ARTICLE pubs.acs.org/JPCA
Cooperativity between S 3 3 3 π and Rg 3 3 3 π in the OCS 3 3 3 C6H6 3 3 3 Rg (Rg = He, Ne, Ar, and Kr) van der Waals Complexes Yanli Zeng, Jing Hao, Shijun Zheng, and Lingpeng Meng* Institute of Computational Quantum Chemistry, College of Chemistry and Material Science, Hebei Normal University, Shijiazhuang 050016, People's Republic of China ABSTRACT: The complexes OCS 3 3 3 C 6 H 6 , C 6 H 6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg (Rg = He, Ne, Ar, and Kr) have been studied by means of MP2 calculations and QTAIM analyses. The optimized geometries of the title complexes have C6v symmetry. The intermolecular interactions in the OCS 3 3 3 C6H6 3 3 3 Rg complexes are comparatively stronger than that in the OCS 3 3 3 C6H6 complex, which prove that the He, Ne, Ar, and Kr atoms have the ability to form weak bonds with the benzene molecule. In QTAIM studies, the π-electron density of benzene was separated from the total electron density. The molecular graphs and topological parameters of the OCS 3 3 3 πC6H6, πC6H6 3 3 3 Rg, and OCS 3 3 3 πC6H6 3 3 3 Rg complexes indicate that the interactions are mainly attributed to the electron density provided by the π-bonding electrons of benzene and the top regions of the S and Rg atoms. Charge transfer is observed from the benzene molecule to SCO/Rg in the formation of the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes. Molecular electrostatic potential (MEP) analyses suggest that the electrostatic energy plays a pivotal role in these intermolecular interactions.
1. INTRODUCTION The intermolecular interactions between π-electron systems and Lewis acids have attracted increasing attention in recent years,14 because such interactions play a key role in certain chemical reactions, particularly those involving aromatic rings.5,6 In the past two decades, van der Waals complexes involving the benzene molecule have attracted much attention, with the objective of probing intermolecular forces, intermolecular energy transfer, vibrational relaxation, and so on. van der Waals complexes have weak binding energies, in general of between 100 and 1000 cm1. In van der Waals complexes involving the benzene molecule, benzene has a large, permanent quadrupole moment,7,8 with negative electrostatic potential above and below the plane of the ring. According to this charge distribution, benzene can easily interact with various partners (rare gas atoms,913 hydrogen halides,14 N2,15 CO,16 HCN,17 H2O,18 NH3,19 SO2,20 C2H2,21 and OCS22,23) as electron donors. Recently, using a tunable diode laser spectrometer to probe a pulsed supersonic jet expansion, Dehghany et al.22 studied the infrared spectrum of the weakly bound OCS 3 3 3 C6H6 complex in the region of the ν1 fundamental band of OCS (∼2050 cm1). It is shifted by 11.1 cm1 compared with the free OCS monomer. This observation was one of the first direct infrared studies of a benzene-containing van der Waals complex. The derived geometry of OCS 3 3 3 C6H6 has an S-bonded configuration with OCS located along the benzene C6 symmetry axis. Similar bands were observed for the trimers OCS 3 3 3 C6H6 3 3 3 He and OCS 3 3 3 C6H6 3 3 3 Ne; the obtained geometries had an r 2011 American Chemical Society
on-axis rare gas atom on the other side of the benzene. The analogous band for OCS 3 3 3 C6H6 3 3 3 Ar was not detected; the authors doubted that the OCS 3 3 3 C6H6 3 3 3 Ar trimer had the same symmetrical geometry as OCS 3 3 3 C6H6 3 3 3 He and OCS 3 3 3 C6H6 3 3 3 Ne. In this work, the intermolecular interactions of the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes (Rg = He, Ne, Ar, and Kr) have been studied by means of reliable ab initio calculations and quantum theory of “atoms in molecules” (QTAIM) investigations. The configurations of these complexes were obtained with no imaginary frequencies. In the QTAIM studies, the π-electron density of benzene was separated from the total electron density, the π-electron density function was obtained, and the bonding character of this kind of π-type interaction could be described visually and quantitatively. Therefore, this work could help us to obtain a detailed understanding of the nature of these interactions, supplementing the knowledge on such intermolecular interactions.
2. COMPUTATIONAL DETAILS Equilibrium geometries were fully optimized with the aug-ccpVDZ24 basis set at the second-order MøllerPlesset (MP2)25 level using the Gaussian03 program package.26 Harmonic frequencies were calculated to confirm the equilibrium geometries Received: July 18, 2011 Revised: August 31, 2011 Published: August 31, 2011 11057
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Table 1. Calculated and Experimental Intermolecular Distances for the OCS 3 3 3 C6H6, OCS 3 3 3 C6H6 3 3 3 Rg (Rg = He, Ne) Complexesa OCS 3 3 3 C6H6 3 3 3 He
OCS 3 3 3 C6H6 d(SX)
b
d(HeX)
c
OCS 3 3 3 C6H6 3 3 3 Ne d(NeX) d
experimental values
3.381
3.570
3.443
B3LYP/6-311++g(d,p)
4.1548
7.0471
3.4430
B3LYP/aug-cc-pVDZ
4.2071
10.5756
MP2/6-311++g(d,p)
3.4804
3.5157
MP2/aug-cc-pVDZ
3.3190
3.2957
3.5462
a
Distances in angstroms (Å). b The distance between the S atom and the benzene centroid. c The distance between the He atom and the benzene centroid. d The distance between the Ne atom and the benzene centroid.
corresponding to energy minima. The keyword Counterpoise was used for the calculation of corrected interaction energies (ΔE) excluding the inherent basis set superposition error (BSSE), as well as for geometry optimization and frequency computation.27 In this work, the molecular electrostatic potentials V(r) were calculated at the MP2/aug-cc-pVDZ level. Electrostatic potential surfaces were generated by mapping the electrostatic potentials onto surfaces of constant molecular electron density (0.01 au). A detailed analysis of the electron density distribution function was made according to QTAIM as proposed by Bader,2830 using the programs AIM200031 and GTA-2010,32 the latter of which was developed by the authors and registered at the QCPE (register number QCPE-661). Properties of the electron density calculated at bond critical points (BCP), ring critical points (RCP), and cage critical points (CCP) of the intermolecular interactions under consideration were characterized. In ref 33, the influences of various basis sets used in the calculations of the values of atoms in molecules (AIM) parameters derived from the electron density distribution were investigated for hydrogenbonded systems. The results showed that the most important AIM parameter values were almost independent of the basis set, but the smallest Dunning-type cc-pVDZ or aug-cc-pVDZ basis sets may lead to poor results. Therefore, the wave functions were obtained at the MP2/6-311++G(d, p)//MP2//aug-cc-pVDZ level in this work. In this work, the π-electron density of benzene was separated from the total electron density, the π-electron density function was obtained, and the bonding character of this kind of π-type interaction could be described visually and quantitatively. To distinguish, OCS 3 3 3 πC6H6, πC6H6 3 3 3 Rg, and OCS 3 3 3 πC6H6 3 3 3 Rg refer to the complexes include only the π-electron density of benzene and the total electron density of SCO and Rg; OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg refer to the complexes include the total electron density of benzene, SCO, and Rg.
3. RESULTS AND DISCUSSION Table 1 lists the optimized geometrical parameters computed at four levels of methods and basis sets, B3LYP/6-311++G(d,p), B3LYP/aug-cc-pVDZ, MP2/6-311++G(d,p), and MP2/aug-ccpVDZ, for complexes OCS 3 3 3 C6H6, OCS 3 3 3 C6H6 3 3 3 He, and OCS 3 3 3 C6H6 3 3 3 Ne. Experimental data are also provided in Table 1. One can see from Table 1 that the MP2/aug-cc-pVDZ calculated geometrical parameters are more consistent with the experimental data than those obtained by the other methods. Many studies also indicate that B3LYP method does not correctly describe dispersion and π-type interactions.3436 MP2 method often overestimates dispersion interactions.37
However, the possible overestimation of dispersion is probably partially compensated by the use of a relatively small basis set. 3.1. Geometries and Interaction Energies. The optimized geometries of the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes (Rg = He, Ne, Ar, and Kr) have C6v symmetry, in which OCS and Rg are oriented perpendicularly to the aromatic ring, along the C6 rotation axis, and the electrophilic S interacts with the benzene molecule (see Figure 1). The optimized geometries are consistent with experimental work.913,22,23 The optimized configurations of the OCS 3 3 3 C6H6 3 3 3 Ar and OCS 3 3 3 C6H6 3 3 3 Kr complexes are similar to those of OCS 3 3 3 C6H6 3 3 3 He and OCS 3 3 3 C6H6 3 3 3 Ne, which is inconsistent with the possibility22 that the stable form of the OCS 3 3 3 C6H6 3 3 3 Ar trimer may not have the same symmetrical structure as OCS 3 3 3 C6H6 3 3 3 He and OCS 3 3 3 C6H6 3 3 3 Ne. Table 2 lists the interaction energies ΔE obtained at the MP2/ aug-cc-pVDZ level, which have been corrected for BSSE and zero-point vibrational energies (ZPVE). The interaction energy for the OCS 3 3 3 C6H6 complex is 12.67 kJ 3 mol1, which is comparable in strength with the reported values for the conventional H 3 3 3 π interactions considered as “weak hydrogen bonds”.38 Therefore, the arenesulfur bond can be considered as a “weak bond”. The interaction energies for the C6H6 3 3 3 Rg complexes are very small, ranging from 0.01 kJ 3 mol1 to 5.37 kJ 3 mol1, which indicates that the interactions between benzene and rare gases are very weak. For the trimers OCS 3 3 3 C6H6 3 3 3 Rg, the interaction energy values are larger than that of the OCS 3 3 3 C6H6 complex, which shows that the intermolecular interactions in the OCS 3 3 3 C6H6 3 3 3 Rg complexes are comparatively stronger than that in the OCS 3 3 3 C6H6 complex. This proves that the He, Ne, Ar, and Kr atoms have the ability to form weak bonds with the benzene molecule. The interaction energy values of C6H6 3 3 3 Rg and OCS 3 3 3 C6H6 3 3 3 Rg become greater along the sequence of Rg = He, Ne, Ar, and Kr. This can be rationalized in terms of the general characteristic of rare gas atoms that their outermost electrons become less strongly bound by the nucleus with increasing atomic weight, and so can form chemical compounds more easily. The interaction energies for the OCS 3 3 3 C6H6 and C6H6 3 3 3 He complexes are 12.67 and 0.01 kJ 3 mol1, while for OCS 3 3 3 C 6 H 6 3 3 3 He is 12.71 kJ 3 mol 1 , decreased by 0.03 kJ 3 mol1 due to the cooperativity. The cooperativity between S 3 3 3 π and Rg 3 3 3 π interactions in the OCS 3 3 3 C6H6 3 3 3 Rg (Rg = He, Ne, Ar, and Kr) van der Waals complexes are 0.03, 0.11, 0.18, and 0.24 kJ 3 mol1, respectively. The trends are along the sequence of Rg = He, Ne, Ar, and Kr. 3.2. Interaction Distances and Infrared Spectra. From Table 2, it can be seen that the distances between the S atom 11058
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Figure 1. Geometries of OCS 3 3 3 C6H6 (a), C6H6 3 3 3 Ar (b), and OCS 3 3 3 C6H6 3 3 3 Ar (c) complexes.
Table 2. Interaction Energies, Main Geometrical Parameters, Frequencies as Well as Their Changes a complexes OCS 3 3 3 C6H6 C6H6 3 3 3 He C6H6 3 3 3 Ne C6H6 3 3 C6H6 3 3
3 Ar 3 Kr
OCS 3 3 OCS 3 3
3 C6H6 3 3 3 C6H6 3 3
3 He
OCS 3 3 OCS 3 3
3 C6H6 3 3 3 C6H6 3 3
3 Ar
ΔEb
d(SX)c
12.67(7.35)
3.3190
0.01(0.55) 0.69(1.13)
3.2952 3.4927
4.12(2.09)
3.5359
5.37(4.19) 3 Ne 3 Kr
d(RgX)d
Δd(SC)
Δν(SC)
Δd(CO)
Δν(CO)
0.0007
2.72
0.0021
9.38
3.6440
12.71(8.23)
3.3200
3.2957
0.0007
2.59
0.0020
9.1
13.47(8.88)
3.3199
3.5462
0.0007
2.63
0.0022
10.15
16.97(10.29)
3.3197
3.5405
0.0007
2.62
0.0020
9.08
18.28(12.97)
3.3173
3.6538
0.0007
2.67
0.0020
9.12
Interaction energies in kJ 3 mol1, distances in angstrom (Å), and frequencies in cm1. b Interaction energies include BSSE and ZPE corrections; the values in brackets are BSSE data. c The distance between the S atom and the benzene centroid. d The distance between the Rg atom and the benzene centroid. a
and the benzene centroid, d(SX), are essentially equal or somewhat longer in the OCS 3 3 3 C6H6 3 3 3 Rg complexes compared with that in the OCS 3 3 3 C6H6 complex. The intermolecular distances between the Rg atoms and the benzene centroid, d(RgX), are also essentially equal or somewhat longer in the OCS 3 3 3 C6H6 3 3 3 Rg complexes compared with those in the C6H6 3 3 3 Rg complexes. That is to say, the interactions between benzene and OCS are almost the same or become somewhat weaker in the OCS 3 3 3 C6H6 3 3 3 Rg complexes compared with that in the OCS 3 3 3 C6H6 complex, and the interactions between benzene and Rg atoms become somewhat weaker in the OCS 3 3 3 C6H6 3 3 3 Rg complexes compared with those in the C6H6 3 3 3 Rg complexes. For all of the complexes, as expected, the SC and CO bonds are lengthened. The elongations of the SC bonds are all
0.0007 Å, and the elongations of the CO bonds are all about 0.0020 Å. The SC and CO stretching vibrations both shift to lower frequencies upon complex formation. The degree of redshift of the CO bonds is larger than that of the SC bonds, which is consistent with their relative elongations. The elongations and red-shifts of the SC and CO bonds show that the stability of OCS decreases upon complex formation. However, all of the changes in the parameters in Table 2 between OCS 3 3 3 C6H6 and OCS 3 3 3 C6H6 3 3 3 Rg are small, showing that the interactions between Rg atoms and the benzene molecule are weak. 3.3. QTAIM Analyses. A. Molecular Graphs and Electron Densities at the Critical Points (CPs). The quantum theory of “atoms in molecules” (QTAIM)2830 is an approach to analyze intra- and intermolecular interactions, the electronic structures of 11059
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Figure 2. QTAIM molecular graphs of total electron density for OCS 3 3 3 C6H6 (a), C6H6 3 3 3 Ar (b), and OCS 3 3 3 C6H6 3 3 3 Ar (c) complexes. The lines connecting the nuclei are the bond paths. Red dots and yellow dots represent BCPs and RCPs, respectively. The position of the CCP is indicated with a green dot.
Table 3. Topological Properties of the Electron Density at the Bond, Ring, and Cage Critical Points in the Intermolecular Interactions of OCS and Benzenea complexes OCS 3 3 3 C6H6
OCS 3 3 3 C6H6 3 3 3 He
OCS 3 3 3 C6H6 3 3 3 Ne
OCS 3 3 3 C6H6 3 3 3 Ar
OCS 3 3 3 C6H6 3 3 3 Kr
a
CPs
Fc
S3 3 3C (3, +1)
0.0051 0.0051
(3, +3) S3 3 3C
0.0039 0.0051
(3, +1) (3, +3) S3 3 3C (3, +1)
r2Fc
Hc
Gc/Vc
0.0028
0.0008
1.2798
0.0027
0.0008
1.2856
0.0037 0.0035
0.0029 0.0028
0.0008 0.0008
1.2713 1.2801
0.0172
0.0035
0.0027
0.0008
1.2858
0.0180
0.0037
0.0029
0.0008
1.2706
0.0051
0.0173
0.0035
0.0028
0.0008
1.2791
0.0051
0.0173
0.0035
0.0027
0.0008
1.2848
(3, +3)
0.0039
0.0180
0.0037
0.0029
0.0008
1.2688
S3 3 3C (3, +1) (3, +3)
0.0051
0.0173
0.0035
0.0028
0.0008
1.2813
0.0051 0.0039
0.0173 0.0180
0.0035 0.0037
0.0027 0.0029
0.0008 0.0008
1.2870 1.2705
S3 3 3C (3, +1)
0.0051
0.0173
0.0036
0.0028
0.0008
1.2814
0.0051
0.0173
0.0035
0.0028
0.0008
1.2872
(3, +3)
0.0039
0.0180
0.0037
0.0029
0.0008
1.2711
Gc
Vc
0.0173
0.0035
0.0173
0.0035
0.0180 0.0172
0.0051 0.0039
All values in au.
molecules, and chemical reactions.3950 In QTAIM, critical points (CPs) play an important role in the characterization of electron density topology. Figure 2 shows three kinds of CPs corresponding to the intermolecular interactions of OCS 3 3 3 C6H6, C6H6 3 3 3 Ar, and OCS 3 3 3 C6H6 3 3 3 Ar. The S 3 3 3 C bond critical points (BCP) connect the S atom and each carbon atom in the benzene molecule, and the Rg 3 3 3 C BCP connect the Rg atom and each carbon atom in the benzene molecule. For each of
the complexes discussed here, there are two other kinds of CPs: the ring critical point (RCP) and the cage critical point (CCP). The topological and energetic properties at the CPs of the interactions between OCS and benzene are listed in Table 3, and those at the CPs between Rg and benzene are listed in Table 4. The electron density at the BCP, FBCP, is often described as an indicator of the strength of an interaction. In general, the larger 11060
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Table 4. Topological Properties of the Electron Density at the Bond, Ring, and Cage Critical Points in the Intermolecular Interactions of Rg and Benzenea CPs
Fc
r2Fc
Gc
Vc
Hc
Gc/Vc
He 3 3 3 C (3, +1) (3, +3)
0.0015
0.0065
0.0013
0.0009
0.0004
1.3760
0.0015 0.0014
0.0065 0.0070
0.0013 0.0014
0.0009 0.0011
0.0004 0.0004
1.3756 1.3335
Ne 3 3 3 C (3, +1)
0.0015
0.0085
0.0016
0.0011
0.0005
1.4933
0.0015
0.0085
0.0016
0.0011
0.0005
1.4930
(3, +3)
0.0013
0.0086
0.0016
0.0011
0.0005
1.4576
Ar 3 3 3 C (3, +1)
0.0033
0.0117
0.0023
0.0017
0.0006
1.3573
0.0033
0.0117
0.0023
0.0017
0.0006
1.3577
(3, +3)
0.0027
0.0121
0.0025
0.0019
0.0006
1.2923
C6H6 3 3 3 Kr
Kr 3 3 3 C (3, +1)
0.0036 0.0036
0.0118 0.0118
0.0024 0.0023
0.0018 0.0018
0.0006 0.0006
1.3388 1.3397
(3, +3)
0.0029
0.0125
0.0026
0.0020
0.0006
1.2830
OCS 3 3 3 C6H6 3 3 3 He
He 3 3 3 C (3, +1)
0.0015
0.0065
0.0013
0.0009
0.0004
1.3954
0.0015
0.0065
0.0013
0.0009
0.0004
1.3951
(3, +3)
0.0014
0.0070
0.0014
0.0010
0.0004
1.3543
Ne 3 3 3 C (3, +1)
0.0013
0.0076
0.0014
0.0009
0.0005
1.5550
0.0013
0.0076
0.0014
0.0009
0.0005
1.5547
(3, +3) Ar 3 3 3 C
0.0012 0.0032
0.0077 0.0116
0.0014 0.0023
0.0009 0.0017
0.0005 0.0006
1.5160 1.3745
(3, +1)
0.0032
0.0116
0.0023
0.0017
0.0006
1.3751
(3, +3)
0.0026
0.0120
0.0024
0.0018
0.0006
1.3135
Kr 3 3 3 C (3, +1)
0.0035
0.0116
0.0023
0.0017
0.0006
1.3569
0.0035
0.0116
0.0023
0.0017
0.0006
1.3579
(3, +3)
0.0028
0.0123
0.0025
0.0019
0.0006
1.3038
complexes C6H6 3 3 3 He
C6H6 3 3 3 Ne
C6H6 3 3 3 Ar
OCS 3 3 3 C6H6 3 3 3 Ne
OCS 3 3 3 C6H6 3 3 3 Ar
OCS 3 3 3 C6H6 3 3 3 Kr
a
All values in au.
the value of FBCP, the stronger the bond.28 From Table 3, it can be seen that for the intermolecular interaction of OCS and benzene, the electron density at the BCPs, FBCP, is equal to the electron density at the RCPs. Meanwhile, the values of the electron density at the CCPs are lower than those at the BCPs and RCPs. More importantly, the topological properties at all CPs show low values of electron density, which can be ascribed to the fact that the S atom interacts simultaneously with each carbon atom of the benzene molecule. The electron densities at the S 3 3 3 C BCP and RCP have the same values for both OCS 3 3 3 C6H6 and OCS 3 3 3 C6H6 3 3 3 Rg, which indicates that the interactions between Rg and benzene do not influence the interactions between S and benzene. From Table 4, it can be seen that for the intermolecular interactions of Rg and benzene, the topological properties at the BCPs, RCPs, and CCPs show low values of electron density, which can be attributed to the fact that the Rg atom interacts simultaneously with each carbon atom of the benzene molecule. The electron densities at the Rg 3 3 3 C BCP and RCP have almost the same values for both C6H6 3 3 3 Rg and OCS 3 3 3 C6H6 3 3 3 Rg, indicating that the interactions between OCS and benzene do not influence the interactions between Rg and benzene. In ref 51, it was shown how the electron density due to a π system can be characterized through QTAIM concepts and definitions. In this work, the π-electron density of benzene was separated from the total electron density, the π-electron density function was obtained, and the bonding character of this kind of π-type interaction could be described visually and quantitatively. Figure 3 displays the molecular graphs of the OCS 3 3 3 πC6H6,
πC6H6 3 3 3 Ar, and OCS 3 3 3 πC6H6 3 3 3 Ar complexes, which only includes the π electrons for benzene and total electrons for OCS and Ar. According to Figure 3, the π bond for benzene is composed of 12 attractors on the top and bottom of the respective nuclei, 12 BCPs at each of the π bonds, and 24 curved bond paths. Tables 5 and 6 present the electron density properties due to the considered π system, and all CPs are merely attributed to the π-electron density of benzene. Comparing the data in Table 5 with those in Table 3, it can be seen that, for the intermolecular interactions of OCS and benzene, all of the topological parameters attributed to π-electron density at the BCPs, RCPs, and CCPs become only a little smaller. Comparing the data in Table 6 with those in Table 4, it can be seen that, for the intermolecular interactions of Rg atoms and benzene, all of the topological parameters attributed to π-electron density at the BCPs, RCPs, and CCPs have almost the same values as those attributed to the total electron density. It can be concluded that the interactions in the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes are mainly attributed to the π-bonding electrons of benzene and OCS or Rg. B. Laplacian of the Electron Density and Energy Properties. The Laplacian values in all of the complexes are positive and are the result of the interaction between two closed-shell systems, such as ionic interaction, van der Waals forces, hydrogen bonding, and so forth.28 The values of r2Fc and Hc (the sum of Gc and Vc) indicate the type of interaction. It has also been claimed that if r2Fc is positive but Hc is negative, then the interaction is partly covalent in nature.52,53 The kinetic electron energy density Gc is positive, while the potential electron energy density Vc is 11061
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Figure 3. QTAIM molecular graphs of π-electron density for OCS 3 3 3 πC6H6 (a), πC6H6 3 3 3 Ar (b), and OCS 3 3 3 πC6H6 3 3 3 Ar (c) complexes. The lines connecting the nuclei are the bond paths. Red dots and yellow dots represent BCPs and RCPs, respectively. The positions of the CCPs are indicated with green dots.
Table 5. Topological Properties of the π-Electron Density at the Bond, Ring, and Cage Critical Points in the Intermolecular Interactions of OCS and Benzenea complexes OCS 3 3 3 πC6H6
OCS 3 3 3 πC6H6 3 3 3 He
OCS 3 3 3 πC6H6 3 3 3 Ne
OCS 3 3 3 πC6H6 3 3 3 Ar
OCS 3 3 3 πC6H6 3 3 3 Kr
a
CPs
Fc
r2Fc
Gc
Vc
Hc
Gc/Vc
S3 3 3C (3, +1)
0.0047
0.0143
0.0046
0.0142
0.0030
0.0024
0.0006
1.2599
0.0029
0.0023
0.0006
(3, +3)
0.0031
1.2654
0.0138
0.0029
0.0024
0.0005
S3 3 3C (3, +1)
0.0041 0.0041
1.2185
0.0133 0.0133
0.0027 0.0027
0.0022 0.0021
0.0006 0.0006
1.2751 1.2785
(3, +3)
0.0031
0.0128
0.0027
0.0022
0.0005
1.2418
S3 3 3C (3, +1)
0.0047
0.0143
0.0030
0.0024
0.0006
1.2587
0.0046
0.0142
0.0029
0.0023
0.0006
1.2640
(3, +3)
0.0032
0.0138
0.0029
0.0024
0.0005
1.2139
S3 3 3C (3, +1)
0.0047
0.0143
0.0030
0.0024
0.0006
1.2612
0.0046
0.0143
0.0029
0.0023
0.0006
1.2666
(3, +3) S3 3 3C
0.0032 0.0047
0.0137 0.0144
0.0029 0.0030
0.0024 0.0024
0.0005 0.0006
1.2159 1.2625
(3, +1)
0.0047
0.0144
0.0030
0.0023
0.0006
1.2680
(3, +3)
0.0032
0.0139
0.0029
0.0024
0.0005
1.2210
All values in au.
negative, and the balance between these two values determines the nature of the interaction. Hence, Gc/Vc may indicate the regions corresponding to covalent or noncovalent interactions. If this ratio is greater than 1, then the interaction is noncovalent. If the ratio is between 0.5 and 1, the interaction is partly covalent in nature, and when Gc/Vc is less than 0.5, the interaction is a shared covalent one.52,53 From Table 3, it can be seen that, for all of the BCPs
between OCS and benzene, the r2Fc values are positive, the Hc values are positive, and the Gc/Vc values are greater than 1. Hence, the interactions between OCS and benzene are noncovalent in nature. From Table 4, it can be seen that for the BCPs between Rg and benzene, the r2Fc values are positive, the Hc values are positive, and the Gc/Vc values are greater than 1. Hence, the interactions between Rg and benzene are also noncovalent. 11062
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Table 6. Topological Properties of the π-Electron Density at the Bond, Ring, and Cage Critical Points in the Intermolecular Interactions of Rg and Benzenea complexes πC6H6 3 3 3 He
πC6H6 3 3 3 Ne
πC6H6 3 3 3 Ar
πC6H6 3 3 3 Kr
OCS 3 3 3 πC6H6 3 3 3 He
OCS 3 3 3 πC6H6 3 3 3 Ne
OCS 3 3 3 πC6H6 3 3 3 Ar
OCS 3 3 3 πC6H6 3 3 3 Kr
a
CPs
Fc
r2Fc
Gc
Vc
Hc
Gc/Vc
He 3 3 3 C (3, +1) (3, +3)
0.0015
0.0057
0.0011
0.0008
0.0003
1.3544
0.0015 0.0013
0.0057 0.0061
0.0011 0.0012
0.0008 0.0010
0.0003 0.0003
1.3536 1.2952
Ne 3 3 3 C (3, +1)
0.0014
0.0075
0.0014
0.0009
0.0005
1.4963
0.0014
0.0075
0.0014
0.0009
0.0005
1.4955
(3, +3)
0.0012
0.0073
0.0014
0.0010
0.0004
1.4389
Ar 3 3 3 C (3, +1)
0.0031
0.0099
0.0020
0.0015
0.0005
1.3331
0.0031
0.0098
0.0020
0.0015
0.0005
1.3315
(3, +3)
0.0024
0.0097
0.0020
0.0017
0.0004
1.2321
Kr 3 3 3 C (3, +1)
0.0033 0.0033
0.0100 0.0100
0.0021 0.0020
0.0016 0.0016
0.0005 0.0004
1.2815 1.2802
(3, +3)
0.0025
0.0101
0.0022
0.0018
0.0004
1.1985
He 3 3 3 C (3, +1)
0.0014
0.0057
0.0011
0.0008
0.0003
1.3786
0.0014
0.0057
0.0011
0.0008
0.0003
1.3779
(3, +3)
0.0012
0.0060
0.0012
0.0009
0.0003
1.3232
Ne 3 3 3 C (3, +1)
0.0013
0.0068
0.0012
0.0008
0.0004
1.5615
0.0013
0.0068
0.0012
0.0008
0.0004
1.5607
(3, +3) Ar 3 3 3 C
0.0011 0.0030
0.0066 0.0098
0.0012 0.0019
0.0008 0.0014
0.0004 0.0005
1.5015 1.3525 1.3512
(3, +1)
0.0030
0.0098
0.0019
0.0014
0.0005
(3, +3)
0.0023
0.0096
0.0020
0.0016
0.0004
1.2570
Kr 3 3 3 C (3, +1)
0.0032
0.0099
0.0020
0.0015
0.0005
1.3122
0.0032
0.0098
0.0020
0.0015
0.0005
1.3111
(3, +3)
0.0024
0.0099
0.0021
0.0017
0.0004
1.2283
All values in au.
The topology of the Laplacian of the electron density can show, through a two-dimensional chart, whether the electron density is either maximally concentrated or maximally depleted. The chart can not only show which sites are able to deliver electronic charge, but also those that can stabilize an overloaded uptake of electronic charge. When an atom is involved in a chemical bond, its valence electronic charge will lose its uniformity.28 Contour maps of the Laplacian of electron density for OCS 3 3 3 πC6H6, πC6H6 3 3 3 Ar, and OCS 3 3 3 πC6H6 3 3 3 Ar are displayed in Figure 4. In Figure 4a, one can see that the S atom exhibits a great region of charge depletion in its valence shell (VS) in the axial orientation. Also, the π-cloud of C6H6 exhibits a great region of electron concentration in its VS in the axial orientation. The S atom in the OCS 3 3 3 πC6H6 complex shows an increased capability for electron attack because it has a region of electron depletion to be filled by the electron density provided by the bonding electrons of benzene. In Figure 4b, one can see that the Ar atom exhibits a region of electron depletion in its VS in the axial orientation, while the π-cloud of C6H6 exhibits a region of electron concentration in its VS in the axial orientation. In Figure 4c, in the OCS 3 3 3 πC6H6 3 3 3 Ar complex, both the S and Rg atoms exhibit regions of electron depletion in their VSs in the axial orientation, and the π-cloud of C6H6 exhibits two regions of electron concentration in its VS in the axial orientation. Consequently, the Laplacian topology clearly shows that the S and Rg atoms can undergo stabilizing interactions with the π-cloud of C6H6. C. Integral Atomic Charge in Atomic Basin. A zero-flux surface is defined by a particular set of rF(r) trajectories, all
Figure 4. Contour maps of Laplacian of the electron density for OCS 3 3 3 πC6H6, (a), πC6H6 3 3 3 Ar, (b) and OCS 3 3 3 πC6H6 3 3 3 Ar (c) complexes.
the members of which terminate at a single point, the bond critical point, where rF(r) = 0.28 The integral of electron density over the zero-flux surface can provide useful intra- and 11063
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intermolecular interaction information on the interacting atoms. Atomic net charge is the sum of the positive charge of the nucleus and the negative charge of the electrons in an atom. From Table 7, it can be seen that in the complexes OCS 3 3 3 C6H6 and OCS 3 3 3 C6H6 3 3 3 Rg, the net charges of the S atom increase, those of the C and O atoms decrease, and the total net charges of SCO decrease. In the complexes C6H6 3 3 3 Rg and OCS 3 3 3 C6H6 3 3 3 Rg, the net charges of the Rg atoms decrease. That is to say, charge transfer is observed from the benzene molecule to SCO/Rg in the formation of the OCS 3 3 3 C6H6, Table 7. Atomic Basin Integrated Properties for the Complexesa complexes
Δq(S)
Δq(C)
Δq(SCO) or Δq(Rg)
0.0107 0.0193 0.0088
0.0174
0.0111 0.0188 0.0097
0.0174
0.0118 0.0191 0.0094
0.0167
0.0116 0.0188 0.0096
0.0168
OCS 3 3 3 C6H6 3 3 3 Kr 0.0107 0.0192 0.0104 C6H6 3 3 3 He C6H6 3 3 3 Ne C6H6 3 3 3 Ar
0.0189
OCS 3 3 3 C6H6 OCS 3 3 3 C6H6 3 3 3 He OCS 3 3 3 C6H6 3 3 3 Ne OCS 3 3 3 C6H6 3 3 3 Ar
C6H6 3 3 3 Kr OCS 3 3 3 C6H6 3 3 3 He OCS 3 3 3 C6H6 3 3 3 Ne OCS 3 3 3 C6H6 3 3 3 Ar a
Δq(O)
OCS 3 3 3 C6H6 3 3 3 Kr
q: integral net charge. All values in au.
0.0053 0.0056 0.0075 0.0047 0.0046 0.0078
C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes, and there is a redistribution of charge in the electron acceptor SCO. 3.4. Molecular Electrostatic Potentials Analysis. Molecular electrostatic potential (MEP) is a theoretical index of quantum chemistry that can be used to judge certain molecular properties, especially molecular reactivity. The MEP is determined naturally by the molecule itself, so the MEPs of different molecules are different in their surrounding space. In this work, the electrostatic potentials have been computed at the MP2/aug-cc-pVDZ level, and the isosurfaces of the electronic density equivalent to F(r) = 0.01 au are considered. Figure 5 shows the three-dimensional MEP maps of SCO, Ar, and benzene. From a visual analysis of the electrostatic potential surfaces, it can be seen that there is a positive electron charge density (in blue) in the top region of the S atom of the SCO molecule, which is consistent with the S-bonded configurations of the complexes presented in Figure 1. The MEP also indicates the smaller positive electrostatic potential (in pale green) on the surface of the Ar atom, which accounts for the fact that the gas atom has the capability of interacting with the π-cloud of benzene to form weak bonds. For the benzene molecule, a negative electrostatic potential (in red) can be found above and below the ring. The MEP maps of the OCS 3 3 3 C6H6, C6H6 3 3 3 Ar, and OCS 3 3 3 C6H6 3 3 3 Ar complexes are also displayed in Figure 5. Upon the complexation of OCS 3 3 3 C6H6, C6H6 3 3 3 Ar, and OCS 3 3 3 C6H6 3 3 3 Rg, the size of the negative electrostatic potential regions of the π-cloud facing OCS or Ar decreases, with color changes from red to orange. The size of the positive electrostatic potential regions also decreases at the outermost
Figure 5. Molecular electrostatic potentials (MEP) for SCO (a), Ar (b), C6H6 (c), OCS 3 3 3 C6H6 (d), C6H6 3 3 3 Ar (e), and OCS 3 3 3 C6H6 3 3 3 Ar (f), mapped on the surface of molecular electron density 0.01 au. 11064
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The Journal of Physical Chemistry A regions of the S and Ar atoms, the blue color on the head of the S atom becomes shallow, and the pale-green color on the surface of the Ar atom facing the benzene turns into red. These results indicate that the S atom and Rg atom are more prone to accept the electron density provided by the π-cloud of the benzene molecule, and that electron displacement occurs in the benzene molecule, directed toward the center of the aromatic ring. All of these observations suggest that electrostatic energy plays a pivotal role in all of the studied intermolecular interactions.
4. SUMMARY The intermolecular interactions in the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes (Rg = He, Ne, Ar, and Kr) have been studied theoretically by means of MP2 calculations and QTAIM analyses. (1) The optimized geometries of these complexes have C6v symmetry, in which OCS and Rg are oriented perpendicularly with respect to the aromatic ring, along the C6 rotation axis, and the electrophilic S interacts with the benzene molecule. (2) The intermolecular interactions in the OCS 3 3 3 C6H6 3 3 3 Rg complexes are comparatively stronger than that in the OCS 3 3 3 C6H6 complex. This proves that the He, Ne, Ar, and Kr atoms have the ability to form weak bonds with the benzene molecule. (3) QTAIM analyses have shown that the interactions between OCS and benzene, as well as between Rg and benzene, are “closed-shell” noncovalent in nature. Charge transfer is observed from the benzene molecule to SCO/ Rg in the formation of the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes, and there is a redistribution of charge in the electron acceptor SCO. (4) π-Electron density of benzene was separated from the total electron density and the π-electron density function was obtained. Molecular graphs and topological parameters of OCS 3 3 3 πC6H6, πC6H6 3 3 3 Rg, and OCS 3 3 3 πC6H6 3 3 3 Rg indicate that the formation of the OCS 3 3 3 C6H6, C6H6 3 3 3 Rg, and OCS 3 3 3 C6H6 3 3 3 Rg complexes results from the interaction between the electron density provided by the π-bonding electrons of benzene and the top regions of the S and Rg atoms, respectively. (5) MEP analyses have indicated that the S atom and Rg atom are more prone to accept the electron density provided by π-bonding electrons of the benzene molecule, and that electron displacement occurs in the benzene molecule, directed toward the center of the aromatic ring. This suggests that electrostatic energy plays a pivotal role in these intermolecular interactions. ’ AUTHOR INFORMATION Corresponding Author
*Tel./Fax: +86-311-86269217. E-mail:
[email protected]. cn.
’ ACKNOWLEDGMENT Thanks for International Science Editing to edit this paper. This project was supported by the National Natural Science Foundation of China (Contract Nos.: 20801017, 20973053, 21073051, 21102033, 21171047), the Natural Science Foundation of Hebei
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Province (Contract Nos.: B2010000371, B2011205058), and the Education Department Foundation of Hebei Province (Contract No.: ZD2010126).
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