Journal of Quantum Informatio n Science, 2011, 1, 26-33
doi:10.4236/jqis.2011.11004 Published Online June 2011 (
Copyright © 2011 SciRes. JQIS
Electronic Structure of some A3
Adenosine-Receptor Antagonist
——A Structure Activity Relationship
Rifaat Hilal*, Mohamed F. Shibl, Moteaa El-Deftar
Chemistry Department, Faculty of Science, Cairo University, Giza, Egypt
Received April 26, 2011; revised May 27, 2011; accepted June 6, 2011.
DFT quantum chemical computations have been carried out at the B3LYP/6-31G(d) level. Full geometry opti-
mization has been performed and equilibrium geometries for a new series of phenyl thiazoles have been located.
Ground state electronic properties, charge density distributions, dipole moments and its components have been
calculated and reported. Effect of substituents on the geometry and on the polarization of the studied series of
compounds are analyzed and discussed. Some structural features have been pinpointed to underline the affinity
and selectivity of the studied compounds as adenosine A3-receptor antagonists. Results of the present work indi-
cate that activity towards A3 receptor sites is directly correlated with both of the polarity and the co-planarity of
the thiazole.
Keywords: DFT/B3LYB, Thiazoles, Substituent Effect, A3-Receptors, Adenosine-Receptor Antagonist
1. Introduction
Adenosine, a metabolite of adenine nucleotides, is a
physiological regulator of several cellular activities and
cellular metabolism. It acts as an autacoid and activates G-
protein-coupled membrane receptors. These receptors are
present on almost every cell. However, receptor subtype
distribution and densities vary greatly. In our previous
work [1] a QSAR model has been developed for 1,3-
dimethylxanthines as adenosine receptor antagonists. The
model is capable of predicting the affinity towards both A1
and A2 receptors. Furthermore, several diverse classes of
heterocyclic compounds have been developed [2-4] and
reported as selective antagonists for A3 receptors. Re-
cently, thiazole and thiadiazole analogues have been de-
scribed as the possible core skeletons of A3 receptor an-
tagonists with moderate affinity and selectivity [5-6].
The current study aims to present the ground state
electronic properties of some new thiazole derivatives
with expected biological activity, namely, A3 Adenosine-
receptor antagonist. A structure-activity correlations
(SAR) will be attempted.
2. Materials and Methods
4-phenylthiazole is considered as the parent to the stud-
ied series of compounds
X = Me, NHMe, NHPh
Y = Ph, 4-ClC
, 4-MeC
, 3,4-CH
, 4-MeOC
, 3-thienyl
Compounds studied in the present work were prepared
[7] through microwave-assisted cross- coupling reactions
in water, and microwave-assisted Suzuki cross-coupling
reactions. These methods have been reviewed [8,9].
Theoretical computations carried out throughout this
work were performed using the Gaussian 2003 program
package [10]. Full geometry optimizations were performed
at the DFT (Density Functional Theory) level of theory
[11]. The B3LYB method [12,13] has been adopted.
3. Results and Discussion
3.1. Electronic Structure of 4-Phenylthiazole
The choice of the appropriate basis set is of prime impor-
Copyright © 2011 SciRes. JQIS
tance. The size of the molecules studied in the present
work is medium to large, hence, a cost-effective study of
basis sets, is in order. Such a study revealed that the 6-
31G(d) basis set provides the minimum acceptable level
of accuracy. This point can be appreciated by inspection
of Ta ble (1), where the optimized geometric parameters,
atomic charges and dipole moments of 4-phenylthiazole
are presented, at the 6-31G and the 6-31G(d) levels of
theory. Inclusion of the d-polarization functions has but
limited effect on the geometric parameters of 4-
phenythiazole. Such effect is confined to the sulphur
atom region where significant deformation is observed.
Upon d-orbital inclusion, the C-S bond length shows
>3% shortening whereas, the C-S-C bond angles show
widening by ~1 degree. This angle widening is due to the
much better extension in space of the d-orbitals. This
extension ensures a better description of the molecular
The effect on the charge density distribution and on
the dipole moment is more pronounced. Thus, the net
charge on “S” is reduced from a value of 0.4 e to a value
of 0.25 e upon inclusion of “d” functions. The “d” po-
larization function enabled a much better description of
the “S” electron-affinity. The effect in this case is not local-
ized; it is transmitted to all atoms of the 5-membered
ring. In case of the 6-31G(d) basis set, the N-atom is able
to accumulate 25% more negative charge, whereas, C5
became more positive. This indicates the direction of
migration of the electron charge density. The 6-
membered ring, on the other hand, shows but little de-
pendence on the d-functions. The overall redistribution
of the charge density is reflected in the increase in the
magnitude of the dipole moment to a value of 1.044 D.
The direction of the dipole moment shows also dra-
matic dependence on the “d” functions. Figur e ( 1 ) shows
the dipole moment vectors upon using the 6-31G and the
6-31G(d). The change in direction is most probably due
to the fact that polarization functions are able to provide
much better description of the lone pair electrons on both
“S” and “N”.
The above discussion indicates clearly that the 6-31G
(d) basis set is much more capable of describing the mo-
lecular electronic properties of the studied molecules.
Consequently, this basis set is adopted throughout the
present study.
3.2. Substituted 4-Phenylthiazole
Substituted 4-phenylthiazoles studied in the present work
fall into two main groups: in the first, substituent (X) is
in the five-membered ring and the second represent
variation of the substituent (Y) in the six-membered ring.
Our discussion of the main molecular features will be
along these two lines.
Figure 1. Perspective view of dipole moment orientation of
4-phenylthiazole using 6-31G and 6-31G (d). The origin of
coordinate system used is located at the center of mass at
point “1” for each molecule; the orientation of dipole mo-
ment is along the bold line from 1 to 2.
3.3. Substituted-2-Methylthiazoles
Substitution by a methyl group is not expected to cause
major geometric deformation. Careful inspection (table
supplementary material) of the main geometric parame-
ters of 4-phenyl-2-methylthiazole reveals that there is no
noticeable change in N1-C2 or C2-S3 bonds in the imme-
diate vicinity of the substitution center. This is true for
all bond lengths. However, there seems to be consider-
able deformation in bond angles. The N1C2S3 bond angle
is reduced by ~2° upon 2-methyl substitution, an effect
which causes an increase in ring strain. However this
effect is not transmitted to the 6-membered ring.
2-methyl substitution causes polarization of the σ-
framework in a direction opposite to that of the polariza-
tion of the π framework. This increase in σ polarization
is reflected in two main effects. First, the increase in the
negative charge density accumulated on the N atom and
the reduction of the dipole moment by ~16%. This po-
larization and the subsequent reduction in polarity would
certainly have the effect of reducing the activity towards
the A3-receptors [1].
Substitution in C9 of the six-membered ring by a halo-
gen atom has a considerable effect on the charge redistri-
bution. While the effect on the C-C bond length is almost
negligible, the dipole moment increases dramatically
Copyright © 2011 SciRes. JQIS
from a value of 0.87 D to 2.98 and 2.88 D for the chloro-
and the bromo-derivatives, respectively. The geometric
and electronic features of the chloro-and the bromo- de-
rivatives are given in tables supplementary material.
The high electronegativity of the halogen atom in-
duces polarization in both the σ- and the π-frameworks,
of the phenylthiazole moiety. Both the chloro-and the
bromo-derivatives show their dipole moment vectors
pointing in the same direction, towards the 5-membered
ring. This indicates a net charge transfer from the 6- to
the 5-membered ring. It is very important to realize that,
the planarity of 4-phenylthiazole is due to the fact that
the π-system extends all over the entire σ-framework.
This planarity is a very important geometric feature for
adenosine receptor antagonist [14]. Substitution by a
chloro-, a bromo-or a methyl group lead to an increase in
the tightness of binding. This has the direct consequence
of keeping the two rings co-planar. Figure (2) presents
the geometries of the studied thiazoles and the corre-
sponding dipole moment vectors.
Substitution by an aryl group in the phenyl ring, would
certainly add to the σ/π polarization. Careful inspection
of the geometric and electronic features of aryl-4-phenyl-
2-methylthiazoles studied in this work (tables supple-
mentary material) reveals that, extending the π-system
has the direct consequence of enhancing the polarity of
the system.
Figure 2. Perspective view of dipole moment orientation of
substituted-2-methylthiazole. The origin of coordinate sys-
tem used is located at the center of mass at point “1” for
each molecule; the orientation of dipole moment is along
the bold line from 1 to 2.
Copyright © 2011 SciRes. JQIS
It is also evident that the conjugation is much tighter
on the aryl-phenyl region. This shift of π-conjugation,
away from the 5-membered ring, has two main effects.
First, reduction in magnitude of the dipole moment by
almost 20%, and lifting of co-planarity. The thiazole ring
is out of the plane of the rest of the molecule. It should
be noticed that, although the dipole moment has been
reduced considerably, yet its direction is not significantly
affected. This is most probably due to the fact that the
directional character of the lone-pair electrons on “S”
and on “N” plays a dominant role in this respect. P-
chlorophenyl substitution has a pronounced effect on the
polarity of the molecule. Thus, the thiazole ring is forced
back towards the molecular plane and the dipole moment
has increased to 3.15 D. The effect of the chlorine atom
substitution is to considerably polarizes the σ-framework
in a direction opposite to that of the π- system. Replace-
ment of 4-chloro by a 4-methyl group causes a reduction
of the magnitude of the dipole moment to 0.462 D and
forcing the thiazole ring out of the molecular plane.
Thus, an electron-withdrawing substituent in the 4-
phenyl moiety is essential for the A3-adenosine antago-
nist receptors reactivity. This is due to the enhanced po-
larity and co-planarity of the molecule.
This is true for all substituted-2-methylthiazole deriva-
tives studied in the present work. Table (2) summarizes
the dipole moment values, its components and the dihe-
dral angles for the studied 2-methylthiazoles.
It is also important to examine the variation of the
electron-donating strength and the electron affinity val-
ues of the studied molecules. Table (3) presents the ioni-
zation energies (I.P) and electron affinities (E.A) of the
studied molecules. Substitution in the 6-membered ring
has but little effect on the donating strength. However,
this substitution has considerable effect on the electron-
affinity. The halogen atom substitution has pronounced
effect in lowering the LUMO i.e. increasing the electron-
affinity of the molecule. This point is of prime impor-
tance in determining the activity as A3 receptor antago-
Table 1. Optimized geometry of 4-phenylthiazole.
Bond (Ao) 6-31G 6-31G(d) Angle 6-31G 6-31G(d) Charge 6-31G 6-31G(d)
N1-C2 1.295 1.296 N1C2S3 114.363 115.138 N1 –0.323 –0.401
C2-S3 1.826 1.748 C2S3C4 86.531 88.379 C2 –0.222 –0.122
S3-C4 1.795 1.73 S3C4C5 111.728 110.883 S3 0.401 0.251
C4-C5 1.371 1.375 C4C5N1 114.089 114.057 C4 –0.498 –0.401
N1-C5 1.409 1.388 C5N1C2 113.289 111.543 C5 0.18 0.265
C5-C6 1.474 1.477 C4C5C6 127.297 126.882 C6 0.098 0.115
C6-C7 1.408 1.404 C5C6C7 119.644 119.716 C7 –0.146 –0.174
C7-C8 1.397 1.394 C6C7C8 120.562 120.644 C8 –0.134 –0.131
C8-C9 1.399 1.396 C7C8C9 120.399 120.403 C9 –0.112 –0.125
C9-C10 1.401 1.397 C8C9C10 119.470 119.423 C10 –0.140 –0.137
C10C11 1.396 1.393 C9C10C11 120.268 120.285 C11 –0.140 –0.181
C11-C6 1.408 1.405 C10C11C6 120.706 120.775 H12 0.189 0.185
C2-H12 1.079 1.084 C11C6C7 118.594 118.468 H13 0.182 0.183
C4-H13 1.077 1.08 N1C2H12 125.703 124.127 H14 0.182 0.16
C7-H14 1.083 1.084 S3C4H13 119.130 120.330 H15 0.128 0.131
C8-H15 1.086 1.087 C6C7H114 118.675 118.716 H16 0.127 0.130
C9-H16 1.085 1.087 C7C8H15 119.549 119.52 H17 0.126 0.130
C10-H17 1.085 1.087 C8C9H16 120.334 120.356 H18 0.126 0.122
C11-H18 1.085 1.086 C9C10H17 120.094 120.134
C10C11H18 119.139 119.071
6-31G 6-31G(d)
E (a.u.) –799.968 –800.108
Dipole moment (Debye) 0.877 1.044
Copyright © 2011 SciRes. JQIS
Table 2. Dipole moment of 4-substituted-2-methyl thiazole using 6-31G(d).
Cpd No substituent PX (D) PY (D) PZ (D) Total (D) Dihedral angle
1 4-phenylthiazole 0.387 –0.97 –0.0002 1.044 0.013
2 H 0.749 –0.447 0.0004 0.872 0.012
3 Cl 2.921 –0.591 –0.0002 2.980 0.043
4 Br 2.833 –0.539 0.0005 2.884 0.012
5 Ph –0.806 –0.379 –0.0505 0.893 3.097
6 4-ClC6H4 –3.113 –0.465 –0.0707 3.149 1.934
7 4-MeC6H4 –0.316 –0.336 –0.0068 0.462 2.973
8 3-thienyl –1.262 –0.068 –0.1842 1.277 1.479
9 3,4-CH2O2C6H4 –0.338 –0.262 –0.3553 0.556 2.749
10 4-MeOC6H4 0.241 –1.422 0.4346 1.506 3.481
11 4-styryl –0.884 –0.296 –0.0007 0.932 –0.108
Table 3. Ionization potential and electron affinity of 4-
substituted-2-methyl thiazole.
Compound No. I.P (eV) E.A (eV)
2 5.79 –9.25
3 5.93 –1.17
4 5.90 –1.17
5 7.58 –1.14
6 5.71 –1.31
7 5.49 –1.09
8 5.52 –1.14
9 5.28 –1.09
10 5.33 –1.03
11 5.25 –1.55
4. 2-N-methylthiaz ole-2-amine and Its
Table (4) summarizes the dipole moment data and dihe-
dral angles of the studied compounds. The π-electron
density redistribution in this series of compounds seems
to be dominated by a localized conjugation in the thia-
zole-amine moiety. This would impose a subsequent
cross-conjugation in the phenylthiazole region. This is
reflected in the magnitude of the dihedral angles reported
in Table (4). In general, the aryl group is out of the plane
of the thiazole amine moiety. Substitution in the 4-
position of the phenyl ring does not change much the non
-coplanarity of the studied molecules. Substitution with a
Cl or with a Br atom enhances the polarity considerably;
both the magnitude and direction of the dipole moments
are affected.
Thiazole amines are of better electron donating and of
less electron-accepting strength then the corresponding
methylthiazoles. Table (5) presents the ionization ener-
gies and electron affinities of the studied thiazole amines.
The geometric and electronic features of aryl-4-phenyl
-2-N-methylthiazoles-2-amine studied in this work are
analyzed (presented in (tables, supplementary material)).
This series of compounds do not show significant ge-
ometry changes upon substitution. However, thiazole
amines are characterized by a pronounced increase (
~20%) of the negative electron density accumulated on
the thiazole nitrogen atom. The variation of the charge
density upon substitution is remarkable and reflects itself
in the alteration of the direction of the dipole moments
(cf. Figure 3).
5. 4-Phenyl-2-N-phenylthiazole-2-amine and
Its Derivatives
Table (6) presents the dipole moments, its components
and dihedral angles of the studied compounds.
Copyright © 2011 SciRes. JQIS
Table 4. Dipole moments of 4-substituted-2-N- methylthia-
zole-2-amine using 6-31G(d).
No substituent PX
12 H –2.133 –0.433 0.582 2.253 2.506
13 Cl –4.342 –0.307 0.546 4.387 2.072
14 Br –4.253 –0.410 0.550 4.308 2.413
15 Ph –2.227 –0.566 0.672 2.394 –2.675
16 4-ClC6H4 –4.567 –0.601 0.488 4.632 4.0978
17 4-MeC6H4 –1.441 0.728 –0.590 1.719 0.733
18 3-thienyl 2.404 0.859 0.518 2.605 –3.920
19 3,4-CH2O2C6H4 1.763 –0.900 0.917 2.182 2.598
Table 5. Ionization potential and electron affinity of 4-subs-
Compound No. I. P (eV) E. A (eV)
11 5.25 –0.62
12 5.41 –0.87
13 5.41 –0.9
14 5.19 –0.03
15 5.30 –1.14
16 5.14 –0.92
17 5.17 –0.98
18 5.09 –0.898
Figure 3. Perspective view of dipole moment orientation of
substituted-2-N-methylthiazole-2-amine. The origin of co-
ordinate system used is located at the center of mass at
point “1” for each molecule; the orientation of dipole mo-
ment is along the bold line from 1 to 2.
Copyright © 2011 SciRes. JQIS
Table 6. Dipole moments of 4-substituted-2-N-phenyl thiazole-2-amine using 6-31G(d).
Cpd No substituent PX (D)PY (D) PZ (D) Total (D)Dihedral angle
20 H 1.1453 –0.11 –0.13381.1583 9.269
21 Cl 3.4309 0.2951–0.20813.4499 4.226
22 Br 3.3616 0.17 –0.19773.3717 3.454
23 Ph 1.1034 –0.82560.05331.3792 –15.122
24 4-ClC6H4 –3.4104 –1.3513–0.04213.6686 –15.758
25 4-MeC6H4 0.6603 –0.61640.09270.908 –15.631
26 3-thienyl 1.4437 1.196 0.12571.879 –15.496
Inspection of geometric data of these compounds (tables
and figures, supplementary material) indicates clearly that:
All the studied molecules show accumulation of the
negative charge density on the thiazole N-atom. This
negative charge facilitates hydrogen bonding which is
a very important structural feature related directly to
the ability to bind to the A3 receptor sites.
The NH-phenyl derivatives are non-coplanar. Indicat-
ing cross-conjugation between the phenyl and the thi-
azole moieties. It should be noted that the chlorine
and bromine atom substituents have exactly the same
effect as noted before. First, it reduced the dihedral
angles forcing the phenyl ring towards coplanarity.
Second, it enhances the polarity of the molecule as
indicated by the magnitude of the dipole moments
(cf. Table 6).
The dipole moment vectors seem but little affected by
substitution in the 6-membered ring. The dipole mo-
ments are dominated by contributions from heteroa-
toms especially “N” lone-pair.
NH-phenyl derivatives have almost the same elec-
tron-donating and electron-accepting strength as that
of the NH-CH3 derivatives.
Substituted 4-phenylthiazoles studied in the present
work fall into three main categories.
Y X groups
Cl, Br, Ph, 4-ClC6H4, 4-MeC6H4,
3,4-CH2O2C6H3, 4-MeOC6H4, 3-Thienyl
Cl, Br, Ph, 4-ClC6H4, 4-MeC6H4,
3,4-CH2O2C6H3, 3-Thienyl
Cl, Br, Ph, 4-ClC6H4, 4-MeC6H4 NHPh III
Substitution in general, has but little effect on the
geometric features of phenylthiazoles, the major geo-
metric effect, however, is traced in the co-planarity of the
molecules studied.
Thus, while 4-phenylthiazole itself is coplanar, substi-
tution in the 5-membered ring lefts this co-planarity. It is
very important to notice the effect of substitution by Cl-
or Br-, in the phenyl ring. This substitution has the geo-
metric effect of restoring the co-planarity back. It seems
that Cl- or Br- substituents would have a marked effect
on the activity of phenylthiazole as A3-receptor antago-
Substitution has a remarkable effect on the dipole
moments, magnitudes and directions. Analysis of dipole
moments show fluctuations of their values by substitu-
tion. It has been indicated that activity towards A3-
receptor sites is directly proportional to the polarity of
the thiazole. In the present work, the enhanced polarity
of some phenylthiazoles has been analyzed and attributed
to σ-/π-polarization. In some cases, especially for N-CH3
and N-Ph substitutents, cross-conjugation has but a very
little effect on the polarity of molecules. This elaborates
upon our previous conclusion that, the contributions
from the lone-pair electrons dominate the dipole mo-
Analysis of the effect of substitution, on the net elec-
tronic charge on the thiazole “N” atom, shows that the
NH-CH3 and NH-Ph derivatives accumulate more than
0.53e on the thiazole “N” atom. On the other hand, sub-
stitution in the phenyl ring has but little effect on the
amount of charge on the thiazole N atom. This charge is
of prime importance in H-bond formation with
A3-receptor sites. This hydrophilic interaction seems to
underlie the selectivity for the human A3-receptor. In
vitro, the thiazole moiety is surrounded by many hydro-
phobic amino acids.
The tendency of the studied phenylthiazoles to act as
electron-donors or electron-acceptors has also been in-
Copyright © 2011 SciRes. JQIS
vestigated. The energies of the HOMO's of the studied
series of thiazoles are around 5 eV. This low ionization
potential indicates a high tendency toward electron dona-
tion. Furthermore, aryl-2-methylthiazoles are character-
ized by low lying LUMO's, indicating considerable elec-
tron-affinity. This is of prime importance in enhancing
the activity towards A3-receptor sites.
The present analysis of the structure and electronic
properties of phenylthiazoles focuses on four main
structural features. The first feature is the co-planarity of
molecules. The second is the polarity, as indicated by the
dipole moments and their directions. The third feature is
the net negative charge on the thiazole “N” atom. This
charge enhances H-bond formation; a property of prime
importance for binding to A3-receptor sites. Finally, the
fourth feature is the electron donating and accepting ten-
dency of the studied thiazoles. A substituent that forces
co-planarity increases the dipole moment and the charge
accumulated on the thiazole “N” atom, and lowers the
LUMO, would certainly enhance the activity as potent and
selective adenosine A3-receptor antagonists.
6. References
[1] S. El-Tahar, K. M. El-Sawy and R. Hilal, “Electronic
Structure of Some Adenosine Receptor Antagonists: V.
QSAR Investigation ,”Journal of Chemical Information
And Computer Science, Vol. 42, No. 2, 2002, pp. 386-392.
doi:10.1021 /ci010307x
[2] Y.-C. Kim and K. A. Jacobson, “Derivatives of the Tri-
zoloquinazoline Adenosine Antagonist (CGS15943) are
Selective for the Human A(3) Receptor Subtype,” Jour-
nal Medicinal Chemistry, Vol. 39, No. 21, 1996, pp.
[3] P. G. Baraldi, B. Cacciari, R. Romagonoli, G. Spalluts,
K.-N. Klotz, E. Leung, S. Gessi, S. Merighi and P. A.
Porea, “Pyrazolo [4,3-e]-1, 2, 4-Triazolo[1,5-c]-Pyrimi-
dine Dervatives as Highly Potent and Selective Human
A(3) Adenosine Peceptor Antagonists,” Journal Medici-
nal Chemistry, Vol. 42, No. 22, 1999, pp, 4473-4478.
[4] K.-Y. Jung, S.-K. Kim, Z.-G. Gao, A. S. Gross, N. Mel-
man, K. A. Jacobson and Y-C. Kim, “Structure-Activity
Relationships of Thiazole and Thiadiazole Derivatives as
Potent and Selective Human Adenosine A(3) Receptor
Antagonists,” Bioorganic and Medicinal Chemistry, Vol.
12, No. 3, 2004, pp. 613-623.
[5] J. E. V. Muijlwijk-Kooezen, H. Timmerman, R. C.
Vollinga, J. F. Kunzel, M. de Goote, S. Visser and A. P.
Ijzernan, “Thiazole and Thiadiazole Analogues as a
Novel Class of Adenosine Receptor Antagonists,” Jour-
nal Medicinal Chemistry, Vol. 44, No. 5, 2001, pp.
[6] N. J. Press, J. R. Fozard, D. Beer, R. Heng, F. Padova, P.
Tranter, A. Trifilieff, C. Walker and T. H. Keller, “New
Highly Potent and Selective Adenosine A3 Receptor An-
tagonists,” Abstracts of Pape rs of the American Chemical
Society, Vol. 224, 2002,1-2, MEDI 419.
[7] K. M. Dawood and M. M. El-Deftar, “Microwave-Assisted
Synthesis of 2-Substituted 4-Biarylyl-1, 3-thiazoles by
Carbon-Carbon Cross-Coupling in Water,” Synthesis, Vol.
6, 2010, pp. 1030-1038.doi:10.1055/s-0029-1218662
[8] F. Bellina, A. Carpita and R. Rossi, “Palladium Catalysts for
the Suzuki Cross-Coupling Reaction: An Overview of Re-
cent Advances,” Synthesis, Vol. 15, 2004, pp. 2419-2440.
[9] L. Botella and C. Nájera, “A Convenient Oxime-Carbap-
alladacycle-Catalyzed Suzuki Cross-Coupling of Aryl
Chlorides in Water,” Angewandte Chemie International
Edition, Vol. 41, No. 1, 2002, pp. 179-181.
[10] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E.
Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Jr.
Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M.
Millam, S. S. Iyengar, J. Tomasi, V. Barone, B.
Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A.
Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota,
R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y.
Honda, O. Kitao, H. Nakai, M. Klene, Li, J. E. Knox, H.
P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J.
Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J.
Austin, R. Cammi, C. Pomelli, J. Ochterski, P. Y. Ayala,
K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg,
V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C.
Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K.
Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G.
Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu,
A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J.
Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A.
Nanayakkara, M. Challacombe, P. M. W. Gill, B. G.
Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A.
Pople, “Gaussian” Revision C.02, Gaussian, Inc.,
Wallingford, CT, 2004.
[11] P. Hohenberg and W. Kohn, “Inhomogenous Electron
Gas,” Physical Review, Vol. 136, No. 3, 1964, pp. 864-871.
[12] A. D. J. Becke, “Density-Functional Thermochemistry. 3.
The Role of Exact Exchange,” The Journal of Chemical
Physics, Vol. 98, No. 7, 1993, pp. 5648-5652.
[13] W. Y. Lee and R. G. Parr, “Development of The Colle-
Salvetti correlation-energy Formula Into A Functional of
The Electron-Density,” Physical Review, Vol. 37, No. 2,
1988, pp, 785-789.doi:10.1103/PhysRevB.37.785
[14] K. A. Jacobson, P. J. M. Van Galen and M. Williams,
Adenosine Receptors-pharmacology, Structure- Activ-
ity-Relationships, and Therapeutic Potential,” Journal
Medicinal Chemistry, Vol. 35, No. 3, 1992, pp. 407-422.