Toward Selection of Efficient Density Functionals for van der Waals

Article pubs.acs.org/JPCA

Toward Selection of Efficient Density Functionals for van der Waals Molecular Complexes: Comparative Study of C−H···π and N−H···π Interactions Guvanchmyrat Paytakov,

†

Tandabany Dinadayalane,*,‡ and Jerzy Leszczynski*,

†

† Interdisciplinary Center for Nanotoxicity, Department of Chemistry and Biochemistry, Jackson State University, J. R. Lynch Street, Jackson, Mississippi 39217, United States ‡ Department of Chemistry, Clark Atlanta University, 223 James P. Brawley Drive, S.W., Atlanta, Georgia 30314, United States S Supporting Information *

ABSTRACT: We have evaluated the performance of two of the recently developed density functionals (M06-2X and B2PLYP-D), which are widely used, by considering three important prototype systems, including benzene−acetylene, benzene− methane, and benzene−ammonia, possessing C−H···π or N−H···π interactions. Computational results are compared with the available experimental data. Considered density functionals are from two different classes: hybrid meta density functional (M06-2X) and double hybrid density functional (B2PLYP-D). The performance of a range of basis sets (6-31G(d), 6-31+G(d), 6-31+G(d,p), 6311G(d,p), 6-311+G(d,p), aug-cc-pVXZ (X = D, T, Q)) with the above-mentioned two density functionals was evaluated. Comparison of the results includes Pople’s basis sets versus Dunning’s correlation consistent basis sets with the M06-2X and B2PLYP-D functionals considered in this study. The basis set effect on geometrical parameters, dissociation energies, and selected vibrational frequency shifts was thoroughly analyzed. We have addressed whether the counterpoise corrections with geometry optimizations and vibrational frequencies are important. Our computational study reveals that calculations carried out with smaller basis sets very well reproduce the reported experimental values of dissociation energies. The present study also shows that using the very large Dunning’s correlation consistent basis set worsens the results. The necessity of including counterpoise correction for binding energies depends on the system and the type of method used. In general, vibrational frequency calculations using these DFT functionals generate characteristic red shifts for the C−H···π or N−H···π interactions in the complexes.

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INTRODUCTION Experimental investigation of the structure of the benzene··· acetylene complex, which is a prototype C−H···π system, has been very recently reported in the gas phase using Fouriertransform microwave spectroscopy.1 Nonbonding interactions of C−H or N−H bond with π-systems were often described as very weak conventional π-hydrogen bonds.2−4 They are of broad interest to many forefront areas of chemistry, biology, and materials science.5−7 The above-mentioned interactions are believed to play important roles in structure, function, and stability of proteins8−12 and in molecular recognition and crystal structures of organic compounds.5,13−15 Apparently, C− H···π or N−H···π interactions are much weaker than cation−π interactions.7,16−19 High-level ab initio calculations showed that the dispersion contribution is the major source of attraction in the C−H···π interactions.20−23 Coupled cluster theory including single, double, and perturbative triple (CCSD(T)) with a large augmented correlation consistent basis set is known to produce accurate results for complexes stabilized by dispersion forces. Sherrill and co-workers studied C−H···π interactions of methane (as proton donor) with benzene, phenol, and indole (as π source) using second-order © XXXX American Chemical Society

perturbation theory (MP2) and very accurate CCSD(T) methods employing augmented correlation consistent doubleand triple-ζ basis sets.21 Crittenden reported accurate results of binding energies, potential energy curves (PEC), and equilibrium intermonomer distances at the CCSD(T) in conjunction with a large augmented quadruple-ζ basis set (aug-cc-pVQZ) to understand noncovalent interactions between benzene and small species that include methane and ammonia.24 Until recently, the majority of density functional methods failed to properly describe the dispersive interactions.25,26 However, newly developed meta-hybrid density functional26,27 and double hybrid density functional methods28,29 have been shown to be promising for evaluation of complexes involving π−π and C−H···π interactions that are dominated by dispersion forces.30−32 The performance of the DFT-D model, which involves a density functional theory (DFT) description augmented by R−6 contribution, proposed by Received: November 15, 2014 Revised: January 19, 2015

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DOI: 10.1021/jp511450u J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Grimme25,29 was rigorously evaluated by considering 143 complexes.33 The DFT-D method was reported to be a viable option for aromatic interactions involving simple to complex organic and biological systems in which dispersion forces are dominant.33,34 It is essential to mention that recently developed density functional theory methods can produce acceptable or even accurate results with far less computational cost compared to the most accurate and highly time-consuming CCSD(T) calculations.29,30,35 In the case of C−H···π interactions, the proton donor (i.e., source of C−H) can be from alkane, alkyne, and aromatic systems, and the representative complexes for these types are methane−benzene, acetylene−benzene, and T-shaped benzene dimer, respectively. The latter complex has already been extensively studied by Dinadayalane and Leszczynski focusing on the structures, binding energies, and C−H stretching vibrational frequency shifts.36,37 The C−H···π interactions in small molecular clusters involving benzene or modified benzene as π source have been computationally investigated using highlevel MP2 and coupled cluster (CCSD(T)) methods. Particular attention was given to examine the structures, binding energies, and the origin for stabilization of C−H···π interactions.19−23,30,35,38 Data including vibrational frequencies at high-level ab initio calculations for those interactions are very limited because such calculations are computationally expensive.37,39,40 Owing to the experimental results on C−H stretching vibrational frequencies and their shifts (blue- or redshifting) have been reported for some model systems (e.g., benzene dimer, benzene−methane complexes),2,41 the computational interest in blue- and red-shifting of the C−H stretching vibrations for the C−H···π interacting complexes has been growing.37,39,40,42 Careful estimation of the interaction energies by computational techniques was considered very informative and quite useful in exploring the origin of C−H···π interactions. Halogen substitution in aliphatic system of proton donor (example, CH4) notably enhanced the strength of C−H···π interactions.4,35,39 Substitution or modification of the π-proton acceptor (benzene) influences the C−H···π interactions involving acetylene as proton donor.7,30 Mishra et al. have recently reported that substitution by electron-withdrawing groups decreases the C−H···π interaction strength whereas the benzene modified by electron-donating groups increases the strength of interaction.30 The Minnesota hybrid metageneralized gradient approximation (GGA) functional M062X has been well-recognized and is a widely used DFT functional for investigations of complexes stabilized by dispersion forces.27,30−32,43 Zhao and Truhlar reported good performance of M05-2X functional with Pople’s basis set of 6311+G(2df,2p) for benzene dimer.44 However, M05-2X and M06-2X functionals with aug-cc-pVTZ basis set were reported to be not accurate in the case of benzene dimer.19 Recent studies have utilized the combination of M06-2X with Dunning’s augmented correlation-consistent basis set.30,43 Previous computational study highlighted that the suitability of the recently developed double-hybrid density functional for studying C−H···π interactions remains an unresolved issue.35 B2PLYP-D is the double-hybrid density functional with longrange dispersion correction, and it has gained attention recently.25,28 Therefore, we decided to evaluate the performance of Pople versus Dunning’s basis set with M06-2X as well as B2PLYP-D functional for the model systems considered in this study.

The experimental reports of binding energies and IR frequencies are available for complexes of benzene−acetylene (Bz-Ac),2,45,46 benzene−methane (Bz-Me)47 and benzene− ammonia (Bz-Am). Therefore, we have considered these systems in the present study. The performance of two recently developed density functionals (M06-2X and B2PLYP-D) and the effect of basis set as well as the influence of counterpoise correction on geometries, binding energies, and vibrational frequency shifts of C−H or N−H stretching has been assessed.

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COMPUTATIONAL DETAILS All calculations were carried out using Gaussian 09 program package.48 Hybrid meta-generalized gradient approximation functional,27 M06-2X and the double-hybrid density functional with long-range dispersion correction,25,28 B2PLYP-D with an array of basis sets (6-31G(d), 6-31+G(d), 6-31+G(d,p), 6311G(d,p), 6-311+G(d,p), aug-cc-pVXZ (X = D, T, Q)) were utilized for geometry optimizations. Vibrational frequency calculations for the complexes and the individual fragments were performed at all the levels with an exception that the calculations for the complexes at the B2PLYP-D/aug-cc-pVQZ level were not feasible computationally within our limited resources. We were not successful in obtaining the configurations with all real frequencies at some levels even though we made several attempts. Initially, we considered 4−6 different configurations (Scheme 1) for each of benzene−acetylene, Scheme 1. Different Configurations Considered for Benzene−Acetylene (A1−A4), Benzene−Methane (B1−B6), and Benzene−Ammonia (C1−C6) Complexes

benzene−methane, and benzene−ammonia complex in performing calculations with smaller 6-31G(d) and 6-31+G(d,p) basis sets. The lowest-energy configuration for each type is shown in Scheme 2, and these three structures were considered for calculations at all the levels to examine the equilibrium geometries, binding energies, and vibrational frequency shifts. Counterpoise (CP) correction proposed by Boys and Bernardi was utilized for obtaining basis set superposition error (BSSE) correction.49 To verify the necessity of CP B


Article

The Journal of Physical Chemistry A

C−H of acetylene pointing above the center of the benzene ring (with C6v point group). In the case of Bz-Me complex, many of the earlier studies considered only C3v symmetric structure (only one C−H bond pointing above the center of benzene ring), but the bent methane with one C−H fragment interacting with benzene configuration possessing Cs symmetry is obtained as the lowest-energy structure (in majority of the calculations) or nearly at the same energy as the abovementioned C3v symmetric structure (Scheme 2). Tsuzuki et al. reported that the orientation of methane changed when the πsystem was changed from benzene to naphthalene or pyrene for C−H···π interactions.55 The N−H fragment of ammonia interacting with benzene is slightly shifted away from the center of benzene in the lowest-energy optimized structure of Bz-Am complex. It is interesting to note that for the lowestenergy Bz-Am complex, the N−H bond is tilted about 45° (Cs) from plane of benzene in the case of M06-2X optimized structures, while it is parallel to C6-axis of benzene in the case of B2PLYP-D optimized structures. However, the structure remained Cs symmetric and the N−H bond is not pointing above the center of benzene ring for the geometries obtained with both functionals. As shown by the data in Table 1, the variation of basis set with either of the DFT functionals has minor effect on the geometries of individual fragments in the complexes. However, the nonbonding interaction distance between hydrogen of X− H (the bond in Ac, Me, and Am that interacts with π-cloud of benzene) and the center of Bz does vary significantly by changing the method and basis set with an exception of Bz-Ac complex. As shown by the data in Table 2, the inclusion of counterpoise correction in the geometry optimization has notable effect on such intermoiety distance, while it does not affect the bond distances of the individual fragments in the complexes. The three complexes considered in this study behave differently for the array of basis sets used. For example, in the case of Bz-Ac complex, the small basis set 6-31G(d) or aug-cc-pVDZ with either M06-2X or B2PLYP-D gives the shortest C−H···BzCM distance compared to the calculations with other basis sets. Furthermore, the M06-2X and B2PLYP-D functionals with other basis sets yield the distance of ∼2.4 and 2.7−2.8 Å for Bz-Ac complex, respectively. The distance of ∼2.4 Å obtained using M06-2X is in excellent agreement with the recent experimental result of 2.492 Å.1 The intermoiety distance (X−H···BzCM) obtained for Bz-Ac is shorter than that for Bz-Me. However, such distance for Bz-Am lies between the values for Bz-Ac and Bz-Me. The bond lengths of interacting X−H in the complexes (Bz-Ac, Bz-Me, and Bz-Am) elongated marginally with respect to the free molecule. This tendency is observed with both the functionals using any of the basis sets considered in this study. Binding Energies and Effects of Counterpoise Correction. In this work, we have calculated the binding energies without counterpoise correction (no CP), those including CP correction with single-point calculation (CPsp), and the CP correction with optimization (CPopt) at all the levels. Table 3 lists the calculated binding energy, dissociation energy, and zero-point vibrational energy correction data along with the available experimental results. Tsuzuki and coworkers45 and Sundararajan et al.46 independently reported the experimental dissociation energy of 2.7 ± 0.2 kcal/mol for the Bz-Ac complex. The experimental dissociation energy of 1.03−1.13 kcal/mol for Bz-Me complex was published by Tsuzuki and co-workers.47 The dissociation energy for Bz-Am

Scheme 2. Most Stable Configuration Obtained at the M062X/6-31+G(d,p) Level for Benzene−Acetylene (Bz-Ac), Benzene−Methane (Bz-Me), and Benzene−Ammonia (BzAm) Complexes

correction in the geometry optimization, the calculations for geometry optimizations were included with counterpoise option. Harmonic vibrational frequency calculations with counterpoise option were also performed for each of the CPcorrected geometries. The frequency calculations were used to examine whether the obtained geometry corresponds to a saddle point or minimum on their potential energy surface (PES) and to analyze the important C−H vibrational stretching frequencies. Selected vibrational frequencies and frequency shifts obtained at all levels were reported without applying any scaling factor (see Supporting Information). Binding energies were calculated as ΔE = −[Ecomplex − (E Bz + Ex )]

where Ecomplex and Ex correspond to the total energy of the complex and total energy of benzene, respectively; Ex means the total energy of acetylene, methane, or ammonia (x = Ac, Me, or Am). Zero-point vibrational energy (ZPVE) corrections were included with binding energies to obtain the dissociation energies (D0). The calculated dissociation energies were compared with the reported experimental data.

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RESULTS AND DISCUSSION Equilibrium Geometries. Selected bond distances for the isolated species and for the lowest-energy configuration of the complexes of Bz-Ac, Bz-Me, and Bz-Am obtained at different levels are provided in Table 1. The corresponding values obtained with counterpoise optimization are given in Table 2. The experimental values for benzene, acetylene, methane, and ammonia are also given in Tables 1 and 2 for comparison. In general, both M06-2X and B2PLYP-D functionals with basis sets 6-311G(d,p), 6-311+G(d,p), and aug-cc-pVTZ yield bond distances that are very close to the reported experimental or high-level ab initio data.50−53 An important point to note here is that the values obtained with aug-cc-pVDZ basis set by using both the functionals significantly deviate from the experimental or accurate computational data.50−53 At each level, the C−H bond distance of acetylene is shorter than that of benzene and methane. The reason for shorter C−H bond distance was explained long before by Politzer and Harris: the π-electronic charge outside of the C−C region in acetylene is concentrated in the C−H region.54 In the case of complexes, we have listed only the average values of C−C and C−H bond distances for benzene (Bz). With the same basis set, M06-2X predicts a distance shorter than that of B2PLYP-D for C−C bond of benzene. The lowestenergy configuration for Bz-Ac complex is the structure with C


a

D

1.393 1.086 1.202 1.067 1.092 1.017 1.394 1.086 1.203 1.070 2.352 1.393 1.086 1.092 2.660 1.393 1.086 1.019 2.594

1.395 1.086 1.204 1.068 1.092 1.016 1.395 1.086 1.205 1.071 2.394 1.395 1.086 1.093 2.695 1.395 1.086 1.018 2.526

631+G(d) 1.394 1.086 1.205 1.067 1.091 1.014 1.395 1.086 1.205 1.070 2.394 1.394 1.086 1.092 2.680 1.395 1.086 1.016 2.536

631+G(d,p) 1.391 1.084 1.196 1.064 1.089 1.014 1.392 1.083 1.197 1.067 2.392 1.391 1.084 1.090 2.641 1.392 1.083 1.016 2.586

6311G(d,p) 1.392 1.084 1.197 1.064 1.089 1.013 1.392 1.083 1.198 1.067 2.393 1.392 1.084 1.090 2.641 1.392 1.084 1.015 2.516

6311+G(d,p) 1.395 1.089 1.206 1.071 1.095 1.017 1.396 1.089 1.207 1.074 2.353 1.395 1.089 1.095 2.638 1.396 1.089 1.018 2.515

aug-ccpVDZ 1.388 1.082 1.194 1.063 1.087 1.012 1.389 1.081 1.195 1.066 2.385 1.388 1.082 1.088 2.628 1.389 1.082 1.014 2.510

aug-ccpVTZ 1.388 1.081 1.193 1.062 1.086 1.012 1.388 1.080 1.194 1.065 2.385 1.388 1.081 1.087 2.678 1.388 1.081 1.014 2.526

aug-ccpVQZ 1.397 1.086 1.210 1.065 1.092 1.017 1.397 1.085 1.211 1.066 2.344 1.397 1.086 1.090 2.618 1.397 1.086 1.018 2.546

631G(d) 1.399 1.086 1.213 1.067 1.092 1.017 1.399 1.086 1.213 1.068 2.379 1.399 1.086 1.091 2.628 1.399 1.086 1.017 2.514

631+G(d) 1.399 1.084 1.213 1.065 1.090 1.013 1.399 1.084 1.214 1.066 2.378 1.399 1.084 1.089 2.632 1.399 1.084 1.014 2.513

631+G(d,p) 1.396 1.084 1.205 1.063 1.090 1.014 1.397 1.084 1.206 1.065 2.377 1.396 1.084 1.089 2.580 1.396 1.084 1.015 2.480

6311G(d,p)

B2PLYP-D

Experimental or accurate computational data. bTaken from ref 50. cTaken from ref 1. dTaken from ref 51. eTaken from ref 52. fTaken from ref 53.

Bz−Am

Bz−Me

Me Am Bz−Ac

Ac

distance (Å)

C−C C−H C−C C−H C−H N−H C−C (Bz) C−H (Bz) C−C (Ac) C−H (Ac) C−H···BzCM C−C (Bz) C−H (Bz) C−H (Me) C−H···BzCM C−C (Bz) C−H (Bz) N−H (Am) N−H···BzCM

struct.

Bz

631G(d)

M06-2X

1.397 1.084 1.206 1.063 1.090 1.014 1.397 1.084 1.207 1.064 2.376 1.397 1.084 1.089 2.581 1.397 1.084 1.014 2.497

6311+G(d,p) 1.402 1.091 1.218 1.072 1.097 1.018 1.403 1.090 1.218 1.073 2.339 1.402 1.091 1.096 2.534 1.402 1.091 1.019 2.450

aug-ccpVDZ 1.393 1.081 1.213 1.060 1.088 1.012 1.393 1.081 1.204 1.063 2.368 1.392 1.081 1.087 2.587 1.393 1.081 1.013 2.475

aug-ccpVTZ

1.391b, 1.4043c 1.080b, 1.0853c 1.203d, 1.1986c 1.062d 1.086e 1.012f

exptl or accurate comp. dataa

Table 1. Selected Bond Distances and Nonbonding Distances (Angstroms) for the Most Stable Configuration of Benzene−Acetylene (Bz-Ac), Benzene−Methane (Bz-Me), and Benzene−Ammonia (Bz-Am) Complexes and the Individual Molecules Obtained at Different Levels

The Journal of Physical Chemistry A Article


a

C−C C−H C−C C−H C−H N−H C−C (Bz) C−H (Bz) C−C (Ac) C−H (Ac) C−H...BzCM C−C (Bz) C−H (Bz) C−H (Me) C−H...BzCM C−C (Bz) C−H (Bz) N−H (Am) N−H...BzCM

Bz

E

1.393 1.086 1.202 1.067 1.091 1.017 1.394 1.086 1.203 1.070 2.413 1.393 1.086 1.092 2.660 1.394 1.086 1.019 2.560

1.395 1.086 1.204 1.068 1.092 1.016 1.395 1.086 1.205 1.071 2.428 1.394 1.086 1.093 2.695 1.395 1.086 1.018 2.560

6631G(d) 31+G(d) 1.394 1.086 1.205 1.067 1.091 1.014 1.395 1.086 1.205 1.070 2.420 1.394 1.086 1.092 2.680 1.395 1.086 1.016 2.556

631+G(d,p) 1.391 1.084 1.196 1.064 1.089 1.014 1.392 1.083 1.197 1.067 2.422 1.391 1.084 1.090 2.640 1.392 1.083 1.016 2.530

6311G(d,p) 1.392 1.084 1.197 1.064 1.089 1.013 1.392 1.083 1.198 1.067 2.429 1.392 1.084 1.090 2.662 1.392 1.084 1.015 2.542

6311+G(d,p) 1.395 1.089 1.206 1.071 1.095 1.017 1.396 1.089 1.207 1.074 2.400 1.395 1.089 1.095 2.695 1.396 1.089 1.019 2.533

aug-ccpVDZ 1.388 1.082 1.194 1.063 1.087 1.012 1.389 1.081 1.195 1.066 2.385 1.388 1.082 1.088 2.637 1.389 1.082 1.014 2.510

aug-ccpVTZ 1.388 1.081 1.193 1.062 1.086 1.012 1.388 1.080 1.194 1.065 2.385 1.388 1.081 1.087 2.678 1.388 1.081 1.014 2.526

aug-ccpVQZ 1.397 1.086 1.210 1.065 1.092 1.017 1.397 1.085 1.211 1.067 2.449 1.397 1.086 1.091 2.747 1.397 1.086 1.018 2.653

631G(d) 1.399 1.086 1.213 1.067 1.092 1.017 1.399 1.086 1.214 1.068 2.469 1.399 1.086 1.092 2.739 1.399 1.086 1.017 2.653

631+G(d) 1.399 1.084 1.213 1.065 1.090 1.013 1.399 1.084 1.214 1.066 2.461 1.399 1.084 1.090 2.724 1.399 1.084 1.014 2.631

631+G(d,p) 1.396 1.084 1.205 1.063 1.090 1.014 1.396 1.084 1.206 1.064 2.445 1.396 1.084 1.090 2.681 1.396 1.084 1.015 2.603

6311G(d,p)

B2PLYP-D

Experimental or accurate computational data. bTaken from ref 50. cTaken from ref 1. dTaken from ref 51. eTaken from ref 52. fTaken from ref 53.

Bz-Am

Bz-Me

Me Am Bz-Ac

Ac

distance ( Å)

struct.

M06-2X

1.397 1.084 1.206 1.063 1.090 1.014 1.397 1.084 1.207 1.065 2.449 1.397 1.084 1.090 2.686 1.397 1.084 1.014 2.595

6311+G(d,p) 1.402 1.091 1.218 1.072 1.097 1.018 1.403 1.091 1.219 1.074 2.422 1.402 1.091 1.097 2.656 1.402 1.091 1.019 2.550

aug-ccpVDZ 1.393 1.081 1.213 1.060 1.088 1.012 1.393 1.081 1.204 1.063 2.397 1.392 1.081 1.087 2.587 1.393 1.081 1.013 2.475

aug-ccpVTZ

1.391b, 1.4043c 1.080b, 1.0853c 1.203d, 1.1986c 1.062d 1.086e 1.012f

exptl or accurate comp. dataa

Table 2. Selected Bond Distances and Nonbonding Distances (Angstroms) for the Most Stable Configuration of Benzene−Acetylene (Bz-Ac), Benzene−Methane (Bz-Me) and Benzene−Ammonia (Bz-Am) Complexes with CPopt (Optimized Geometry with Counterpoise Option) and the Individual Molecules Obtained at Different Levels



F

f

3.44 −1.03 2.41 1.87 0.84 2.08 −0.54 1.54

ΔE ΔZPVE D0 h ΔECP D0 h ΔECP, opt ΔZPVECP D0 h

No CPe

CPf

No CPe

CPf

BZ-Me

exptl D0 = 1.03−1.13c

BZ-Am

exptl D0 = 1.84 ± 0.12d

CPg

CPg

2.78 −0.58 2.20 2.38 1.80 2.37 −0.61 1.75

1.57 −0.25 1.33 1.43 1.18 1.43 −0.25 1.18

3.00 −0.50 2.50 2.73 2.23 2.74 −0.52 2.22

2.71 −0.65 2.06 2.38 1.73 2.38 −0.67 1.71

1.62 −0.27 1.35 1.48 1.21 1.48 −0.27 1.21

3.12 −0.53 2.59 2.82 1.97 2.82 −0.52 2.30

631+G(d,p)

3.42 −1.10 2.32 2.17 1.07 2.34 −0.78 1.56

2.00 −0.28 1.72 1.64 1.36 1.64 −0.30 1.34

3.41 −0.55 2.86 2.94 2.39 2.95 −0.56 2.39

6311G(d,p)

2.92 −0.75 2.16 2.59 1.83 2.59 −0.77 1.82

1.86 −0.27 1.58 1.34 1.07 1.37 −0.33 1.04

3.22 −0.59 2.63 2.91 2.32 2.92 −0.57 2.35

6311+G(d,p)

2.92 −0.65 2.27 2.42 1.78 2.43 −0.71 1.71

2.12 −0.08 2.04 1.55 1.47 1.55 −0.19 1.36

3.60 −0.49 3.10 2.77 2.28 2.79 −0.32 2.47

augccpVDZ

2.53 −0.94 1.58 2.37 1.43 2.37 −0.81 1.56

1.51 −0.45 1.06 1.35 0.90 1.35 −0.38 0.97

2.97 −0.72 2.25 2.73 2.01 2.73 −0.66 2.07

augccpVTZ

2.36 −0.86 1.51 2.32 1.46 2.32 −0.84 1.47

1.43 −0.10 1.33 1.37 1.27 1.37 −0.10 1.27

2.77 −0.80 1.97 2.70 1.90 2.70 −0.75 1.94

augccpVQZ

3.28 −0.62 2.65 1.54 0.92 1.99 −0.57 1.42

1.64 −0.46 1.17 0.76 0.29 0.76 −0.36 0.39

3.78 −0.61 3.17 2.55 1.94 2.55 −0.42 2.13

631G(d)

2.84 −0.77 2.06 1.90 1.13 1.96 −0.57 1.39

1.49 −0.51 0.98 0.89 0.39 0.92 −0.35 0.57

3.49 −0.83 2.66 2.47 1.64 2.53 −0.45 2.07

631+G(d)

2.76 −0.79 1.98 1.93 1.14 1.97 −0.57 1.41

1.54 −0.52 1.02 0.95 0.43 0.95 −0.35 0.59

3.54 −0.81 2.73 2.50 1.69 2.54 −0.44 2.11

631+G(d,p)

3.10 −0.61 2.49 1.68 1.07 2.00 −0.58 1.42

1.68 −0.46 1.22 1.04 0.58 1.04 −0.34 0.69

3.55 −0.57 2.97 2.68 2.10 2.71 −0.44 2.26

6311G(d,p)

B2PLYP-D

2.83 −0.90 1.93 2.03 1.14 2.07 −0.57 1.50

1.67 −0.65 1.02 1.06 0.41 1.10 −0.34 0.76

3.56 −0.93 2.63 2.60 1.67 2.64 −0.45 2.19

6311+G(d,p)

3.07 −0.73 2.34 2.14 1.40 2.18 −0.57 1.61

2.13 −0.51 1.62 1.21 0.70 1.27 −0.37 0.90

4.18 −0.75 3.43 2.78 2.03 2.83 −0.42 2.41

augccpVDZ

2.61 −0.70 1.91 2.30 1.61 2.30 −0.59 1.71

1.64 −0.49 1.15 1.36 0.87 1.36 −0.42 0.94

3.38 −0.62 2.76 2.95 2.33 2.96 −0.52 2.43

augccpVTZ

All values are in kilocalories per mole. bTaken from refs 45 and 46. cTaken from ref 47. dTaken from ref 56. eNo counterpoise correction was done for calculating ΔE and dissociation energy (D0). Counterpoise correction was performed for optimized geometry. gCounterpoise correction was utilized in both geometry optimization and frequency calculations. hD0 includes ΔZPVE.

a

1.88 −0.30 1.58 1.14 0.84 1.14 −0.33 0.81

ΔE ΔZVPE D0 h ΔECP D0 h ΔECP, opt ΔZPVECP D0 h

CPf

exptl D0 = 2.7 ± 0.2b

CPg

3.37 −0.47 2.90 2.66 2.19 2.68 −0.47 2.21

ΔE ΔZPVE D0 h ΔECP D0 h ΔECP, opt ΔZPVECP D0 h

No CPe

complex

BZ-Ac

6631G(d) 31+G(d)

M06-2X

Table 3. Binding Energy (ΔE), Change in Zero-Point Vibrational Energy (ΔZPVE), and Dissociation Energy (D0) Data Obtained Using M06-2X and B2PLYP-D Functionals with Various Basis Setsa



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Figure 1. Dissociation energy (kilocalories per mole) obtained at M06-2X and B2PLYP-D with different basis sets for (a) benzene−acetylene (BzAc), (b) benzene−methane (Bz-Me), and (c) benzene−ammonia (Bz-Am) complexes. The blue solid line indicates the experimental value, and the red lines above and below the blue lines correspond to the experimental correction.

higher cost, and steeper dependence of cost on system size, compared to M06-2X. As depicted in Figure 1a, the choice of the DFT functional and basis set is not uniform for all three complexes. In the case of Bz-Ac complex, the CP correction is not required for both functionals with any of the basis sets to reproduce experimental binding energy values. Both M06-2X and B2PLYP-D with 631+G(d), 6-31+G(d,p), or 6-311+G(d,p) reproduce the experimentally reported dissociation energies of 2.7 ± 0.2 kcal/mol.45,46 In general, the M06-2X functional with any of Pople’s basis sets considered here gives the dissociation energy values within the experimental range. Also in the case of Bz-Me complex (Figure 1b), CP correction is not required for almost all the levels except M062X/6-311+G(d,p). B2PLYP-D functional with any one of the basis sets of 6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-311+G(d,p), and aug-cc-pVTZ produces dissociation energies, which are free of CP correction, close to or in agreement with the experimental value of 1.03−1.13 kcal/mol.47 For large complex systems of C−H···π interactions, we recommend M06-2X/631+G(d) or B2PLYP-D/6-31+G(d) level without CP correction for calculating the dissociation energies. For the Bz-Am complex, counterpoise correction is required for M06-2X functional with the basis sets of 6-31+G(d), 631+G(d,p), 6-311+G(d,p), and aug-cc-pVDZ to obtain experimentally reported dissociation energies (Figure 1c). However, the B2PLYP-D functional in conjunction with 6311+G(d,p) or aug-cc-pVTZ basis set without CP correction reproduces the experimental D0 value. It should be noted that B2PLYP-D/6-31+G(d,p) and B2PLYP-D/aug-cc-pVTZ levels without CP correction and with CPopt correction give dissociation energy values close to experimental result, respectively. Figure 1a−c shows that diffuse function has substantially larger effect on the dissociation energy of this complex, compared to that of Bz-Ac and Bz-Me complexes. Although both M06-2X/6-31+G(d) and M06-2X/6-311+G(d,p) levels are excellent for N−H···π interactions, we recommend the former level because of computational effectiveness for larger systems.

complex determined experimentally by Mons et al. amounts to 1.84 ± 0.12 kcal/mol.56 We have provided Figure 1 for a quick and clear visualization of the variation of dissociation energies using different basis sets with two functionals (M06-2X and B2PLYP-D). This figure also displays how much the computed dissociation energies deviate with respect to the experimental data for all three complexes. The data provided in Table 3 indicate that calculated CPsp and CPopt corrected binding energies are very similar at M062X functional with almost all the basis sets for the complexes considered. However, B2PLYP-D functional usually produces slightly smaller values of CPsp correction compared to CPopt with some of the basis sets. Our detailed study reveals that inclusion of counterpoise correction with geometry optimization is not required because it is computationally expensive and not worthwhile. Using M06-2X or B2PLYP-D, Pople’s basis sets including diffuse function generate dissociation energies that are in good agreement (or very close) to the experimental values. It is known that Dunning’s correlation consistent augmented basis sets are much more expensive than Pople’s basis sets. M06-2X functional with Dunning’s correlation consistent basis set does not yield the dissociation energies in agreement with the experimental data. Therefore, we do not recommend Dunning’s correlation consistent basis set with M06-2X functional for C−H···π and N−H···π interactions. In the case of the latter type of interactions, M06-2X/aug-ccpVDZ level may be considered, but the energies should be included with counterpoise correction. It should be noted that increasing the quality of the basis set from aug-cc-pVDZ to augcc-pVQZ with M06-2X functional leads to the worst results for both C−H···π and N−H···π interactions. On the other hand, B2PLYP-D functional with aug-cc-pVTZ basis set yields dissociation energies that are comparable (or the same) as the experimental values. B2PLYP-D/aug-cc-pVDZ level is not adequate for obtaining dissociation energies, but the results are improved by moving from aug-cc-pVDZ to aug-cc-pVTZ basis set. As mentioned in an earlier study by Zhao and Truhlar,57 the double hybrid density functional, B2PLYP-D, method has G


Article

The Journal of Physical Chemistry A Vibrational Frequency Shifts: Effect of Basis Sets and Counterpoise Correction. Infrared (IR) spectroscopy was used to characterize the C−H stretching frequency of C−H···π interactions in the complexes.2,41,46,47,58,59 Vibrational spectroscopy is also useful in characterizing N−H···π interactions in small clusters involving pyrrole.3,6 Experimental investigations reported the red shift (Fujii et al., −22 cm−1;2 Sundrarajan et al., −16 and −13 cm−1)46 for the vibrational mode of interacting C−H of acetylene when it forms complex with benzene. Theoretical calculations predicted “improper blue shifting” H bond for the C−H···π interactions in the benzene dimer rather than “classical red shifting”. MP2 method predicted considerable blue shift.39,40 However, two of us, Dinadayalane and Leszczynski, reported the importance of including the counterpoise correction in the vibrational frequency calculations at the MP2/aug-cc-pVDZ level to reproduce experimental results41 of the small “red shifts” of C−H stretching frequencies.37 In this section, we have analyzed the effect of basis set and the role of counterpoise correction for the C−H or N−H stretching frequency shifts with two DFT functionals. Figure 2 depicts all calculated C−H and N−H vibrational frequency shifts at M06-2X and B2PLYP-D functionals with various basis sets. The general trend of vibrational frequency shift shown in Figure 2 with CP optimization and frequency with or without

CP is very similar. One can see a negligible difference between them for almost all the basis sets with both M06-2X and B2PLYP-D functionals. It is known that the computational cost for calculations including counterpoise corrections in optimizations and frequencies is significant. Therefore, we do not recommend including counterpoise correction for calculating the frequency shifts. The experimental frequency shift of C−H stretching of Ac was reported to be Δν = −13, −16, and −22 cm−1 in the case of the Bz-Ac complex. The graph in Figure 2 was plotted by taking the largest magnitude. First of all, both M06-2X and B2PLYP-D functionals with all of the basis sets (except aug-cc-pVQZ) produce the red shift. However, the magnitude of the red shift varies depending on the method and basis set used. M06-2X/aug-cc-pVQZ level gives a blue shift of small magnitude for the C−H stretching of Ac, and this is in contrast to the experimental report. It is interesting to note that the M06-2X method with all of the Pople type basis sets considered here reproduces the experimental results. However, the B2PLYP-D method with any applied Pople basis set underestimates the C−H vibrational frequency shift. B2PLYPD with aug-cc-pVTZ basis set gives vibrational frequency shifts that are in reasonably good agreement with the experimental report. The experimental result for C−H vibrational frequency shift of CH4 in the Bz-Me complex is −5 cm−1.2 Although M06-2X functional with all of the considered basis sets reproduces the red shift, the magnitude of frequency shift is much higher, compared to the experimental value, for almost all the basis sets except 6-31+G(d). Thus, we recommend M06-2X/6-31+G(d) level without CP correction for predicting C−H stretching frequency shift of C−H···π interacting complexes, where alkane or alkyne interacts with π-systems. B2PLYP-D functional with majority of the basis sets underestimates the frequency shift in the case of Bz-Me complex. The B2PLYP-D/6-31G(d) level even predicts the controversial “blue shift”. Therefore, caution is required in using the 6-31G(d) basis set for larger complex systems. Although B2PLYP-D/6-31+G(d) level reproduces the experimental value, the calculation at this level is somewhat more expensive, compared to the M06-2X/6-31+G(d) level. It is worthwhile to mention that the vibrational frequency shift (asymmetric mode) of interacting C−H of CH4 in the Bz-Me complex was predicted to be a blue shift using B2PLYP-D consistently with all the basis sets (see Supporting Information, Table S2). This observation is in contrast to the experimental result of the red shift of 14 cm−1. In the case of N−H···π interactions in the pyrrole−benzene complex, the N−H stretch is red-shifted by 59 cm−1, relative to the N−H stretch of free pyrrole.6 Similarly, the red shift of 87 cm−1 was obtained for N−H stretching in pyrrole dimer.3 It is important to mention here that there is no data available in the literature for N−H stretching frequency shift of neutral Bz-Am complex. However, Mizuse et al. reported N−H stretching frequencies for radical cation of Bz-Am complex [C6H6NH3]+.60 Similar to the experimental reports of red shift of N−H stretching frequency in N−H···π intermolecular interaction complexes, the red shift of N−H stretching frequency was predicted for Bz-Am complex from our extensive calculations. The magnitude for the red shift of N−H stretching frequency of Bz-Am complex using M06-2X is notably higher than B2PLYP-D functional with the same basis set. M06-2X functional performs better than B2PLYP-D functional in predicting the vibrational frequency shifts involving C−H···π and N−H···π interactions.

Figure 2. Selected symmetric C−H and N−H stretching frequency shifts obtained at M06-2X and B2PLYP-D with different basis sets for benzene−acetylene (Bz-Ac), benzene−methane (Bz-Me), and benzene−ammonia (Bz-Am) complexes. The influnence of counterpoise correction with optimization and frequency (CPopt) is assessed. Experimental values are also plotted for comparison. H


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the Prototypical C-H···π Interaction. Phys. Chem. Chem. Phys. 2014, 16, 8886−8894. (2) Fujii, A.; Morita, S.-i.; Miyazaki, M.; Ebata, T.; Mikami, N. A Molecular Cluster Study on Activated CH/π Interactions: Infrared Spectroscopy of Aromatic Molecule−Acetylene Clusters. J. Phys. Chem. A 2004, 108, 2652−2658. (3) Dauster, I.; Rice, C. A.; Zielke, P.; Suhm, M. A. N−H···π Interactions in Pyrroles: Systematic Trends from the Vibrational Spectroscopy of Clusters. Phys. Chem. Chem. Phys. 2008, 10, 2827− 2835. (4) Jantimapornkij, P.; Jundee, P.; Uttamapinant, N.; Pianwanit, S.; Karpfen, A. A−H···π Hydrogen Bonding to Acetylene and Benzene: The Role of Intramolecular Coupling. Comput. Theor. Chem. 2012, 999, 231−238. (5) 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. (6) Pfaffen, C.; Infanger, D.; Ottiger, P.; Frey, H.-M.; Leutwyler, S. N−H···π Hydrogen-Bonding and Large-Amplitude Tipping Vibrations in Jet-Cooled Pyrrole−Benzene. Phys. Chem. Chem. Phys. 2011, 13, 14110−14118. (7) Dinadayalane, T. C.; Paytakov, G.; Leszczynski, J. Computational Study on C−H···π Interactions of Acetylene with Benzene, 1,3,5Trifluorobenzene and Coronene. J. Mol. Model. 2013, 19, 2855−2864. (8) Pace, C. J.; Kim, D.; Gao, J. Experimental Evaluation of CH−π Interactions in a Protein Core. Chem.Eur. J. 2012, 18, 5832−5836. (9) Plevin, M. J.; Bryce, D. L.; Boisbouvier, J. Direct Detection of CH/π Interactions in Proteins. Nat. Chem. 2010, 2, 466−471. (10) Chakrabarti, P.; Samanta, U. CH/π Interaction in the Packing of the Adenine Ring in Protein Structures. J. Mol. Biol. 1995, 251, 9−14. (11) Brandl, M.; Weiss, M. S.; Jabs, A.; Sühnel, J.; Hilgenfeld, R. CH···π-Interactions in Proteins. J. Mol. Biol. 2001, 307, 357−377. (12) Maresca, M.; Derghal, A.; Carravagna, C.; Dudin, S.; Fantini, J. Controlled Aggregation of Adenine by Sugars: Physicochemical Studies, Molecular Modelling Simulations of Sugar−Aromatic CH−π Stacking Interactions, and Biological Significance. Phys. Chem. Chem. Phys. 2008, 10, 2792−2800. (13) Seth, P.; Bauzá, A.; Frontera, A.; Massera, C.; Gamez, P.; Ghosh, A. Analysis of the Contribution of the π-Acidity of the s-Tetrazine Ring in the Crystal Packing of Coordination Polymers. CrystEngComm 2013, 15, 3031−3039. (14) Thakur, T. S.; Sathishkumar, R.; Dikundwar, A. G.; Row, T. N. G.; Desiraju, G. R. Third Polymorph of Phenylacetylene. Cryst. Growth Des. 2010, 10, 4246−4249. (15) Boese, R.; Clark, T.; Gavezzotti, A. Cocrystallization with Acetylene. The 1:1 Complex with Benzene: Crystal Growth, X-Ray Diffraction and Molecular Simulations. Helv. Chim. Acta 2003, 86, 1085−1100. (16) Dinadayalane, T. C.; Hassan, A.; Leszczynski, J. A Theoretical Study of Cation−π Interactions: Li+, Na+, K+, Be2+, Mg2+ and Ca2+ Complexation with Mono- and Bicyclic Ring-Fused Benzene Derivatives. Theor. Chem. Acc. 2012, 131, 1131. (17) Hassan, A.; Dinadayalane, T. C.; Grabowski, S. J.; Leszczynski, J. Structural, Energetic, Spectroscopic and QTAIM Analyses of Cation-π Interactions Involving Mono- and Bi-Cyclic Ring Fused Benzene Systems. Phys. Chem. Chem. Phys. 2013, 15, 20839−20856. (18) Mahadevi, A. S.; Sastry, G. N. Cation−π Interaction: Its Role and Relevance in Chemistry, Biology, and Material Science. Chem. Rev. (Washington, DC, U.S.) 2013, 113, 2100−2138. (19) Sherrill, C. D.; Takatani, T.; Hohenstein, E. G. An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H2S. J. Phys. Chem. A 2009, 113, 10146−10159. (20) Tarakeshwar, P.; Choi, H. S.; Kim, K. S. Olefinic vs Aromatic π− H Interaction: A Theoretical Investigation of the Nature of Interaction of First-row Hydrides with Ethene and Benzene. J. Am. Chem. Soc. 2001, 123, 3323−3331.

CONCLUSIONS The performance of recently developed and also widely used density functionals (M06-2X and B2PLYP-D) with arrays of basis sets (6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-311G(d,p), 6-311+G(d,p), aug-cc-pVXZ (X = D, T, Q)) was assessed for C−H···π and N−H···π interactions. This particularly includes geometries, dissociation energies, and important C−H and N− H vibrational frequency shifts. Three prototype complexes, namely, benzene−acetylene, benzene−methane, and benzene− ammonia, were considered. Computational results were compared with the available experimental data. Unlike the calculations at MP2 level with Dunning’s correlation consistent basis sets for C−H···π interactions in the case of benzene dimer reported earlier,37 inclusion of counterpoise in optimizations and frequencies is generally not required for the abovementioned DFT calculations. The effect of basis set on the geometries of individual fragments in the complexes is negligible, whereas the intermolecular distance in the complexes differs notably for various methods and basis sets. M06-2X or B2PLYP-D with Pople’s basis sets that include diffuse function produces the dissociation energies that are in good agreement (or are close to the experimental values) for the complexes considered in this study. The M06-2X functional performs better than the B2PLYP-D functional in predicting the vibrational frequency shifts involving C−H···π and N− H···π interactions. The counterpoise correction is not important in calculating the dissociation energies and frequency shifts with either of the functionals. Our study clearly indicates that the combination of M06-2X and Dunning’s correlation consistent basis sets of aug-cc-pVXZ (X = D, T, or Q) should not be used for nonbonding interactions of C−H···π and N− H···π types. The M06-2X/6-31+G(d) level is reliable and economical for investigations of C−H···π and N−H···π interactions in predicting the dissociation energies and vibrational frequency shifts for larger molecular complexes.

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ASSOCIATED CONTENT

* Supporting Information S

Selected vibrational frequency data for the complexes and fragments at all the computational levels. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*T.D.: tel., +1-404-880-6969; e-mail, [email protected]. *J.L.: tel., +1-601-979-3482; e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.P. and J. L. acknowledge the support of the NSF CREST Interdisciplinary Nanotoxicity Center, Grant HRD-0833178; NSF-EPSCoR Award 362492-190200-01\NSFEPS-0903787. DoD High Performance Computing Modernization Program (HPCMP) is thanked for computational resources through the Office of Naval Research (ONR). Mississippi Center for Supercomputing Research (MCSR) is also acknowledged for generous computational facilities.

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Toward Selection of Efficient Density Functionals for van der Waals

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