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Journal of Molecular Modeling

, 24:258 | Cite as

Co-operativity in non-covalent interactions in ternary complexes: a comprehensive electronic structure theory based investigation

  • Shyam Vinod Kumar Panneer
  • Mahesh Kumar Ravva
  • Brijesh Kumar Mishra
  • Venkatesan SubramanianEmail author
  • Narayanasami Sathyamurthy
Original Paper
  • 115 Downloads
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

The structure and stability of various ternary complexes in which an extended aromatic system such as coronene interacts with ions/atoms/molecules on opposite faces of the π-electron cloud were investigated using ab initio calculations. By characterizing the nature of the intermolecular interactions using an energy decomposition analysis, it was shown that there is an interplay between various types of interactions and that there are co-operativity effects, particularly when different types of interactions coexist in the same system.

Graphical abstract

Weak OH-π, π-π and van der Waals-π ternary systems are stabilized through dispersion interactions. Cation-π ternary systems are stabilized by through-space electrostatic interactions.

Keywords

Non-covalent interactions Ternary complexes Coronene DFT SAPT QTAIM 

Introduction

Cation–π interactions have been studied over the years (for example, see refs [1, 2, 3]) and the subject has been reviewed elsewhere [4]. Interaction of different molecules with π-systems has also been the subject of considerable investigation (for example, see [5]). An interesting question arises: how does an ion/atom/molecule on one face of a π-system influence the interaction of another ion/atom/molecule on the other face of the π-system. Sastry and coworkers have examined such cooperativity in noncovalent interactions in such ternary systems and have reviewed the literature on the subject recently [6, 7].

It can be anticipated that wherever there is electrostatic interaction, interactions will be additive and there is likely to be little cooperativity. On the other hand, wherever there are other interactions such as with exchange or dispersion dominating, there could be cooperativity or anti-cooperativity.

Although the coupled clusters singles and doubles and perturbative triples [CCSD(T)] method is the gold standard for the calculation of correlation energy of systems involving non-covalent interactions [8], Møller-Plesset second order (MP2) perturbation theory and density functional theory (DFT) using different functionals have been employed to decipher these interactions after rigorous benchmarking [9]. Energy values calculated at the Hartree-Fock level of theory account for the electrostatic contributions. In unraveling the non-covalent interactions, molecular electrostatic potential has been used as a guiding tool to position non-covalently interacting molecular systems [10]. In addition, several energy decomposition schemes have been used to probe the origin and nature of these interactions [11]. Bader’s quantum theory of atoms in molecules (QTAIM) has been employed to characterize the nature of non-covalent interactions [12, 13]. Its utility has been demonstrated in a number of investigations [14, 15, 16, 17].

Several studies on non-covalent interactions involving π-system dimers comprising a π-system and neutral atoms/molecules and charged species have been carried out [18, 19]. The role of charge and dipole and quadrupole moments in the stabilization of these inter-molecular complexes has been investigated [5]. However, the number of studies on the ternary systems involving π-systems is rather limited [20, 21].

Considering the growing interest on the subject of ions/atoms/molecules interacting with graphene and other extended π-systems from both sides, we have undertaken an ab initio electronic structure investigation of the interaction of Na+, Cl, water (W), benzene (Bz) and argon (Ar) from the top side and bottom side of coronene (Cor) as a prototype. A total of 13 ternary systems involving combinations of cation–π, anion–π, OH–π, π–π, and van der Waals–π type interactions have been studied.

Computational details

The geometry of coronene and the intermolecular complexes was optimized at the MP2/6-31+G(d,p) level of theory. The interaction energy (∆Eint) values were computed at the same level of theory for the optimized geometries. For binary complexes, basis set superposition error (BSSE)-corrected ∆Eint values were determined using the counterpoise method described by Boys and Bernardi [22] employing Eq. (1):
$$ {\Delta E}_{int}(AB)=\left[E(AB)-\left(E(A)+E(B)\right)\right], $$
(1)
where E (AB) is the total energy of the binary complex, and E(A) and E(B) are the total energies of the monomers A and B, respectively.
Similarly, for ternary systems, the BSSE corrected ∆Eint (ABC) values were calculated by determining the total energy of the ternary complex and the total energy of individual monomers using counterpoise method as shown in Eq.(2):
$$ {\Delta E}_{int}(ABC)=\left[E(ABC)-\left(E(A)+E(B)+E(C)\right)\right], $$
(2)
where E (ABC) is the total energy of the ternary complex, and E(A), E(B) and E(C) are the total energies of the monomers A, B and C, respectively, calculated for the monomer geometry in the complex.

To gain a deeper understanding of the nature of intermolecular interactions, an energy decomposition analysis was carried out using symmetry-adapted perturbation theory (SAPT) and the cc-pVDZ basis set [23, 24]. In this approach, the total interaction energy can be partitioned into various physically meaningful contributions: the electrostatic, exchange-repulsion, induction (permanent dipole-induced dipole), and dispersion (induced dipole-induced dipole) interactions. All MP2 and SAPT calculations were performed using the Gaussian 09 [25] and PSI-4 [26] packages, respectively. The QTAIM topological analysis of the electron density distribution was carried out for the binary and ternary complexes. QTAIM reference values were obtained from the wave functions obtained at the MP2/6-31+G(d,p) level of theory using the AIM2000 software package [27].

The inherent charge and dipole and quadrupole moments of individual atomic/molecular units play an important role in the stabilization of the ternary complex. Hence, the charge⋯dipole (∆Eq-D), charge⋯quadrupole (∆Eq-Q), dipole⋯dipole (∆ED-D), dipole⋯quadrupole (∆ED-Q) and quadrupole⋯quadrupole (∆EQ-Q) interaction energies were estimated as follows [28]:
$$ \Delta {E}_{q-D}=\frac{q_{ion}\times \mu cos\theta}{R^2}, $$
(3)
$$ \Delta {E}_{q-Q}=\frac{q_{ion}\times {Q}_{zz}}{R^3}, $$
(4)
$$ \Delta {E}_{D-D}=\pm 2\times \frac{\mu^A\times {\mu}^B}{R^3}, $$
(5)
$$ \Delta {E}_{D-Q}=\pm 3\times \frac{\mu^A\times {Q}_{zz}^B}{R^4}, $$
(6)
$$ \Delta {E}_{Q-Q}=\pm 6\times \frac{Q_{zz}^A\times {Q}_{zz}^B}{R^5}, $$
(7)
where q represents the charge of the ion, μ represents the dipole moment and Q the quadrupole moment of the molecule. R is the center-of-mass separation. The “+” and “−” signs are applicable depending upon the direction of μ and Q of the interacting units.

Results and discussion

Geometries

The main purpose of the present study was to understand the interplay of various intermolecular interactions and cooperativity in the 13 ternary complexes under investigation. They consist of charge–π–charge (Na+–Cor–Cl), charge–π–dipole (Na+–Cor–W and Cl–Cor–W), charge–π–quadrupole (Na+–Cor–Bz and Cl–Cor–Bz), charge–π–van der Waals (Na+–Cor–Ar and Cl–Cor–Ar), dipole–π–dipole (W–Cor–W), dipole–π–quadrupole (W–Cor–Bz), dipole–π–van der Waals (W–Cor–Ar), quadrupole–π–quadrupole (Bz–Cor–Bz), quadrupole–π–van der Waals (Bz–Cor–Ar), and van der Waals-π-van der Waals (Ar–Cor–Ar) systems. All geometries were fully optimized at the MP2/6-31+G(d,p) level of theory and the results are shown in Fig. 1 along with the R values. It is important to point out that the ions, atoms and molecules are adsorbed on the central ring of coronene.
Fig. 1

Optimized geometries of various ternary complexes as obtained from ab initio calculations at MP2/6–31+G(d,p) level of theory. The color codes used for different atoms are as follows: gray carbon, white hydrogen, red oxygen, violet Na+, green Cl, blue argon. The dashed blue line represents the distance between coronene and the respective atom/ion/molecule

Interaction energies

Earlier studies had estimated the ∆Eint value for Na+–Bz to be −24.7 kcal mol−1 at the CCSD(T)/CBS level of theory [29], compared to −28.0 kcal mol−1 obtained from experiments [30]. The interaction of a metal cation with coronene has been investigated using different electronic structure theory based methods. Dunbar and coworkers [31] investigated the monomer and dimer complexes of coronene with atomic ions. They calculated the interaction energy for the Na+–Cor complex using MPW1PW91, B3LYP, and B3P86 functionals with an optimal basis set combination of 6-31G(d) for carbon atoms, 6-31+G(d) for hydrogen atoms and 6-311+G(d) basis sets for Na+. They reported the ∆Eint values to be −31.6 kcal mol−1, −32.0 kcal mol−1, and − 30.8  kcal mol−1, respectively. Patra et al. [32] explored the dynamics of Na+, Li+, Cl and F ions binding to graphene nanostructures employing various model systems including coronene. They found that the anions were either physisorbed on the surface of coronene or covalently bound to selected regions. It was also found that the cations were physisorbed on coronene. In the present study, ∆Eint for Na+-Cor at MP2/6-31+G(d,p) level of theory was found to be −27.0 kcal mol−1.

Several experimental and theoretical studies have examined the anion–π interaction [18, 33, 34, 35]. An earlier study [36] showed the ∆Eint value to be −0.17 kcal mol−1 for the Cl–Bz complex, at the MP2/6-311++G(d,p) level of theory. In contrast, ∆Eint for the Cl-hexafluorobenzene complex at the same level of theory was found to be −12.19 kcal mol−1 [37]. This is presumably due to a dramatic change in the quadrupole moment from −8.5 B for benzene to +9.5 B for hexafluorobenzene. It has been shown that introducing an electron-withdrawing/-donating group in an arene system strongly influences its interaction with anions [33]. DFT calculations using the M06-2X functional and the 6-311++G(d,p) basis set yielded a value of −2.8 kcal mol−1 for ∆Eint for the Cl-Cor complex [34]. Our calculations at the MP2/6-31+G(d,p) level of theory yielded a ∆Eint value of −1.6 kcal mol−1.

The interaction of water molecules with π-systems has been the subject of several earlier investigations. In fact, in most of the studies, the water–benzene interaction has been taken to be the prototype for the OH–π interaction [38, 39]. A water molecule interacts with a π-system in different ways: (1) one of the O–H bonds of the water molecule interacts directly with the π-cloud, (2) the two O–H bonds of the water molecule interact with the π-cloud and (3) the lone pair (lp) of the oxygen atom (of the water molecule) interacts with the π-system. Both high-resolution spectroscopic and electronic structure calculations using wave function and DFT-based methods have been applied to unravel the interaction between benzene and water. With a view to modeling the interaction of water molecules with graphite and wetting of graphene, different model systems such as anthracene, pentacene, coronene, and dodecabenzocoronene have been selected. Jenness and Jordan [40] found the water-coronene interaction energy to be −2.5 kcal mol−1 using the DF-DFT-SAPT based method and a modified aug-cc-pVTZ basis set. We have calculated the ∆Eint value for the water-coronene system to be −2.6 kcal mol−1 at the MP2/6-31+G(d,p) level of theory.

The Bz-Cor system has been investigated to model π–π interactions in biological molecules including the three-dimensional (3D) structure of DNA and proteins [41]. In addition, these interactions provide useful information on the functionalization of graphene and stacking interactions in the formation of graphite and van der Waals solids. Previous studies [41] showed ∆Eint to be −9.3 kcal mol−1 for Bz–Cor at MP2/6-31G(d) level of theory. We find ∆Eint for the Bz–Cor binary complex using the MP2/6-31+G(d,p) level of theory to be −9.7 kcal mol−1.

It is well known that the strength of non-covalent interaction ranges from very weak to very strong, bordering on covalent, energy [42]. The interaction of rare gas atoms with π-systems is one of the weakest. It has been used to ascertain the accuracy of various electronic structure methods and the role of electron correlation in the stabilization of these systems. Several high-resolution spectroscopic and theoretical studies have been carried out in the last three decades on rare gas–π systems [43]. In the present study, Ar–Cor was chosen as the model system to examine the role of other interactions in the stabilization of the third partner in ternary systems. Previously, the Ar–Cor interaction has been studied using the CCSD(T) level of theory in the complete basis set (CBS) limit [44]. The reported value of −1.9 kcal mol−1 for ∆Eint has to be compared with the value of −0.9 kcal mol−1 obtained by us at the MP2/6-31+G(d,p) level of theory.

We start our discussion with Na+- and coronene-based ternary systems, where Na+ binds on one face of the coronene molecule and Cl, water, benzene or argon binds on the other face (Fig. 1). In the ternary complexes investigated, the calculated intermolecular distance between the cation and the center of the coronene molecule varies from 2.295 to 2.380 Å due to the presence of different ion/atom/molecule on the other side of coronene (Fig. 1). In a binary Na+–Cor complex, the distance between Na+ and coronene is 2.380 Å (Fig. 2). The presence of Cl on the other side leads to a slight decrease (~0.1 Å) in the R value due to through-space electrostatic interaction between the two ions mediated by coronene. In the cases of Na+–Cor–W, Na+–Cor–Bz, and Na+–Cor–Ar, the through-space interaction is weaker and hence there is a marginal impact on R. Earlier reports [45] on the explicit solvation of cation–π systems had shown that when water molecules were present below the plane of the benzene ring (with the cation on top of the benzene ring), there was a reduction in the R value, when compared to the isolated cation–π system.
Fig. 2

Optimized geometries of various dimer complexes with charge–π, dipole–π, and quadrupole–π type interactions as obtained from ab initio calculations at MP2/6-31+G(d,p) level of theory. The color codes used for different atoms are as follows: gray carbon, white hydrogen, red oxygen, violet Na+, green Cl, blue argon. The dashed blue line represents the distance between coronene and the respective atom/ion/molecule

To understand the role of the third partner in an anion-π system, Cl–π was considered as a model system, with Na+, water, benzene or argon as the third partner. It can be noted from the geometrical parameters in Fig. 1 that the addition of Na+ to the other side of coronene decreases the distance between the anion and the center of coronene, whereas the presence of a neutral molecule/atom increases the distance between the anion and coronene. As expected, the anion-π interaction is strengthened by the presence of Na+ due to the through-space electrostatic interaction. In other cases, the anion-π distances are marginally longer than the distance between Cl and coronene in the absence of a third molecule (calculated anion-π distance in Cl-Cor complex is 3.091 Å, Fig. 2).

Geometry optimization for the W-Cor complex at the MP2/6-31+G(d,p) level of theory yielded a geometry in which both hydrogen atoms of the water molecule pointed towards the π-plane, in accord with the earlier reports. In the case of water- and coronene-based ternary systems, five different ternary complexes, where one water molecule was adsorbed on one face of coronene and Na+, Cl, water, benzene or argon was adsorbed on the other face of the same coronene molecule. As noted above, water molecules prefer to interact with the aromatic ring through one of their hydrogen atoms (OH–π interaction in W–Cor, shown in Fig. 2). However, when a Na+ ion is present on the opposite side of coronene (Na+–Cor–W), the water molecule changes its orientation in such a way that its oxygen atom interacts with the π-cloud through its lone pair. The through-space electrostatic interaction makes the electron-rich oxygen atom interact with Na+ even though coronene is inserted in between. In all other ternary systems, the water molecule prefers to interact with the aromatic ring through the OH–π interaction (Fig. 1). Marginal changes in the intermolecular distance were observed in the other ternary systems investigated, due to through-space interactions.

The ∆Eint values for the binary complexes of coronene obtained from ab initio calculations at the MP2/6-31+G(d,p) level of theory are listed in Table 1. As expected, the ∆Eint value for the Na+–Cor system is much larger than that for Cl–Cor and Bz–Cor. The calculated values of ∆Eint for W–Cor and Ar–Cor systems clearly indicate the presence of a weak interaction in them. All these ∆Eint values are in good agreement with the earlier reports. To see if the binary interaction energies are additive or not in a ternary complex, we computed the cooperativity effect (∆Ecoop) [6, 45, 46] as:
$$ \Delta {E}_{\mathrm{coop}}=\Delta {E}_{\mathrm{int}}\ \left( AB C\right)\hbox{--} \left\{\Delta {E}_{\mathrm{int}}\ (AB)+\Delta {E}_{\mathrm{int}}\ (BC)+\Delta {E}_{\mathrm{int}}\ (CA)\right\} $$
(8)
where, ∆Eint (AB), ∆Eint (BC) and ∆Eint (CA) were calculated using Eq. (2) by employing the optimized geometries of the components of the ternary complexes by excluding other participating units. For example, in the case of Na+–Cor–Cl, to calculate the Na+–Cor interaction energy, Cl was not included. For calculating the Cor–Cl interaction energy, Na+ was not included. And to calculate the Na+–Cl interaction energy, Cor was not included. A similar approach was followed for all 13 ternary systems. A negative value of ∆Ecoop is a clear sign of the existence of cooperativity. By the same logic, a positive value can be considered as anti-cooperativity. Values of three-body and two-body interaction energies and ∆Ecoop are listed in Table 2. It is clear from the data presented that ∆Ecoop is positive for Na+–Cor–Cl, Na+–Cor–W and Na+–Cor–Bz. It is negative for Na+–Cor–Ar. It is also positive for Cl–Cor–W and Cl–Cor–Bz. For Cl–Cor–Ar, it is practically zero, indicating that there is no cooperativity. In all other cases, there is very little cooperativity.
Table 1

Calculated interaction energy (∆Eint) values in kcal mol−1 units for binary complexes of coronene, obtained from MP2/6-31+G(d,p) calculations

System

Present study

Earlier reports

Na+-Cor

−27.0

−28.0 [30]

Cl-Cor

−1.6

−2.8 [33]

W-Cor

−2.7

−2.5 [40]

Bz-Cor

−9.7

−9.3 [41]

Ar-Cor

−0.9

−1.9 [43]

Table 2

Calculated interaction energy (∆Eint) values in kcal mol−1 for ternary and binary complexes as obtained from MP2/6-31+G(d,p) calculations

System

Eint (ABC)

Eint (AB)

Eint (BC)

Eint (CA)

Ecoop

Na+-Cor-Cl

−89.3

−26.4

0.3

−65.7

2.5

Na+-Cor-W

−31.5

−26.9

−0.4

−5.8

1.6

Na+-Cor-Bz

−38.8

−27.0

−9.4

−3.7

1.3

Na+-Cor-Ar

−28.1

−27.0

−0.8

−0.1

−0.2

Cl-Cor-W

−7.3

−1.2

−2.5

−4.2

0.6

Cl-Cor-Bz

−11.2

−1.4

−9.6

0.8

−1.0

Cl-Cor-Ar

−2.5

−1.5

−0.9

−0.1

0.0

W-Cor-W

−5.1

−2.7

−2.7

0.4

−0.1

W-Cor-Bz

−12.5

−2.6

−9.6

−0.4

0.1

W-Cor-Ar

−3.6

−2.6

−0.9

−0.0

−0.1

Bz-Cor-Bz

−19.0

−9.3

−9.3

−0.1

−0.3

Bz-Cor-Ar

−10.6

−9.6

−0.8

0.0

−0.2

Ar-Cor-Ar

−1.8

−0.9

−0.9

0.0

0.0

It is clear from Table 2 that the value of ∆Eint for the cation-π systems is nearly the same in all ternary complexes. It is interesting to note that the anion-π interaction in Na+–Cor–Cl shows a positive interaction energy (0.3 kcal mol−1, Table 2) whereas in other cases such as Cl–Cor–W, Cl–Cor–Bz, and Cl–Cor–Ar systems, it shows a negative interaction energy. This observation suggests that the binary interaction between Cl and coronene in Na+-Cor-Cl is repulsive in nature, in spite of the fact that the anion-π distance in the ternary complex Na+–Cor–Cl is shorter than in the binary system Cl–Cor by ~ 0.22 Å (Figs. 1, 2), indicating a stronger interaction. This unusual behavior has to be interpreted in terms of the through-space interaction between Na+ on one side of coronene and Cl on the other side. The through-space interaction between the cation (Na+) on one side of coronene and ion/atom/molecule on the other side is much stronger for Na+–Cor–Cl, Na+–Cor–W, Na+–Cor–Bz, and Na+–Cor–Ar than for Cl–Cor–W, Cl–Cor–Bz, and Cl–Cor–Ar.

To understand the nature of these intermolecular interactions further, the ∆Eint value was decomposed into four physically meaningful energy terms: electrostatic, exchange-repulsion, induction, and dispersion energies. Using the geometries of the ternary complexes, energy decomposition analysis was carried out only for constituent binary systems of ternary complexes and classified according to the type of intermolecular interaction. For instance, in the case of the Na+–Cor–Cl complex, two different energy decomposition analyses were carried out: first, between Na+ and coronene by removing Cl (cation-π interaction) and then between Cl and coronene by removing Na+ (anion-π interaction) for the same Na+–Cor–Cl complex. Similar calculations were carried out for the rest of the ternary complexes and the results are listed in Table 3 according to the type of intermolecular interaction involved. The ∆Eint values calculated using the SAPT0/cc-pVDZ method were in good agreement with those obtained from MP2/6-31+G(d,p) calculations. It can be seen from Table 3 that the cation-π interaction is largely stabilized by electrostatic and induction energies. A major contribution from induction and dispersion energies accounts for the anion-π interaction. As demonstrated in earlier studies [47], the weak OH–π, π–π, and van der Waals interactions–π in ternary complexes are stabilized by dispersion interactions. The π–π and van der Waals–π interactions in ternary complexes are slightly stronger than in binary Bz-Cor and Ar-Cor complexes (Table 3).
Table 3

Calculated ∆Eint values in kcal mol−1 for binary systems of ternary complexes in the absence of the third moiety obtained from symmetry-adapted perturbation theory (SAPT0/cc-pVDZ) calculations

System

Electrostatic

Exchange

Induction

Dispersion

SAPT0

Cation-π

  Na+-Cor

−12.9

8.0

−23.6

−2.0

−30.5

  Na+-Cor-Cl

−13.2

10.4

−25.2

−2.3

−30.2

  Na+-Cor-W

−12.9

8.1

−23.7

−2.0

−30.5

  Na+-Cor-Bz

−12.8

8.2

−23.8

−2.0

−30.4

  Na+-Cor-Ar

−12.9

8.0

−23.6

−2.0

−30.5

Anion-π

  Cl-Cor

0.2

16.9

−11.5

−10.7

−5.1

  Na+-Cor-Cl

−5.9

28.9

−13.5

−14.4

−5.0

  Cl-Cor-W

−1.5

20.2

−12.2

−11.5

−4.9

  Cl-Cor-Bz

−0.5

18.4

−11.9

−10.9

−4.9

  Cl-Cor-Ar

−0.3

18.0

−11.7

−10.9

−5.0

OH-π

 W-Cor

−2.9

4.4

−0.9

−3.2

−2.6

  Na+-Cor-W

−1.2

5.5

−1.0

−4.9

−1.6

  Cl-Cor-W

−2.7

5.1

−1.3

−4.8

−3.6

 W-Cor-W

−2.4

4.2

−1.0

−4.4

−3.7

 W-Cor-Bz

−2.4

4.4

−1.1

−4.5

−3.6

 W-Cor-Ar

−2.5

4.4

−1.1

−4.5

−3.7

π–π

 Bz-Cor

−11.0

26.1

−2.0

−22.2

−9.1

  Na+-Cor-Bz

−11.7

28.1

−2.0

−28.9

−14.6

  Cl-Cor-Bz

−11.4

27.2

−2.0

−28.4

−14.7

 W-Cor-Bz

−11.4

27.2

−2.0

−28.4

−14.7

 Bz-Cor-Bz

−11.5

27.4

−2.0

−28.2

−14.3

 Bz-Cor-Ar

−11.3

27.0

−2.0

−28.4

−14.8

van der Waals

  Ar-Cor

−1.4

3.8

−0.2

−2.5

−0.4

  Na+-Cor-Ar

−1.5

4.3

−0.3

−5.1

−2.5

  Cl-Cor-Ar

−1.3

3.7

−0.3

−4.7

−2.5

 W-Cor-Ar

−1.3

3.8

−0.3

−4.8

−2.5

 Bz-Cor-Ar

−1.4

4.0

−0.3

−4.8

−2.5

  Ar-Cor-Ar

−1.3

3.8

−0.3

−4.8

−2.6

To shed more light on how different intermolecular interactions influence each other when they coexist in a given system, another set of energy decomposition calculations was carried out. Unlike in the previous case, here we decomposed the interaction energy of binary complexes of a ternary system in the presence of a third monomer. For instance, in the case of the Na+–Cor–Cl complex, two different energy decomposition analyses were carried out: first, between Na+ and coronene–Cl (cation-π interaction) by considering coronene and Cl as one collective entity, and then between Cl and Na+-Cor (anion-π interaction) for the same Na+–Cor–Cl complex. Here, coronene and Na+ together are considered as one entity. Results obtained from these calculations were compared with those for the binary complexes without the third monomer. Similar calculations were carried out for the rest of the ternary complexes and the values are listed according to the type of intermolecular interaction in Table 4.
Table 4

Calculated ∆Eint values in kcal mol−1 for binary complexes in the presence of the third moiety obtained from SAPT0/cc-pVDZ calculations. The binary system in square brackets is treated as one fragment in the calculation of SAPT interaction energy

System

Electrostatic

Exchange

Induction

Dispersion

SAPT0

Cation-π

  Na+-Cor

−12.9

8.0

−23.6

−2.0

−30.5

  [Na+-Cor]-Cl

−77.8

12.3

−26.4

−2.4

−94.3

  [Na+-Cor]-W

−17.3

8.4

−24.0

−2.0

−34.8

  [Na+-Cor]-Bz

−14.9

8.5

−24.6

−2.1

−33.1

  [Na+-Cor-]Ar

−13.2

8.1

−23.8

−2.0

−30.8

Anion-π

  Cl-Cor

0.2

16.9

−11.5

−10.7

−5.1

  [Na+-Cor]-Cl

−68.5

28.5

−14.7

−14.4

−69.1

  [Cl-Cor]-W

−4.7

20.2

−12.3

−11.5

−8.3

  [Cl-Cor]-Bz

0.4

18.6

−12.4

−11.1

−4.5

  [Cl-Cor]-Ar

−0.2

18.0

−11.8

−10.9

−4.9

OH-π

 W-Cor

−2.9

4.4

−0.9

−3.2

−2.6

  [Na+-Cor]-W

−4.9

5.0

−1.2

−4.9

−6.0

  [Cl--Cor]-W

−6.5

5.8

−1.6

−4.9

−7.2

  [W-Cor]-W

−2.7

4.4

−0.9

−3.2

−2.4

  [W-Cor]-Bz

−3.2

4.8

−1.0

−3.4

−2.8

  [W-Cor]-Ar

−3.0

4.6

−0.9

−3.3

−2.6

π-π

 Bz-Cor

−11.0

26.1

−2.0

−22.2

−9.1

  Na+-[Cor-Bz]

−12.4

26.7

−2.6

−28.5

−16.8

  Cl--[Cor-Bz]

−11.6

28.7

−2.7

−29.1

−14.7

 W-[Cor-Bz]

−11.5

27.0

−2.1

−22.7

−9.3

 Bz-[Cor-Bz]

−11.5

28.0

−2.1

−28.7

−14.3

 Bz-[Cor-Ar]

−11.3

27.0

−2.0

−28.4

−14.8

van der Waals

  Ar-Cor

−1.4

3.8

−0.2

−2.5

−0.4

  Na+-[Cor-Ar]

−1.2

3.8

−0.4

−5.0

−2.8

  Cl-[Cor-Ar]

−1.6

4.3

−0.4

−4.9

−2.6

 W-[Cor-Ar]

−1.4

3.9

−0.2

−2.6

−0.4

 Bz-[Cor-Ar]

−1.4

4.1

−0.3

−4.9

−2.5

  Ar-[Cor-Ar]

−1.4

3.9

−0.2

−2.6

−0.4

It is clear from Table 4 that the nature of cation-π interaction in ternary complexes is similar to that in binary complexes as they are stabilized mostly by electrostatic and induction energies. However, in the Na+–Cor–Cl complex, the presence of Cl on the opposite side of coronene substantially enhances the electrostatic contribution. In Na+–Cor, electrostatic contribution for the cation-π interaction is ~42% whereas in Na+–Cor–Cl, the same goes up to 83%. This clearly indicates the through-space electrostatic interaction between Na+ and Cl in the presence of coronene. The electrostatic contribution in the Cl–Cor complex is actually repulsive due to the repulsion between the anion and the π-cloud of coronene. Cl–Cor is stabilized by the contribution from induction and dispersion energies. However, the introduction of Na+ on the other side of coronene completely changes the scenario for the anion-π interaction. The presence of Na+ increases the electrostatic energy contribution between Cl and Na+–Cor complex. In cases where benzene and argon are adsorbed on opposite faces of coronene (Cl–Cor–Bz and Cl–Cor–Ar), the complexes are largely stabilized by induction and dispersion energies (Table 4).

It is worth mentioning that when Na+ or Cl is present on the other side of coronene, the nature of interaction in OH–π (in Na+–Cor–W and Cl–Cor–W), π–π (in Na+–Cor–Bz and Cl–Cor–Bz), and van der Waals (in Na+–Cor–Ar and Cl–Cor–Ar) is substantially changed. The contribution of the exchange-repulsion energy, which is due to the orbital overlap between individual monomers, is altered when charged species are adsorbed on the other side of the same coronene molecule.

For example, in the case of the binary W-Cor complex, the exchange-repulsion energy contribution towards the total interaction is ~ −167% (repulsive in nature). The same energy is reduced to ~ −80%, when there is a cation-π interaction on the other side of the aromatic ring. This is due mainly to the through-space interaction between the cation and the water molecule. Also, the cation present on the other side pulls the electron density towards itself and reduces the orbital overlap between water and coronene. Marginal or no change in interaction energy terms is observed when neutral molecules are present on both sides of the coronene molecule.

Point charge and multipole analysis

To gain further insight into various interactions from a multipole perspective, the electrostatic interaction between the participating units was calculated using Eqs. (37). The zz component of the quadrupole moment of coronene is −21.42 B. During the formation of the Na+-Cor complex, the contribution from ∆Eq-Q is −109.9 kcal mol−1. The zz component of the quadrupole moment of the Na+–Cor dimer is −17.60 B. In the formation of ternary complexes involving Na+–Cor, the charge/dipole/quadrupole moment of the third partner such as Cl, W, Ar and Bz interacts with the zz component of the quadrupole moment of Na+–Cor. To shed light on the cooperativity in the formation of the ternary complex, for example, Na+–Cor–W, the resultant dipole and quadrupole moments of the Cor–W complex were used to interact with the charge of Na+. The calculated dipole and quadrupole moments of the individual units, binary and ternary complexes along with the respective center-of-mass distances are listed in Tables 5 and 6. The interaction of Ar, Na+, Cl, water, and benzene with coronene leads to a significant reorganization of charge distribution. As a result, the values of the interacting dipole and quadrupole moments of binary complexes change from their inherent values. The possible role of ∆Eq-D, ∆Eq-Q, ∆Eq-D, ∆ED-D, ∆ED-Q and ∆EQ-Q is evident from these results.
Table 5

Molecular dipole and quadrupole moments at MP2/6-31+G(d,p) level of theory

System

Dipole moment (μ/D)

Quadrupole moment (Q/B)

Present study

Previous reports

Present study

Previous reports

Qxx

Qyy

Qzz

Qxx

Qyy

Qzz

Coronene

0.00

+10.71

+10.71

−21.42

−20.2 [34]

Benzene

0.00

+3.17

+3.17

−6.33

−8.7 [51]

Water

−2.28

1.85 [52]

−1.61

+1.87

−0.26

−2.50

+2.64

−0.13 [28]

Na+-Cor

+6.94

+8.80

+8.80

−17.60

Cl-Cor

−10.04

+19.12

+19.27

−38.40

W-Cor

−2.48

+14.92

+17.12

−32.04

Bz-Cor

−0.20

+13.62

+14.20

−27.82

Ar-Cor

−0.03

+10.86

+10.86

−21.71

Table 6

Charge-dipole (∆Eq-D), charge-quadrupole (∆Eq-Q), dipole-dipole (∆ED-D), quadrupole-quadrupole (∆EQ-Q) and dipole-quadrupole (∆ED-Q) interaction energy values in kcal mol−1 units for the considered complexes calculated using the point multipole approach. In binary complexes, ∆EAB is the interaction energy computed between coronene and various interacting partners. In ternary systems, ∆EAB represents the interaction energy between the net dipole/quadrupole moment of the binary complex and the third interacting partner. Similarly, ∆EBC represents the interaction energy between the first interacting partner and the net dipole/quadrupole moment of the binary system

Systems

Interaction type

Center-of-mass separation R (Å)

EAB

EBC

Etot = ∆EAB + ∆EBC

Binary complexes

 Na+-Cor

q-Q

2.380

−109.9

 

−109.9

 Cl-Cor

q-Q

3.092

50.1

 

50.1

 W-Cor

D-Q

2.840

−35.2

 

−35.2

 Bz-Cor

Q-Q

3.282

30.8

 

30.8

 Ar-Cor

q-Q

3.230

0.00

 

0.00

Ternary complexes

Charge-π-charge

 Na+-Cor-Cl

 Na+-Cor

q-Q

2.295

−122.8

 

−122.8

 Cor-Cl

Q-q

2.869

62.7

 

62.7

 [Na+-Cor]-Cl

D-q + Q-q

2.861

−58.6

51.9

−6.6

 Na+-[Cor-Cl]

q-D + q-Q

2.440

−116.6

−182.7

−299.3

Charge-π-dipole

 Na+-Cor-W

 Na+-Cor

q-Q

2.374

−110.6

 

−110.6

 Cor-W

Q-D

2.833

32.8

 

32.8

 [Na+-Cor]-W

D-D + Q-D

2.873

−501.5

122.4

−379.2

 Na+-[Cor-W]

q-D + q-Q

2.646

−24.4

−119.6

−144.0

Charge-π-Quadrupole

 Na+-Cor-Bz

 Na+-Cor

q-Q

2.372

−109.9

 

−109.9

 Cor-Bz

Q-Q

3.261

31.8

 

31.8

 [Na+-Cor]-Bz

D-Q + Q-Q

3.150

−19.3

31.0

11.8

 Na+-[Cor-Bz]

q-D + q-Q

3.219

−1.1

−57.6

−58.8

Charge-π-Charge

 Na+-Cor-Ar

 Na+-Cor

q-Q

2.378

−110.1

 

−110.1

 Cor-Ar

Q-q

3.163

0.0

 

0.0

 [Na+-Cor]-Ar

D-q + Q-q

3.228

0.0

0.0

0.0

 Na+-[Cor-Ar]

q-D + q-Q

2.484

0.0

0.0

0.0

Charge-π-Dipole

 Cl-Cor-W

 Cl-Cor

q-Q

3.144

47.6

 

47.6

 Cor-W

Q-D

2.750

36.9

 

36.9

 [Cl-Cor]-W

D-D + Q-D

3.329

26.8

−58.3

−31.4

 Cl-[Cor-W]

q-D + q-Q

3.326

15.5

60.2

75.7

Charge-π-Quadrupole

 Cl-Cor-Bz

 Cl-Cor

q-Q

3.116

48.9

 

48.9

 Cor-Bz

Q-Q

3.312

15.5

 

15.5

 [Cl-Cor]-Bz

D-Q + Q-Q

3.385

−11.0

599.4

588.4

 Cl-[Cor-Bz]

q-D + q-Q

3.959

0.8

31.0

31.7

Charge-π-Charge

 Cl-Cor-Ar

 Cl-Cor

q-Q

3.140

47.8

 

47.8

 Cor-Ar

Q-q

3.254

0.0

 

0.0

 [Cl-Cor]-Ar

D-q + Q-q

3.336

0.0

0.0

0.0

 Cl-[Cor-Ar]

q-D + q-Q

3.201

0.0

0.0

0.0

Dipole-π-Dipole

 W-Cor-W

 W-Cor

D-Q

2.762

−36.3

 

−36.3

 Cor-W

Q-D

2.740

−37.5

 

−37.5

 [W-Cor]-W

D-D + Q-D

3.466

3.9

−21.9

−18.0

 W-[Cor-W]

D-D + D-Q

3.461

3.9

−22.0

−18.1

Dipole-π-Quadrupole

 W-Cor-Bz

 W-Cor

D-Q

2.738

−37.6

 

−37.6

 Cor-Bz

Q-Q

3.267

16.6

 

16.6

 [W-Cor]-Bz

D-Q + Q-Q

3.438

−2.6

462.8

460.3

 W-[Cor-Bz]

D-D + D-Q

4.043

−0.2

−118.3

−118.5

Dipole-π-Charge

 W-Cor-Ar

 W-Cor

D-Q

2.775

−35.6

 

−35.6

 Cor-Ar

Q-q

3.230

0.0

 

0.0

 [W-Cor]-Ar

D-q + Q-q

3.142

0.0

0.0

0.0

 W-[Cor-Ar]

D-D + D-Q

3.316

0.0

0.0

0.0

Quadrupole-π-Quadrupole

 Bz-Cor-Bz

 Bz-Cor

Q-Q

3.281

30.8

 

30.8

 Cor-Bz

Q-Q

3.280

30.9

 

30.9

 [Bz-Cor]-Bz

D-Q + Q-Q

4.042

−0.2

14.1

13.9

 Bz-[Cor-Bz]

Q-D + Q-Q

4.041

−0.2

14.1

13.9

Charge-π-Quadrupole

 Ar-Cor-Bz

 Ar-Cor

q-Q

3.266

0.0

 

0.0

 Cor-Bz

Q-Q

3.282

30.8

 

30.8

 [Ar-Cor]-Bz

D-Q + Q-Q

3.314

0.0

0.0

0.0

 Ar-[Cor-Bz]

q-D + q-Q

4.049

0.0

0.0

0.0

Charge-π-Charge

 Ar-Cor-Ar

 Ar-Cor

q-Q

3.220

0.0

 

0.0

 Cor-Ar

Q-q

3.219

0.0

 

0.0

 [Ar-Cor]-Ar

D-q + Q-q

3.133

0.0

0.0

0.0

 Ar-[Cor-Ar]

q-D + q-Q

3.307

0.0

0.0

0.0

AIM analysis

Several reports in the past have demonstrated the utility of AIM theory in quantifying weak interactions in various systems [48, 49, 50]. Hence, the electron density topography features of binary and ternary systems were analyzed in the present study. The calculated values of the electron density, ρ and its Laplacian, ∇2ρ are listed in Table 7. Non-bonded critical points (NBCPs) were observed between the two (three) binding partners in addition to the covalent bonds in the interacting systems, as illustrated in Figs. 3 and 4. The calculated values of ρ(rc) and ∇2ρ(rc) at these NBCPs for all the complexes range from 0.005 to 0.018 and 0.005 to 0.014 au, respectively. These values clearly indicate the presence of non-covalent interactions between these systems. It is important to note that, in point multipole approximation, the center-of-mass separation between interacting partners significantly influences the various multipole interactions.
Table 7

Values (au) of electron density ρ(rc) and its Laplacian ∇2ρ(rc) at bond critical points (rc) for the considered binary and ternary systems calculated at MP2/6-31+G(d,p) level of theory

Molecules

A–Ba

B–Ca

ρ(rc)

2ρ(rc)

ρ(rc)

2ρ(rc)

Binary systems

  Na+–Cor

0.010

0.012

  

  Cl–Cor

0.010

0.007

  

 W–Cor

0.003

0.003

  

 Bz–Cor

0.009

0.007

  

  Ar–Cor

0.001

0.001

  

Ternary systems

  Na+–Cor–Cl

0.012

0.015

0.012

0.010

  Na+–Cor–W

0.008

0.007

0.010

0.013

  Na+–Cor–Bz

0.009

0.006

0.011

0.013

  Na+–Cor–Ar

0.010

0.012

0.006

0.005

  Cl–Cor–W

0.008

0.007

0.014

0.011

  Cl–Cor–Bz

0.008

0.006

0.012

0.009

  Cl–Cor–Ar

0.005

0.004

0.009

0.008

 W–Cor–W

0.007

0.006

0.007

0.006

 W–Cor–Bz

0.007

0.006

0.010

0.007

 W–Cor–Ar

0.007

0.006

0.005

0.005

 Bz–Cor–Bz

0.009

0.006

0.009

0.006

 Bz–Cor–Ar

0.006

0.005

0.009

0.006

  Ar–Cor–Ar

0.002

0.002

0.002

0.002

aA–B represents [ρ(rc)] and [∇2ρ(rc)] values when the interaction is between the first interacting partner and coronene, whereas B–C represents the same values when the interaction is between coronene and the third partner

Fig. 3

Molecular topography analysis of the electron density map at the MP2/6-31+G(d,p) level of theory for various binary complexes considered in this study. Red dots Bond critical points (BCP), yellow dots ring critical points (RCP), green dots cage critical points (CCP), black spheres carbon atoms, gray spheres hydrogen atoms

Fig. 4

Molecular topography analysis of the electron density map at the MP2/6-31+G(d,p) level of theory for various ternary complexes considered in this study. Red dots Bond critical points (BCP), yellow dots ring critical points (RCP), green dots cage critical points (CCP), black spheres carbon atoms, gray spheres hydrogen atoms

Summary and conclusions

In the present study, a set of 13 non-covalently interacting ternary complexes representing cation–π, anion–π, OH–π, π–π and van der Waals–π interactions was studied using ab initio calculations at the MP2/6-31+G(d,p) level of theory. Cooperativity and anti-cooperativity between various intermolecular interactions in these ternary complexes was examined systematically through SAPT calculations. Further, electrostatic interactions between the binary partners of the ternary systems under the influence of the third partner were analyzed in terms of point multipole approximations. Atoms-in-molecules analysis was carried out to quantify the weak interactions in the chosen model systems.

The results show that through-space electrostatic interaction plays an important role in the stabilization of cation-π ternary systems (Na+–Cor–Cl) and (Na+–Cor–W). For other cation–π complexes, this effect is found to be weaker. The calculated interaction energy values between various systems suggest that the presence of Na+ and Cl influences the nature of OH–π, π–π and van der Waals–π interactions. An energy decomposition analysis revealed that weak OH–π, π–π and van der Waals interactions are stabilized by dispersion interactions in ternary systems. The point multipole analysis demonstrated a significant reorganization in the charge distribution of the interacting dipoles and quadrupoles, thereby influencing the stabilization of ternary complexes. The AIM analysis reiterates the existence of non-covalent interactions in ternary systems.

It is hoped that the results reported in this paper will provide an impetus for further theoretical and experimental investigations in understanding the adsorption of ionic liquids/surfactants on the surface of carbon nanomaterials and their interaction mechanism in energy storage devices.

Notes

Acknowledgments

The authors acknowledge the project, Design and Development of Two Dimensional van der Waals Solids and their Applications (No. EMR/2015/000447) funded by Department of Science and Technology (DST), India. M.K.R. thanks the SRM Supercomputer Center, SRM Institute of Science and Technology for providing computational facilities.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Shyam Vinod Kumar Panneer
    • 1
  • Mahesh Kumar Ravva
    • 2
  • Brijesh Kumar Mishra
    • 3
  • Venkatesan Subramanian
    • 1
    Email author
  • Narayanasami Sathyamurthy
    • 4
  1. 1.Chemical LaboratoryCSIR-Central Leather Research InstituteChennaiIndia
  2. 2.Department of ChemistrySRM University – APAmaravatiIndia
  3. 3.Indian Institute of Information TechnologyBangaloreIndia
  4. 4.Jawaharlal Nehru Centre for Advanced Scientific ResearchBangaloreIndia

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