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
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
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.21-23 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. 3.90 kcal/mol).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 analysis26 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 M062X/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 = Edimer – (Emonomer1 + Emonomer2)
… (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.29-34 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 package35 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 (Ees), dispersion (Edisp), induction (Eind),
exchange (Eex) and δHF components as shown in the
Eq. (2). The exchange-induction (Eex-ind) and
exchange-dispersion (Eex-disp) components are
included into the Eind and Edisp components
respectively, to simplify the discussion as done by
others.30, 36
BEdft-sapt = Ees + Eex + Edisp + Eind + δHF
… (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
PREMKUMAR et al.: QUANTIFYING DISPERSION INTERACTION IN ALKANE AND ALKENE DIMERS
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 (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
1.19
1.99
2.76
3.46
4.43
E2-E2
E3-E3
E4-E4
E5-E5
E6-E6
2.06
2.00
3.58
2.05
4.40
6.24
cE3-cE3
cE4-cE4
cE5-cE5
cE6-cE6
cE10-cE10
cE14-cE14
A-A
A2-A2
A3-A3
A4-A4
A5-A5
A6-A6
cA-cA
cA3-cA3
cA4-cA4
cA5-cA5
cA6-cA6
cA10-cA10
cA14-cA14
987
BE (kcal/mol)
Dimer
0.92
2.44
2.75
3.83
4.69
A2-E2
A3-E3
A4-E4
A5-E5
A6-E6
1.55
3.13
4.50
2.63
6.36
9.71
cA3-cE3
cA4-cE4
cA5-cE5
cA6-cE6
cA10-cE10
cA14-cE14
E-E
BE (kcal/mol)
A-E
cE-cE
1.00
2.06
2.85
3.96
4.77
cA-cE
2.77
2.96
3.59
3.20
6.92
10.08
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-workers15 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 0.005 au
and 0.008 au for all the considered dimers.37 These
values are close to the reported intermolecular
RH...HR interactions38 (0.003−0.014 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 (0.200−0.400 au), but similar
to those observed in the Ar...HF and Ne...HF van der
Waals complexes (0.008 au and 0.010 au,
respectively).25 In addition, the values of the
Laplacian at the BCPs (0.012−0.030 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 (Edisp), has been found to have larger
contribution to the overall BE. The electrostatic
component of energy (Ees), has been found to be the
second higher attractive component. The energy
difference between Edisp and Ees 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.
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].
INDIAN J CHEM, SEC A, AUG-SEPT 2014
990
Table 2
The DFT-SAPT results of cyclic and acyclic
hydrocarbon dimers calculated at PBE0/cc-pvDZ level
Hydro-carbon Ees
dimers
(kcal/
mol)
Eex
(kcal/
mol)
Eind
(kcal
/mol)
Edisp
(kcal/
mol)
δHF
(kcal/
mol)
BE
(kcal/
mol)
A2-A2
A3-A3
A4-A4
A5-A5
A6-A6
0.40
0.73
1.07
1.55
2.00
-1.36
-2.50
-3.63
-5.08
-6.49
0.01
0.03
0.05
0.06
0.08
1.21
2.22
3.17
4.34
5.53
0.05
0.12
0.19
0.26
0.34
0.31
0.60
0.84
1.13
1.45
E2-E2
E3-E3
E4-E4
E5-E5
0.83
1.41
2.26
2.71
-1.59
-3.02
-4.31
-5.94
0.04
0.10
0.12
0.16
1.06
2.09
2.89
4.22
0.13
0.24
0.30
0.39
0.47
0.81
1.26
1.55
E6-E6
3.85
-7.46
0.21
5.13
0.50
2.24
A2-E2
A3-E3
A4-E4
A5-E5
A6-E6
0.51
0.96
1.54
2.40
2.96
-1.50
-2.58
-4.58
-6.67
-8.11
0.04
0.08
0.09
0.15
0.17
1.09
2.02
3.38
4.95
5.95
0.13
0.17
0.34
0.49
0.58
0.27
0.66
0.78
1.32
1.55
cA3-cA3
cA4-cA4
cA5-cA5
cA6-cA6
1.13
1.07
2.12
1.37
-3.40
-3.32
-6.40
-4.55
0.07
0.05
0.08
0.07
2.62
2.73
4.74
3.77
0.16
0.17
0.35
0.27
0.58
0.69
0.88
0.93
cE3-cE3
cE4-cE4
cE5-cE5
cE6-cE6
2.23
3.32
4.21
3.16
-6.15
-6.91
-8.58
-10.33
0.16
0.23
0.41
0.25
3.56
3.36
4.97
8.13
0.95
1.03
0.71
0.90
0.75
1.04
1.72
2.11
cA3-cE3
cA4-cE4
cA5-cE5
cA6-cE6
1.83
2.23
2.61
2.57
-4.23
-5.71
-6.85
-6.44
0.09
0.17
0.16
0.22
2.87
3.68
4.76
4.41
0.38
0.52
0.56
0.52
0.94
0.88
1.24
1.29
The contribution of the repulsive Eex component
becomes higher as the hydrocarbon size increases.
The sum of attractive components (Edisp+Ees+Eind)
clearly
overcomes
the
opposing
exchange
repulsive interactions (Eex). 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 12th five year
plan projects, INTELCOAT (CSC-0114) and GENESIS
(BSC-0121). JRP and DU thank CSIR for SRF.
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