Vol.2, No.1, 32-36 (2011) Journal of Biophysical Chemistry
doi: 0.4236/jbpc.2011.21005
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/ journal/JBPC/
Interaction of small aromatic molecules: An ab initio
studies on benzene and pyridine molecules
Bipul Bezbaruah, P. Hazarika, A. Gogoi, O.K. Medhi, C. Medhi*
Chemistry Department, Gauhati University, Guwahati, Assam, India; *Corresponding Author: chitrani@sify.com
Received 10 September 2010; revised 1 November 2010; accepted 22 November 2010.
The use of appropriate level of theories for
studying weak interactions such as stacking of
aromatic molecules has been an important as-
pect, since the high level methods have limita-
tions for application to large molecules. The
differences in the stacking energies of various
structures are found significant for identifying
the most favored stacked benzene rings and the
pyridine rings. The most favored structure of
benzene rings obtained from various methods
are similar, and also comparable with that of
reported accurate CCSD(T) method. The effect
of basis set in the stacking energies of MP2
calculations is small. Thus the moderately ac-
curate methods may be feasible for studying the
stacking interactions as demonstrated for ben-
zene and pyridine molecules.
Keywords: Ab Initio; Stacking; Basis Set; Benzene;
The non bonded interactions between aromatic com-
pounds are considered to be an important aspect in bio-
logical systems, and other relevant areas like drug dis-
covery. These attractive intermolecular interactions are
also responsible for macromolecular aggregation, where
the medicinal property of a drug molecule may partly
depend on its recognition for a biological system [1-4].
The majority of medicinal agents contain aromatic sub-
stituents that provide one of the important groups related
to medicinal property. For example, the biological activ-
ity of many anticancer drugs, Amsacrine and Daunomy-
cin is believed to be related to the drug intercalation
within sequences of DNA, where the stacking interac-
tions between aromatic rings and base pairs usually take
place [1-4]. As a part of designing new intercalative
drugs, the stacking interactions between the aromatic
rings have been analyzed to achieve the sufficient struc-
tural requirement of the DNA binding domain of drugs.
So it is rather important to choose the most reliable
method to understand the structure and non-bonded in-
teractions of aromatic molecules. We note that the ben-
zene and the pyridine rings are the basic molecular parts
that constitute most biomolecules and drugs. At the first
sight, the stacking interactions of benzene-benzene and
pyridine-pyridine could represent the constituent units
for the stabilization of many large aromatic molecules.
So the studies on small aromatic molecules may be
given particular importance for better understanding of
stacking interactions among large aromatic molecules.
Ab initio calculations have been shown useful for
studying the non bonded interactions of aromatic mole-
cules [5-10]. The various levels of theories and basis sets
have been carefully chosen to calculate the interaction
energies of aromatic(-) and stacking types of interac-
tions that are responsible for the stabilization of double
helical DNA. It is evident that the studies of molecular
stacking require high level ab initio calculations. Many
theoretical studies are reported to predict the preferred
stacking interactions of benzene dimers, and thereby
provoking the importance of dipole-dipole and quadru-
pole-quadrupole interaction [5-6]. Similar studies on the
intermolecular interactions of cytosine dimers have been
calculated with MP2/6-31G** level, whereas less accu-
rate approach, the AMBER force field is also found use-
ful in certain cases despite of the lack of estimating dis-
persion energies in the calculations. The dispersion
forces, the short range exchange repulsions and electron
correlation are the essential factors for the overall as-
sessment of stacking interaction of molecules [7-10].
Comparison of different level of theories used in certain
investigations clearly indicate the choice of reasonably
accurate method that include proper basis set as well as
electron correlation in the calculations. As we know that
the London dispersion force is the instrumental binding
of stacked molecules, which is not described by Har-
tree-Fock theory. Therefore, the correlated descriptions
of electrons are must to produce even a qualitatively
accurate picture of weakly interacted molecules. It
B. Bezbaruah et al. / Journal of Biophysical Chemistry 2 (2 011) 32-36
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/ journal/JBPC/
should be noted that several newly developed functional
have shown to provide acceptable results for this type of
intermolecular interactions [10-13].
However, this method is still rather expensive for
large molecules, and it can only be applied to small
molecules such as benzene dimers. The CCSD(T)
method is currently believed to be the most accurate for
computing dispersion interactions provided the basis set
of aug-cc-pVTZ is included in the calculations [9-14].
The computational cost required for larger molecules
does not permit the application of accurate ab initio
methods. After thorough survey of the available studies
on the molecular stacking of small aromatic rings, there
are certain issues that need to be reinvestigated. The
present investigation aims to test the different level of ab
initio methods in predicting the stability of benzene and
pyridine dimers [15].
The completely optimized geometries of benzene and
pyridine molecules with HF/6-31G** were taken for
calculating stacking energies. Single point calculations
on the stacked models have been carried out with MP2
as well as HF methods with some chosen basis set. The
two benzene rings may stack either in eclipsed (exact
- sandwiched form) or in staggered configuration
(Figure 1a). All the stacked configurations of benzene
rings have been analyzed by rotating the upper benzene
through different angles about the vertical axis at fixed
vertical separation (optimum distance of 3.3 Å). The
(b) (c)
Figure 1. (a) Staggered model of two stacked benzene mole-
cules, (b) Optimum stacked structure for lateral shifting along
positive axes with origin(0,0) for complete stacking, and (c)
Optimum stacked structure for lateral shifting along negative
axes with origin(0,0) for complete stacking.
single point calculations have been performed for all the
structures. The eclipsed form has been taken for con-
structing various stacked models by shifting one benzene
ring laterally along the plane of the other, and the most
favorable structures are shown in Figures 1b and 1c.
The interaction energies are computed from the fol-
lowing equation.
Interaction energies= EST – 2EM
EST and EM are the energies of stacked model and
monomer. All the calculations are carried out with Gaus-
sian 03 program code [15].
The relative changes of the stacking energies (MP2)
of different stacked benzene rings are shown in Figure 2,
and certain stable structures are located from the local
minima in the potential energy plots. However the cor-
responding potential energy plots of HF calculations
shown in Figure 3 cannot explain the stacking stabiliza-
tion of two benzene rings. The single point calculations
of all stacked models have been performed in this study,
since the complete geometry optimization may not be
advantageous to locate the local optimum structures. The
nature of the potential energy plots of MP2 and HF cal-
culations shown in Figures 2 and 3 is similar, but the HF
calculation fail to locate the local minima for stable
structures. The values are found significantly different,
and the MP2/6-31+G(d,p) and MP2/6-31+G(df,p) cal-
culations could estimate large negative interaction ener-
gies compared to that of HF calculations.
It is not surprising that the interaction energies of
HF/6-31G** and HF/6-31+G(d,p) calculations are all
positive, which is definitely due to the lack of dispersion
energies with these calculations. The series of results
could provide prior necessity of dispersion forces for the
stabilization of these stacked molecules. The results of
HF and MP2 level of theories reflect the extent of dis-
persion energies accounted in all these calculations. In-
deed, the electron correlations included in MP2 level
with diffused function in the basis set could estimate
more negative stacking energies, where the increase of
diffuse function in the basis set provides little change in
the energy values.
As we know that the stacking energies obtained from
HF calculation include columbic, induction, exchange
and some electron correlation energies, and the intermo-
lecular electron correlation necessary for the stabiliza-
tion of these stacked molecules cannot be calculated
with this method. However the stacking energies ob-
tained from this method may be taken for comparison
with the MP2 results. The present studies focus how the
stacking energies can be improved with the inclusion of
B. Bezbaruah et al. / Journal of Biophysical Chemistry 2 (2 011) 32-36
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/ journal/JBPC/
-3.5 -2.5-1.5 -
Lateral shifting (Ǻ)
Stacking energies
MP2/6-31G** MP2/6-31+G(d,p) MP2/6-31+G(df,p)
Figure 2. Plots of benzene-benzene stacking energies versus lateral shifting in angstrom
with different basis sets in the MP2 method (for benzene-benzene staggered models).
-3.5-2.5 -1.5 -
Lateral shifting (Ǻ)
Stacking energies
HF/6-31G** HF/6-31+G(d,p)
Figure 3. Plots of benzene-benzene stacking energies versus lateral shifting in
angstrom with different basis sets in the HF method (for benzene-benzene stag-
gered models).
Table 1. Computed stacking energies of benzene-benzene and pyridine-pyridine rings for optimized stacked models with different
basis sets.
Stacking energies (kcal/mol)
Benzene-Benzene Pyridine-Pyridine
Basis sets
Eclipsed Staggered Eclipsed Staggered
HF/6-31G** 2.174 3.051 1.611 2.886
HF/6-31+G(d,p) 3.318 3.105 2.571 3.515
MP2/6-31G** -3.149 -3.898 -3.075 -6.236
MP2/6-31+G(d,p) -5.447 -5.594 -4.971 -6.448
MP2/6-31+G(df,p) -4.591 -5.506 -3.258 -6.462
diffused functions in the HF and MP2 level of calcula-
tions. The computed stacking energies of optimum
structures with various levels of calculations are summa-
rized in Table 1.
It may be noted that the difference of stacking ener-
gies obtained from HF/6-31G** and MP2/6-31G** cal-
culations is significantly large, whereas values of
MP2/6-31G**, MP2/6-31+G(d,p) and MP2/6-31+G(df,p)
are not so different (Table 1). However the most expen-
sive method, MP4 level of theory is particularly used in
most calculations on stacking interactions, but such high
level calculations cannot be applied to large molecule of
research interests. For general application one must test
the low level methods as well to extract some informa-
B. Bezbaruah et al. / Journal of Biophysical Chemistry 2 (2 011) 32-36
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/ journal/JBPC/
-3.5 -2.5-1.5 -
Lateral shifting (Ǻ)
Stacking energies
BB-3.0 BB-3.2 BB-3.4 BB-3.6 BB-3.8
Figure 4. Plots of stacking energies versus lateral shifting in angstrom (Ǻ) of ben-
zene molecules at different intermolecular distances with MP2/6-31+G(d,p)
tion. The change in stacking energies determined by
MP2 method with 6-31+G(d,p) and 6-31+G(df,p) may
be appropriate for qualitative explanations of these
non-bonded weak interactions. Our results show that the
stacking energies do not considerably vary with the in-
clusion of more diffuse functions in the basis set. The
stacking energies obtained from MP2/6-31+G(d,p) cal-
culations are found much better than the reported values
of MP2 and CCSD(T) methods with aug-cc-pVQZ and
aug-cc-pVDZ basis set [7,9]. The reported CCSD(T)
energy is –2.72 kcal/mol with basis set correction,
whereas the values for MP2/6-31+G(d,p) and
MP2/6-31+G(df,p) without basis set correction are
–5.447 kcal/mol and –4.591 kcal/mol. The single-point
MP2 calculations with 6-31+G(d,p) basis set have been
found useful in describing the stability of stacked ben-
zene and pyridine molecules. The calculated interaction
energies with 6-31+G(df,p) basis set does not show
much variation from that of 6-31+G(d,p) basis set (Table
1, Figure 2). The basis set superposition error at the
MP2 level is not so essential although there may be
slight effect on the dispersion energies.
Although the HF and other low level methods cannot
be used to calculate accurate stacking energies, it may be
useful for predicting at least the stabilization of counter
molecules qualitatively. As we can see that both the HF
and MP2 methods can locate similar regions for the sta-
bilization of stacked structures (Figures 2 and 3).
It is also important to locate the most favored -
stacking distance, so the stacking energies of two ben-
zene molecules at different vertical separations have
been calculated and the distance(vertical and lateral)
dependent variation of stacking energies are shown in
Figure 4. The stacked structures located within certain
conformational spaces of two benzene are found favor-
able as predicted from the results of MP2/6-31G(d,p)
calculations. The maxima and minima in the curves in-
dicate the two distinguishable regions of total and partial
stacking of aromatic rings(Figure 2, Figures 1(a-c)).
The repulsive interaction is found prominent in the total
stacking of the aromatic rings, and the maximum points
in the curves represent the unstable structures. Also the
repulsive interaction is found maximum at 3.0 Ǻ, and
gradually decreases due to the increase of electrostatic
interaction energies at longer distances.
As shown in Table 1, the extent of dispersion energies
included in the stacking energies of MP2/6-31G**,
MP2/6-31+G(d,p) and MP2/6-31+G(df,p) calculations
of benzene and pyridine molecules is distinct, whereas
the HF/6-31G** calculation cannot usually estimate
dispersion energies.
The extent of dispersion forces included in various cal-
culations may be useful for monitoring relative variation
of stacking interactions of aromatic molecules. The re-
sults of MP2 studies and the reported CCSD(T) calcula-
tions can provide similar information on the stacking of
benzene rings. Hence the MP2/6-31G+(d,p) and
MP2/6-31+G(df,p) may be feasible for explaining the
- type of stacking interaction qualitatively, and the
method may be applied to the computation of large
stacked molecules instead of other high level expensive
The authors thank Department of Science and Technology and Coun-
cil of Scientific Research, New Delhi, India, for financial assistance.
B. Bezbaruah et al. / Journal of Biophysical Chemistry 2 (2 011) 32-36
Copyright © 2011 SciRes. Openly accessible at http:// www.scirp.org/ journal/JBPC/
[1] Castonguay, L.A., Rappe´, A.K. and Casewit, C.J. (1991)
Π-stacking and the platinum-catalyzed asymmetric hy-
droformylation reaction: A molecular modeling study.
Journal of the American Chemical Society, 113(19),
[2] Kolb, H.C., Andersson, P.G. and Sharpless, K.B. (1994)
Toward an understanding of the high enantioselectivity in
the osmium-catalyzed asymmetric dihydroxylation (AD).
1. Kinetics. Journal of the American Chemical Society,
116(4), 1278–1291.
[3] Smith, D.A., Ulmer II, C.W., and Gilbert M.J. (1992)
Structural studies of aromatic amines and the dna
intercalating compounds m-amsa and o-amsa:
Comparison of mndo, am1, and pm3 to experimental and
ab initio results. Journal of Computational Chemistry, 13
(5), 640.
doi: 10.1002/jcc.540130514
[4] Barone, G., Guerra, C.F., Gambino, N., Silvestri, A.,
Lauria, A., Almerico, A.M. and Bickelhaupt, F.M. (2008)
Intercalation of daunomycin into stacked DNA base pairs.
DFT study of an anticancer drug. Journal of Biomolecu-
lar Structure and Dynamics, 26(1), 115-30.
[5] Gilman, A.G., Rall, T.W., Mies, A.S. and Taylor, P. (1993)
The pharmaceutical basis of therapeutics. 8th Ed.,
McGraw Hill, Inc., New York.
[6] Ishida, T., Doi, M., Ueda, H., Inoue, M. and Scheldrick,
G.M. (1988) Specific ring stacking interaction on the
tryptophan-7-methylguanine system: Comparative crys-
tallographic studies of indole derivatives-7-methylguani-
ne base, nucleoside, and nucleotide complexes. Journal
of the American Chemical Society, 110 (7), 2286–2294
[7] Hobza, P., Selzle, H.L. and Schlag, E.W. (1994) Potential
energy surface of the benzene dimer: Ab initio theoretical
study. Journal of the American Chemical society, 116(8),
[8] Bernstein, E.R., Sun, S. (1996) Aromatic van der waals
clusters: Structure and nonrigidity. Journal of Physical
Chemistry, 100(32), 13348-13366.
[9] Hobza, P., Selzle, H.L., Schlag, E.W. (1996) Potential
energy surface for the benzene dimer. Results of ab initio
CCSD(T) calculations show two nearly isoenergetic
structures: T-Shaped and parallel-displaced. Journal of
Physical Chemistry, 100(48), 18790.
[10] Tsuzuki, S., Honda, K., Uchimaru, T., Mikami, M. and
Tanabe, K. (2002) Origin of attraction and directionality
of the π-π interaction: Model chemistry calculations of
benzene dimer interaction. Journal of the American
Chemical Society, 124(1), 104-112.
[11] Sinnokrot, M.O., Valeev, E. F. and Sherrill, C.D. (2002),
Estimates of the ab initio limit for π-π interactions: The
benzene dimer. Journal of the American Chemical Soci-
ety, 124(36), 10887-10893.
[12] Zhikol, O.A., Shishkin, O.V., Lyssenko, K.A. and
Leszczynski, J. (2005) Electron density distribution in
stacked benzene dimers: A new approach towards the es-
timation of stacking interaction energies. Journal of
Chemical Physics, 122(14), 144104.
[13] Parthasarathi, R., Subramanian, V. (2005) Stacking in-
teractions in benzene and cytosine dimers: From mo-
lecular electron density perspective. Structural Chemistry,
16(3), 243-255.
[14] Steven, E.W., Anne, J.M, Peter, M, Timothy, M.S, and
Houk, K.N. (2010) Probing substituent effects in
aryl-aryl interactions using stereoselective diels-alder
cycloadditions. Journal of the American Chemical Soci-
ety, 132(10), 3304-3311.
[15] Frisch, M.J., Trucks, G.W., Schlegel, H.B., Gill, P.M.W.,
Johnson, B.G., Robb, M.A., Cheeseman, J.R., Keith, T.,
Petersson, G.A., Montgomery, J.A., Raghavachari, K.,
Al-Laham, M.A., Zakrzewaki, V.G., Ortiz, J.V., Fores-
mann, J.B., Ciolowski, J., Stefanov, B.B., Namayakkara,
A., Challacombe, M., Peng, C.Y., Ayala, P.Y., Chen, W.,
Wong, M.W., Andres, J.L., Replogle, E.S., Gomperts, R.,
Martin, R.L., Fox, D.J., Binkley, J.S., Defrees, D.J.,
Baker, J., Stewart, J. P., Head-Gordon, M., Gonzalez, C.,
and Pople, J.A.. Gaussian 03, Gaussian Inc., Pittsburgh