Quantifying Dispersion Interaction: a Study of Alkane and Alkene Dimers
Indian Journal of Chemistry Vol. 53A, Aug-Sept 2014, pp. 985-991
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 500 607, India Email: [email protected] 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 CH⋅⋅⋅π over π-π type in the cluster aggregates.12 The the fields of biology, supramolecular chemistry and π-π networks in proteins and their connectivity materials science such as structure, stability, pattern have been studied in a recent database.13 The 1,2 solvation, and crystal packing. Understanding the saturated hydrocarbon molecules are held together in various factors influencing the noncovalent the crystal state by apparently weak dihydrogen interactions is indispensable to appreciate phenomena (CH⋅⋅⋅HC) interactions. Ab initio calculations carried such as protein folding, structure of DNA, molecular out in order to find the interaction energies of 3-5 recognition and drug binding in biology. Factors n-alkane dimers report that the interaction energies of influencing the noncovalent interactions such as size n-hexane and n-heptane are close to that of the and curvature of the π system have been studied hydrogen bond of the water dimer.14 Echeverría et al.15 6-9 extensively. In the case of unsaturated studied the intermolecular interactions in the dimers hydrocarbons, the noncovalent interactions such as of n-alkanes and polyhedranes and identified the π-π and CH⋅⋅⋅π has been well-recognized in the strength and nature of these dihydrogen contacts. The literature.10 Among these, π-π interaction is known to cooperative effect of π-π stacking interaction in the play a key role in imparting functional properties to presence of other noncovalent interactions has also bio-molecules. The study of intermolecular been studied extensively.16,17 interactions between saturated and unsaturated Apart from the significance of these interactions in hydrocarbon is a topic of high importance. Clearly, controlling the structure and function of molecules, the fact that the boiling point of hydrocarbon the noncovalent interactions involving hydrocarbons increases as the alkyl chain length increases, indicates play a significant role in nanomaterials and nano-bio stronger intermolecular interaction in alkanes and interface.18 The interlayer interactions in graphene have alkenes. A recent study reveals that simple substituent been explored by studying the weak noncovalent on the π-systems can have a dramatic impact on the interactions between the stacked layers of graphene.19 11 local orientation of π-π stacked complexes. Saturated hydrocarbon model systems have been A recent report investigated the relative strengths employed to study the interaction between multilayered of CH⋅⋅⋅π and π-π interactions in benzene cluster graphanes in order to explore its electronic properties. aggregates and illustrated the apparent preference of Dispersion components play an important role in the 986 INDIAN J CHEM, SEC A, AUG-SEPT 2014
interactions between saturated hydrocarbons.20 The reported in literature that the calculated BEs using noncovalent interactions of various metal ions, small M06-2X functional without including the BSSE molecules and bio-molecules on the models of carbon corrections are comparable to the CCSD(T) results for materials have also been explored.21-23 Supramolecular the π-π dimers.29-34 AIM analysis developed by Bader chemistry is one of the most strongly developing and co-workers was carried out to map the electron research areas which involves noncovalent interactions density in order to characterize the different type of to explain the self-assembly of molecules.24 Benzene noncovalent interactions.26 EDA was done using and cyclohexane have similar boiling points of 80 ºC, symmetry adapted perturbation theory (SAPT) at DFT indicating that they have similar intermolecular level as implemented in MOLPRO-2009 package35 in interactions. The boiling point of benzene can be order to understand the contribution of various energy attributed to the C-H...π and π−stacking interaction components to the overall BE. These analyses were between the benzene molecules as indicated by their done at PBE0/cc-pVDZ level on the M06-2X/6-31G* crystal structure. However, the equally higher boiling geometries. The BE of a dimer can be split into point of cyclohexane which has no unsaturated π−bond electrostatic (Ees), dispersion (Edisp), induction (Eind), indicates the presence of equally stronger dispersion exchange (Eex) and δHF components as shown in the forces between the saturated cyclohexane molecules. Eq. (2). The exchange-induction (Eex-ind) and According to accurate CCSD(T) computations, the exchange-dispersion (Eex-disp) components are stacked benzene dimer exhibits smaller binding energy included into the Eind and Edisp components (BE) than the pentane dimer (2.80 vs. 3.90 kcal/mol).25 respectively, to simplify the discussion as done by These observations triggered our interest to enumerate others.30, 36 the dispersion interactions in alkane and alkene dimers. The preceding section clearly indicates the BEdft-sapt = Ees + Eex + Edisp + Eind + δHF … (2) occurrence of dispersion interactions and the importance to quantify such interactions. In the current Results and Discussion study, we have systematically studied the interactions A large number of possible conformations of of various acyclic and cyclic hydrocarbon dimers in hydrocarbon dimers have been considered and only the both saturated and unsaturated forms. The different minimum energy conformations have been reported types of possible dispersion interactions between these here. In this section, we discuss the BEs of various hydrocarbons have been analyzed. This is followed by acyclic and cyclic hydrocarbons in both saturated and AIM analysis26 in order to differentiate the various unsaturated forms. The topological analysis of the hydrocarbon dimers. Energy decomposition analysis electron density at M06-2X/cc-pVTZ level of theory (EDA) has been done to study the contribution of has been presented and analyzed. The EDA has been various energy components to the overall BEs. discussed for the acyclic as well as cyclic dimers. The nomenclature used in this discussion is as follows Computational Details acyclic alkanes (A), acyclic alkenes (E), cyclic alkanes All the structures were subjected to geometry (cA) and cyclic alkenes (cE) (Scheme 1). optimizations without any constraints at the M06- 27 2X/6-31G* level of theory. The stationary points Energetics obtained by the geometry optimization were The BE of acylic and cyclic hydrocarbon dimers has characterized as minima after verifying the presence been calculated and given in Table 1. The BE are of all real frequencies. The energies of the optimized clearly dependent on the size of the interacting hydrocarbon dimers were further fine tuned with hydrocarbons. For A-A dimer, the binding strength slightly the higher triple-ζ quality basis set, increases systematically as a function of the alkane ‘cc-pVTZ’. The BEs of the hydrocarbons were size, however the increase in BE as we go from calculated by subtracting the sum of the total energies ethane → propane, propane → n-butane and n-butane of the monomers with the total energy of the dimer in → n-pentane have been found to be 0.80, 0.77 and their distorted environment as shown in Eq. (1). 0.70 kcal/mol respectively and from n-pentane to n-hexane the difference is 0.97 kcal/mol. Thus the BE = Edimer – (Emonomer1 + Emonomer2) … (1) magnitude of the modulation in the BE values as a All the above mentioned calculations carried out function of the hydrocarbon size is anomalous, using the Gaussian 09 suite of program.28 It has been however there seems to be an increase in the BE for PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS 987
each addition of a methyl group. Tsuzuki et al.24 dimers as 2.76, 3.46, and 4.43 kcal/mol respectively reported the ab initio BE of n-butane, n-pentane and have been found to be nearer to those reported values n-hexane as 2.80, 3.57, and 4.58 kcal/mol, of Tsuzuki et al.24 It appears that the A-E dimers are respectively. Our BE results obtained at M06-2X/cc- relatively stronger compared to the E-E and A-A pVTZ level for the n-butane, n-pentane and n-hexane dimers.
Table 1Biding energies (kcal/mol) 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 (kcal/mol) Dimer BE (kcal/mol) Dimer BE (kcal/mol) A-A E-E A-E A2-A2 1.19 E2-E2 0.92 A2-E2 1.00 A3-A3 1.99 E3-E3 2.44 A3-E3 2.06 A4-A4 2.76 E4-E4 2.75 A4-E4 2.85 A5-A5 3.46 E5-E5 3.83 A5-E5 3.96 A6-A6 4.43 E6-E6 4.69 A6-E6 4.77 cA-cA cE-cE cA-cE cA3-cA3 2.06 cE3-cE3 1.55 cA3-cE3 2.77 cA4-cA4 2.00 cE4-cE4 3.13 cA4-cE4 2.96 cA5-cA5 3.58 cE5-cE5 4.50 cA5-cE5 3.59 cA6-cA6 2.05 cE6-cE6 2.63 cA6-cE6 3.20 cA10-cA10 4.40 cE10-cE10 6.36 cA10-cE10 6.92 cA14-cA14 6.24 cE14-cE14 9.71 cA14-cE14 10.08
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In acyclic hydrocarbon dimers, it has been atoms and in the cases of E-E dimers the BCPs are observed that the BE increases as the size of found between intermolecular carbon atoms and in the hydrocarbon increases. However, such linear A-E dimers, the BCPs are observed between dependency of BE on size of the hydrocarbon has not hydrogen atom of the saturated hydrocarbons and been observed in case of cyclic-hydrocarbon dimers. carbon atom of the unsaturated hydrocarbons. The In the optimized geometries of acyclic hydrocarbons, ρ values of the BCPs range between 0.005 au … the CH HC bond contacts increase systematically as and 0.008 au for all the considered dimers.37 These a function of alkane size, while it is not very values are close to the reported intermolecular systematic for cyclic hydrocarbon dimers. Thus, it RH...HR interactions38 (0.003−0.014 au). It indicates appears that in the case of cyclic hydrocarbon dimers, that the hydrocarbon interactions come under the van … the number of CH HC contacts and the BE of der Waals interactions. As expected, these electron hydrocarbons are well correlated. The dimer of densities are significantly smaller than those found for cyclopropane, cyclobutane, and cyclohexane which … typical covalent bonds (0.200−0.400 au), but similar have three intermolecular CH HC contacts each, to those observed in the Ar...HF and Ne...HF van der exhibit closer BEs. The unusual higher BE of Waals complexes (0.008 au and 0.010 au, cyclopentane dimer when compared to the respectively).25 In addition, the values of the cyclohexane can be explained by the presence five … Laplacian at the BCPs (0.012−0.030 au) are positive, intermolecular CH HC contacts in the cyclopentane as expected for closed shell interactions.25 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. Energy decomposition analysis When we compare the BE of acyclic and cyclic As discussed before the strength of hydrocarbon hydrocarbons of similar sizes, the BEs of cyclic interactions is manifested as a function of hydrocarbons have been found to be higher than their hydrocarbon size. The energy decomposition analysis acyclic counterpart in most of the cases, though the has been done to ascertain the nature of these cyclic hydrocarbons have less number of hydrogen to interactions and also to identify the force attributed to establish CH…HC bond contacts. This contradiction to the modulation of these interaction as a function of the previous conclusion is due to the relatively strong hydrocarbon size. To gain knowledge about the CH…HC interactions of cyclic hydrocarbon dimers fundamental forces of hydrocarbon-hydrocarbon compared to the acyclic hydrocarbon dimers. Further binding, we have carried out the DFT-SAPT for evidence for the foresaid insight can be obtained by cyclic and acylic hydrocarbon dimers at PBE0/cc- the recent work of Alvarez and co-workers15 where pVDZ level. The BE obtained in this level is lower they have observed higher melting points of cyclic than the energy values at M06-2X/cc-pVTZ level, hydrocarbons and polyhedranes compared to the which has been considered for energetics throughout n-alkanes even though the latter has more number of the discussion. However, the BEs obtained in this hydrogens to establish CH…HC contacts. 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 Topological analysis of the electron density energy (Edisp), has been found to have larger A systematic study of the topography of all the contribution to the overall BE. The electrostatic considered dimers has been done by AIM analysis. It component of energy (Ees), has been found to be the has been shown from our study that, the hydrocarbon second higher attractive component. The energy dimers show different intermolecular bond critical difference between Edisp and Ees components is found points (BCPs) between C⋅⋅⋅C, CH⋅⋅⋅C, and CH...HC to increase dramatically when the hydrocarbon size groups, thus indicating the different types of the increases, except for cE4-cE4, where the electrostatic dispersion interactions. The ρ values between C⋅⋅⋅C and dispersion components are very close in energy. groups have been found to be higher when compared Induction component of hydrocarbons shows the least to the value of CH⋅⋅⋅C, which in turn show slightly variation with the hydrocarbon size and exhibits poor higher electron density values than CH...HC. A contribution to the overall BE. A glimpse at the Table 2 cursory look at the Fig. 1 shows the BCPs for A-A indicates that, the induction and the electrostatic dimers are present between intermolecular hydrogen components are linearly correlated. PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS 989
Fig. 1Atomic 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]. 990 INDIAN J CHEM, SEC A, AUG-SEPT 2014
Table 2The DFT-SAPT results of cyclic and acyclic most of the dimers, except in a few cases where hydrocarbon dimers calculated at PBE0/cc-pvDZ level the A-E dimers shows higher repulsive energy as compared to the E-E dimers. The largely Hydro-carbon Ees Eex Eind Edisp δHF BE dimers (kcal/ (kcal/ (kcal (kcal/ (kcal/ (kcal/ contributing dispersion component of hydrocarbons mol) mol) /mol) mol) mol) mol) shows a clear difference in the trend between acyclic and cyclic dimer. In the case of acyclic dimers, t A2-A2 0.40 -1.36 0.01 1.21 0.05 0.31 A3-A3 0.73 -2.50 0.03 2.22 0.12 0.60 he A-A dimers or the A-E dimers show higher A4-A4 1.07 -3.63 0.05 3.17 0.19 0.84 dispersion energy and hence the trend will be A5-A5 1.55 -5.08 0.06 4.34 0.26 1.13 A-A ~ A-E > E-E. However, in cyclic systems the A6-A6 2.00 -6.49 0.08 5.53 0.34 1.45 E-E dimers showed the higher dispersion except for cE4-cE4 and thus the general trend observed for E2-E2 0.83 -1.59 0.04 1.06 0.13 0.47 cyclic-dimers is E-E > A-E > A-A. E3-E3 1.41 -3.02 0.10 2.09 0.24 0.81 E4-E4 2.26 -4.31 0.12 2.89 0.30 1.26 E5-E5 2.71 -5.94 0.16 4.22 0.39 1.55 Conclusions A systematic study of hydrocarbon dimers has been E6-E6 3.85 -7.46 0.21 5.13 0.50 2.24 done by employing DFT method. We have considered A2-E2 0.51 -1.50 0.04 1.09 0.13 0.27 hydrocarbon dimers of saturated and unsaturated A3-E3 0.96 -2.58 0.08 2.02 0.17 0.66 forms in both cyclic and acylic geometries. The EDA A4-E4 1.54 -4.58 0.09 3.38 0.34 0.78 results obtained by employing the DFT-SAPT method A5-E5 2.40 -6.67 0.15 4.95 0.49 1.32 showed that the interaction between hydrocarbons is A6-E6 2.96 -8.11 0.17 5.95 0.58 1.55 predominantly due to the dispersion component, with
cA3-cA3 1.13 -3.40 0.07 2.62 0.16 0.58 a surprisingly substantial electrostatic component. cA4-cA4 1.07 -3.32 0.05 2.73 0.17 0.69 Importantly, both dispersion and electrostatic cA5-cA5 2.12 -6.40 0.08 4.74 0.35 0.88 components play nearly equal roles in modulation of cA6-cA6 1.37 -4.55 0.07 3.77 0.27 0.93 the strength of hydrocarbon-hydrocarbon interaction as a function of size and nature, viz., alkane or alkene. cE3-cE3 2.23 -6.15 0.16 3.56 0.95 0.75 Our results indicate that these hydrocarbons tend to cE4-cE4 3.32 -6.91 0.23 3.36 1.03 1.04 show various types of dispersive noncovalent cE5-cE5 4.21 -8.58 0.41 4.97 0.71 1.72 ...... cE6-cE6 3.16 -10.33 0.25 8.13 0.90 2.11 interactions such as π π, CH π and CH HC. Further evidence for the existence of these different types of cA3-cE3 1.83 -4.23 0.09 2.87 0.38 0.94 noncovalent interactions between the hydrocarbon cA4-cE4 2.23 -5.71 0.17 3.68 0.52 0.88 dimers have been obtained from the topographic cA5-cE5 2.61 -6.85 0.16 4.76 0.56 1.24 analysis by AIM calculations. The BCPs cA6-cE6 2.57 -6.44 0.22 4.41 0.52 1.29 corresponding to the π...π, CH...π and CH...HC
interactions have been obtained for C...C, H...C, H...H The contribution of the repulsive Eex component becomes higher as the hydrocarbon size increases. moieties respectively. The sum of attractive components (Edisp+Ees+Eind) clearly overcomes the opposing exchange Acknowledgement repulsive interactions (Eex). Hence, the analysis We thank Council of Scientific and Industrial concludes that the overall BE of the hydrocarbon Research (CSIR), New Delhi, India for the 12th five year dimer is predominantly controlled by the plan projects, INTELCOAT (CSC-0114) and GENESIS dispersive component and secondarily by (BSC-0121). JRP and DU thank CSIR for SRF. the electrostatic component. The induction component of the BE is expectedly much lower in value, since References the interactions are essentially between neutral 1 Mahadevi A S & Sastry G N, Chem Rev, 113 (2013) 2100. molecules. The electrostatic interaction between 2 Song Z, Gao H, Li G, Yu Y, Shi Z & Feng S, Cryst Eng Comm, the different type of hydrocarbon dimers has 11 (2009) 1579. 3 Michael G M, Saraboji K, Ahmad S, Ponnuswamy M N & been found to be in the hierarchy of E-E > A-E > E-E. Suwa M, Biophys Chem, 107 (2004) 263. The repulsive component of the BE also follows 4 Yurenko Y P, Novotny J, Sklenar V & Marek R, Phys Chem a trend similar to that of electrostatic interaction in Chem Phys, 16 (2014) 2072. PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS 991
5 Snyder R D, Holt P A, Maguire J M & Trent J O, Environ Mol 24 Ruiz-Osés M, de Oteyza D G, Fernández-Torrente I, Mutagen, 54 (2013) 668. Gonzalez-Lakunza N, Schmidt-Weber P M, Kampen T, 6 Premkumar J R, Vijay D & Sastry G N, Dalton Trans, 41 (2012) Horn K, Gourdon A, Arnau A & Ortega J E, 4965. ChemPhysChem, 10 (2009) 896. 7 Priyakumar U D, Punnagai M, Mohan G P K & Sastry G N, 25 Sinnokrot M O & Sherrill C D, J Phys Chem A, 110 (2006) Tetrahedron, 60 (2004) 3037. 10656. 8 Umadevi D & Sastry G N, J Phys Chem C, 115 (2011) 9656. 26 Bader R F W, Atoms in Molecules. A Quantum Theory, (Oxford, 9 Vijay D & Sastry G N, Phys Chem Chem Phys, 10 (2008) 582. UK) 1990. 10 Salonen L M, Ellermann M & Diederich F, Angew Chem Int Ed, 27 Zhao Y & Truhlar D, Theor Chem Acc, 120 (2008) 215. 50 (2011) 4808. 28 Gaussian 09, Rev. C.01, (Gaussian Inc, Wallingford, CT) 2009. 11 Wheeler S E, Acc Chem Res, 46 (2012) 1029. 29 Sinnokrot M O, Valeev E F & Sherrill C D, J Am Chem Soc 124 12 Mahadevi A S, Rahalkar A P, Gadre S R & Sastry G N, J Chem (2002) 10887. Phys, 133 (2010) 164308. 30 Šponer J & Hobza P, J Phys Chem A, 104 (2000) 4592. 13 Chourasia M, Sastry G M & Sastry G N, Int J Biol Macromol, 31 Rutledge L R, Churchill C D M & Wetmore S D, J Phys 48 (2011) 540. Chem B, 114 (2010) 3355. 14 Tsuzuki S, Honda K, Uchimaru T & Mikami M, J Chem Phys, 32 Leavens F M V, Churchill C D M, Wang S & Wetmore S D, 124 (2006) 114304. J Phys Chem B, 115 (2011) 10990. 15 Echeverría J, Aullón G, Danovich D, Shaik S & Alvarez S, Nat Chem, 3 (2011) 323. 33 Jurecka P, Sponer J, Cerny J & Hobza P, Phys Chem Chem 16 Vijay D & Sastry G N, Chem Phys Lett, 485 (2010) 235. Phys, 8 (2006) 1985. 17 Vijay D, Zipse H & Sastry G N, J Phys Chem B, 112 (2008) 34 Vijay D, Sakurai H & Sastry G N, Int J Quant Chem, 111 (2011) 8863. 1893. 18 Umadevi D & Sastry G N, Curr Sci, 106 (2014) 1224. 35 MOLPRO, Ver. 2009.1, A Package of ab initio Programs, see 19 Chen W, Duan L & Zhu D, Environ Sci Technol, 41 (2007) http://www.molpro.net. 8295. 36 Mishra B K, Karthikeyan S & Ramanathan V, J Chem Theor 20 Grimme S, Angew Chem Int Ed, 47 (2008) 3430. Comp, 8 (2012) 1935. 21 Umadevi D & Sastry G N, J Phys Chem Lett, 2 (2011) 1572. 37 Robertson K N, Knop O & S C T, Can J Chem, 81 (2003) 727. 22 Umadevi D & Sastry G N, Chem Phys Lett, 549 (2012) 39. 38 Alkorta I, Elguero J & Foces-Foces C, Chem Commun, (1996) 23 Umadevi D & Sastry G N, ChemPhysChem, 14 (2013) 2570. 1633.