The Nature of the Noncovalent Interactions between Benzene and

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The Nature of the Noncovalent Interactions Between Benzene and C Fullerene Ming-Ming Li, Yi-Bo Wang, Yu Zhang, and Weizhou Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06492 • Publication Date (Web): 01 Jul 2016 Downloaded from http://pubs.acs.org on July 6, 2016

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The Journal of Physical Chemistry

The Nature of the Noncovalent Interactions between Benzene and C60 Fullerene Ming-Ming Li,† Yi-Bo Wang,*,† Yu Zhang,‡ and Weizhou Wang*,‡ †

Department of Chemistry, and Key Laboratory of Guizhou High Performance Computational

Chemistry, Guizhou University, Guiyang 550025, P. R. China ‡

College of Chemistry and Chemical Engineering, and Henan Key Laboratory of

Function-Oriented Porous Materials, Luoyang Normal University, Luoyang 471934, P. R. China

ABSTRACT: The noncovalent interactions between aromatic compounds and fullerenes have received considerable attention from various fields of science and technology. Employing the benzene (C6H6) and C60 fullerene as model molecules, in the present study, the nature of this kind of noncovalent interactions has been explored theoretically. Our results show clearly that the π···π stacking configurations of the complex C6H6···C60 are more strongly bound than the C−H···π analogues, and the C−H···π interactions in the C−H···π configurations of C6H6···C60 are not of the hydrogen bond. According to symmetry adapted perturbation theory analyses, all of the configurations of C6H6···C60 are dominated by dispersion forces. The percentage of the dispersion components in the overall attractive interactions for the π···π stacking configurations is smaller than the percentage of the dispersion components in the overall attractive interactions for the C−H···π configurations, whereas the percentage of the electrostatic terms in the overall attractive interactions for the π···π stacking configurations is larger than the percentage of the electrostatic terms in the overall attractive interactions for the C−H···π configurations. This is distinctly different from the case of the benzene dimer.

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1. INTRODUCTION Since C60 was first discovered by Smalley and his coworkers at Rice University in the mid-1980s,1 the fullerenes have attracted increasing research attention in areas ranging from electronics to medicine due to their outstanding chemical, physical, and electronic properties.2 The main obstacles for large scale application of fullerenes lie in the following two aspects: a) poor solubility of fullerenes in polar solvents, and b) separation and purification of different fullerenes. It is well known that good solvents for fullerenes are mainly aromatic.3 The relatively high solubility of fullerenes in aromatic solvents is presumably associated with the π···π stacking interactions. On the other hand, research in the field of supramolecular chemistry has shown that traditional host molecules, which are mainly composed of electron-rich aromatic rings, can be employed for separation and purification of fullerenes.4 Here, obviously, the π···π stacking interactions also play a key role. Although many experimental studies have been undertaken and reported, very little is known about the strength and nature of the noncovalent interactions between fullerenes and aromatic molecules. Hence, it is important to quantify these noncovalent interactions and also to identify the forces that govern their strength through high-level quantum chemical calculations. In this work, we investigated the noncovalent interactions between fullerenes and aromatic molecules by employing C6H6···C60 as a model complex. According to the X-ray single-crystal structures of benzene-solvated C60,5-7 there are two types of configurations for the complex C6H6···C60. One is the C−H···π configuration in which one C−H bond or two C−H bonds of C6H6 point(s) to the vertex, edge or face

2


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of C60. The other is the π···π stacking configuration in which one face of C6H6 is over the face or edge of C60. Figure 1 shows that the electrostatic potential surfaces of C6H6 and C60. The positive electrostatic potentials in C6H6 are associated with hydrogens, and the negative electrostatic potentials in C6H6 are strongest above and below the aromatic ring. The major regions of positive electrostatic potential in C60 are located above the five-membered rings and six-membered rings of C60, and the negative regions are located above the edges shared by two adjacent six-membered rings. In 2011, an IUPAC task group reexamined the definition of the hydrogen bond and published the final report.8 According to the new definition of the hydrogen bond, a hydrogen bond is formed if there is an attractive interaction between a hydrogen atom and an atom or a group of atoms.8 As shown in Figure 1, there is a repulsion between the hydrogen atom of C6H6 and the five-membered ring or six-membered ring of C60, so the C−H···π interactions in which one C−H bond of C6H6 points to the five-membered ring or six-membered ring of C60 are not of the hydrogen bond. In the C−H···π configurations in which one or two C−H bonds of C6H6 point(s) to the edge(s) shared by two adjacent six-membered rings of C60, are the C−H···π interactions of the hydrogen bond? This study will address this issue. Although the topic of π···π interaction and C−H···π interaction is very hot in recent years,9-15 there are only a few theoretical studies on these interactions in the complex C6H6···C60. Strutyński and Gomes investigated theoretically the subtle effect of noncovalent interactions on the structure of the C60 fullerene by using the complexes formed by C60 with different number of benzene molecules.16 The

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geometries and interaction energies of C6H6···C60 were determined at the RF/6-31G theory level.16 To more fully understand the nature of the noncovalent interactions between benzene and C60 fullerene, we still need to know, in addition to the highly accurate interaction energies, the contribution of different interaction energy components (electrostatic, exchange, induction, dispersion, etc.). No energy component analysis of the noncovalent interactions has been reported for the complex C6H6···C60, maybe because the complex is a little larger. In this study, we have performed energy component analyses for the noncovalent interactions in C6H6···C60 using symmetry adapted perturbation theory (SAPT).17

2. COMPUTATIONAL DETAILS The standard density functional theory with dispersion correction (DFT-D3) has been shown to describe noncovalent interactions with considerable success.18 In this study, the geometries of the different configurations of the complex C6H6···C60 were fully optimized and the energies were calculated at the PBE0-D3/def2-TZVPP theory level.19,20 Becke-Johnson damping was used with PBE0-D3.21 An “ultrafine” integration grid was utilized for all the PBE0-D3 calculations to minimize the integration grid errors. Although the performance of DFT-D3 method was pretty good for the study of the dispersion-dominated complexes,18 in order to avoid the possible computational artifacts and further confirm the reliability of the PBE0-D3/def2-TZVPP calculations, we have performed a series of computations to determine the interaction energies at

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the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set (CBS) limit level.22 The CCSD(T)/CBS values are often considered as the golden standard of energy calculations. The CCSD(T)/CBS energy can be constructed on the basis of the following formulae:23 ECCSD(T)/CBS = EMP2/CBS + ∆CCSD(T) ∆CCSD(T) = ECCSD(T)/aug-cc-pVDZ – EMP2/aug-cc-pVDZ MP2 calculations are performed with the basis sets aug-cc-pVTZ (aVTZ) and aug-cc-pVQZ (aVQZ), and extrapolated to the CBS limit with the Helgaker’s two-point scheme.24 The large number of electrons and the linear dependence problem of the Dunning basis sets aug-cc-pVNZ (N = D,T,Q) have been a bottleneck for CCSD(T)/CBS calculations of the large hydrocarbon systems such as the complex C6H6···C60. In this study, we use the following formulae instead to estimate the CCSD(T)/CBS energy: ECCSD(T)/CBS = EMP2/CBS + c ∆CCSD(T) ∆CCSD(T) = ECCSD(T)/cc-pVDZ – EMP2/cc-pVDZ Here, MP2/CBS(VTZ,VQZ) values are obtained with a cc-pVTZ (VTZ) and cc-pVQZ (VQZ) two-point Helgaker extrapolation, and the coefficient c is derived in terms of a training set. PBE0-D3 calculations were performed employing the GAUSSIAN 09 electronic structure program package.25 MP2 calculations were made with the ORCA program suite.26 CCSD(T) calculations were done with the MOLPRO suite of ab initio programs.27 The basis set superposition errors for all the interaction energies were

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eliminated with the function counterpoise technique of Boys and Bernardi.28 The bonding characteristic of the H···C and H···π noncovalent bonds was analyzed with the Bader’s well-established theory of atoms in molecules.29 Atoms in molecules analysis was conducted with the AIM2000 program employing the PBE0-D3/def2-TZVPP wave functions as input.30 The cost of conventional SAPT computations becomes prohibitive for the large complex C6H6···C60. In recent years, it was found that the zeroth-order SAPT (SAPT0) approach could give comparable results to those obtained with the conventional SAPT approach in many cases.31-35 Note that the computational cost of the SAPT0 approach is very low. Our previous results showed that the spin-component scaled SAPT0 (SCS-SAPT0), when judiciously coupled with suitable basis sets, performs very well for accurately characterizing the noncovalent π···π interactions between aromatic molecules.36-38 In the present study, energy decomposition analysis was carried out using the SCS-SAPT0 approach in junction with the jun-cc-pVDZ basis set (cc-pVDZ on hydrogens, aug-cc-pVDZ less the diffuse d functions on the other atoms).31,32 SCS-SAPT0 calculations were carried out with the PSI4 program.34 Density fitting approximations have been employed to enhance the efficiency of the SCS-SAPT0 method.

3. RESULTS AND DISCUSSION 3.1. CCSD(T)/CBS calculations. The interaction energies at the CCSD(T)/CBS theory level are estimated by adding to MP2/CBS a correction, c*∆CCSD(T),

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calculated in a small basis set. The key of this method is to select a suitable training set to determine the coefficient c. Considering that both C6H6 and C60 are nonpolar aromatic molecules, it is reasonable to construct a training set consisting of different configurations

of

the

benzene···naphthalene

(C6H6···C10H8)

complex.

The

CCSD(T)/CBS benchmark data of C6H6···C10H8 can be obtained from a recent study by our group.37 Table 1 lists the interaction energies and coupled-cluster corrections of the different configurations of the complexes C6H6···C10H8 and C6H6···C60 calculated at different levels of theory. The configurations T-6 and S-2 of C6H6···C60 are shown in Figure 2. The MP2/CBS(VTZ,VQZ) calculations are very expensive, so we did not consider the other configurations of C6H6···C60. For the three configurations of C6H6···C10H8, the MP2/CBS(aVTZ,aVQZ) interaction energies are almost the same as the MP2/CBS(VTZ,VQZ) ones, which proves that our method to evaluate the CCSD(T)/CBS interaction energy is reasonable. The coefficient c is found to be 1.30 after comparing the CCSD(T)/CBS(VTZ,VQZ) values of the three configurations of C6H6···C10H8 with the CCSD(T)/CBS benchmark data from Ref. 37. With this coefficient, the CCSD(T)/CBS(VTZ,VQZ) interaction energies for the configurations T-6 and S-2 of C6H6···C60 are estimated to be -2.58 and -5.36 kcal/mol, respectively. Comparably, the PBE0-D3/def2-TZVPP interaction energies for the configurations T-6 and S-2 of C6H6···C60 are -2.59 and -5.49 kcal/mol, respectively. Evidently, for the complexes studied here, the fast and low-cost PBE0-D3/def2-TZVPP calculations have high accuracy compared to gold-standard values.

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3.2. Structures, energies and electronic properties. The PBE0-D3/def2-TZVPP optimized configurations of the complex C6H6···C60 are illustrated in Figure 2. The Cartesian coordinates of the PBE0-D3/def2-TZVPP optimized configurations of the complex C6H6···C60 are available in the Supporting Information. T-1 and T-2 are the configurations in which one C−H bond of C6H6 points to the five-membered ring or six-membered ring of C60. In T-3, T-4, T-5 and T-6, two C−H bonds of C6H6 point to the edge or face of C60. S-1 is the configuration in which the benzene is above a C=C bond shared by a five-membered ring and a six-membered ring, and S-2 is the configuration in which the benzene is above a C=C bond shared by two adjacent six-membered rings. In S-3 and S-4, the benzene is above the five-membered ring and six-membered ring of C60, respectively. Table 2 summarizes the interaction energies, C−H bond lengths, selected distances, natural bond orbital charges, HOMO and LUMO levels for the different configurations of the complex C6H6···C60 calculated at the PBE0-D3/def2-TZVPP theory level. For comparison, some values of the monomers are also listed in Table 2. In the configurations T-1 and T-2, the C−H bonds of C6H6 are contracted about 0.0014 and 0.0016 Å upon C6H6···C60 formation. This is understandable because there is an attraction between C6H6 and C60 and a repulsion between the hydrogen atom of C6H6 and the five-membered ring or six-membered ring of C60. For the configurations T-3, T-4, T-5 and T-6, the values of R1 are all greater than the sum of the van der Waals radii of C and H (2.90 Å),39 which indicates that the C−H···π interactions in T-3, T-4, T-5 and T-6 are also not of the hydrogen bond. Charge

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transfer occurs accompanying the formation of C6H6···C60, but the magnitude of charge transfer is very small. Also, it can be clearly observed from Table 2 that the HOMO and LUMO levels do not change significantly upon the formation of C6H6···C60. The last column of Table 2 lists the counterpoise-corrected interaction energies. The interaction energies range from -4.13 to -5.49 kcal/mol for the π···π stacking configurations of C6H6···C60, and from -2.10 to -2.74 kcal/mol for the C−H···π configurations of C6H6···C60. The π···π stacking configurations of the complex C6H6···C60 are more strongly bound than the C−H···π configurations. The configuration where benzene lies on top of a C=C double bond shared by two adjacent six-membered rings of C60 is the most stable structure, followed by the configuration where benzene lies on top of a C=C double bond shared by a five-membered ring and a six-membered ring. To further confirm whether the C−H···π interactions in C6H6···C60 are indeed not of the hydrogen bond, we performed atoms in molecules analysis on the configurations T-1, T-2, T-3, T-4, T-5 and T-6. Bader’s theory of atoms in molecules,29 which is mainly based on a topological analysis of the electron density distribution, has proven to be a feasible approach in successfully characterizing different types of noncovalent bonds.29,40 According to Baer’s theory of the atoms in molecules, Popelier proposed several criteria to assess whether there exists a hydrogen bond.40 The first criterion to determine the presence of a hydrogen bond is that there is a bond path and a concomitant bond critical point (BCP) between the hydrogen atom and the acceptor atom. The second criterion is that the electron density

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of the BCP lies in the range between 0.002 and 0.035 au. Another important criterion for the presence of a hydrogen bond is that the Laplacian of the electron density of the BCP lies in the range between 0.024 and 0.139 au.40 Figure 3 clearly demonstrates that there is a BCP in each H···A (A = C, or BCP of a C=C double bond) noncovalent bond. The bond path associated with the BCP of each H···A noncovalent bond can also be observed in Figure 3. The values of the electron density at the BCPs of the H···A noncovalent bonds are given in Table 3. These values all lie in the allowed range between 0.002 and 0.035 au for a hydrogen bond. Therefore, the first two criteria are met for the presence of a H···A hydrogen bond, and the key is the third criterion. The electron density Laplacian at a BCP is a sum of three Hessian eigenvalues λ1, λ2 and λ3 at that point. It reveals the region where electron density is locally accumulated or depleted. A negative value of the electron density Laplacian is a sign of shared electrons between the atoms and the positive Laplacian indicates a noncovalent bond such as a halogen bond or a hydrogen bond.29 As expected, in Table 3 the values of the electron density Laplacian are all positive. However, these values are too small to fall within the allowed range between 0.024 and 0.139 au for a hydrogen bond. Here, the topological properties of the H···A noncovalent bonds do not meet the proposed criteria for the presence of a hydrogen bond, which proves again that the C−H···π interactions in the C−H···π configurations of C6H6···C60 are not of the hydrogen bond. In Bader’s quantum theory of atoms in molecules, ellipticity is an indicator of the bond stability; large values of ellipticity means that the bond is unstable.22 As shown in the last column of Table 3, large values

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of the ellipticity reflect the instability of the H···A noncovalent bonds; that is, the H···A noncovalent bonds can be easily ruptured. 3.3. Energy component analysis. Table 4 lists the results of the total interaction energy decomposition analysis for various configurations of the complex C6H6···C60. SCS-SAPT0/jun-cc-pVDZ

computations

were

performed

at

the

PBE0-D3/def2-TZVPP equilibrium geometries. It is noticed from Table 2 and Table 4 that

the

SCS-SAPT0/jun-cc-pVDZ

total

interaction

energies

for

various

configurations of the complex C6H6···C60 are in well agreement with the corresponding ones obtained at the PBE0-D3/def2-TZVPP theory level, which confirms the reliability of the SCS-SAPT0 method for the study of the complex C6H6···C60. As clearly shown in Table 4, all of the configurations of C6H6···C60 are dominated by dispersion forces. For the C−H···π configurations, the electrostatic forces represent 13%-18% of the overall attractive forces. In contrast, the electrostatic components account for 22%-30% of the overall attractions for the π···π stacking configurations. On the contrary, the percentage of the dispersion components in the overall attractive interactions for the π···π stacking configurations is smaller than the percentage of the dispersion components in the overall attractive interactions for the C−H···π configurations. This is distinctly different from the case of the benzene dimer.41 For the sandwich configuration of the benzene dimer, the electrostatics is repulsive because of the unfavorable quadrupole-quadrupole interactions.41,42 The attractive electrostatic interactions for the π···π stacking configurations of C6H6···C60 can be attributed to the favorable quadrupole-quadrupole interactions and charge

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penetration effects.42 On the other hand, these results also prove indirectly that the C−H···π interactions in the C−H···π configurations of C6H6···C60 are not of the hydrogen bond.

4. CONCLUSIONS The magnitude and nature of noncovalent interactions between C6H6 and C60 fullerene have been investigated by extensive state-of-the-art quantum chemical calculations. At the PBE0-D3/def2-TZVPP theory level, the interaction energies range from -4.13 to -5.49 kcal/mol for the π···π stacking configurations of C6H6···C60, and from -2.10 to -2.74 kcal/mol for the C−H···π configurations of C6H6···C60. The π···π stacking configurations of the complex C6H6···C60 are more strongly bound than the C−H···π configurations. The CCSD(T)/CBS calculations have been performed to enhance the reliability of the PBE0-D3/def2-TZVPP results. The results of surface electrostatic potential analysis, atoms in molecules analysis and energy component analysis show that all the C−H···π interactions in the C−H···π configurations of C6H6···C60 are not of the hydrogen bond. According

to

the

interaction

energy

decomposition

analysis

at

the

SCS-SAPT0/jun-cc-pVDZ level of theory, all the configurations of C6H6···C60 are dominated by dispersion forces. Different from the case of the benzene dimer, the percentage of the dispersion components in the overall attractive interactions for the π···π stacking configurations of C6H6···C60 is smaller than the percentage of the dispersion components in the overall attractive interactions for the C−H···π

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configurations of C6H6···C60, whereas the percentage of the electrostatic terms in the overall attractive interactions for the π···π stacking configurations of C6H6···C60 is larger than the percentage of the electrostatic terms in the overall attractive interactions for the C−H···π configurations of C6H6···C60. The results presented herein provide new insight into the fundamental structural and energetic properties of the noncovalent interactions between C6H6 and C60 fullerene. It is hoped that the conclusions will be helpful for the study on the strength and nature of the noncovalent interactions between fullerenes and other aromatic compounds.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: The

Cartesian

coordinates

of

the

PBE0-D3/def2-TZVPP

optimized

configurations of the complex C6H6···C60, the enlarged version of Figure 2 and the enlarged version of Figure 3 (PDF) AUTHOR INFORMATION Corresponding Authors *E-mail [email protected]; Tel +86 851 8829 2009 (Y.B.W.). *E-mail [email protected]; Tel +86 379 6861 8820 (W.W.). Notes The authors declare no competing financial interest. ACKNOWLEDGMENT Financial support from the Program for Science & Technology Innovation Talents in Universities of Henan Province (13HASTIT015) is gratefully acknowledged.

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REFERENCES (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. C60: Buckminsterfullerene. Nature 1985, 318, 162-163. (2) Sheka, E. FULLERENES Nanochemistry, Nanomagnetism, Nanomedicine, Nanophotinics; CRC Press: Boca Raton, 2011. (3) Mchedlov-Petrossyan, N. O. Fullerenes in Liquid Media: An Unsettling Intrusion into the Solution Chemistry. Chem. Rev. 2013, 113, 5149-5193. (4) Martin, N.; Nierengarten, J.-F. Supramolecular Chemistry of Fullerenes and Carbon Nanotubes; Wiley-VCH Verlag & Co. KGaA: Weinheim, 2012. (5) Meidine, M. F.; Hitchcock, P. B.; Kroto, H. W.; Taylor, R.; Walton, D. R. M. Single Crystal X-Ray Structure of Benzene-solvated C60. J. Chem. Soc., Chem. Commun. 1992, 1534-1537. (6) Balch, A. L.; Lee, J. W.; Noll, B. C.; Olmstead, M. M. Disorder in a Crystalline Form of Buckminsterfullerene: C60·4C6H6. J. Chem. Soc., Chem. Commun. 1993, 56-58. (7) Buergi, H. B.; Restori, R.; Schwarzenbach, D.; Balch, A. L.; Lee, J. W.; Noll, B. C.; Olmstead, M. M. Nanocrystalline Domains of a Monoclinic Modification of Benzene Stabilized in a Crystalline Matrix of C60. Chem. Mater. 1994, 6, 1325-1329. (8) Arunan, E.; Desiraju, G. R.; Klein, R. A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D. C.; Crabtree, R. H.; Dannenberg, J. J.; Hobza, P., et al. Definition of the Hydrogen Bond (IUPAC Recommendations 2011). Pure Appl. Chem. 2011, 83, 1637-1641. (9) Riley, K. E.; Pavel Hobza, P. On the Importance and Origin of Aromatic Interactions in Chemistry and Biodisciplines. Acc. Chem. Res. 2013, 46, 927-936.

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(10) Cho, Y.; Cho, W. J.; Youn, I. S.; Lee, G.; Singh, N. J.; Kim, K. S. Density Functional Theory Based Study of Molecular Interactions, Recognition, Engineering, and Quantum Transport in π Molecular Systems. Acc. Chem. Res. 2014, 47, 3321-3330. (11) Lee, E. C.; Kim, D.; Jurečka, P.; Tarakeshwar, P.; Hobza, P.; Kim, K. S. Understanding of Assembly Phenomena by Aromatic−Aromatic Interactions: Benzene Dimer and the Substituted Systems. J. Phys. Chem. A 2007, 111, 3446-3457. (12) Singh, N. J.; Min, S. K.; Kim, D. Y.; Kim, K. S. Comprehensive Energy Analysis for Various Types of π-Interaction. J. Chem. Theory Comput. 2009, 5, 515-529. (13) Tkatchenko, A.; Alfè, D.; Kim, K. S. First-Principles Modeling of Non-Covalent Interactions in Supramolecular Systems: The Role of Many-Body Effects. J. Chem. Theory Comput. 2012, 8, 4317-4322. (14) Podeszwa, R.; Bukowski, R.; Szalewicz, K. Potential Energy Surface for the Benzene Dimer and Perturbational Analysis of π−π Interactions. J. Phys. Chem. A 2006, 110, 10345-10354. (15) Alonso, M.; Woller, T.; Martín-Martínez, F. J.; Contreras-García, J.; Geerlings, P.; De Proft, F. Understanding the Fundamental Role of π/π, σ/σ, and σ/π Dispersion Interactions in Shaping Carbon-Based Materials. Chem.-Eur. J. 2014, 20, 4931-4941. (16) Strutyński, K.; Gomes, J. A.N.F. The Subtle Effect of vdW Interactions upon the C60 Fullerene Structure. Comput. Theor. Chem. 2013, 1026, 12-16. (17) Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes. Chem. Rev. 1994, 94, 1887-1930. (18) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate ab initio

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Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (19) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158-6169. (20) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297-3305. (21) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. (22) Bartlett, R. J.; Purvis, G. D. Many-Body Perturbation Theory, Coupled-Pair Many-Electron Theory, and the Importance of Quadruple Excitations for the Correlation Problem. Int. J. Quantum Chem. 1978, 14, 561-581. (23) Sinnokrot, M. O.; Sherrill, C. D. Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer: Sandwich, T-Shaped, and Parallel-Displaced Configurations. J. Phys. Chem. A 2004, 108, 10200-10207. (24) Halkier, A.; Helgaker, T.; Jørgensen, P.; Klopper, W.; Koch, H.; Olsen, J.; Wilson, A. K. Basis-Set Convergence in Correlated Calculations on Ne, N2, and H2O. Chem. Phys. Lett. 1998, 286, 243-252. (25) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc., Wallingford CT, 2013. (26) Neese, F. The ORCA Program System. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2,

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73-78. (27) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G., et al. MOLPRO, version 2012.1, a package of ab initio programs; Cardiff University: Cardiff, U.K., 2012; see http://www.molpro.net. (28) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553-566. (29) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon; Oxford, U.K., 1990. (30) Biegler-König F.; Schönbohm, J.; Bayles, D. AIM2000—A Program to Analyze and Visualize Atoms in Molecules. J. Comput. Chem. 2001, 22, 545-559. (31) Hohenstein, E. G.; Sherrill, C. D. Density Fitting and Cholesky Decomposition Approximations in Symmetry-Adapted Perturbation Theory: Implementation and Application to Probe the Nature of π-π Interactions in Linear Acenes. J. Chem. Phys. 2010, 132, 184111. (32) Hohenstein, E. G.; Sherrill, C. D. Density Fitting of Intramonomer Correlation Effects in Symmetry-Adapted Perturbation Theory. J. Chem. Phys. 2010, 133, 014101. (33) Hohenstein, E. G.; Parrish, R. M.; Sherrill, C. D.; Turney, J. M.; Schaefer, H. F. Large-Scale Symmetry-Adapted Perturbation Theory Computations via Density Fitting and Laplace Transformation Techniques: Investigating the Fundamental Forces of DNA-Intercalator Interactions. J. Chem. Phys. 2011, 135, 174107. (34) Turney, J. M.; Simmonett, A. C.; Parrish, R. M.; Hohenstein, E. G.; Evangelista, F. A.; Fermann, J. T.; Mintz, B. J.; Burns, L. A.; Wilke, J. J.; Abrams, M. L., et al. PSI4: An Open-Source ab initio Electronic Structure Program. WIREs Comput. Mol. Sci. 2012, 2, 556-565.

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(35) Sherrill, C. D. Energy Component Analysis of π Interactions. Acc. Chem. Res. 2013, 46, 1020-1028. (36) Wang, W.; Zhang, Y.; Wang, Y.-B. Noncovalent π···π Interaction between Graphene and Aromatic Molecule: Structure, Energy and Nature. J. Chem. Phys. 2014, 140, 094302. (37) Wang, W.; Sun, T.; Zhang, Y.; Wang, Y.-B. The Benzene···Naphthalene Complex: A More Challenging System than the Benzene Dimer for Newly Developed Computational Methods. J. Chem. Phys. 2015, 143, 114312. (38) Wang, W.; Sun, T.; Zhang, Y.; Wang, Y.-B. Benchmark Calculations of the Adsorption of Aromatic Molecules on Graphene. J. Comput. Chem. 2015, 36, 1763-1771. (39) Bondi, A. van der Waals Volumes and Radii. J. Phys. Chem. A 1964, 68, 441-451. (40) Popelier, P. L. A. Characterization of a Dihydrogen Bond on the Basis of the Electron Density. J. Phys. Chem. A 1998, 102, 1873-1878. (41) Wang, W.; Zhao, Y.; Zhang, Y.; Wang, Y.-B. The Nature of the I···I Interactions and a Comparative Study with the Nature of the π···π Interactions. Comput. Theor. Chem. 2014, 1030, 1-8. (42) Hohenstein, E. G.; Duan, J.; Sherrill, C. D. Origin of the Surprising Enhancement of Electrostatic Energies by Electron-Donating Substituents in Substituted Sandwich Benzene Dimers. J. Am. Chem. Soc. 2011, 133, 13244-13247.

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Table 1. The Interaction Energies and Coupled-Cluster Corrections of the Different Configurations of the Complexes C6H6···C10H8 and C6H6···C60 Calculated at Different Levels of Theory. All Units Are in kcal/mol Method

C6H6···C10H8 C6H6···C10H8 C6H6···C10H8 C6H6···C60 (T-6) (PD)a (S)a (T)a

CCSD(T)/CBSa

-4.25

-4.09

-4.31

PBE0-D3/def2-TZVPP

-4.13

-4.00

-4.33

MP2/CBS(aVTZ,aVQZ)

-7.75

-7.41

-5.88

MP2/CBS(VTZ,VQZ)

-7.77

-7.42

CCSD(T)/VDZ

-0.91

MP2/VDZ

C6H6···C60 (S-2)

-2.59

-5.49

-5.95

-4.26

-10.94

-0.93

-2.24

-1.72

-2.96

-3.56

-3.44

-3.52

-3.01

-7.26

∆CCSD(T)/VDZ

2.65

2.51

1.29

1.29

4.29

1.30*∆CCSD(T)/VDZ

3.44

3.26

1.67

1.68

5.58

CCSD(T)/CBS(VTZ,VQZ)

-4.33

-4.16

-4.28

-2.58

-5.36

a

The geometries and CCSD(T)/CBS interaction energies of the different configurations of C6H6···C10H8 are from Ref. 37.

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Page 20 of 27

CP

Table 2. The Interaction Energies ( Eint , kcal mol-1), C−H Bond Lengths (r1, Å), Selected Distances (R1, Å), Natural Bond Orbital Charges (q, e), HOMO and LUMO Levels (eV) for the Different Configurations of the Complex C6H6···C60 Calculated at the PBE0-D3/def2-TZVPP Theory Level Configuration

r1a

R1

qC6H6

qC60

HOMOb

LUMOb

CP Eint

T-1

1.0816 (1.0830)

2.5272

0.0034

-0.0034

-6.59 (-6.57)

-3.60 (-3.57)

-2.10

T-2

1.0814

2.4468

0.0028

-0.0028

-6.60

-3.60

-2.37

T-3

1.0832

2.9923

0.0040

-0.0040

-6.59

-3.60

-2.62

T-4

1.0827

2.9906

0.0033

-0.0033

-6.59

-3.60

-2.74

T-5

1.0829

2.9101

0.0021

-0.0021

-6.60

-3.60

-2.60

T-6

1.0830

2.9829

0.0033

-0.0033

-6.59

-3.60

-2.59

S-1

1.0834

3.4156

0.0160

-0.0160

-6.46

-3.50

-5.06

S-2

1.0833

3.2707

0.0252

-0.0252

-6.47

-3.49

-5.49

S-3

1.0834

3.5338

0.0168

-0.0168

-6.46

-3.50

-4.75

S-4

1.0834

3.6708

0.0067

-0.0067

-6.47

-3.52

-4.13

a

b

Number in parenthesis is the corresponding value of C6H6 monomer. Number in parenthesis is the corresponding value of C60 monomer.

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Table 3. Density (ρ), Density Laplacian (▽2ρ), Eigenvalues of the Hessian Matrix (λ1, λ2, λ3) and Ellipticity (ε) at the Bond Critical Points of the C−H···π Configurations of the Complex C6H6···C60. All Units Are Atomic Units Configuration Interaction

ρb

▽2ρb

λ1

λ2

λ3

ε

T-1

H···C

0.0071

0.0230

-0.0045

-0.0012

0.0299

2.7831

T-2

H···C

0.0064

0.0222

-0.0043

-0.0006

0.0272

5.8644

H···C

0.0059

0.0173

-0.0041

-0.0038

0.0252

0.0793

H···BCP

0.0044

0.0156

-0.0026

-0.0007

0.0189

2.8930

H··· BCP

0.0045

0.0153

-0.0030

-0.0016

0.0200

0.9041

H··· BCP

0.0045

0.0170

-0.0025

-0.0001

0.0197

23.2408

H··· BCP

0.0045

0.0142

-0.0035

-0.0015

0.0192

1.2854

H··· BCP

0.0046

0.0141

-0.0035

-0.0018

0.0195

0.9792

H··· BCP

0.0047

0.0157

-0.0032

-0.0019

0.0207

0.7056

H··· BCP

0.0046

0.0154

-0.0030

-0.0017

0.0201

0.7249

T-3

T-4

T-5

T-6

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Table 4. SCS-SAPT0/jun-cc-pVDZ Decomposition of the Interaction Energies (kcal/mol) for the Different Configurations of the Complex C6H6···C60 Configuration

ESCS-SAPT0

Eelst

Eexch

Eind

Escs-disp

Eelst%a

Eind%a

Escs-disp%a

T-1

-1.92

-0.72

3.53

-0.45

-4.28

13%

8%

79%

T-2

-2.12

-1.00

4.04

-0.45

-4.71

16%

7%

77%

T-3

-2.40

-0.91

3.43

-0.44

-4.47

16%

7%

77%

T-4

-2.49

-0.84

3.40

-0.38

-4.67

15%

6%

79%

T-5

-2.31

-0.80

2.76

-0.31

-3.95

16%

6%

78%

T-6

-2.37

-0.95

2.85

-0.31

-3.95

18%

6%

76%

S-1

-5.54

-3.99

9.04

-1.09

-9.50

27%

7%

66%

S-2

-6.09

-5.39

11.82

-1.64

-10.88

30%

9%

61%

S-3

-5.13

-3.38

7.97

-0.97

-8.75

26%

7%

67%

S-4

-4.12

-2.31

6.27

-0.44

-7.64

22%

4%

74%

a

Contribution to the overall attractive interactions.

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9.41

-16.94

Figure 1. The electrostatic potential surfaces of C6H6 and C60 calculated at the PBE0-D3/def2-TZVPP theory level with a scale of –16.94 (red) to 9.41 (blue) kcal/mol.

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Figure 2. The PBE0-D3/def2-TZVPP optimized configurations of the complex C6H6···C60.

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Figure 3. Schematic drawing of the C−H···π configurations of the complex C6H6···C60 showing the geometry of all its critical points. The small light spheres represent the hydrogen atoms, and the small dark spheres are the carbon atoms. Small red dots represent the bond critical points. In circles are the bond critical points considered in this study.

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TOC graphic:

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232x212mm (72 x 72 DPI)


The Nature of the Noncovalent Interactions between Benzene and

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