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Cooperative or Anticooperative: How Noncovalent Interactions Influence Each Other Soumen Saha and G. Narahari Sastry* Centre for Molecular Modeling, CSIR-Indian Institute of Chemical Technology, Tarnaka, Hyderabad 500007, Andhra Pradesh, India S Supporting Information *

ABSTRACT: This computational study examines the key factors that control the structures and energetics of the coexistence of multiple noncovalent interactions. 4-Amino-2-iodophenol is taken as a model that exhibits nine different kinds of noncovalent interactions, viz., cation−π (CP), hydrogen bond (HB) through O (OHB), HB through N (NHB), halogen bond (XB), π−π (PP), metal ion− lone pair (ML) through O (OML), ML through N (NML), charge assisted hydrogen bond (CHB) through O (OCHB), and CHB through N (NCHB). Through all possible combinations of these noncovalent interactions, based on energy, geometry, charge, and atoms in molecules (AIM) analysis, we have systematically analyzed the cooperativity among 40 ternary systems and 105 quaternary systems. We have observed that CP−HB, CP−XB, CP−PP, HB−HB, HB−XB, HB−PP, HB−ML, HB−CHB, XB−PP, XB−ML, XB−CHB, PP−ML, and PP−OCHB can form cooperative ternary systems. While studying the quaternary systems, we have observed that HB, XB, and PP work together by enhancing each other’s strength. The study highlights that the positively charged species enhances HB−HB and HB−PP interactions and forms cooperative HB−HB−CHB, HB−HB−ML, HB−PP−ML, and HB−PP−CHB systems. Surprisingly, OHB−OML−NML, OHB−OML−OCHB, OHB− OML−NCHB, OHB−NML−OCHB, NHB−OML−NML, NHB−OML−NCHB, and NHB−NML−OCHB are also cooperative in nature despite the electrostatic repulsion between two positive charge species. The current study shows the widespread presence of cooperativity as well as anticooperativity in supramolecular assembles.

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bonding (XB) has also been reported.64−66 The CP−PP, CP−HB, and PP−XB have been scrutinized in detail.53−56,67,68 Thus, knowing how two or more noncovalent interactions mutually influence each other is a question of paramount importance. For explaining the extent of manifestation of cooperativity and anticooperativity, we have chosen a model system, 4-amino-2-iodophenol (AIP), that has the potential to exhibit CP, HB, XB, PP, metal ion−lone pair (ML), and charge assisted hydrogen bond (CHB). However, the possibility of anion−π interactions has been ruled out with AIP, owing to the presence of substituents which make the model system electron rich. AIP can exhibit HB, ML, and CHB via oxygen atoms as well as through nitrogen atoms. It may form CP interactions with NH3CH3+. Note that NH3CH3+ also can form NH/π interaction58,69 with AIP. Thus, a total of 10 different types of noncovalent interactions, namely, CP with Li+; HB through O (OHB) and N (NHB) with NH2CH3; XB with NH2CH3; PP with benzene; ML through O (OML) and N (NML) with Li+; CHB through O (OCHB) and N (NCHB) with NH3CH3+ and CP with NH3CH3+ (NCP), may be shown by AIP. Generally,

INTRODUCTION Recent advances in the fields of supramolecular chemistry, molecular biology, and materials science appear to have a strong bearing on the way in which various noncovalent interactions manifest themselves. Fundamental understanding in the molecular processes, such as self-assembly, molecular recognition, chemical transport, and catalysis, is traced to the interplay of noncovalent interactions.1−12 Among the noncovalent interactions, hydrogen bonding, cation−π (CP), and π−π interactions may be considered as the most extensively studied ones.13−35 Recent years have also witnessed a number of studies addressing anion−π, halogen bond, metal ion−lone pair, cation− hydrocarbon, carbon bond, etc.36−48 Usually, several noncovalent interactions operate simultaneously in biological systems, and how these interactions mutually influence each other is a question of interest in its own right.49−52 When two or more noncovalent interactions operate simultaneously and in concert enhance each others’ strength, they are said to be acting cooperatively.48−60 Conversely, anticooperativity refers to a situation where noncovalent interactions weaken each others’ strength. The cooperativity effects involving hydrogen bonds in living organisms are well-known phenomena.50−52,59,60 The water cluster is an excellent example of the cooperativity of hydrogen bonds.35,59 Many groups have explored the cooperativity effects between π−π (PP) and hydrogen bonding (HB).61−63 The cooperativity between HB and halogen © 2015 American Chemical Society

Special Issue: Biman Bagchi Festschrift Received: March 29, 2015 Revised: April 30, 2015 Published: May 4, 2015 11121

DOI: 10.1021/acs.jpcb.5b03005 J. Phys. Chem. B 2015, 119, 11121−11135

Article

The Journal of Physical Chemistry B

write the following eq 1 for ΔECoop(T) (for details, see the Supporting Information)

the computational investigations on cooperativity have been mostly based on ternary systems, which focused only on one or two type(s) of noncovalent interaction(s). The importance of quantifying the cooperativity and/or anticooperativity among the several noncovalent interactions holds significance in supramolecular chemistry. Clearly, knowledge on the manifestation of intermolecular interactions and their relative preferences is crucial in rational design of materials with desired properties. Thus, instead of studying the cooperativity between a pair of nonbonded interactions, we intend to quantify cooperativity and/or anticooperativity among all of these noncovalent interactions. We aimed to study all the possible combinations of these interactions which can be formed in the ternary systems. These systems are the simplest way to understand the influence between two different noncovalent interactions. Moreover, a very few studies have been reported on the cooperativity effect of quaternary structures.67,70−73 In order to explore whether the cooperativity among various nonbonded interactions is the only factor for stabilization of the systems or anticooperativity can also have some effects in such stabilization, we decided to investigate the quaternary systems for quantifying the cooperativity (and/or anticooperativity) among three different multiple noncovalent interactions. It is our opinion that studying the cooperativity among all these nonbonded interactions together might shed new light on the cooperativity effect in biological as well as supramolecular chemistry.

ΔECoop(T ) = EABC(T ) − EAB(T ) − E BC(T ) − ECA (T ) + EA (T ) + E B(T ) + EC(T )

(1)

Similarly, the cooperativity energy in quaternary systems (ΔECoop(Q))72 can be simplified as (see the Supporting Information for theoretical details) ΔECoop(Q ) = EABCD(Q ) − EAB(Q ) − E BC(Q ) − ECD(Q ) − E DA (Q ) − ECA (Q ) − E BD(Q ) + 2EA (Q ) + 2E B(Q ) + 2EC(Q ) + 2E D(Q )

(2)

The complexation and cooperativity energies so obtained were corrected for the basis set superposition error (BSSE)88 by using the counterpoise method of Boys−Bernardi.89 A negative value of the cooperativity energy indicates that the two noncovalent interactions work cooperatively, while a positive value indicates that the two interactions work anticooperatively. In this study, the cooperativity effects were quantified in terms of cooperativity energies, geometries, charge derived from Mulliken population analysis (MPA) schemes,90 and Bader’s theory of atoms-in-molecules91 (AIM). Cage critical points were evaluated for CP and PP, whereas bond critical points were evaluated for OHB, NHB, XB, OML NML, OCHB, and NCHB. AIM analysis was carried out using the AIM 2000 program.92 The electron density (ρ) and the Laplacian of the electron density (∇2ρ) values were calculated from the wave function of the equilibrium geometry of the systems at the M06-2X/6-31G(d) (I: DGDZVP) level of theory.

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COMPUTATIONAL DETAILS The optimizations of all the systems considered in this study were initially done at the M06-2X/6-31G(d) level of theory followed by single point calculations with the 6-311+G(d,p) and cc-pVTZ basis sets. The DGDZVP basis set74 was used for iodine in all of these calculations. The selection of the method was directed by the extensive computational investigations77−86 on different noncovalent interactions, where the performance of M06-2X75,76 is in good agreement with high level postHartree−Fock ab initio methods at a very decent computational cost. Frequency calculations have been performed for all structures considered to unequivocally characterize them as minima on the potential energy surface. The focus of the current study is to examine the cooperative and anticooperative interactions in a given local minimum, rather than locating the global minimum on the potential energy surface. We feel that the local minima structures are representative as model systems corresponding to truncated real bio- or macromolecular structures. These calculations were performed using the Gaussian 09 program package.87 The complexation energy of systems (binary, ternary, and quaternary) corresponds to the difference between the total energy of the systems and its constituent monomers; see the Supporting Information. In order to enumerate the reorganization effect of monomers in the complexation energy of a system, the monomers’ geometries were taken from the optimized system and followed by single point calculation to compute the energies of the individual monomers (see the Supporting Information for the reorganization energy values of different systems obtained at the M06-2X/6-31G(d) (I: DGDZVP) level of theory). The cooperativity energy in ternary systems (ΔECoop(T))54,55 was calculated as the difference between the complexation energy of the ternary system and the sum of the complexation energy of its constituent binary systems. Thus, by simplifying, one can

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RESULTS AND DISCUSSION In this section, a study based on energy, geometry, charge, and AIM analysis for the binary systems has been discussed. The impact of various levels of theory employed in the calculations along with the effect of BSSE on complexation energy values of the binary systems have also been explored. To study the interplay between various noncovalent interactions, a discussion on cooperativity/anticooperativity of ternary systems has been presented. This has been ensued by crucial evaluations of the complexation and cooperativity energy values of ternary systems with variations in bond distances, charges, ρ, and ∇2ρ. An evaluation of the cooperativity/anticooperativity of different quaternary systems has been presented. The cooperative/ anticooperative nature of quaternary systems is correlated with bond distances, charges, ρ, and ∇2ρ. Binary Systems. The geometry optimization studies indicate that AIP can form CP with Li+; OHB, NHB, and XB with NH2CH3; PP with benzene; OML and NML with Li+; OCHB and NCHB with NH3CH3+, but it cannot form CP (and/or NH/π interaction) with NH3CH3+ (NCP) (Figure 1). The NCP structure converged to OCHB during the optimization process, and hence, we ruled out these possibilities (i.e., NCP and NH/π interaction) for further investigation. The optimized binary geometries and the optimized nonbonded distances of binary systems are presented in Figure S1 (in the Supporting Information). Throughout the discussion, the distance between the centroid of AIP (or benzene) and the metal is referred to as CP. Similarly, the distance between the centroid of AIP and the centroid of benzene is considered as PP. As the trends of complexation energies for the considered 11122


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Figure 1. Schematic representation of monomers and binary systems considered in the study.

bond distances of AIP, respectively, have increased with respect to the model system (i.e., AIP). For example, the O−H bond distance in the OHB (b) system has elongated relative to the O−H bond distance of AIP. We have observed that the charge values of H(O) and H(N) of AIP in OHB and NHB, respectively, are more than those atoms of AIP (Table S12 in the Supporting Information). Similarly, the charges on O and N of AIP in OML (and OCHB) and NML (and NCHB), respectively, are more than the corresponding atoms of AIP. In the case of XB, the I atom of AIP is more negative than that present in XB. The charge values also indicate the formation of subsequent noncovalent interaction with AIP. All the observed distances of different noncovalent interactions in binary systems are in good agreement with earlier studies.40,47 Furthermore, the complexation energy value for CP interaction between Li+ and AIP is −46.27 kcal/mol, whereas that of Li+ and benzene is −41.49 kcal/mol, respectively. These complexation energy values indicate that AIP forms strong CP interaction relative to benzene. This may be traced to the presence of two electron donating groups (OH and NH2) and a polarizable atom (iodine) in AIP, and therefore forms stronger CP interaction than benzene. Ternary Systems. The cooperativity effect in the ternary systems is investigated by considering all the possible combinations of these nine different noncovalent interactions. Thus, there will be 36 (9C2, among nine different noncovalent interactions only two are needed to form ternary systems) possible combinations and apart from these combinations four more possibilities, viz., CP−CP (xxxvii), CPin−PP (xxxviii), OML− CP2 (xxxix), and NML−CP2 (xl), are also considered (Figure 2). In the CP−CP system, AIP is sandwiched between two Li+; in CPin−PP, Li+ is in between AIP and benzene, whereas, in OML−CP2, Li+ is forming OML with AIP and simultaneously CP with benzene (CP2); in the case of NML−CP2, Li+ is

systems obtained at different levels are identical (Figure S2 in the Supporting Information), the discussion will be centered on the results obtained at the M06-2X/6-31G(d) level of theory (DGDZVP basis set used for iodine). We have found that the calculated complexation energy values for the binary systems are negative (Table 1; see Table S1a in the Supporting Table 1. Complexation (ΔEcom) Energy (in kcal/mol) with and without BSSE Correction Evaluated at the M06-2X/631G(d)a Level of Theory for Binary Systemsb no.

binary systems

ΔEcom (BSSE)

a. b. c. d. e. f. g. h. i. j.

CP OHB NHB XB PP OML NML OCHB NCHB NCP

−46.27 (−44.21) −14.98 (−12.58) −8.90 (−7.17) −5.28 (−3.85) −6.13 (−3.25) −54.94 (−52.87) −48.42 (−46.34) −29.96 (−28.48) −30.44 (−29.08) c

a The DGDZVP basis set used for iodine. bBSSE corrected values are in parentheses. cStructure is converged to “OCHB” during the optimization process.

Information for different levels of theory). ρ and ∇2ρ values evaluated from AIM calculations clearly indicate that AIP can form nine different noncovalent interactions, viz., CP (a), OHB (b), NHB (c), XB (d), PP (e), OML (f), NML (g), OCHB (h), and NCHB (i) (Table S2a in the Supporting Information). It is evident from Table S11 (in the Supporting Information) that, while forming OHB, NHB, XB, OML, NML OCHB, and NCHB, the O−H, N−H, C−I, C−O, C−N, C−O, and C−N 11123


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Figure 2. Schematic representation of all ternary systems considered in the study. The structures shown in red color boxes do not exist on the potential energy surface.

the AIP’s π system is stacked in between two Li+ and hence there is a confrontation between two cations to interact with the electron cloud of the π systems. This confrontation between two Li+ cations makes the CP−CP structure either unstable or even not be formed. Figure S3 (in the Supporting Information) represents the optimized geometries and the optimized nonbonded distances for the studied ternary systems. The complexation and cooperativity energies evaluated at the M06-2X/6-31G(d) level of theory (DGDZVP basis set used for iodine) for ternary systems are tabulated in Table 2 (see Figure S2b,c and Table S3 in the Supporting Information for comparisons of different levels of theory). Among the remaining 37 ternary structures, CP−OHB

forming ML through N (NML) and at the same time CP with benzene (CP2). Altogether 40 ternary structures are considered which are depicted in Figure 2. Among these 40 ternary systems, OML−OCHB (xxxii) and NML−NCHB (xxxv) are converged to OML−NCHB and CP−NCHB, respectively, during the geometrical optimization process, whereas the CP−CP (xxxvii) structure does not exist on the potential energy surface. In these cases, it is seen that two charged species are acting on the same atoms. For instance, in (xxxii), two cations (Li+and NH3CH3+) are acting on the O atom of AIP, thereby repelling each other and forming OML−NCHB. Similarly, in the case of (xxxv), due to electrostatic repulsion between two cations, Li+ is going away and forming CP−NCHB. While forming (xxxvii), 11124


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Table 2. Complexation (ΔEcom) and the Cooperativity (ΔEcoop) energies (in kcal/mol) with and without BSSE Correction Evaluated at the M06-2X/6-31G(d)a Level of Theory for Ternary Systemsb no.

ternary systems

ΔEcom (BSSE)

ΔEcoop (BSSE)

no.

ternary systems

ΔEcom (BSSE)

ΔEcoop (BSSE)

i ii iii iv v vi vii viii ix x xi xii xiii xiv xv xvi xvii xviii xix xx

CP−OHB CP−NHB CP−XB CP−PP CP−OML CP−NML CP−OCHB CP−NCHB OHB−NHB OHB−XB OHB−PP OHB−OML OHB−NML OHB−OCHB OHB−NCHB NHB−XB NHB−PP NHB−OML NHB−NML NHB−OCHB

−73.89 (−69.40) −63.31 (−59.41) −61.52 (−57.33) −56.37 (−51.36) −24.76 (−20.88) −14.57 (−10.29) −10.33 (−7.47) −5.28 (−2.24) −23.48 (−19.32) −20.69 (−16.83) −22.65 (−17.57) −89.58 (−84.52) −73.45 (−69.16) −62.10 (−58.10) −53.17 (−49.67) −15.01 (−11.82) −16.41 (−11.56) −69.87 (−66.12) −67.51 (−63.19) −44.70 (−41.38)

−4.55 (−4.92) −2.25 (−2.54) −7.49 (−6.78) 0.08 (1.59) 8.96 (8.88) 9.17 (9.31) 7.72 (7.70) 7.78 (7.79) −1.08 (−1.08) 0.50 (0.53) −0.12 (−0.12) −4.71 (−5.34) −5.46 (−5.48) −6.36 (−6.55) −4.44 (−4.44) 0.39 (0.42) −0.08 (−0.20) −2.90 (−2.87) 0.35 (−0.31) −2.22 (−2.23)

xxi xxii xxiii xxiv xxv xxvi xxvii xxviii xxix xxx xxxi xxxii xxxiii xxxiv xxxv xxxvi xxxvii xxxviii xxxix xl

NHB−NCHB XB−PP XB−OML XB−NML XB−OCHB XB−NCHB PP−OML PP−NML PP−OCHB PP−NCHB OML−NML OML−OCHB OML−NCHB NML−OCHB NML−NCHB OCHB−NCHB CP−CP CPin−PP OML−CP2 NML−CP2

−117.48 (−114.00) −12.85 (−8.63) −68.77 (−64.73) −61.64 (57.69) −42.56 (−39.33) −42.87 (−39.73) −63.02 (−58.15) −58.04 (−52.98) −38.17 (−34.15) −40.26 (−35.98) −39.43 (−35.41) c −27.50 (−24.54) −21.13 (−18.20) c −8.07 (−5.95) c −77.19 (−71.72) −82.56 (−77.62) −80.39 (−75.20)

−8.12 (−8.36) −0.08 (−0.09) 0.92 (0.22) −5.45 (−5.43) −2.36 (−2.25) −3.88 (−3.81) 0.84 (0.62) −0.85 (−0.98) −0.86 (−0.85) −0.84 (−0.82) 13.79 (13.85) c 11.50 (11.50) 10.47 (10.48) c 8.98 (9.02) c 10.41 (10.11) 12.50 (12.29) 10.52 (10.28)

a The DGDZVP basis set used for iodine. bBSSE corrected values are in parentheses. cStructure does not exist on the potential energy surface (see details in the Results and Discussion).

or N for the OHB and NHB systems, respectively, in Table S12 in the Supporting Information), which in turn forms strong interactions with positively charged species present in the system. As a result, the complexation with positively charged species is expected to be stronger when AIP is involved as a HB donor, which may be the origin of cooperativity for (i), (ii), (xii), (xiii), (xiv), (xv), (xviii), (xix), (xx), and (xxi). The (xxviii), (xxix), and (xxx) systems are cooperative because positively charged species can withdraw π-electron density of AIP through the O (or N) atom; as a consequence, the charge value on the carbon atom attached with O (or N) decreases for the OCHB (or NCHB) binary system, and thus, OCHB (or NCHB) will enhance the PP interactions. The presence of electron-withdrawing moieties in the backbone enhances the anisotropy of the electron distribution on the attached halogen atom, and as a result, the strength of the XB interaction will increase. For instance, in CP, Li+ interacts with the electron cloud of π systems, will try to drag its electron density and thus will behave like an electron-withdrawing moiety. This maximizes the magnitude of the σ-hole, rendering the XB interactions stronger. Hence, CP and XB are cooperative in nature. Similarly, for the XB−OML, XB−NML, XB−OCHB, and XB−NCHB systems, positively charged species can drag the electron density of π systems either via the O or N atom and thus they are cooperative in nature. Likewise, the presence of benzene facilitates the formation of PP interaction with AIP, which in turns enhances the XB, resulting in cooperativity of XB−PP (xxii). However, the 11 ternary systems, viz., CP−OML (v), CP− NML (vi), CP−OCHB (vii), CP−NCHB (viii), OML−NML (xxxi), OML−NCHB (xxxiii), NML−OCHB (xxxiv), OCHB− NCHB (xxxvi), CPin−PP (xxxviii), OML−CP2 (xxxix), and NML−CP2 (xl), are anticooperative in nature, as they have positive values of cooperativity energy. In the case of anticooperative ternary systems, complexation energies have decreased, nonbonded distances have increased, and ρ and

(i), CP−NHB (ii), CP−XB (iii), OHB−NHB (ix), OHB−PP (xi), OHB−OML (xii), OHB−NML (xiii), OHB−OCHB (xiv), OHB−NCHB (xv), NHB−PP (xvii), NHB−OML (xviii), NHB−OCHB (xx), NHB−NCHB (xxi), XB−PP (xxii), XB−NML (xxiv), XB−OCHB (xxv), XB−NCHB (xxvi), PP−NML (xxviii), PP−OCHB (xxix), and PP−NCHB (xxx) are found to be cooperative in nature, as they have negative values of cooperativity energy. In these 20 ternary systems, the calculated nonbonded distances (Figure S3 in the Supporting Information) are observed to be shorter than the corresponding binary systems. AIM analysis suggests that the variations of ρ and ∇2ρ (Table S4 in the Supporting Information) are also increased for these ternary systems as compared to their individual values in isolated binary systems. For example, in CP−OHB (i), the complexation energy value is −73.89 kcal/mol. The observed nonbonded distances for CP and OHB in (i) are 1.844 and 1.582 Å, respectively, which are shorter compared to those for isolated CP and OHB (1.876 and 1.771 Å, respectively). The values of ρ for CP and OHB in (i) are 0.014 and 0.073 au, respectively, which are larger than that of isolated CP and OHB (Tables S2 and S4 in the Supporting Information). Likewise, the magnitudes of ∇2ρ for CP and OHB in (i) are also increased compared to the related binary systems (i.e., CP and OHB). Some of the ternary systems, such as CP−PP (iv), OHB−XB (x), NHB−XB (xvi), NHB−NML (xix), XB−OML (xxiii), and PP−OML (xxviii), are having negligible values of cooperativity energies (less than 1 kcal/mol). The nonbonded distances for (iv), (xix), (xxiii), and (xxviii) are shorter than the corresponding binary systems, whereas, for (x) and (xvi), they are slightly longer as compared to their isolated binary systems. Moreover, AIM analysis for these six systems suggests that ρ and ∇2ρ values are almost the same relative to their individual values in isolated binary systems. The cooperativity of these 26 systems can be explained as follows. In HB complexes, electron density shift from the acceptor to AIP makes O (or N) more negative (see the charge value on O 11125


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Figure 3. Complexation energy of the ternary systems, sum of complexation energy of binary systems (in free state) present in the ternary systems, and cooperativity energy of the ternary systems as obtained at the M06-2X/6-31G(d) (I: DGDZVP) level of theory.

∇2ρ values have decreased relative to their respective individual values in binary systems. The anticooperativity of (v), (vi), (vii), (viii), (xxxi), (xxxiii), (xxxiv), and (xxxvi) can be explained in terms of the electrostatic repulsion between two positively charged species. For example, in CP−OML (v), because of the electrostatic repulsion, the difference between the sum of two individual Li+ energies (present in CP−OML) and the “through space Li+−Li+ energy” is 65.34 kcal/mol (from Table S14 in the Supporting Information). In CPin−PP, OML−CP2, and NML−CP2, Li+ is forming two different kinds of interactions with both AIP and benzene, resulting in anticooperativity. Figure 3 depicts the complexation energy values of the ternary systems, the sum of the complexation energy values of binary systems (in free state) present in the ternary systems, and the cooperativity energy values of the ternary systems as obtained at the M06-2X/6-31G(d) (I: DGDZVP) level of theory. For cooperative systems, we have found that the complexation energy values of the ternary systems are higher than the sum of complexation energy values of related binary systems (Table S5 in the Supporting Information). Oppositely, in the case of anticooperative systems, the sum of complexation energy values of related binary systems is larger than the complexation energy values of the corresponding ternary systems. For instance, in the case of the cooperative CP−OHB (i) system, the difference between the complexation energy value of (i) and the sum of the complexation energy values of related binary systems (i.e., CP and OHB) is −12.64 kcal/mol. On the other hand, in the anticooperative CP−OML (v) system, the

complexation energy value of (v) is −24.76 kcal/mol, while the sum of the complexation energy values of CP and OML is −101.22 kcal/mol. Some exceptions are also observed in the cases of CP−PP (iv), OHB−NHB (ix), OHB−XB (x), NHB− XB (xvi), NHB−NML (xix), XB−OML (xxiii), and PP−OML (xxviii) systems, as these systems have very small cooperativity/ anticooperativity energy values (Table 2). Note that the difference between the complexation energy values of the ternary systems and the sum of the complexation energy values of related binary systems is not exactly the same as the cooperativity energy of the ternary systems. This is because the cooperativity energy of the ternary systems contains an extra term called the “through space energy”.54,55 As evident from Table 2 and Figure 3, the ternary system (xxi) is having the highest cooperativity effect, whereas the highest anticooperativity effect is observed in (xxxi). In NHB−NCHB (xxi), the N−H (the H atom is responsible for forming NHB) distance is 1.080 Å (Table S11 in the Supporting Information), the NHB nonbonded distance is 1.717 Å, and the NCHB nonbonded distance between N of AIP and H of NH3CH3+ is 1.098 Å (Figure S3 in the Supporting Information), whereas, in the case of the isolated NHB binary system the nonbonded distance is 2.081 Å and in the isolated NCHB systems, the nonbonded distance is 1.674 Å (Figure S1 in the Supporting Information). This indicates that, in NHB−NCHB (xxi), both NHB and NCHB are forming very strong interactions, which is well supported by AIM analysis (Table S4 in the Supporting Information). In general, in covalent bonding, ρ is greater than 0.20 au and ∇2ρ is less than 0, whereas in the case of 11126


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Figure 4. Sum of the electron density of the ternary systems, sum of the electron density of the binary systems (in free state) present in the ternary systems, and the difference between them. The electron density values as obtained by using the wave function from M06-2X/6-31G(d) (I: DGDZVP) calculation.

noncovalent bonding ρ is less than 0.10 au and ∇2ρ is greater than 0.93−95 Our observed ρ and ∇2ρ values of NCHB in (xxi) are 0.254 and 0.283 au, respectively, which is the signature of forming a covalent-like bond. On the contrary, for the OML− NML (xxxi) system, both nonbonded distances have increased and as a result ρ and ∇2ρ values have decreased relative to their respective individual values in binary systems. Moreover, we have observed (Table S6a in the Supporting Information) that, in the case of cooperative ternary systems, the sum of two ρ (i.e., ∑ρ) values for two different critical points present in a ternary system is higher than the sum of two ρ (i.e., ∑ρ (binary)) values for two critical points of corresponding two free binary systems. In contrast, in the case of anticooperative ternary systems, ∑ρ (binary) values of related free binary systems are larger than values ∑ρ for the ternary systems. These observations are represented in Figure 4. The calculated values of ∑∇2ρ and ∑∇2ρ (binary) are also listed and plotted in Table S6b and Figure S4, respectively, in the Supporting Information. As ρ and ∇2ρ of NCHB in (xxi) are 0.254 and −0.283 au, respectively, indicating the formation of a covalent-like bond, while presenting these values in Figure 4 and Figure S4 (in the Supporting Information), we have omitted the (xxi) system. Thus, one may correlate the cooperativity energy of ternary systems with the difference between ∑ρ (and/or ∑∇2ρ) of the ternary systems and ∑ρ (binary) (and/or ∑∇2ρ (binary)) of the corresponding free binary systems. In (iv), (ix), (xvi), (xix), (xxiii), (xxviii), (xxix), and (xxx) systems, we have found that either the difference between ∑ρ (and/or ∑∇2ρ) and ∑ρ (binary) (and/or ∑∇2ρ (binary)) or the cooperativity energy of systems are very small.

To the best of our knowledge, the cooperativity effect of CP−HB, CP−PP, HB−HB, HB−XB, and HB−PP is already demonstrated in the earlier literature.53−57,59−68 It is pertinent to mention that our results also indicate that CP−OHB (i), CP−NHB (ii), CP−PP (iv), OHB−NHB (ix), OHB−XB (x), NHB−XB (xiv), OHB−PP (xi), and NHB−PP (xvii) are cooperative in nature. Moreover, we have observed that CP−XB, HB−ML, HB−CHB, XB−PP, XB−ML, XB−CHB, PP−ML, and PP−CHB can also work together by enhancing each others’ strength. These results demonstrated that positively charged species exert a strong influence on HB, XB, and PP which may be of significant value in understanding the biological and supramolecular systems. Quaternary Systems. In order to further investigate the cooperativity effect among multiple noncovalent interactions, we have considered all the possible combinations of the nine different noncovalent interactions. Altogether, 105 quaternary systems are considered which are shown in Figure 5. Among these 105 systems, 27 structures are collapsed to other structures upon the geometry optimization process. In these 27 structures either two charged species are acting on the same atoms or the presence of three charged species in a system makes them unstable. For instance, OHB−NML−NCHB (48), Li+, and NH3CH3+ are acting on the N atom of AIP; as a consequence, they repel each other and form OHB−NML−OCHB (47). Similarly, in NHB−OML−OCHB (60), NHB−NML− NCHB (63), XB−OML−OCHB (70), XB−NML−NCHB (73), PP−OML−OCHB (76), PP−NML−NCHB (79), OCHB− OML−CP2 (97), and NCHB−NML−CP2 (105) systems are collapsed to NHB−OML−NCHB (61), NHB−NML−OCHB 11127


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CP2 (104), OML−NML−CP2 (103), and NML−OML−CP2 (96), respectively, upon geometry optimization. As evident from Table 3 (and Table S7 in the Supporting Information), apart from the above-mentioned systems, 41 systems are showing the cooperative effect, as they have negative values of cooperativity energy (see Figure S2d,e in the Supporting Information for comparisons of different levels of theory). For instance, in CP−OHB−NHB (1), the complexation energy and cooperativity energy values are −87.03 and −6.11 kcal/mol, respectively. The observed nonbonded distances for CP, OHB, and NHB in (1) are 1.825, 1.610, and 1.904 Å (Figure S5 in the Supporting Information), respectively, whereas the nonbonded distances for isolated CP, OHB, and NHB are 1.876, 1.771, and 2.081 Å, respectively. The values of ρ for CP, OHB, and NHB in (1) are 0.014, 0.068, and 0.037 au (Table S8 in the Supporting Information), respectively, which are larger than those of isolated CP, OHB, and NHB. Likewise, the magnitudes of ∇2ρ for CP,

(62), XB−OML−NCHB (71), CP−XB−NCHB (18), NCHB−OML−CP2 (98), OCHB−NML−CP2 (104), NCHB−OML−CP2 (98), and NCHB−NML−CP2 (104), respectively. However, in the case of CP−OML−OCHB (24), CP−OML−NCHB (25), CP−NML−OCHB (26), CP− NML−NCHB (27), CP−OCHB−NCHB (28), OML− NML−OCHB (81), OML−NML−NCHB (82), OML− OCHB−NCHB (83), and NML−OCHB−NCHB (84) systems, because of electrostatic repulsion among three charged species, these systems are not formed. The desired structure of PP− OCHB−NCHB (80) is not found. Further, the structures CP− PP−OML (19), CP−PP−NML (20), CP−PP−NCHB (22), PP−OML−NML (75), PP−OML−NCHB (77), PP−NML− OCHB (78), CPin−PP−OML (88), and CPin−PP−NML (89) collapsed to already existing structures, viz., CP−OML−CP2 (92), CP−NML−CP2 (99), CP−PP−OCHB (21), OML− NML−CP2 (103), NCHB−OML−CP2 (98), OCHB−NML−

Figure 5. continued 11128


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Figure 5. Schematic representation of all quaternary systems considered in the study: (a) 1 to 54 and (b) 55 to 105. The structures shown in red color boxes do not exist on the potential energy surface.

distances (and/or ρ and ∇2ρ values) are also observed in the cases of CP−OHB−OML (4), CP−OHB−NML (5), CP− NHB−OCHB (12), CP−XB−OML (15), CP−XB−NML (16), CP−XB−NCHB (18), OHB−NHB−PP (30), OHB− PP−OML (40), OHB−PP−OCHB (42), OHB−PP−NCHB (43), OHB−OML−NML (44), OHB−OML−OCHB (45), OHB−OML−NCHB (46), OHB−NML−OCHB (47), NHB− XB−OCHB (53), NHB−PP−OML (55), NHB−PP−NML (56), NHB−PP−OCHB (57), NHB−PP−NCHB (58), XB− PP−NML (66), XB−PP−OCHB (67), and XB−PP−NCHB (68). However, their cooperativity energy values are negative. Furthermore, nine quaternary systems, viz., CP−OHB−OCHB (6), CP−NHB−OML (10), CP−XB−OCHB (17), OHB− NHB−XB (29), OHB−XB−PP (35), OHB−OCHB−NCHB (49), NHB−XB−PP (50), NHB−OML−NCHB (61), and XB−PP−OML (65), are having slightly negligible values (∼1 kcal/mol) of cooperativity energies (Table 3). In these

OHB, and NHB in (1) are also increased more than the related binary systems. Similarly, in the case of CP−OHB−XB (2), CP−OHB−PP (3), CP−OHB−NCHB (7), CP−NHB−XB (8), CP−NHB−PP (9), CP−XB−PP (14), OHB−NHB−OML (31), OHB−NHB−NML (32), OHB−NHB−OCHB (33), OHB−NHB−NCHB (34), OHB−XB−OML (36), OHB− XB−NML (37), OHB−XB−OCHB (38), OHB−XB−NCHB (39), OHB−PP−NML (41), NHB−XB−OML (51), NHB− XB−NML (52), and NHB−XB−NCHB (54), all the complexation energy and cooperativity energy values are negative (Table 3), the observed nonbonded distances are shorter (Figure S5 in the Supporting Information), and the ρ and ∇2ρ values have increased (Table S8 in the Supporting Information) relative to the corresponding free binary systems. Thus, the observed nonbonded distances, ρ and ∇2ρ values, along with the cooperativity energy values indicate that these quaternary systems are cooperative in nature. Exceptions in nonbonded 11129


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ΔEcoop (BSSE) −6.11 (−6.74) −6.87 (−7.22) −3.43 (−4.20) −34.43 (−35.57) −33.85 (−33.86) 0.26 (−0.39) −30.82 (−30.94) −8.81 (−9.05) −2.09 (−2.80) 0.73 (0.35) 10.59 (9.30) −0.48 (−0.77) 5.62 (5.13) −6.36 (−6.59) −1.45 (−2.00) −8.01 (−7.85) 1.53 (1.49) −8.24 (−8.23) c c 7.30 (7.04) c 27.84 (27.89) c c c c c 1.12 (1.21) −1.00 (−1.14) −6.94 (−7.50) −3.74 (−4.42) −7.69 (−7.84) −12.89 (−13.17) 0.35 (0.43)

ΔEcom (BSSE)

−87.03 (−81.08) −86.17 (−79.62) −80.62 (−73.06) −148.41 (−141.31) −162.36 (−154.76) −47.77 (−42.34) −143.22 (−136.72) −76.00 (−70.02) −70.00 (−63.00) −49.48 (−43.73) −40.86 (−34.31) −29.85 (−25.31) −26.56 (−21.42) −70.71 (−63.59) −51.34 (−44.67) −37.68 (−30.88) −31.34 (−26.08) −26.01 (−20.53) c c −21.45 (−15.48) c 65.04 (70.71) c c c c c −27.41 (−21.81) −31.45 (−24.27) −101.63 (−94.96) −89.37 (−82.83) −72.89 (−67.07) −142.43 (−136.62) −24.52 (−17.91) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

no. OHB−XB−OML OHB−XB−NML OHB−XB−OCHB OHB−XB−NCHB OHB−PP−OML OHB−PP−NML OHB−PP−OCHB OHB−PP−NCHB OHB−OML−NML OHB−OML−OCHB OHB−OML−NCHB OHB−NML−OCHB OHB−NML−NCHB OHB−OCHB−NCHB NHB−XB−PP NHB−XB−OML NHB−XB−NML NHB−XB−OCHB NXB−XB−NCHB NHB−PP−OML NHB−PP−NML NHB−PP−OCHB NHB−PP−NCHB NHB−OML−NML NHB−OML−OCHB NHB−OML−NCHB NHB−NML−OCHB NHB−NML−NCHB NHB−OCHB−NCHB XB−PP−OML XB−PP−NML XB−PP−OCHB XB−PP−NCHB XB−OML−NML XB−OML−OCHB

quaternary systems −99.86 (−92.79) −82.54 (−76.53) −70.79 (−64.96) −60.66 (−55.64) −158.97 (−150.96) −79.06 (−71.40) −69.57 (−63.45) −62.42 (−56.43) −140.06 (−133.21) −127.98 (−121.14) −115.27 (−109.33) −104.02 (−98.17) c −40.99 (−36.34) −18.64 (−12.20) −81.68 (−76.04) −76.76 (−70.52) −54.23 (−49.03) −128.48 (−123.22) −75.27 (−68.09) −73.00 (−65.71) −48.32 (−42.13) −132.64 (−126.30) −62.95 (−56.54) c −105.24 (−99.86) −42.71 (−37.32) c −28.26 (−24.27) −74.23 (−67.27) −70.13 (−63.28) −47.05 (−41.05) −48.11 (−42.09) −60.89 (−54.51) c

ΔEcom (BSSE) −5.45 (−6.64) −9.01 (−8.97) −7.27 (−11.42) −6.52 (−6.43) −21.43 (−22.66) −5.40 (−5.71) −7.82 (−7.88) −5.39 (−5.42) −16.25 (−16.92) −41.10 (−42.05) −13.57 (−14.23) −16.55 (−16.76) c 1.18 (1.04) 0.38 (0.30) −1.20 (−1.90) −7.54 (−8.05) −8.47 (−8.39) −16.07 (−16.24) −7.36 (−7.63) −4.30 (−5.35) −9.40 (−9.37) −10.35 (−10.80) 9.41 (8.83) c 0.91 (0.64) 5.76 (5.08) c 4.57 (4.44) 1.59 (0.90) −5.45 (−5.52) −3.10 (−3.00) −4.17 (−4.10) 8.63 (7.92) c

ΔEcoop (BSSE) 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

no. XB−OML−NCHB XB−NML−OCHB XB−NML−NCHB XB−OCHB−NCHB PP−OML−NML PP−OML−OCHB PP−OML−NCHB PP−NML−OCHB PP−NML−NCHB PP−OCHB−NCHB OML−NML−OCHB OML−NML−NCHB OML−OCHB−NCHB NML−OCHB−NCHB CPin−PP−OHB CPin−PP−NHB CPin−PP−XB CPin−PP−OML CPin−PP−NML CPin−PP−OCHB CPin−PP−NCHB CP−OML−CP2 OHB−OML−CP2 NHB−OML−CP2 XB−OML−CP2 NML−OML−CP2 OCHB−OML−CP2 NCHB−OML−CP2 CP−NML−CP2 OHB−NML−CP2 NHB−NML−CP2 XB−NML−CP2 OML−NML−CP2 OCHB−NML−CP2 NCHB−NML−CP2

quaternary systems −47.11 (−41.75) −37.45 (−32.27) c −22.70 (−18.62) c c c c c c c c c c −104.44 (−96.48) −91.98 (−84.61) −89.84 (−82.36) c c −45.41 (−39.14) −45.05 (−38.51) −64.06 (−57.15) −113.25 (−104.86) −95.63 (−89.05) −94.16 (−87.14) −74.12 (−67.24) c −60.51 (−54.62) −54.94 (−47.77) −102.55 (−95.50) −97.15 (−89.62) −91.69 (−84.45) −77.28 (−70.42) −55.97 (−50.16) c

ΔEcom (BSSE)

The DGDZVP basis set used for iodine. bBSSE corrected values are in parentheses. cStructure does not exist on the potential energy surface (see details in the Results and Discussion).

CP−OHB−NHB CP−OHB−XB CP−OHB−PP CP−OHB−OML CP−OHB−NML CP−OHB−OCHB CP−OHB−NCHB CP−NHB−XB CP−NHB−PP CP−NHB−OML CP−NHB−NML CP−NHB−OCHB CP−NHB−NCHB CP−XB−PP CP−XB−OML CP−XB−NML CP−XB−OCHB CP−XB−NCHB CP−PP−OML CP−PP−NML CP−PP−OCHB CP−PP−NCHB CP−OML−NML CP−OML−OCHB CP−OML−NCHB CP−NML−OCHB CP−NML−NCHB CP−OCHB−NCHB OHB−NHB−XB OHB−NHB−PP OHB−NHB−OML OHB−NHB−NML OHB−NHB−OCHB OHB−NHB−NCHB OHB−XB−PP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

a

quaternary systems

no.

8.08 (7.36) 7.08 (7.10) c 5.98 (5.94) c c c c c c c c c c 9.54 (8.90) 11.10 (10.63) 7.28 (7.20) c c 10.64 (10.38) 14.98 (14.61) 13.76 (13.44) 10.60 (9.68) 9.93 (9.73) 15.60 (14.56) 20.51 (20.41) c 19.33 (19.18) 10.42 (10.90) 6.70 (6.42) 11.66 (10.82) 6.76 (6.65) 16.82 (17.20) 14.35 (14.72) c

ΔEcoop (BSSE)

Table 3. Complexation (ΔEcom) and the Cooperativity (ΔEcoop) Energies (in kcal/mol) with and without BSSE Correction Evaluated at the M06-2X/6-31G(d)a Level of Theory for Quaternary Systemsb

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Figure 6. Complexation energy of the quaternary systems, sum of the complexation energy of the binary systems (in free state) present in the quaternary systems, and cooperativity energy of the quaternary systems as obtained at the M06-2X/6-31G(d) (I: DGDZVP) level of theory.

case of anticooperative quaternary systems, the sum of complexation energy values of related binary systems is larger than the complexation energy values of the quaternary systems. For example, in CP−NHB−NML (11), the complexation energy value of (11) is −40.86 kcal/mol, whereas the sum of complexation energy values of CP, NHB, and NML is −103.58 kcal/mol. However, the eight exceptions also have been observed in the case of the CP−NHB−OCHB (12), CP−XB−OML (15), CP−XB−NML (16), CP−XB−NCHB (18), NHB−OML− NCHB (61), XB−PP−OML (65), CPin−PP−OHB (85), and OHB−OML−CP2 (93) systems. We have also observed that the difference between the complexation energy values of the quaternary systems and the sum of the complexation energy values of related binary systems is not exactly the same as the cooperativity energy values of respective quaternary systems. These deviations may be attributed to the fact that the cooperativity energy of the quaternary systems contains three extra terms called the “through space energy”.54,55 In the case of cooperative quaternary systems, we have also observed (Table S10a in the Supporting Information) the sum of three ρ (i.e., ∑ρ) values for three different critical points present in a ternary system is higher than the sum of three ρ (i.e., ∑ρ (binary)) values for the corresponding three free binary systems. Oppositely, in the case of anticooperative systems, ∑ρ (binary) values of related free binary systems are larger than ∑ρ values for the quaternary systems. The calculated values of ∑∇2ρ and ∑∇2ρ (binary) for the optimized quaternary systems are listed in Table S10b in the Supporting Information. We have observed that the ρ and ∇2ρ values for OHB in (4), (5), (7), (40), (44), (45), (46), and (47) and for NCHB in (34), (54), (58), and (61) systems are more than 0.2 au and less than 0, respectively, which indicates that in these systems OHB or NCHB are forming a covalent kind of bond.94 In the case of (23), (35), (90), and (91), we

nine systems, the nonbonded distances are slightly longer compared to their isolated binary systems. The AIM analysis for these systems suggests that the magnitudes of ρ and ∇2ρ are almost the same relative to their individual values in isolated binary systems. However, Table 3 also depicts that the 28 quaternary systems, viz., CP−NHB−NML (11), CP−NHB−NCHB (13), CP−PP−OCHB (21), CP−OML−NML (23), NHB−OML− NML (59), NHB−NML−OCHB (62), NHB−OCHB−NCHB (64), XB−OML−NML (69), XB−OML−NCHB (71), XB− NML−OCHB (72), XB−OCHB−NCHB (74), CPin−PP− OHB (85), CPin−PP−NHB (86), CPin−PP−XB (87), CPin− PP−OCHB (90), CPin−PP−NCHB (91), CP−OML−CP2 (92), OHB−OML−CP2 (93), NHB−OML−CP2 (94), XB− OML−CP2 (95), NML−OML−CP2 (96), NCHB−OML− CP2 (98), CP−NML−CP2 (99), OHB−NML−CP2 (100), NHB−NML−CP2 (101), XB−NML−CP2 (102), OML− NML−CP2 (103), and OCHB−NML−CP2 (104), are anticooperative in nature, as they have positive values of cooperativity energy. All other systems, except CP−OML−NML (23), are having negative complexation energy values. Figure 6 illustrates the complexation energy values of the quaternary systems, the sum of the complexation energy values of binary systems (in free state) present in the quaternary systems, and the cooperativity energy values of the quaternary systems as obtained at the M06-2X/6-31G(d) (I: DGDZVP) level of theory. For cooperative quaternary systems, the complexation energy values of the quaternary systems are higher than the sum of the complexation energy values of related binary systems (Table S9 in the Supporting Information). For instance, in the case of CP−OHB−NHB (1), the difference between the complexation energy value of (1) and the sum of the complexation energy values of related binary systems (i.e., CP, OHB, and NHB) is −16.88 kcal/mol. In contrast, in the 11131


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Figure 7. Sum of the electron density of the quaternary systems, sum of the electron density of the binary systems (in free state) present in the quaternary systems, and the difference between them. The electron density values obtained by using the wave function from M06-2X/6-31G(d) (I: DGDZVP) calculation.

(Table 3), CP−OML−NML (23) (which is having a positive complexation energy value also), all of the related ternary systems, CP−OML (v), CP−NML (vi), and OML−NML (xxxi), are showing anticooperative effects (Table 2). The remaining all optimized quaternary systems (altogether 43), including the most cooperative system (i.e., OHB−OML− OCHB (45)), consist of two cooperative ternary systems and one anticooperative ternary system. For instance, in CP− OHB−OML (4) systems, CP−OHB (i) and OHB−OML (xii) are cooperative, whereas CP−OML (v) is anticooperative in nature (see Table 2). It is important to note that, in these 43 quaternary systems, the anticooperative ternary system is playing an important role to quantify the cooperativity/ anticooperativity of quaternary systems. Furthermore, we have observed that all of the neutral quaternary systems, OHB−NHB−XB (29), OHB−NHB−PP (30), OHB−XB−PP (35), and NHB−XB−PP (50), are cooperative in nature; that means HB, XB, and PP can work together by enhancing each others’ strength. Apart from these neutral systems, CP−HB−HB, CP−HB−XB, CP−HB−PP, CP−HB−ML, CP−HB−CHB, CP−XB−ML, CP−XB−CHB, HB−HB−ML, HB−HB−CHB, HB−XB−ML, HB−XB−CHB, HB−PP−ML, HB−PP−CHB, XB−PP−ML, and XB−PP−CHB can also work together and form cooperative systems. We have observed that HB−HB, HB−PP, or HB−HB−PP interactions are cooperative, which are primarily responsible for forming the helical structure of DNA. It is also found that CP− HB, CP−PP, HB−ML, HB−CHB, PP−ML, PP−CHB, CP− HB−HB, HB−HB−CHB, HB−HB−ML, HB−PP−ML, and HB−PP−CHB are also cooperative. These observations indicate that the positively charged species can play a crucial role in many cases, particularly in biological systems. The negatively charged phosphate backbone of DNA is generally neutralized by forming noncovalent interactions with positive charges on proteins, metal ions, and polyamines.96 It is interesting to note

have not observed the cage critical point either for CP or for PP. Note that system (23) is having a positive complexation energy value and (90) and (91) are having high positive values of cooperativity energy (more than +10 kcal/mol). Except for these cases, the observed trends for ∑ρ values of quaternary systems, ∑ρ (binary) values for three free binary systems, and the difference (i.e., ∑ρ − ∑ρ (binary)) between them are plotted in Figure 7. A similar kind of plot for ∇2ρ has also been presented in Figure S6 in the Supporting Information. We have found that ∑ρ − ∑ρ (binary) (and/or ∑∇2ρ − ∑∇2ρ (binary)) may be considered as a signature of cooperativity for the system. It has been observed that among 50 cooperative quaternary systems, in 33 systems, i.e., CP−OHB−NHB (1), CP−OHB− XB (2), CP−OHB−PP (3), CP−NHB−XB (8), CP−NHB− PP (9), CP−XB−PP (14), OHB−NHB−XB (29), OHB− NHB−PP (30), OHB−NHB−OML (31), OHB−NHB−NML (32), OHB−NHB−OCHB (33), OHB−NHB−NCHB (34), OHB−XB−PP (35), OHB−XB−OML (36), OHB−XB−NML (37), OHB−XB−OCHB (38), OHB−XB−NCHB (39), OHB−PP−OML (40), OHB−PP−OML (41), OHB−PP− OCHB (42), OHB−PP−NCHB (43), NHB−XB−PP (50), NHB−XB−OML (51), NHB−XB−NML (52), NHB−XB− OCHB (53), NHB−XB−NCHB (54), NHB−PP−OML (55), NHB−PP−NML (56), NHB−PP−OCHB (57), NHB−PP− NCHB (58), XB−PP−OML (65), XB−PP−OCHB (67), and XB−PP−NCHB (68), all three constituent ternary systems are cooperative in nature. For instance, CP−OHB−NHB (1) contains three ternary systems, CP−OHB (i), CP−NHB (ii), and OHB−NHB (ix), and all of them are cooperative in nature (Table 2). Hence, it is expected that, when these three ternary systems form a quaternary system, i.e., CP−OHB−NHB, it will also be cooperative in nature (Table 3). On the contrary, if all three constituent ternary systems are anticooperative in nature, their associative quaternary system is also expected to be anticooperative in nature. In the most anticooperative system 11132


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between these two aspects results in imparting stability to macromolecular assemblies.

that the positively charged species enhances HB−HB and HB−PP interactions and forms cooperative HB−HB−CHB, HB−HB−ML, HB−PP−ML, and HB−PP−CHB which correlated well with the earlier observations. Thus, it is our opinion that the positively charged species not only neutralizes the DNA, but the presence of charged species on the backbone may also help to form stronger hydrogen bond and/or π−π interactions. Surprisingly, more than one positively charged species are binding to the DNA backbone despite the electrostatic repulsion between them, indicating the strong presence of anticooperative interactions. As our study also indicates that two charged species can be confronted and from cooperative systems, like, OHB−OML−NML, OHB−OML− OCHB, OHB−OML−NCHB, OHB−NML−OCHB, NHB− OML−NML, NHB−OML−NCHB, and NHB−NML−OCHB, although OML−NML, OML−NCHB, and NML−OCHB systems are anticooperative in nature. It is evident that the backbone neutralization increases duplex DNA flexibility in protein− DNA recognition processes.97,98 Therefore, it may be noted that the anticooperativity effect plays a decisive role in the overall stability of DNA.

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ASSOCIATED CONTENT

S Supporting Information *

Theoretical details, figures, and the values of different energy terms of the systems are given along with bond distances, charges, ρ and ∇2ρ values, and the full citation for Gaussian 09. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b03005.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-40-27193016. Fax: +91-40-27160512. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS CSIR, New Delhi, is thanked for financial support in the form of GENESIS (BSC-121), a 12th five year project.

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CONCLUSIONS In the current study, we have analyzed the structures and energetics of the coexistence of multiple noncovalent interactions. 4-Amino-2-iodophenol as a model system has been chosen to understand cooperativity among the nine different kinds of noncovalent interactions, viz., cation−π (CP) hydrogen bond (HB) through O (OHB), HB through N (NHB), halogen bond (XB), π−π (PP), metal ion−lone pair (ML) through O (OML), ML through N (NML), charge assisted hydrogen bond (CHB) through O (OCHB) and CHB through N (NCHB). Through all possible combinations of these noncovalent interactions, based on energy, geometry, charge, and AIM analysis, we have systematically analyzed the cooperativity among 40 ternary systems and 105 quaternary systems. We have found that CP−HB, CP−PP, HB−HB, HB−XB, and HB−PP interactions are cooperative in nature, as shown in earlier studies.53−57,59−68 We have explicitly observed that CP−XB, HB−ML, HB−CHB, XB−PP, XB−ML, XB−CHB, PP−ML, and PP−OCHB can also form cooperative ternary systems. While studying the quaternary systems, we have observed that HB, XB, and PP work together by enhancing each others’ strength. While analysizing our results, we have found that ∑ρ − ∑ρ (binary) (and/or ∑∇2ρ − ∑∇2ρ (binary)) may be considered as a signature of cooperativity for the system. It is interesting to observe that HB−HB, HB−PP, or HB−HB−PP interactions are cooperative, which are primarily responsible for forming the helical structure of DNA. In our study, we have found that CP−HB, CP−PP, HB−ML, HB−CHB, PP−ML, PP−CHB, CP−HB−HB, HB−HB−CHB, HB−HB−ML, HB−PP−ML, and HB−PP−CHB are also cooperative. These findings indicate that the positively charged species can play a crucial role in biological systems. From this study, we have observed that the positively charged species enhances HB−HB and HB−PP interactions and forms cooperative HB−HB−CHB, HB−HB−ML, HB−PP−ML, and HB−PP−CHB systems. Surprisingly, OHB−OML−NML, OHB−OML−OCHB, OHB−OML−NCHB, OHB−NML− OCHB, NHB−OML−NML, NHB−OML−NCHB, and NHB−NML−OCHB are also cooperative in nature despite the electrostatic repulsion between two positive charge species. The current study explains the coexistence of cooperative and anticooperative effects and highlights that a fine balance

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