Benzene, an Unexpected Binding Unit in Anion– π Recognition: The Critical Role of CH/ π Interactions

: We report high-level ab initio calculations (CCSD(T)(full)/CBS//SCS-RI-MP2(full)/aug-cc-pwCVTZ) that demonstrate the importance of cooperativity effects when Anion– π and CH/ π interactions are simultaneously established with benzene as the π -system. In fact, most of the complexes exhibit high cooperativity energies that range from 17% to 25.3% of the total interaction energy, which is indicative of the strong inﬂuence of the CH/ π on the Anion– π interaction and vice versa. Moreover, the symmetry-adapted perturbation theory (SAPT) partition scheme was used to study the different energy contributions to the interaction energies and to investigate the physical nature of the interplay between both interactions. Furthermore, the Atoms in Molecules (AIM) theory and the Non-Covalent Interaction (NCI) approach were used to analyze the two interactions further. Finally, a few examples from the Protein Data Bank (PDB) are shown. All results stress that the concurrent formation of both interactions may play an important role in biological systems due to the ubiquity of CH bonds, phenyl rings, and anions in biomolecules.


Introduction
Comprehension of non-covalent interactions lays the foundation of the interdisciplinary field of supramolecular chemistry. In particular, interactions with aromatic rings play a vital role in a great deal of chemical and biological processes, such as molecular recognition, crystal engineering, and conformational changes [1].
Anion-π interactions are a prominent type of attractive non-covalent force that was put in the spotlight of the scientific community from the pioneering computational studies that first appeared back in 2002 [2][3][4][5], igniting great interest in further analyzing the nature and quantification of these interactions from both theoretical and experimental points of view [6]. Since then, many theoretical studies have been reported focusing on this type of interaction [7][8][9][10][11]. In fact, several reviews of these studies have appeared in the literature [12][13][14][15][16][17][18], converting Anion-π interactions into a live topic nowadays. For instance, very recently, i-corona [3]arene [3]tetrazines have been reported to regulate their macrocyclic conformation and cavity structures to recognize anions by forming interdependent and synergistic Anion-π/and hydrogen bond interactions [19]. In another recent study, Anionπ interactions of azacalix [3]triazines alter their ionization potentials and capture protons as organic superbases, despite the electron-deficient nature of triazine [20]. Another very recent study reports a series of rotaxane-based Anion-π catalysts in which the mechanical bond between a bipyridine macrocycle and an axle containing a naphthalene diimide unit that catalyses an otherwise disfavoured Michael addition in >60 fold selectivity over a competing decarboxylation pathway [21].
In Anion-π complexes, the π system is usually an electron-deficient arene and, thus, the interaction is often dominated by electrostatic due to its positive quadrupole moment and ion-induced polarization terms [2][3][4]8,9]. Therefore, from an electrostatic perspective, Recently, we and others reported theoretical and experimental evidence for cooperativity effects in complexes in which different interactions coexist, namely, Anion-π and π-π stacking [64,65], Anion-π and hydrogen-bonding interactions [66][67][68][69], Anion-π and Ar/π [70], Anion-π and halogen-bonding interactions [71][72][73] and Anion-π and triel bond interactions [74]. It has been found that such interplays can lead to strong cooperativity effects. In this manuscript, we present a computational study using high-level ab initio calculations (CCSD(T)(full)/CBS//SCS-RI-MP2(full)/aug-cc-pwCVTZ) in which we address cooperativity effects between CH/π ανδ Anion-πinteractions and analyze their importance in biological systems due to the ubiquity of CH bonds (as in methyl groups), phenyl rings (as in the side chains in Phe and Tyr) and anions (as in Asp and Glu). We selected the benzene molecule as a model of phenyl moieties, the methane molecule as a model of an alkyl chain, and formate and nitrate anions as models for carboxylate anions. We first computed the geometric and energetic features of the CH/π complexes 1-3 and Anion-π complexes 4-7. Secondly, we calculated CH/π-anion complexes 8-11 to study cooperativity effects between both types of interactions, viz., how the Anion-π interaction is affected by the CH/π interaction and vice versa. Moreover, the symmetry-adapted perturbation theory (SAPT) energy partitioning scheme was used to investigate the different energy contributions to the interactions energies and to examine the physical nature of the interplay between both interactions. Finally, the Atoms in Molecules (AIM) theory and the Non-Covalent Interaction (NCI) approach were used to further analyze the two interactions. To the best of our knowledge, no computational studies have been reported on the study of the interaction between either carboxylate or nitrate anions with benzene.

Computational Details
The geometry of the compounds under study was optimized using the resolution of the identity MP2 (RI-MP2) [75,76], with all electrons correlated and imposing the highest group symmetry for each case. In addition, the spin-component scaled MP2 method (SCS-RI-MP2) has been used [77,78]. The SCS-RI-MP2 correlation treatment yields better structures than the standard MP2, especially in systems dominated by dispersion effects [79]. The calculations were carried out using Dunning's correlation-consistent polarized weightedcore valence basis sets of triple-ζ (aug-cc-pwCVTZ, abbreviated as AVTZ). Furthermore, we used a truncated AVTZ basis, denoted AVTZ', which removes diffuse functions from the hydrogen atoms not involved in hydrogen bonding.
The energies of the compounds were improved by using the CCSD(T)/CBS level of theory [80]. The CCSD(T) method provides reliable interaction energies only when brought together with extended atomic orbitals basis sets. It is recommended that the relevant calculations be performed at the complete basis-set (CBS) limit. The extrapolation scheme of Helgaker et al. [81,82] has become the most widely used. Here, the HF and MP2 energies are separately extrapolated as follows: where E CBS and E X are the energies for the complete basis set and for the basis set with the largest angular momentum X, respectively. The CCSD(T)/CBS level can be achieved following an extrapolation of the MP2 and higher-order correlation energies towards the basis-set limit (equation 3). In this case, each of the components shows different sensitivity to the atomic orbital basis set: the MP2 correlation energy is the one that converges more slowly, and the larger the basis set used in the extrapolation, the better. In our manuscript, we used a two-point extrapolation scheme using the AVTZ and the aug-cc-pVQZ basis sets. The third term, called the CCSD(T) correction term (∆E CCSD(T) − ∆E MP2 ), converges much faster than the MP2 correlation energy and is obtained as the difference between the CCSD(T) and MP2 energies. In our case, we have used the AVTZ' basis set to calculate the CCSD(T) correction. All the geometry optimizations were performed by using TURBOMOLE version 7.0 [83], and CBS calculations were carried out with the help of the MOLPRO program [84]. The interaction energies were determined as the difference between the energy of the complex and the energies of the optimized isolated monomers.
In complexes in which CH/π and an Anion-π interactions coexist, we computed the cooperativity energy E coop using Equation (4) where E(Hπ) and E(Aπ) and E(Hπ + Aπ) terms correspond to the interaction energies of the corresponding optimized two-component CH/π and Anion-π complexes and the three-component CH/π-anion complexes, respectively, and E(HA) is the interaction between methane and the anion in the CH/π-anion complexes. This equation has been successfully used to investigate cooperativity effects when two different interactions coexist in a variety of systems, namely π systems as simultaneous hydride-and hydrogen-bond acceptors, the concurrent interaction of tetrafluoroethylene with anions and hydrogen-bond donors [66,67], Anion-π and halogen-bonding interactions [71], and ion-π and Argon/π interactions [68]. The bonding features were studied by using the Atoms-in-Molecules (AIM) theory [85,86]. For this purpose, we have found the most relevant bond and cage critical points (BCP and CCP, respectively) and evaluated the electron density at each CP with the help of the AIMAll program package [87].
The SAPT (Symmetry Adapted Perturbation Theory) [88] method permits the decomposition of the interaction energy into different contributions related to physically well-defined components, such as those arising from induction, electrostatic, dispersion, and exchange terms. Within the framework of the SAPT method, the interaction energy can be expressed as [89]: where E el is the electrostatic interaction energy of the monomers; E exch is the first-order exchange energy term; E ind represents the second-order induction energy; E disp is the second-order dispersion energy. The density fitting DFT-SAPT (DF-DFT-SAPT) method has been utilized to analyze the interaction energies of the complexes. In this method, the energies of interacting monomers are expressed in terms of orbital energies obtained from the Kohn-Sham density functional theory [90,91]. Besides the terms listed in Equation (5), a Hartree-Fock correction term δHF, which accounts for third-and higher-order induction and exchange corrections, has been included [92]. The DF-DFT-SAPT calculations have been carried out by using the PBE0/aug-cc-pVQZ/aug-cc-pwCVTZ-PP computational method [93]. The JK-fitting basis of Weigend [94] was used as an auxiliary fitting basis set. The cc-pV5Z JK-fitting basis was employed for all atoms. For the intermolecular correlation terms, i.e., the dispersion and exchange-dispersion terms, the related aug-cc-pVQZ MP2-fitting basis of Weigend, Köhn, and Hättig [95] were employed. All SAPT calculations have been performed with the MOLPRO program [84].
To further characterize CH/π and Anion-π interactions in real space based on the electron density, the noncovalent interaction NCI analysis based on the reduced density gradient (RDG) method [96] has been performed using the AIMAll program package [87].

Results and Discussion
3.1. Energetic and Geometric Details of CH/π and Anion-π Complexes Table 1 and Figure 1 summarize the binding energies and equilibrium distances of complexes 1-7. First, we will address the CH/π complexes 1-3. The interaction energies of complexes between benzene and methane are small and vary from −1.21 to −1.46 kcal/mol depending on the number of CH bonds pointing at the benzene molecular plane. The most favorable configuration of the benzene-methane complex is found for complex 1, i.e., the one that only points one CH bond at the ring, with interaction energy of −1.46 kcal/mol, comparable to previously reported results at the CCSD(T)/CBS level of theory [39]. In complexes 2a and 2b, the methane molecule points to two CH bonds at the benzene ring either at carbon atoms or at the middle point of CC bonds. The binding energies of 2a and 2b are almost the same, −1.37 and −1.38 kcal/mol, respectively, and slightly smaller than the one obtained for 1. In complexes 3a and 3b, the methane molecule positions three hydrogen atoms on the benzene molecule, either pointing at carbon atoms or at the middle point of CC bonds, yielding binding energies of −1.21 and −1.23 kcal/mol, respectively. Therefore, depending on the positioning of the methane molecule, the binding energy for the interaction with benzene will only vary around 0.25 kcal/mol between the most and least favorable configurations, thus confirming the weak orientation dependence of the CH/π interaction [97]. The equilibrium distance in CH/π complexes (R Hπ , Table 1 and Figure 1), defined as the distance between the carbon atom of the methane molecule and the molecular plane of benzene, ranges from 3.753 Å for complex 1 to 3.634 Å for complexes 3a and 3b. Thus, as expected by the similar binding energies, there is a small variation of the equilibrium distances (only 0.119 Å) between the most and least favorable configurations for the CH/π complexes. Let us continue with the Anion-π complexes, starting with the ones with formate (complexes 4a and 4b). Due to symmetry constraints, we have only considered the complexes shown in Figure 1. The binding energies of the carboxylate complexes are tiny and positive (not favorable, Table 1 and Figure 1), as expected from an electrostatic point of view for the interaction of an anion with an electron-rich aromatic system, such as benzene, that exhibits a negative quadrupole moment. The orientation of the formate anion, with both O atoms either pointing at C atoms of benzene or pointing at CC middle bonds, does not have any significant impact on the energetics and geometric features of the anion complexes, as can be inferred from the data collected in Table 1. For the nitrate-π complexes, we have explored different configurations shown in Figure 1 with one, two, and three of its O atoms pointing at the benzene molecule (complexes 5, 6a-b, and 7a-b, respectively). As expected, the interaction energy for complex 5 is not favorable (0.53 kcal/mol) with an equilibrium distance (R Aπ , Table 1 and Figure 1) of 3.200 Å, defined as the distance between the O atom and the molecular plane of benzene. Ongoing from complex 5 to 6a or 6b, the interaction energy becomes less positive (0.20 kcal/mol) with equilibrium distances slightly larger than the one found in complex 5. However, the complexes where all three O atoms of the nitrate anion point at the ring (complexes 7a and 7b) yield favorable configurations with negative interaction energies of −1.02 kcal/mol and −0.99 kcal/mol, depending on the orientation of the anion. Therefore, surprisingly, the interaction of benzene with nitrate is favorable only if the anion is stacked with the aromatic system. In these cases, the equilibrium distances are very similar to the ones found in complexes 6a and 6b. This behavior is likely related to the electrophilic role of the central N-atom of the nitrate anion in these complexes. In fact, it has been demonstrated that nitrate anion can act as an electrophile in the solid state [98]. kcal/mol depending on the number of CH bonds pointing at the benzene molecular plane. The most favorable configuration of the benzene-methane complex is found for complex 1, i.e., the one that only points one CH bond at the ring, with interaction energy of −1.46 kcal/mol, comparable to previously reported results at the CCSD(T)/CBS level of theory [39]. In complexes 2a and 2b, the methane molecule points to two CH bonds at the benzene ring either at carbon atoms or at the middle point of CC bonds. The binding energies of 2a and 2b are almost the same, −1.37 and −1.38 kcal/mol, respectively, and slightly smaller than the one obtained for 1. In complexes 3a and 3b, the methane molecule positions three hydrogen atoms on the benzene molecule, either pointing at carbon atoms or at the middle point of CC bonds, yielding binding energies of −1.21 and −1.23 kcal/mol, respectively. Therefore, depending on the positioning of the methane molecule, the binding energy for the interaction with benzene will only vary around 0.25 kcal/mol between the most and least favorable configurations, thus confirming the weak orientation dependence of the CH/π interaction [97]. The equilibrium distance in CH/π complexes (RHπ, Table 1 and Figure 1), defined as the distance between the carbon atom of the methane molecule and the molecular plane of benzene, ranges from 3.753 Å for complex 1 to 3.634 Å for complexes 3a and 3b. Thus, as expected by the similar binding energies, there is a small variation of the equilibrium distances (only 0.119 Å) between the most and least favorable configurations for the CH/π complexes.

Energetic and Geometric Details of Three-Component CH/π and Anion-π Complexes
The geometric and energetic results computed for multicomponent complexes 8-11 are summarized in Table 1  the three-component complexes under study because we expect they would yield similar results to those of formate complexes. Thus, we have only considered the configurations where nitrate is establishing stacking interactions due to its uniqueness (11a-b).
N-atom of the nitrate anion in these complexes. In fact, it has been demonstrated that nitrate anion can act as an electrophile in the solid state [98].

Energetic and Geometric Details of Three-Component CH/π and Anion-π Complexes
The geometric and energetic results computed for multicomponent complexes 8-11 are summarized in Table 1 and Figure 2. We have considered both orientations of formate in the three-component complexes (complexes 8-10). In the case of nitrate, configurations where either one or two O atoms are pointing at the ring, have not been considered in the three-component complexes under study because we expect they would yield similar results to those of formate complexes. Thus, we have only considered the configurations where nitrate is establishing stacking interactions due to its uniqueness (11a-b). Some interesting points can be extracted from the geometrical results. In all cases, the equilibrium distance of the anion-π interactions in CH/π-anion complexes 8-11 is shorter than in their respective two-component complexes 4-7 (see ΔRAπ in Table 1), i.e., the presence of the CH/π interaction reinforces the anion-π interactions. Moreover, the equilibrium distance of the CH/π interaction RHπ in complexes 8-11 is also shorter compared to complexes 1-3, i.e., the presence of the anion-π interactions also reinforces the CH/π Some interesting points can be extracted from the geometrical results. In all cases, the equilibrium distance of the Anion-π interactions in CH/π-anion complexes 8-11 is shorter than in their respective two-component complexes 4-7 (see ∆R Aπ in Table 1), i.e., the presence of the CH/π interaction reinforces the Anion-π interactions. Moreover, the equilibrium distance of the CH/π interaction R Hπ in complexes 8-11 is also shorter compared to complexes 1-3, i.e., the presence of the Anion-π interactions also reinforces the CH/π interaction. There are three exceptions, the complexes 10a-c, for which ∆R Hπ is positive but almost negligible.
In all three-component complexes, the interaction energies are negative (see Table 1), with values that are larger than the sum of the interaction energies of the related CH/π and Anion-π two-component systems. With the intention of analyzing the mutual influence between the Anion-π interaction and the CH/π interaction, we have computed what we entitle the cooperativity energies (E coop in Table 2) for complexes 8a-b, 9a-d, 10a-d, and 11a-b. The cooperativity energy is the result of subtracting the binding energies of geometry optimized two-component complexes and the binding energy of the interaction between the anion and methane as in 8-11 complexes from the binding energy of the three-component complexes. For instance, in complex 9a (methane···benzene···formate) we have computed the E coop by subtracting the sum of three pair interaction energies: (i) benzene···formate (4b), (ii) methane···benzene (2a) and (iii) methane···formate as in 9a from the binding energy of 9a. This value gives important information regarding the interplay between both noncovalent interactions present in the complexes. It is worth mentioning that this term is negative in all complexes (it ranges from −0.37 to −0.54 kcal/mol, see Table 2), confirming the synergetic effects of both interactions, in agreement with the shortening of the equilibrium distances previously mentioned. The largest E coop values are obtained for complexes 8 and 11 (−0.51 and −0.54 kcal/mol, respectively). However, E coop is more important in complexes 9a and 9b because it amounts to 25.3% and 25.2%, respectively, of the total interaction energy ( Table 2). In any case, it is worth noting that cooperativity energy values are remarkable because they represent between 17.6% and 25.3% (%E coop ) of the total interaction energies. These results demonstrate that either the CH/π interaction influences the Anion-π interaction or the Anion-π interaction influences the CH/π interaction, or both. To further evaluate the effect of the Anion-π interaction on the CH/π bonding and vice versa, we have computed the binding energy of the three-component complexes 8-11 using two different approaches (see Table 2 and Figure 3). First, we have computed the binding energies of complexes 8-11 considering that the CH/π complex has been previously formed and evaluating the interaction with the anion as a two-component system (Aπ2 with binding energy E Aπ2 , for instance, 2a + HCO 2 − → 9a). Second, we have computed the binding energies of complexes 8-11, considering that the Anion-π complex has been previously formed and evaluating the interaction with methane as a two-component system (Hπ2 with binding energy E Hπ2 , for instance, 4a + CH 4 → 9b). Finally, we have compared these binding energy values (E Aπ2 and E Hπ2 ) with the corresponding binding energies of the two-component complexes 1-7, which we refer to as E Aπ1 and E Hπ1 , present in Table 1. Therefore, we have also summarized in Table 2 the difference between the binding energies computed for the ternary complexes and the binding energies of the corresponding binary complexes (denoted as ∆E Aπ and ∆E Hπ ). The ∆E Aπ and ∆E Hπ values allow us to evaluate which noncovalent interaction is more strengthened in the ternary complexes with respect to the two-component complexes. Therefore, a negative value would mean that the interaction is strengthened, and a positive value would mean that the interaction is weakened in the three-component complex with respect to the corresponding two-component complex. The values of ∆E Aπ and ∆E Hπ computed for complexes 8-11 are negative in all cases, in agreement with the previously discussed energetic (E coop ) and geometric (∆R Hπ and ∆R Aπ ) results. In fact, the largest ∆E Hπ values correspond to the complexes with the largest ∆R Hπ values (8a-b and 11a-b). Therefore, both the Anion-π and CH/π interactions are Sci 2022, 4, 32 9 of 20 reinforced with respect to their two-component counterparts when the benzene ring is interacting with methane on one side and with either formate or nitrate anion on the other side of the π system. Curiously, ∆E Aπ and ∆E Hπ have exactly the same values for each complex, and thus, according to these parameters, both interactions are equally reinforced on going from the two-component to the three-component complexes. All these interesting results allow us to learn which interaction in the multi-component system is reinforced. This information cannot be obtained from the cooperativity energies E coop .
complexes with respect to the two-component complexes. Therefore, a negative value would mean that the interaction is strengthened, and a positive value would mean that the interaction is weakened in the three-component complex with respect to the corresponding two-component complex. The values of ΔEAπ and ΔEHπ computed for complexes 8-11 are negative in all cases, in agreement with the previously discussed energetic (Ecoop) and geometric (ΔRHπ and ΔRAπ) results. In fact, the largest ΔEHπ values correspond to the complexes with the largest ΔRHπ values (8a-b and 11a-b). Therefore, both the anion-π and CH/π interactions are reinforced with respect to their two-component counterparts when the benzene ring is interacting with methane on one side and with either formate or nitrate anion on the other side of the π system. Curiously, ΔEAπ and ΔEHπ have exactly the same values for each complex, and thus, according to these parameters, both interactions are equally reinforced on going from the two-component to the three-component complexes. All these interesting results allow us to learn which interaction in the multi-component system is reinforced. This information cannot be obtained from the cooperativity energies Ecoop. Figure 3. Schematic representation of the two routes to form the CH/π-Anion complexes that allows computation of the ΔEHπ and ΔEAπ differences.

SAPT, AIM and NCI Analysis
To analyzing the electrostatic contribution of the anion-π interaction and how it is affected by the formation of the CH/π complex, we computed the electrostatic potential maps of benzene and complexes 1 and 2a on their van der Waals surfaces. The computed ESP value on the center of the benzene molecule is −15.41 kcal/mol (Figure 4). For complex 1, the computed ESP value on the side of the aromatic ring where methane is not located is −14.90 kcal/mol, i.e., on going from benzene to complex 1, the ESP value on the benzene molecule becomes less negative by 0.51 kcal/mol and thus less repulsive if we would consider an anion-π interaction on this side of the benzene molecular plane. Very similar results are obtained for complex 2a (0.32 kcal/mol ESP difference). Therefore, as soon as the methane molecule begins to interact with benzene through CH/π interactions as in complex 1, the electron density of each molecule is polarized by the electric field of the

SAPT, AIM and NCI Analysis
To analyzing the electrostatic contribution of the Anion-π interaction and how it is affected by the formation of the CH/π complex, we computed the electrostatic potential maps of benzene and complexes 1 and 2a on their van der Waals surfaces. The computed ESP value on the center of the benzene molecule is −15.41 kcal/mol (Figure 4). For complex 1, the computed ESP value on the side of the aromatic ring where methane is not located is −14.90 kcal/mol, i.e., on going from benzene to complex 1, the ESP value on the benzene molecule becomes less negative by 0.51 kcal/mol and thus less repulsive if we would consider an Anion-π interaction on this side of the benzene molecular plane. Very similar results are obtained for complex 2a (0.32 kcal/mol ESP difference). Therefore, as soon as the methane molecule begins to interact with benzene through CH/π interactions as in complex 1, the electron density of each molecule is polarized by the electric field of the other, resulting in a better Anion-π interaction on the free surface of the benzene molecule in complex 1, than in free benzene.
These results urge us to expand the study and analysis of the physical nature of the interactions by carrying out SAPT calculations. The individual contributions to the interaction energy as obtained from the SAPT partitioning scheme are listed in Table 3 for selected complexes 1, 2a, 4b, 9a, 7b, and 11b. The values of the sum of all energy terms, E SAPT , are close to the computed interaction energies at the CCSD(T) level of theory, as deduced from Table 3. other, resulting in a better anion-π interaction on the free surface of the benzene molecule in complex 1, than in free benzene. These results urge us to expand the study and analysis of the physical nature of the interactions by carrying out SAPT calculations. The individual contributions to the interaction energy as obtained from the SAPT partitioning scheme are listed in Table 3 for se- lected complexes 1, 2a, 4b, 9a, 7b, and 11b. The values of the sum of all energy terms, ESAPT, are close to the computed interaction energies at the CCSD(T) level of theory, as deduced from Table 3. Table 3. DF-DFT-symmetry-adapted perturbation theory (SAPT) electrostatic, exchange, induction, dispersion and Hartree-Fock higher-order energy contributions (Eel, Eexch, Eind, Edisp and δHF, respectively), SAPT interaction energy (ESAPT) and binding energies (E) of selected complexes. Energies in kcal/mol. We first analyze the CH/π interactions in complexes 1 and 2a. We found that the electrostatic component (Eel in Table 3) is attractive for all the CH/π complexes considered (1 and 2a, −0.89 and −0.68 kcal/mol, respectively). In these complexes, the induction term is very small, and the most important attractive contribution comes from dispersion effects (−2.46 and −2.45 kcal/mol) with a relative weight within all attractive forces of 65.7% and 71.2% for complexes 1 and 2a, respectively. For the anion-π complexes, the electrostatic term is repulsive (3.75 and 2.65 kcal/mol) as expected because of the large and negative quadrupole moment of benzene. For these complexes (4b and 7b), the most important attractive contribution comes from Eind and Edisp, respectively. Therefore,  We first analyze the CH/π interactions in complexes 1 and 2a. We found that the electrostatic component (E el in Table 3) is attractive for all the CH/π complexes considered (1 and 2a, −0.89 and −0.68 kcal/mol, respectively). In these complexes, the induction term is very small, and the most important attractive contribution comes from dispersion effects (−2.46 and −2.45 kcal/mol) with a relative weight within all attractive forces of 65.7% and 71.2% for complexes 1 and 2a, respectively. For the Anion-π complexes, the electrostatic term is repulsive (3.75 and 2.65 kcal/mol) as expected because of the large and negative quadrupole moment of benzene. For these complexes (4b and 7b), the most important attractive contribution comes from E ind and E disp , respectively. Therefore, according to the SAPT calculations, the source of stabilization of the Anion-π stacking interaction in 7b, compared to 4b, is based on large dispersion effects (−4.99 kcal/mol) also keeping large induction effects (−3.22 kcal/mol) and a reduced electrostatic repulsive contribution.

Compound
To analyze the nature of the cooperativity effects in complexes 8-11, we selected complexes 9a and 11b and computed the SAPT of three-component complexes using the approaches described in the previous section (see Figure 3). First, we computed the SAPT of 9a and 11b, considering that the Anion-π complex has been previously formed and examining the interaction with methane as a two-component system (e.g., 4b + CH 4 → 9a).
Second, we computed the SAPT of 9a and 11b, considering that the CH/π complex has been previously formed and examining its interaction with the anion (e.g., 2a + anion → 9a).
Let us first analyze the CH/π interaction. For complexes 9a and 11b, all attractive contributions have been increased. For instance, the E el , E ind , and E disp for the CH/π interaction in 9a have been increased by −0.31, −0.48, and −0.32 kcal/mol, respectively, with respect to complex 2a. Similar results were obtained for complex 11b. Despite dispersion being the major contributor to the CH/π binding, with a relative weight of 61.2% and 59.2% for complexes 9a and 11b, respectively, the observed synergistic effects have their origin in the enhancement of all contributions, with a special mention on the induction term.
Let us continue with the analysis of the Anion-π interaction. For these complexes we observed that all energy contributions become more negative, except for the induction contribution in 11b. As observed in complexes 4b and 7b, the major source of stabilization in 9a and 11b comes from induction and dispersion terms, respectively. It can be seen that the strengthening of the Anion-π interaction in 9a is due primarily to an increase of all the attractive contributions, specifically the induction term (−0.35 kcal/mol) and a considerable decrease of the repulsive electrostatic term (−0.40 kcal/mol) on going from 4b to 9a. On the other hand, the observed strengthening in 11b has a different nature since it comes primarily from a substantial reduction of the repulsive electrostatic contribution (−0.46 kcal/mol) and a slight increase in the dispersion term (−0.22 kca·mol −1 ) on going from 7b to 11b.
Moreover, for all ternary complexes, the δHF contribution always favours the interaction on going from two-to three-component complexes.
To further analyze the noncovalent character of these interactions, the AIM methodology was applied to assess the properties of the charge density for our systems. The molecular graphs of several two-component complexes are shown in Figure 5. The AIM analysis of the electron density in CH/π complexes reveals the presence of two intermolecular bond critical points (BCP) that connect one (complex 1), two H (complex 2a), and three H atoms (complex 3a) of methane with two (1 and 2a) and three C atoms (3a) of benzene (supplementary information, Figure S1). In addition, complexes 2b and 3b show two and three intermolecular BCP connecting methane with two and three intramolecular CC BCP of benzene, respectively. Analogously, very similar results are obtained for the Anion-π complexes ( Figure 5 and Figure S1). For instance, the same number of BCP is obtained depending on the number of anion O atoms pointing at either C atoms or CC BCP of the aromatic ring. All intermolecular BCP is associated with the corresponding bond path connecting either H atoms of methane or O atoms of the anions with the benzene molecule. The values of the electron densities of BCP range between 0.0046 (complex 1) and 0.0029 a.u. (complex 3b) for CH/π derivatives, and between 0.0047 (complexes 4a,b) and 0.0035 a.u. (complex 5) for Anion-π complexes (Table 4). Moreover, positive values of the Laplacian for all complexes were obtained, ranging between 0.0165 a.u. (complex 1) and 0.0097 a.u. (complexes 3a,b), and between 0.0152 (complexes 6a,b) and 0.0135 (complex 5) for CH/π and Anion-π complexes, respectively, indicating close shell regime interactions. All these interactions are also characterized by the presence of one cage critical point (CCP). In Table 4 we gather the values of the electron density (ρ), and its Laplacian (∇ 2 ρ) computed at the cage critical points for complexes 1-7. The molecular graphs of the three-component complexes are shown in Figure 6 and Figure S2. As can be observed, the distribution of the intermolecular BCP and CCP associated with both interactions is the same as the one obtained for the two-component complexes, except for complexes 11a,b, where six BCP for the CH/π interaction are located, as opposed to the two BCPs found in complex 1. In Table S1, we also summarize the variation of the values of ρ and its Laplacian (∇ 2 ρ) in the complexes 8-11 with respect to the binary complexes 1-7 for the BCP and CCP. These values give information about the interplay between the noncovalent interaction involved in the complexes. It is worth remarking that the value of the charge density and its Laplacian computed at both BCP and CCP are greater in the three-component complexes than in the two-component complexes, in agreement with the geometrical (shortening of equilibrium distances) and energetic results (E coop values), thus confirming the synergetic effect of the simultaneous formation of the CH/π and Anion-π interactions. and CCP associated with both interactions is the same as the one obtained for the twocomponent complexes, except for complexes 11a-b, where six BCP for the CH/π interaction are located, as opposed to the two BCPs found in complex 1. In Table S1, we also summarize the variation of the values of ρ and its Laplacian (∇ 2 ρ) in the complexes 8-11 with respect to the binary complexes 1-7 for the BCP and CCP. These values give information about the interplay between the noncovalent interaction involved in the complexes. It is worth remarking that the value of the charge density and its Laplacian computed at both BCP and CCP are greater in the three-component complexes than in the two-component complexes, in agreement with the geometrical (shortening of equilibrium distances) and energetic results (Ecoop values), thus confirming the synergetic effect of the simultaneous formation of the CH/π and anion-π interactions. Figure 5. Molecular graphs of a selection of two-component complexes (1, 2a, 2b, 4a, 4b, 7a). The BCPs, ring and cage critical points are represented by green, red, and blue dots, respectively. Only bond paths are depicted (intermolecular bond paths are shown as dashed lines). Carbon, nitrogen, oxygen, and hydrogen atoms are indicated in grey, blue, red, and white color, respectively. Table 4. Electron density (ρBCP and ρCCP) and Laplacian (∇ 2 ρBCP and ∇ 2 ρCCP), in a.u., for the intermolecular bond critical points and cage critical points, respectively, in two-component complexes.
Compound Given that noncovalent interactions are characterized by low density (ρ) and reduced density gradient (RDG) values, they can be located using the NCIPLOT program [96]. These regions are mapped in real space by plotting an RDG isosurface for a low value of RDG, showing noncovalent interactions as broad regions of real space instead of simple pairwise contacts between atoms. Moreover, the sign of the second eigenvalue (λ2) of the Given that noncovalent interactions are characterized by low density (ρ) and reduced density gradient (RDG) values, they can be located using the NCIPLOT program [96]. These regions are mapped in real space by plotting an RDG isosurface for a low value of RDG, showing noncovalent interactions as broad regions of real space instead of simple pairwise contacts between atoms. Moreover, the sign of the second eigenvalue (λ 2 ) of the density Hessian times the density is color-mapped onto the isosurfaces. Moreover, the sign of λ 2 can be used to distinguish between bonded (λ 2 < 0) and non-bonded (λ 2 > 0) interactions, and, therefore, it can help to differentiate between different types of noncovalent interactions. The regions of very low density (ρ < 0.005 a.u.) correspond to weak dispersion interactions, while those of slightly higher density values (0.005 < ρ < 0.05 au) correspond to stronger noncovalent interactions [96]. Figure 7 shows the gradient isosurfaces for a selection of twoand three-component complexes (The gradient isosurfaces for the rest of the complexes are gathered in Figures S3-S5 of the Supplementary information). As can be observed, there is an area of noncovalent interaction between the aromatic system and the methane molecule and the anion that covers the ring, just where the CH/π and Anion-π interactions are expected. Similar gradient isosurfaces are obtained for the rest of the complexes. In Figure 7, the sign(λ 2 )ρ values obtained at the intersection between the isosurfaces and the AIM bond paths are included. In all cases, these values are <0 and correspond to the maxima of electron density for each interaction, confirming the nature of these bonding interactions. Moreover, for a given interaction, the ρ values are increased in the threecomponent complexes in relation to the two-component complexes, thus reinforcing the given interaction. For instance, the ρ value for the CH/π interaction is increased from complex 2 (0.0040 au) to complex 9a (0.0044 au). Similarly, the density for the Anion-π interaction increases on going from complex 4 (0.0049 au) to complex 9a (0.0051 au). These results agree with previous results where we observe that the CH/π interaction reinforces the Anion-π interaction and vice versa in the three-component complexes.
interactions, and, therefore, it can help to differentiate between different types of noncovalent interactions. The regions of very low density (ρ < 0.005 a.u.) correspond to weak dispersion interactions, while those of slightly higher density values (0.005 < ρ < 0.05 au) correspond to stronger noncovalent interactions [96]. Figure 7 shows the gradient isosurfaces for a selection of two-and three-component complexes (The gradient isosurfaces for the rest of the complexes are gathered in Figures S3-S5 of the Supplementary information). As can be observed, there is an area of noncovalent interaction between the aromatic system and the methane molecule and the anion that covers the ring, just where the CH/π and anion-π interactions are expected. Similar gradient isosurfaces are obtained for the rest of the complexes. In Figure 7 , the sign(λ2)ρ values obtained at the intersection between the isosurfaces and the AIM bond paths are included. In all cases, these values are < 0 and correspond to the maxima of electron density for each interaction, confirming the nature of these bonding interactions. Moreover, for a given interaction, the ρ values are increased in the three-component complexes in relation to the two-component complexes, thus reinforcing the given interaction. For instance, the ρ value for the CH/π interaction is increased from complex 2 (0.0040 au) to complex 9a (0.0044 au). Similarly, the density for the anion-π interaction increases on going from complex 4 (0.0049 au) to complex 9a (0.0051 au). These results agree with previous results where we observe that the CH/π interaction reinforces the anion-π interaction and vice versa in the three-component complexes.

Experimental Evidences
Taking advantage of our previous study on Anion-π interactions in biomolecules [63], here we include two examples retrieved from the PDB in which Anion-π interactions with phenyl rings are operating concomitantly with CH/π interactions coming from alkyl groups (Figure 8). In the first example, the authors report studies on the cellular protein cyclophilin A (CypA) and how it interacts with the HIV-1 capsid domain [99]. They found that the capsid sequence 87 His-Ala-Gly-Pro-Ile-Ala 92 ( 87 HAGPIA 92 ) encompasses the primary cyclophilin A binding site, as shown in the reported X-ray crystal structure of the CypA/HAGPIA complex. Although it was either not discussed or not noticed by the authors, the inspection of the structure reveals the presence of an Anion-π interaction between three carboxylate moiety of the C-terminal alanine of HAGPIA hexapeptide with the phenyl ring of phenylalanine 60 of CypA which, at the same time, is CH/π interacting with a methylene group of methionine 61 of CypA (Figure 8, left).

Experimental Evidences
Taking advantage of our previous study on anion-π interactions in biomolecules [63], here we include two examples retrieved from the PDB in which anion-π interactions with phenyl rings are operating concomitantly with CH/π interactions coming from alkyl groups (Figure 8). In the first example, the authors report studies on the cellular protein cyclophilin A (CypA) and how it interacts with the HIV-1 capsid domain [99]. They found that the capsid sequence 87 His-Ala-Gly-Pro-Ile-Ala 92 ( 87 HAGPIA 92 ) encompasses the primary cyclophilin A binding site, as shown in the reported X-ray crystal structure of the CypA/HAGPIA complex. Although it was either not discussed or not noticed by the authors, the inspection of the structure reveals the presence of an anion-π interaction between three carboxylate moiety of the C-terminal alanine of HAGPIA hexapeptide with the phenyl ring of phenylalanine 60 of CypA which, at the same time, is CH/π interacting with a methylene group of methionine 61 of CypA (Figure 8, left). In the second example, the authors report a deswapping study of a mutant bovine Odorant Binding Protein (bOBP), describing its crystal structure and ligand binding properties, to decipher the evolutionary advantage of a domain swapping in native bOBP [100]. A partial view of the crystal structure of bOBP in a complex with 3,6-bis(methylene)decanoic acid (LIK) is shown in Figure 8. As can be seen, an unnoticed anion-π interaction by the authors is established between the carboxylate group of the ligand and the aromatic ring of phenylalanine 89 of bOBP, which is simultaneously forming a CH/π interaction on the opposite side of the aromatic ring with the conveniently located methylene group of tyrosine 79.

Conclusions
The results reported in this manuscript demonstrate the importance of the mutual influence between CH/π and anion-π interactions when the benzene molecule acts as the π-system, leading to strong synergetic effects. From the geometrical point of view, these In the second example, the authors report a deswapping study of a mutant bovine Odorant Binding Protein (bOBP), describing its crystal structure and ligand binding properties, to decipher the evolutionary advantage of a domain swapping in native bOBP [100]. A partial view of the crystal structure of bOBP in a complex with 3,6-bis(methylene)decanoic acid (LIK) is shown in Figure 8. As can be seen, an unnoticed Anion-π interaction by the authors is established between the carboxylate group of the ligand and the aromatic ring of phenylalanine 89 of bOBP, which is simultaneously forming a CH/π interaction on the opposite side of the aromatic ring with the conveniently located methylene group of tyrosine 79.

Conclusions
The results reported in this manuscript demonstrate the importance of the mutual influence between CH/π and Anion-π interactions when the benzene molecule acts as the π-system, leading to strong synergetic effects. From the geometrical point of view, these effects are translated into a shortening of the equilibrium distances (0.02-0.05 Å) of both interactions on going from the two-component to the three-component complexes. From the energetics point of view, we obtained values of cooperativity energies E coop ranging from −0.37 to −0.54 kcal/mol. These values are high since they represent between 17% and 25% of the total interaction energy, demonstrating that either the CH/π interaction has an influence on the Anion-π interaction or the Anion-π interaction has an influence on the CH/π interaction or both. By means of the approaches described in Figure 3, we have concluded that both Anion-π and CH/π interactions are strengthened with respect to their two-component counterparts when the benzene ring is interacting with methane on one side and with an anion on another side of the π-system. All these interesting results allow us to learn which interaction in the multi-component system is more reinforced, information that cannot be obtained from E coop . Moreover, the SAPT energy partitioning scheme gives us valuable information on the origin of the observed synergetic effects. In this regard, the reinforcement of the CH/π interaction has its origin in the enhancement of all contributions, with a special mention on the induction term, whereas the reinforcement of the Anion-π interaction is based on an increase of all attractive contributions coupled with a considerable decrease of the repulsive electrostatic term, except for the stacked complex 11b, where the variation of the induction term is almost negligible. AIM and NCI results are also in agreement with the observed cooperativity effects and the strengthening of both interactions. Bearing in mind that many biomolecules and substrates contain phenyl groups, alkyl chains, and anionic groups, these synergetic effects might be crucial in different areas of biological chemistry.