3-methylindole···Ca2+ 0.74 298 (66.7) 77.0 (31.7)benzene···Mg(H2O)2

2+ 0.74 248 (17.4) 83.1 (68.8)p-methylphenol···Mg(H2O)2

2+ 0.78 264 (14.1) 70.2 (60.1)3-methylindole···Mg(H2O)2

2+ 0.82 273 (16.2) 79.5 (52.3)benzene···Ca(H2O)2

2+ 0.40 204 (14.5) 65.9 (53.3)p-methylphenol···Ca(H2O)2

2+ 0.55 218 (12.1) 62.0 (45.1)3-methylindole···Ca(H2O)2

2+ 0.58 228 (15.0) 63.9 (35.8)benzene···NH4

+ 0.14 174 (3.5) 34.8 (27.3)202 (77.0)e

p-methylphenol···NH4+ 0.15 207 (11.0) 31.4 (30.8)

222 (63.9)e

3-methylindole···NH4+ 0.16 221 (22.0) 34.4 (18.1)

202 (38.7)e

aRespective IRI and intensity enhancements for Sz and νopCHb are alsoincluded in the Table (within parentheses). bThese values at theG4MP2 level are extracted after the optimization step. Obviouslyresults are from DFT/B3LYP optimized geometries using high-levelbasis set (as prescribed in the G4MP2 method). cΔq values arecalculated from the Mulliken population analysis results. The Mullikencharges considered here could be expected to some error bars, as inmany cases elements of different rows are involved. dΔνopCHb and thecorresponding intensity increments are computed using the results ofthe respective π-systems of the cation−π complexes. eThese alternatefrequencies also resemble Sz modes of the respective cation−πcomplexes, but the respective intensities do not reflect the ΔEBcomplexes nor do they show any linear correlation with respect tothe other ΔEb values (as discussed in Figure 2). Thus they are notfurther discussed in the text.

Figure 2. Correlation of Δq (see Table 5) with the respective ΔEB ofvarious cation−π complexes.

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distinguishes between strong and weak interactions in a specificπ-system. The IR intensities (IRI) of the respective modes alsoshow linear changes with respect to the binding energies of thecation−π complexes (Figure 5c,d). The linearity is not alwaysas good as those in the corresponding frequency cases, but thechange of IRI for the respective modes could be seen to bemore or less regular with respect to the corresponding ΔEB ofthe complexes.It is well known that IRI is proportional to the square of the

magnitude of the dipole derivative, and it has been recentlyshown that intensity enhancement of a particular modeshowing the interactions of constituent components in aweak complex is proportional to the charge flux involving thecounterpart molecule/molecules in such a complex.46 In thepresent complexes, the enhancement of IRI of the νopCHb modescould be related to the measure of intermolecular charge flux,like the previously studied hydrogen bonded complexes.48

These IRI could also be shown to bear the signature of higherorder moment contributions through a simple analysis of the ofthe total energy of the complex. Following the treatment ofQian and Krimm for hydrogen-bonded systems,49 we considerthe present cation−π complexes in simple Onsagar reactionfield. Such a constant external field is being created by theacceptor atoms of the complexes.The total energy (E) of the molecular system in such a

homogeneous electric field (V) could be written as50,51

μ α β γ= − − −!

−!

··· − ∇ ··· − ∇ ···

− ∇

E E V VV VV V VV V V

A V V B VV V

C V V

12

13

14

13

16

115

i i ij i j ijk i j k ijkl i j k l

i jk i jk ij kl i j kl

i jkl i jkl

00

, ,

,2

(4)

E0 denotes the energy without any external perturbation. Theterms μ0 and α denote dipole moment and polarizability, β andγ are the higher order polarizabilities, Ai,kj is the dipole−dipole-quadrupole hyperpolarizability, and Bij,kl and Ci,jkl are dipole−quadrupole and dipole−octopole polarizabilities, respectively.The subscripts i, j, k, and l are the ranks of these tensorial terms.The dipole moment μi generated in the electric field V isdefined as

μ = − ∂∂

EVi

i (5)

Thus, using eq 4, μi could be written as50,51

μ μ α β γ= + + + ··· + ∇ ···

+ ∇ ··· + ∇ ···

V V V V V V A V

B V V C V

12

16

13

13

115

ij j ijk j k ijkl j k l i jk kj

ij kl j kl i jkl jkl

0,

, ,2

(6)

Figure 3. Plots of total electrostatic interaction energies (T-El) and its other multipolar components as a function of r (defined in Figure 1) for thecomplexes of Mg2+ and Ca2+ ions with benzene (Bz), p-methylphenol (PMP), and 3-methylindole (3MI). Panels a and b represent the curves for theMg2+ complexes, while panels c and d are for the Ca2+ ion complexes. In the Figures, C−C, D−C, Q−C, and O−C represent the multipolarelectrostatic interaction energy components (C−C: charge−charge; D−C: dipole−charge; Q−C: quadrupole−charge; O−C: octopole−charge).

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Similar higher order induced moment terms are neglectedbecause they are quite unlikely to contribute in such a weakfield. If Q represents the relevant normal coordinates, then thederivative of μl with respect to Q is given by

μ μ α β

α β

∂∂

=∂∂

+∂∂

+∂

∂···

+∂∂

+∂∂

+ ···

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜

⎞⎠⎟

Q Q QV

QV V

VQ

VQ

V

12

i i ijj

ijkj k

iji

ijki

k

0

(7)

Here Q could be defined as representing the normalcoordinates of the cation−π mode. The enhancement of IRIof a particular mode in cation−π complex could be measuredfrom the change in dipole derivative defined as:

μ μ μ∂ ∂∂

= ∂∂

− ∂∂

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟Q Q Q

complex isolated (8)

The enhancement of IRI is directly measurable from theintensities of νopCHb modes of the complex and the isolatedspecies, and they bear linear relation with the ΔEB of thecomplexes (Figure 5d). It has already been demonstrated that(∂μ/∂Q) is directly related to the charge flux.48 Thus the

combination of eqs 6−8 reveals that this charge flux during thecation−π complex formation has contributions from the dipolemoment, polarizability, and higher order polarizabilites andhence from the higher order moments. The combinedproperties of the eqs 7 and 8 further prove that the multipolarcomponents of electrostatic interactions play an important rolein the stabilization of cation−π complexes because the ∂(∂μ/∂Q) term is related to the ΔEB of such complexes. It is to benoted that although Q−C and O−C interactions are present inthe cation−π complexes the possibility of detecting suchcontributions from experiment (except indirect IR intensityevidence) is quite slim. The quadrupolar effects could beobserved in some cases from the polar plots of the hyperRayleigh scattering intensities52 (if the complexes satisfy thenecessary conditions for such observation), but the presence ofO−C contribution is conceivable from theoretical viewpointonly.

■ CONCLUSIONSTheoretical investigation has been carried out on several strongand weak cation−π complexes to monitor the nature ofelectrostatic forces, which contribute to the stabilization of suchcomplexes in the gas phase. Three model π-systems, viz.benzene, p-methylphenol, and 3-methylindole, are chosen to

Figure 4. Plots of total electrostatic interaction energies (T-El) and their multipolar components as a function of r (defined in Figure 1) for thecomplexes of NH4

+ ion with benzene (Bz) (a), p-methylphenol (PMP) (b), and 3-methylindole (3MI) (c). See Figure 3 for the definition of thecurves representing the cases of C−C, D−C, Q−C, and O−C.

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bind Mg2+, Ca2+, and NH42+ ions. These investigations also

included partially hydrated (dihydrated) metal ions to monitorthe effect of hydration on the strong cation−π interactions. Thestructure of the complexes has been optimized initially at theDFT/B3LYP and MP2 levels with further modification of thefinal binding energies (ΔEB, ΔHB

298, and ΔGB298) using

CCSD(T) and G4MP2 techniques. It is observed that thecation shares electronic charges (Δq) from the π-systems andthe computed Δq of various complexes is linearly correlatedwith their ΔEB. This result shows that both the strong and weakcation−π interactions have similar electrostatic origin. Thedecomposition of interaction energies of the complexesrevealed that the electrostatic component of interactions isimportant in such complexes, and further decomposition ofelectrostatic interaction contribution into its multipolarcomponents revealed the importance of higher order electro-static energy components (charge−dipole, charge−quadrupole,and charge−octopole) in shaping the total electrostatic forcesin such interactions. The cation−π interaction modes (Sz andΔνopCHb) of such complexes are analyzed from their computedvibrational spectra, and it has been demonstrated that theintensity enhancement of these modes could be correlated withthe multipolar electrostatic behavior of such interactions.

■ ASSOCIATED CONTENT*S Supporting InformationComplete reference of Gaussian 09 code and Figures S1−S4.This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: jerzy@icnanotox.org (J.L.), devashis@icnanotox.org(D.M.), szczepan.roszak@pwr.wroc.pl (S.R).NotesThe authors declare no competing financial interest.⊥K.C.-M. and W.A.E. worked in the project as CREST-supported ICN summer school students.

■ ACKNOWLEDGMENTSWe acknowledge the support of NSF CREST funding for thiswork (No. HRD-0833178). This research was furthersupported by the Extreme Science and Engineering DiscoveryEnvironment (XSEDE) by National Science Foundationgrantnumber OCI-1053575 and XSEDE award allocationnumber DMR110088. S.R. acknowledges the financial support

Figure 5. (a,b) Correlation of ΔEB with the intermolecular stretching (Sz, panel a) and blue-shifted out-of-plane CH bending mode of aromaticmoiety (ΔνopCHb, panel b) modes of various cation−π complexes. (b) Red, blue, and green lines respectively, represent the complexes of the cationswith benzene, p-methylphenol, and 3-methylindole. (c,d) Correlation of ΔEB with IRI for the respective Sz (panel c) and the intensity enhancementfor the respective ΔνopCHb (panel d) modes of the various cation−π complexes. The red line in panel c represents the correlation with all thecomplexes, while the blue line represents correlation excluding the hydrated metal ions. The red, blue, and green lines in panel d representcorrelations for the similar cases in panel b.

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by a statutory activity subsidy from Polish Ministry of Scienceand Technology of Higher Education for the Faculty ofChemistry of Wroclaw University of Technology. We thank theMississippi Center for Supercomputing Research and WroclawSupercomputing and Networking Centers for a generousallotment of computer time.

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The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp404245q | J. Phys. Chem. A 2013, 117, 7989−80008000