Quantifying dispersion interaction: A study of alkane and alkene dimers

Transcription

1 Indian Journal of Chemistry Vol. 53A, Aug-Sept 2014, pp Quantifying dispersion interaction: A study of alkane and alkene dimers J Richard Premkumar, Deivasigamani Umadevi & G Narahari Sastry* CSIR-Centre for Molecular Modelling, Indian Institute of Chemical Technology, Hyderabad , India gnsastry@gmail.com Received 20 April 2014; revised and accepted 2 May 2014 In this study, the interaction pattern and energies of a series of hydrocarbon dimers have been investigated by using a highly reliable quantum chemical method (M06-2X/cc-pVTZ). Saturated and unsaturated hydrocarbons in both cyclic and acyclic forms have been modelled to study their interaction. These dimers are found to involve different types of noncovalent interactions such as π-π (dimer of unsaturated hydrocarbons), CH π (dimer of saturated-unsaturated hydrocarbons) and CH HC (dimer of saturated hydrocarbons). Atoms in molecules analysis provides further insight into the presence of these different noncovalent interactions. Interestingly, the saturated hydrocarbon dimers (A-A) are found to have binding energy strengths comparable with those of the dimers of their unsaturated counterparts (E-E). Strong interactions have been observed between the saturated monomers with the corresponding unsaturated monomers (A-E). The energy decomposition analysis using DFT-SAPT method reveals that both dispersion and electrostatic components play nearly equal roles in modulation of the strength of the hydrocarbon-hydrocarbon interaction. Keywords: Theoretical chemistry, Density functional calculations, Dispersion, Noncovalent interactions, Hydrocarbon interactions, Alkane dimers, Alkene dimers, Dimers, Hydrocarbon dimers, Energy decomposition analysis Noncovalent interactions direct diverse phenomena in the fields of biology, supramolecular chemistry and materials science such as structure, stability, solvation, and crystal packing. 1,2 Understanding the various factors influencing the noncovalent interactions is indispensable to appreciate phenomena such as protein folding, structure of DNA, molecular recognition and drug binding in biology. 3-5 Factors influencing the noncovalent interactions such as size and curvature of the π system have been studied extensively. 6-9 In the case of unsaturated hydrocarbons, the noncovalent interactions such as π-π and CH π has been well-recognized in the literature. 10 Among these, π-π interaction is known to play a key role in imparting functional properties to bio-molecules. The study of intermolecular interactions between saturated and unsaturated hydrocarbon is a topic of high importance. Clearly, the fact that the boiling point of hydrocarbon increases as the alkyl chain length increases, indicates stronger intermolecular interaction in alkanes and alkenes. A recent study reveals that simple substituent on the π-systems can have a dramatic impact on the local orientation of π-π stacked complexes. 11 A recent report investigated the relative strengths of CH π and π-π interactions in benzene cluster aggregates and illustrated the apparent preference of CH π over π-π type in the cluster aggregates. 12 The π-π networks in proteins and their connectivity pattern have been studied in a recent database. 13 The saturated hydrocarbon molecules are held together in the crystal state by apparently weak dihydrogen (CH HC) interactions. Ab initio calculations carried out in order to find the interaction energies of n-alkane dimers report that the interaction energies of n-hexane and n-heptane are close to that of the hydrogen bond of the water dimer. 14 Echeverría et al. 15 studied the intermolecular interactions in the dimers of n-alkanes and polyhedranes and identified the strength and nature of these dihydrogen contacts. The cooperative effect of π-π stacking interaction in the presence of other noncovalent interactions has also been studied extensively. 16,17 Apart from the significance of these interactions in controlling the structure and function of molecules, the noncovalent interactions involving hydrocarbons play a significant role in nanomaterials and nano-bio interface. 18 The interlayer interactions in graphene have been explored by studying the weak noncovalent interactions between the stacked layers of graphene. 19 Saturated hydrocarbon model systems have been employed to study the interaction between multilayered graphanes in order to explore its electronic properties. Dispersion components play an important role in the

2 986 INDIAN J CHEM, SEC A, AUG-SEPT 2014 interactions between saturated hydrocarbons. 20 The noncovalent interactions of various metal ions, small molecules and bio-molecules on the models of carbon materials have also been explored Supramolecular chemistry is one of the most strongly developing research areas which involves noncovalent interactions to explain the self-assembly of molecules. 24 Benzene and cyclohexane have similar boiling points of 80 ºC, indicating that they have similar intermolecular interactions. The boiling point of benzene can be attributed to the C-H... π and π stacking interaction between the benzene molecules as indicated by their crystal structure. However, the equally higher boiling point of cyclohexane which has no unsaturated π bond indicates the presence of equally stronger dispersion forces between the saturated cyclohexane molecules. According to accurate CCSD(T) computations, the stacked benzene dimer exhibits smaller binding energy (BE) than the pentane dimer (2.80 vs kcal/. 25 These observations triggered our interest to enumerate the dispersion interactions in alkane and alkene dimers. The preceding section clearly indicates the occurrence of dispersion interactions and the importance to quantify such interactions. In the current study, we have systematically studied the interactions of various acyclic and cyclic hydrocarbon dimers in both saturated and unsaturated forms. The different types of possible dispersion interactions between these hydrocarbons have been analyzed. This is followed by AIM analysis 26 in order to differentiate the various hydrocarbon dimers. Energy decomposition analysis (EDA) has been done to study the contribution of various energy components to the overall BEs. Computational Details All the structures were subjected to geometry optimizations without any constraints at the M06-2X/6-31G* level of theory. 27 The stationary points obtained by the geometry optimization were characterized as minima after verifying the presence of all real frequencies. The energies of the optimized hydrocarbon dimers were further fine tuned with slightly the higher triple-ζ quality basis set, cc-pvtz. The BEs of the hydrocarbons were calculated by subtracting the sum of the total energies of the monomers with the total energy of the dimer in their distorted environment as shown in Eq. (1). BE = E dimer (E monomer1 + E monomer2 ) (1) All the above mentioned calculations carried out using the Gaussian 09 suite of program. 28 It has been reported in literature that the calculated BEs using M06-2X functional without including the BSSE corrections are comparable to the CCSD(T) results for the π-π dimers AIM analysis developed by Bader and co-workers was carried out to map the electron density in order to characterize the different type of noncovalent interactions. 26 EDA was done using symmetry adapted perturbation theory (SAPT) at DFT level as implemented in MOLPRO-2009 package 35 in order to understand the contribution of various energy components to the overall BE. These analyses were done at PBE0/cc-pVDZ level on the M06-2X/6-31G* geometries. The BE of a dimer can be split into electrostatic (E es ), dispersion (E disp ), induction (E ind ), exchange (E ex ) and δ HF components as shown in the Eq. (2). The exchange-induction (E ex-ind ) and exchange-dispersion (E ex-disp ) components are included into the E ind and E disp components respectively, to simplify the discussion as done by 30, 36 others. BE dft-sapt = E es + E ex + E disp + E ind + δ HF (2) Results and Discussion A large number of possible conformations of hydrocarbon dimers have been considered and only the minimum energy conformations have been reported here. In this section, we discuss the BEs of various acyclic and cyclic hydrocarbons in both saturated and unsaturated forms. The topological analysis of the electron density at M06-2X/cc-pVTZ level of theory has been presented and analyzed. The EDA has been discussed for the acyclic as well as cyclic dimers. The nomenclature used in this discussion is as follows acyclic alkanes (A), acyclic alkenes (E), cyclic alkanes (ca) and cyclic alkenes (ce) (Scheme 1). Energetics The BE of acylic and cyclic hydrocarbon dimers has been calculated and given in Table 1. The BE are clearly dependent on the size of the interacting hydrocarbons. For A-A dimer, the binding strength increases systematically as a function of the alkane size, however the increase in BE as we go from ethane propane, propane n-butane and n-butane n-pentane have been found to be 0.80, 0.77 and 0.70 kcal/mol respectively and from n-pentane to n-hexane the difference is 0.97 kcal/mol. Thus the magnitude of the modulation in the BE values as a function of the hydrocarbon size is anomalous, however there seems to be an increase in the BE for

3 PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS 987 each addition of a methyl group. Tsuzuki et al. 24 reported the ab initio BE of n-butane, n-pentane and n-hexane as 2.80, 3.57, and 4.58 kcal/mol, respectively. Our BE results obtained at M06-2X/ccpVTZ level for the n-butane, n-pentane and n-hexane dimers as 2.76, 3.46, and 4.43 kcal/mol respectively have been found to be nearer to those reported values of Tsuzuki et al. 24 It appears that the A-E dimers are relatively stronger compared to the E-E and A-A dimers. Table 1 Biding energies of various possible hydrocarbon dimers at M06-2X/cc-pVTZ//M06-2X/6-31G* level. [Acyclic saturated (A); acyclic unsaturated (E); cyclic saturated (ca); cyclic unsaturated (ce)] Dimer BE Dimer BE Dimer BE A-A E-E A-E A2-A E2-E A2-E A3-A E3-E A3-E A4-A E4-E A4-E A5-A E5-E A5-E A6-A E6-E A6-E ca-ca ce-ce ca-ce ca3-ca ce3-ce ca3-ce ca4-ca ce4-ce ca4-ce ca5-ca ce5-ce ca5-ce ca6-ca ce6-ce ca6-ce ca10-ca ce10-ce ca10-ce ca14-ca ce14-ce ca14-ce

4 988 INDIAN J CHEM, SEC A, AUG-SEPT 2014 In acyclic hydrocarbon dimers, it has been observed that the BE increases as the size of hydrocarbon increases. However, such linear dependency of BE on size of the hydrocarbon has not been observed in case of cyclic-hydrocarbon dimers. In the optimized geometries of acyclic hydrocarbons, the CH HC bond contacts increase systematically as a function of alkane size, while it is not very systematic for cyclic hydrocarbon dimers. Thus, it appears that in the case of cyclic hydrocarbon dimers, the number of CH HC contacts and the BE of hydrocarbons are well correlated. The dimer of cyclopropane, cyclobutane, and cyclohexane which have three intermolecular CH HC contacts each, exhibit closer BEs. The unusual higher BE of cyclopentane dimer when compared to the cyclohexane can be explained by the presence five intermolecular CH HC contacts in the cyclopentane dimer. These observations indicate the importance of the number of CH HC bond contacts for higher BE and also explain the trends of hydrocarbons BE. When we compare the BE of acyclic and cyclic hydrocarbons of similar sizes, the BEs of cyclic hydrocarbons have been found to be higher than their acyclic counterpart in most of the cases, though the cyclic hydrocarbons have less number of hydrogen to establish CH HC bond contacts. This contradiction to the previous conclusion is due to the relatively strong CH HC interactions of cyclic hydrocarbon dimers compared to the acyclic hydrocarbon dimers. Further evidence for the foresaid insight can be obtained by the recent work of Alvarez and co-workers 15 where they have observed higher melting points of cyclic hydrocarbons and polyhedranes compared to the n-alkanes even though the latter has more number of hydrogens to establish CH HC contacts. Topological analysis of the electron density A systematic study of the topography of all the considered dimers has been done by AIM analysis. It has been shown from our study that, the hydrocarbon dimers show different intermolecular bond critical points (BCPs) between C C, CH C, and CH... HC groups, thus indicating the different types of the dispersion interactions. The ρ values between C C groups have been found to be higher when compared to the value of CH C, which in turn show slightly higher electron density values than CH... HC. A cursory look at the Fig. 1 shows the BCPs for A-A dimers are present between intermolecular hydrogen atoms and in the cases of E-E dimers the BCPs are found between intermolecular carbon atoms and in the A-E dimers, the BCPs are observed between hydrogen atom of the saturated hydrocarbons and carbon atom of the unsaturated hydrocarbons. The ρ values of the BCPs range between au and au for all the considered dimers. 37 These values are close to the reported intermolecular RH... HR interactions 38 ( au). It indicates that the hydrocarbon interactions come under the van der Waals interactions. As expected, these electron densities are significantly smaller than those found for typical covalent bonds ( au), but similar to those observed in the Ar... HF and Ne... HF van der Waals complexes (0.008 au and au, respectively). 25 In addition, the values of the Laplacian at the BCPs ( au) are positive, as expected for closed shell interactions. 25 Energy decomposition analysis As discussed before the strength of hydrocarbon interactions is manifested as a function of hydrocarbon size. The energy decomposition analysis has been done to ascertain the nature of these interactions and also to identify the force attributed to the modulation of these interaction as a function of hydrocarbon size. To gain knowledge about the fundamental forces of hydrocarbon-hydrocarbon binding, we have carried out the DFT-SAPT for cyclic and acylic hydrocarbon dimers at PBE0/ccpVDZ level. The BE obtained in this level is lower than the energy values at M06-2X/cc-pVTZ level, which has been considered for energetics throughout the discussion. However, the BEs obtained in this level have shown linear dependence on the size of the hydrocarbons. The EDA results show that in all forms of hydrocarbon dimers, dispersion component of energy (E disp ), has been found to have larger contribution to the overall BE. The electrostatic component of energy (E es ), has been found to be the second higher attractive component. The energy difference between E disp and E es components is found to increase dramatically when the hydrocarbon size increases, except for ce4-ce4, where the electrostatic and dispersion components are very close in energy. Induction component of hydrocarbons shows the least variation with the hydrocarbon size and exhibits poor contribution to the overall BE. A glimpse at the Table 2 indicates that, the induction and the electrostatic components are linearly correlated.

5 PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS 989 Fig. 1 Atomic positions and critical points of acyclic hydrocarbon dimers as obtained at M06-2X/cc-pVTZ level. [BCPs are represented by red color dots, CCPs are represented by green color dots and RCPs are represented yellow].

6 990 INDIAN J CHEM, SEC A, AUG-SEPT 2014 Table 2 The DFT-SAPT results of cyclic and acyclic hydrocarbon dimers calculated at PBE0/cc-pvDZ level Hydro-carbon dimers E es E ex E ind (kcal / E disp δ HF BE A2-A A3-A A4-A A5-A A6-A E2-E E3-E E4-E E5-E E6-E A2-E A3-E A4-E A5-E A6-E ca3-ca ca4-ca ca5-ca ca6-ca ce3-ce ce4-ce ce5-ce ce6-ce ca3-ce ca4-ce ca5-ce ca6-ce The contribution of the repulsive E ex component becomes higher as the hydrocarbon size increases. The sum of attractive components (E disp +E es +E ind ) clearly overcomes the opposing exchange repulsive interactions (E ex ). Hence, the analysis concludes that the overall BE of the hydrocarbon dimer is predominantly controlled by the dispersive component and secondarily by the electrostatic component. The induction component of the BE is expectedly much lower in value, since the interactions are essentially between neutral molecules. The electrostatic interaction between the different type of hydrocarbon dimers has been found to be in the hierarchy of E-E > A-E > E-E. The repulsive component of the BE also follows a trend similar to that of electrostatic interaction in most of the dimers, except in a few cases where the A-E dimers shows higher repulsive energy as compared to the E-E dimers. The largely contributing dispersion component of hydrocarbons shows a clear difference in the trend between acyclic and cyclic dimer. In the case of acyclic dimers, t he A-A dimers or the A-E dimers show higher dispersion energy and hence the trend will be A-A ~ A-E > E-E. However, in cyclic systems the E-E dimers showed the higher dispersion except for ce4-ce4 and thus the general trend observed for cyclic-dimers is E-E > A-E > A-A. Conclusions A systematic study of hydrocarbon dimers has been done by employing DFT method. We have considered hydrocarbon dimers of saturated and unsaturated forms in both cyclic and acylic geometries. The EDA results obtained by employing the DFT-SAPT method showed that the interaction between hydrocarbons is predominantly due to the dispersion component, with a surprisingly substantial electrostatic component. Importantly, both dispersion and electrostatic components play nearly equal roles in modulation of the strength of hydrocarbon-hydrocarbon interaction as a function of size and nature, viz., alkane or alkene. Our results indicate that these hydrocarbons tend to show various types of dispersive noncovalent interactions such as π... π, CH... π and CH... HC. Further evidence for the existence of these different types of noncovalent interactions between the hydrocarbon dimers have been obtained from the topographic analysis by AIM calculations. The BCPs corresponding to the π... π, CH... π and CH... HC interactions have been obtained for C... C, H... C, H... H moieties respectively. Acknowledgement We thank Council of Scientific and Industrial Research (CSIR), New Delhi, India for the 12 th five year plan projects, INTELCOAT (CSC-0114) and GENESIS (BSC-0121). JRP and DU thank CSIR for SRF. References 1 Mahadevi A S & Sastry G N, Chem Rev, 113 (2013) Song Z, Gao H, Li G, Yu Y, Shi Z & Feng S, Cryst Eng Comm, 11 (2009) Michael G M, Saraboji K, Ahmad S, Ponnuswamy M N & Suwa M, Biophys Chem, 107 (2004) Yurenko Y P, Novotny J, Sklenar V & Marek R, Phys Chem Chem Phys, 16 (2014) 2072.

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