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Ab Initio Calculations on Halogen-Bonded Complexes and
Comparison with Density Functional Methods
YUN-XIANG LU,1,2 JIAN-WEI ZOU,1 JI-CAI FAN,3 WEN-NA ZHAO,1 YONG-JUN JIANG,1 QING-SEN YU1,3
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Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China
Drug Discovery and Design Center, Shanghai Institute of Materia Medica,
Chinese Academy of Sciences, Shanghai, 201203, China
3
Department of Chemistry, Zhejiang University, Hangzhou, 310027, China
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Received 24 March 2008; Revised 3 June 2008; Accepted 6 July 2008
DOI 10.1002/jcc.21094
Published online in Wiley InterScience (www.interscience.wiley.com).
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Abstract: A systematic theoretical investigation on a series of dimeric complexes formed between some halocarbon molecules and electron donors has been carried out by employing both ab initio and density functional methods.
Full geometry optimizations are performed at the Moller–Plesset second-order perturbation (MP2) level of theory
with the Dunning’s correlation-consistent basis set, aug-cc-pVDZ. Binding energies are extrapolated to the complete
basis set (CBS) limit by means of two most commonly used extrapolation methods and the aug-cc-pVXZ (X 5 D,
T, Q) basis sets series. The coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] correction term, determined as a difference between CCSD(T) and MP2 binding energies, is estimated with the aug-ccpVDZ basis set. In general, the inclusion of higher-order electron correlation effects leads to a repulsive correction
with respect to those predicted at the MP2 level. The calculations described herein have shown that the CCSD(T)
CBS limits yield binding energies with a range of 20.89 to 24.38 kcal/mol for the halogen-bonded complexes
under study. The performance of several density functional theory (DFT) methods has been evaluated comparing the
results with those obtained from MP2 and CCSD(T). It is shown that PBEKCIS, B97-1, and MPWLYP functionals
provide accuracies close to the computationally very expensive ab initio methods.
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q 2008 Wiley Periodicals, Inc.
J Comput Chem 00: 000–000, 2008
Key words: ab initio; halogen bonding; density functional methods
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Introduction
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Correspondence to: J. W. Zou; e-mail: [email protected] and Y. X.
Lu; e-mail: [email protected]
q 2008 Wiley Periodicals, Inc.
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In recent years, there has been widespread interest in understanding a specific intermolecular interaction involving halogen atoms
as acceptors of electron density.1 Such interactions endowed with
unprecedented properties are now referred to as halogen bonding
to emphasize their striking similarities with classical hydrogen
bonding. Indeed, most of the energetic and structural features
found in hydrogen-bonded complexes are reproduced in halogenbonded complexes as well. Owing to its strength, selectivity, and
directivity, halogen bonding has led to a number of applications
in fields, as diverse as molecular recognition, enantiomers’s separation, crystal engineering, and supramolecular architectures.2–28
In particular, the utilization of this specific interaction in the context of drug design is nowadays coming to light clearly.3,29–35 In
a recent survey of halogen bonding (short XO contacts) in biological molecules, it apparently demonstrated the potential importance of this interaction in ligand binding and recognition, as well
as molecular folding.29
The formation of halogen bonding can be rationalized on the
basis of two computational findings. (1) The presence of a small
positive electrostatic potential end cap along the C
X bond
vectors (except for fluorine),36 as shown in Figure 1a. In recent
articles, the positive cap of halogen atoms was referred to as the
‘‘r-hole’’ that intersects the C-X axis.37–39 The same concept has
now been extended to some atoms of group V and VI to elucidate their ability to form directional noncovalent interactions.40,41(2) The anisotropic distribution of electron density
around halogen atoms42 (see Fig. 1b), i.e., there are two different radii of halogens: a shorter one along the C
X bond and a
longer one perpendicular to it. Murray and coworkers have
pointed out that the two explanations for halogen bonds are
completely compatible with each other.38 Of particular interest
is that halogens exhibit both electrophilic character along the
axes of the C
X bonds and nucleophilic character along the
vectors that are perpendicular to these bonds. That is to say, halogen atoms can form both a halogen bond with nucleophiles
(electronegative atoms/groups) displaying roughly linear arrange-
Lu et al. • Vol. 00, No. 00 • Journal of Computational Chemistry
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Figure 1. (a) Negative and positive electrostatic potentials of halocarbons and (b) anisotropic atomic
charge distribution around halogens.
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Theoretical Methods
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All of the calculations reported in this work were carried out
with the help of Gaussian 03 suite of programs.68 The geometries of all the monomers and complexes were fully optimized
without including basis set superposition error (BSSE) correction
at the MP2 level69 in conjugation with the augmented Dunning’s
basis set, aug-cc-pVDZ (aVDZ). For the systems containing iodine, we employed aug-cc-pVXZ-PP (X 5 D, T, Q), which uses
pseudopotentials to describe the inner core orbitals, and aVXZ
for all other atoms. The MP2 calculations were performed using
the frozen core approximation. All optimized structures were
characterized as potential energy minimums at the MP2/aVDZ
level by verifying that all the vibrational frequencies are real.
The BSSE associated with the halogen bonding energies was
computed and corrected by means of the counterpoise method.70
The hierarchy of Dunning’s correlation-consistent basis sets
has been developed for recovering electron correlation in a systematic fashion. When a series of these basis sets are applied,
the total correlation energy is shown to convergence toward the
limit of one-electron atomic basis functions, that is, the CBS
limit. In view of the asymptotic convergence of the electronic
correlation energy provided by these basis sets, the CBS limit
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Journal of Computational Chemistry
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In a recent database survey of short halogenoxygen interactions in protein and nucleic acid structures, it was discovered
that most of the XO interactions (95 out of 113) contain carbonyl (C¼
¼O) and hydroxyl (O
H) groups.29 Therefore, formaldehyde and water are selected as electron donors in this study.
Also, ammonia is included with a view to complete the data-
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(1)
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CCSDðTÞ
DEMP2 Þsmall basis set
DECCSDðTÞ ¼ DEMP2
CBS þ ðDE
base. Several small model halogen-bonded complexes,
CH2¼
¼CHClOCH2, CHBCClOH2, CHBCClOCH2, CH2¼
¼
CHBrOH2, CH2¼
¼CHBrOCH2, CHBCBrOH2, CHBCBr
OCH2, CH2¼
¼CHClNH3, CHBCClNH3, CH2¼
¼CHBrNH3,
CHBCBrNH3, CH2¼
¼CHIOH2, and CHBCIOH2, are calculated using the aug-cc-pVXZ basis sets series. Binding energies are extrapolated to the CBS limit at the MP2 level. We
then assess the higher-order contributions to the correlation
energy at the CCSD(T) level with the aug-cc-pVDZ basis set.
The calculations described herein allow us to examine the performance of several density functional theory (DFT) methods to
reproduce the CCSD(T)/CBS halogen bonding energies, since
DFT offers an alterative treatment of electron correlation and
has been successfully applied to investigate a large number of
molecular species. Such a systematic theoretical study provides
reference ab initio structures and binding energies of halogen
bonding, which may be used to test the accuracy of less reliable
theoretical approaches developed in the future.
On
ment and a hydrogen bond with electrophiles (hydrogen bond
donors) occurring in the side-on fashion. The type of the interaction via side-on mode is often referred to as hydrogen bonding
or dipole interaction,43,44 and the benchmark tests on some representative systems can be found in the literatures.45
Halogen bonding has obviously been the subject of numerous
theoretical studies.46–60 The key structural and energetic aspects
of this interaction are fairly well established. For example, the
attractive nature of the interaction gives rise to halogen bonding
lengths less than the sum of van der Waals (vdW) radii of
involved atoms. The stronger the interaction, the shorter the halogen bond length is.3 Calculations have also been unveiled that
the strength of the interaction decreases in the following order:
I [ Br [ Cl.59 An accurate description of halogen-bonded systems appears to be of vital importance for our understanding of
crystal packing and molecular recognition processes in biological systems.4,29 There is a wide range of ab initio theoretical
methods available to account for electron correlation that plays
an important role in nonbonded interactions. Among them, the
coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] approach61 in combination with the complete
basis set (CBS) extrapolation approximation using Dunning’s
correlation-consistent basis sets62 is capable of achieving an
exact solution in a systematic way. At present, a direct CBS
extrapolation is, however, not feasible for CCSD(T). Here, it is
assumed that the energy difference between Moller–Plesset second-order perturbation (MP2) and CCSD(T), denoted as
DCCSD(T), will change marginally when there is an increase in
the basis set quality.63–67 Therefore, the CCSD(T) binding
energy at the basis set limit, DECCSD(T), can be evaluated from
MP2
the MP2 one at the CBS limit, DECBS
, combined with the
DCCSD(T) correction term calculated with a small basis set, as
shown in eq. (1).
DOI 10.1002/jcc
Calculations on Halogen-Bonded Complexes and Comparison with DFT Methods
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Table 1. Selected Optimized Geometrical Parameters of the
Results and Discussion
Halogen-Bonded Complexes.a
Complexes
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XO)
3.150
3.180
2.967
2.963
3.031
2.968
3.237
3.035
3.106
3.086
3.092
2.936
2.930
3.027
2.915
3.127
2.958
3.151
2.978
2.952
3.058
167.6
163.0
179.9
180.0
179.9
168.7
179.8
179.8
179.0
169.8
168.5
179.6
179.8
179.9
171.5
179.9
179.9
179.7
179.9
179.6
179.8
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d(XO)
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where X 5 2, 3, 4 represents the aVDZ, aVTZ, aVQZ basis
sets, respectively. The MP2 limit binding energy DECBSMP2
reported in this work was determined as the average values of
the extrapolated BSSE-corrected and BSSE-uncorrected binding
CP
energies, DECBS
, and DECBS, respectively.
Geometries and binding energies of the dimeric complexes
were also calculated by means of 14 DFT methods with the Pople’s standard basis set, 6-31111G(d,p). For the iodine containing systems, the Lanl2DZ basis set, augmented by one set of six
d polarization functionals (Lanl2DZ*) with the following exponents, aC 5 aO 5 aN 5 0.80, and aI 5 0.29, was adopted. The
functionals were selected on the basis of popularity and availability: PW91,73 PBE,74 PBEKCIS,74–76 B97-1,77 PBE1PBE,74
B3LYP,78,79 B3P86,78,80 BH and HLYP,78,79,81 BLYP,78,79
BP86,80,82 B98,82 MPWPW91,73,83 MPWPBE,74,83 and
MPWLYP.79,83 In the same way, the BSSE was corrected using
the standard counterpoise method mentioned above.
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(3)
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DEðXÞ ¼ DECBS þ B=X3
(2)
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DEðXÞ ¼ DECBS þ A exp½ðX 1Þ þ B exp½ðX 1Þ2 ew
binding energies DECBS were extrapolated by two most commonly used three- and two-point extrapolation schemes71,72 for
both the BSSE-corrected and BSSE-uncorrected binding energies, as shown in eqs. (2) and (3).
The key geometrical parameters of the complexes under investigation are presented in Table 1. The MP2/aVDZ optimized molecular structures of the chlorine containing systems are displayed in Figure 2. The majority of the systems examined here
present multiple minima. In this work, however, we consider
only the minimum associated with halogen bonding, albeit in
some cases, it may not be the global minimum on the potential
energy surface. From Table 1, it is clear that the intermolecular
contacts are in a range from 2.915 to 3.180 Å. These separations
are less than the sum of vdW radii of the halogen and oxygen
atoms.84 Noticeably, most of the predicted XO distances are
somewhat shorter than the average statistical value of those
found in biological molecules (3.06 Å for ClO, 3.15 Å for
BrO, and 3.24 Å for IO),29 which is probably a result of the
steric effects in large systems (e.g., protein environment). It
should be pointed out that, for the systems involving H2CO,
there might exist a secondary interaction between the halogen
atom and one of the hydrogen atoms of H2CO. In fact, the XH
distances in these systems computed at the MP2/aVDZ level of
theory are within a range of 2.98–3.16 Å, which are appreciably
larger than the sum of the vdW radii of H and halogen atoms.
For the complexes H2C¼
¼CHClOCH2 and H2C¼
¼
CHBrOCH2, two stationary structures associated with halogen
bonding, as shown in Figure 2, have been observed. In complexes A, all of the atoms in the formaldehyde and halocarbon
molecules are in the same plane, while in complexes B, the H
atoms of formaldehyde are in a plane almost perpendicular to
the H2C¼
¼CHCl or H2C¼
¼CHBr molecular plane. In the perpendicular structure B, it is the p-electron density rather than the O
lone pair electrons that serves as electron donor. MP2/aVDT calculations also reveal that complexes B are more stable, about
0.05 kcal/mol, than the corresponding complexes A. In order to
quantitatively evaluate the accuracy of the computed energy difference, single-point calculations on the MP2/aVDZ geometries
are also carried out at the MP2/aVTZ and CCSD(T)/aVDZ levels. It is shown that the energy differences between complexes
A and B are 0.07 and 0.08 kcal/mol, respectively, by the two
methods, which are in good agreement with the observations
through MP2/aVDZ. The two series of complexes should behave
similarly in subsequent analyses, and therefore, only complexes
B are used for further investigation. In fact, the energetic preference of the p systems as electron donors cannot be neglected in
protein structures, because the O lone pair electrons of the C¼
¼O
are often involved in hydrogen bonds with the N
H group of a
neighboring peptide backbone chain.29
For all the dimers studied, it has been shown that the optimized equilibrium C
XO contacts are essentially linear. At
the MP2/aVDZ level, the C
XO angles are predicted to be
within a range of 1638–1808. This structural feature further supports the electrostatic nature of halogen bonds in the complexes
considered, since an electronegative atom/group prefers to be
located in a position to meet the electrostatic positive cap along
the C
X vectors of halocarbons (see Fig. 1a) that results in a
linear arrangement. It is noteworthy that the C
XO angles in
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Distances are in angstroms, angles in degrees.
The MP2/aVTZ parameters.
c
CP-corrected parameters at the MP2/aVDZ level.
b
Geometries and Binding Energies
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¼CHClOCH2 (A)
H2C¼
H2C¼
¼CHClOCH2 (B)
CHBCClOH2
CHBCClOH2b
CHBCClOH2c
CH¼
¼CClOCH2
¼CHClNH3
H2C¼
CHBCClNH3
H2C¼
¼CHBrOH2
H2C¼
¼CHBrOCH2 (A)
¼CHBrOCH2 (B)
H2C¼
CHBCBrOH2
CHBCBrOH2b
CHBCBrOH2c
CHBCBrOCH2
H2C¼
¼CHBrNH3
CHBCBrNH3
H2C¼
¼CHIOH2
CHBCIOH2
CHBCIOH2b
CHBCIOH2c
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DOI 10.1002/jcc
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Figure 2. Optimized geometries of the complexes containing chlorine at the MP2/aVDZ level.
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The calculated binding energies of the dimeric complexes are
collected in Table 2. From these data, it is apparent that the
uncorrected binding energies become monotonically less negative with the increase in the basis set, in parallel with the monotonic decreases in the absolute value of BSSE. Taking into consideration these two factors, the counterpoise corrected binding
energies are shown to enlarge with the increase in basis set size.
For example, in the case of CH2¼
¼CHClOCH2, on going from
aVDZ to aVQZ, the uncorrected binding energy (DE) are calculated to be 21.78, 21.70, and 21.61 kcal/mol, respectively,
whereas the BSSE values are found to reduce from 0.67 to 0.33
and further to 0.14 kcal/mol. The BSSE-corrected binding energies (DECP) therefore become more negative with the basis set
quality for this dimer (the DECP values are estimated to be
21.11 kcal/mol for aVDZ, 21.37 kcal/mol for aVTZ, and
21.47 kcal/mol for aVQZ). As anticipated, the BSSE values
strongly depend on the basis set. At the MP2/aVDZ level, the
BSSE corrections amount to about 45% in some complexes.
When using the largest basis set aVQZ, the corrections are only
ca. 15% for the binding energy. However, basis set saturation is
not reached yet, and in some cases, the BSSE is still around 1.0
kcal/mol for aVQZ (cf. Table 2). Hence, in this work the MP2
limit binding energy is taken to be the average value of the extrapolated BSSE-corrected and BSSE-uncorrected binding energies. The rationality of this protocol has been validated in several benchmark studies of hydrogen-bonded systems.87,88 At the
MP2/CBS level, the halogen bonding energies are within a range
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Journal of Computational Chemistry
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the dimers RXOCH2 deviate from the linearity significantly as
compared with those in RXOH2. A simple explanation for this
behavior may be that the carbonyl O atom shows an effect on
polarity that is stronger than that of the hydroxyl one. The values of C
XO angles in RXOCH2 computed at the MP2/
aVDZ level, indeed fall into the statistical range of halogen
bonding found in biological molecules (1608–1708).29 Geometry
optimizations of CHBCClOH2, CHBCBrOH2, and
CHBCIOH2 have also been performed at the level of MP2/
aVTZ, and the relevant structural parameters are given in Table
1. It can be seen that the differences of the geometrical parameters with the two methods are quite limited. Consistently, the
binding energy of this dimer depends only marginally on the
geometries attained with the two basis sets (vide infra). Bearing
these in mind, we expect that the basis set used in this work
(aVDZ) is adequate for a precise description of the geometries
of the halogen-bonded complexes.
To assess the effect of BSSE on optimized geometries,
the structures of three studied systems, HCBCClOH2,
HCBCBrOH2, and HCBCIOH2, are also optimized by
including BSSE corrections, and the results are also listed in
Tables 1 and 2. It can be seen that the halogen bond length
from the CP-corrected PES is longer by about 0.08 Å than that
from a standard PES for the three complexes, which is similar
to that in H-bonded systems.85,86 However, the binding energies
are rather insensitive to small changes on the equilibrium geometries, as shown in Table 2.
DOI 10.1002/jcc
Calculations on Halogen-Bonded Complexes and Comparison with DFT Methods
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Table 2. Calculated Binding Energies Along with BSSE for the Halogen-Bonded Dimers.
Complexes
MP2/aVTZ
CBS (D?T?Q)b
MP2/aVQZ
CBS (T?Q)c
DE
BSSE
DE
BSSE
DE
BSSE
DECBS
DECP
CBS
MP2
DECBS
DECBS
DECP
CBS
MP2
DECBS
21.78
22.36
22.37
22.33
22.75
21.10
23.08
21.90
22.87
23.73
23.73
23.66
24.36
22.62
25.17
23.03
25.05
25.03
24.99
0.67
0.54
0.54
0.49
0.75
0.47
0.72
0.86
1.32
1.11
1.12
0.98
1.58
1.13
1.49
1.14
1.35
1.40
1.23
21.70
22.19
22.19
22.17
22.57
20.96
22.74
21.67
22.67
23.36
23.35
23.29
23.96
22.19
24.55
23.00
25.01
25.01
24.90
0.33
0.24
0.23
0.21
0.34
0.20
0.24
0.52
0.82
0.63
0.62
0.55
0.93
0.57
0.76
0.96
1.16
1.21
1.05
21.61
22.15
22.15
22.13
22.50
20.93
22.73
21.56
22.59
23.29
23.29
23.22
23.87
22.15
24.52
22.95
24.95
24.95
24.80
0.14
0.11
0.11
0.10
0.16
0.09
0.13
0.35
0.62
0.47
0.47
0.42
0.69
0.45
0.61
0.80
1.00
1.04
0.89
21.54
22.12
22.13
22.11
22.45
20.91
22.74
21.48
22.53
23.24
23.24
23.18
23.80
22.15
24.53
22.90
24.90
24.89
24.71
21.55
22.11
22.08
22.09
22.43
20.91
22.69
21.26
22.07
22.90
22.90
22.85
23.30
21.77
23.99
22.24
24.03
24.01
23.96
21.55
22.12
22.11
22.10
22.44
20.91
22.72
21.37
22.30
23.07
23.07
23.02
23.55
21.96
24.26
22.57
24.47
24.45
24.34
21.54
22.12
22.12
22.10
22.45
20.91
22.70
21.48
22.53
23.24
23.25
23.17
23.80
22.12
24.47
22.91
24.91
24.91
24.73
21.54
22.11
22.10
22.08
22.39
20.90
22.65
21.25
22.06
22.89
22.89
22.84
23.29
21.76
23.97
22.23
24.02
23.99
23.95
21.54
22.12
22.11
22.09
22.42
20.91
22.68
21.37
22.30
23.07
23.07
23.01
23.55
21.94
24.23
22.57
24.47
24.45
24.34
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H2C¼
¼CHClOCH2
CHBCClOH2
CHBCClOH2d
CHBCClOH2e
CHBCClOCH2
H2C¼
¼CHClNH3
CHBCClNH3
H2C¼
¼CHBrOH2
H2C¼
¼CHBrOCH2
CHBCBrOH2
CHBCBrOH2d
CHBCBrOH2e
CHBCBrOCH2
¼CHBrNH3
H2C¼
CHBCBrNH3
H2C¼
¼CHIOH2
CHBCIOH2
CHBCIOH2d
CHBCIOH2e
MP2/aVDZ
or
All values in kcal/mol. DE are binding energies without BSSE corrections. DECBS and DECP
CBS are BSSE-uncorrected
MP2
is their average value.
and BSSE-corrected energies, respectively, at CBS limits, and DECBS
b
Three-point extrapolation.
c
Two-point extrapolation.
d
Geometries optimized with aVTZ basis set for comparison purpose.
e
Geometries optimized with including BSSE corrections.
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binding energy to a lesser degree, which is consistent with the
findings described earlier. The MP2/aVDZ method is then recommended for accurately determining geometrical and energetic
properties of small systems containing halogen bonding elements.
Here, it should be noted that the average difference in the aVDZ
results relative to the CBS data is 0.34 kcal/mol, whereas the
aVTZ values are on average 0.10 kcal/mol below the CBS limit.
This gives an unequivocal indication that the energies are rapidly
converging with the aVTZ basis set. Additionally, in all cases, the
aVQZ binding energies are very close to the CBS results.
As mentioned earlier, the difference between the CCSD(T)
and MP2 binding energies exhibits only a small basis set dependence. With this in mind, we have calculated the DCCSD(T)
correction terms with a small basis set aVDZ, and the results are
given in Table 3. It can be seen that the DCCSD(T) correction
terms are non-negligible and become repulsive, which can be
ascribed to an extreme attractive dispersion contribution
included in the supermolecular MP2 energy. These repulsive
DCCSD(T) corrections are as large as 0.10 kcal/mol in some
cases and quite variable. The CCSD(T) CBS limits yield binding
energies with a range between 20.89 and 24.38 kcal/mol, as
shown in Table 3.
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Journal of Computational Chemistry
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of 20.91 24.47 kcal/mol, thus indicating that the interactions
in the dimers under study are comparable in strength to classical
hydrogen bonds. Halogen bonding seems to be very significant
as a driving force that influences the alignment of molecules in
crystals. Inspection of Table 2 reveals that larger interaction
energies are predicted for the complexes RXOCH2 as compared with the corresponding RXOH2, reflecting the stronger
halogen bond in the former complex. This can be ascribed to the
greater basicity of carbonyl oxygen relative to the hydroxyl one.
In addition, the strength of the interaction increases in the following order: Cl \ Br \ I, which reproduces the well-documented properties of halogen bonding.3,59
As seen in Table 2, the DECBS values obtained using the
three- and two-point extrapolations differ by only 0.00–0.03
kcal/mol and, consequently, the effect of different extrapolation
approaches would be very small. Notably, albeit the extrapolation to the CBS limit affects the absolute values of binding energies to a great extent, the relative order of the halogen bonding
strength unveiled by MP2/aVDZ remains unaltered.
For the CHBCClOH2, CHBCBrOH2, and CHBCIOH2
complexes, the structure optimized at the MP2/aVTZ level is also
employed to the extrapolation. As shown in Table 2, the CBS limit
extrapolated binding energy depends only marginally on whether
the structures optimized with the aVDZ or aVTZ basis set. The
largest gap is only 0.03 kcal/mol between the two binding energy
series. According to these results, we can assume that BSSE-corrected gradient optimizations with lager basis sets will affect the
DOI 10.1002/jcc
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Table 3. DCCSD(T) Corrections with the aVDZ Basis Set and CCSD(T)
Binding Energies for the Complexes under Study.a
MP2
DECBS
DCCSD(T)
DECCSD(T)b
H2C¼
¼CHClOCH2
CHBCClOH2
CHBCClOCH2
CH2¼CHClNH3
CHBCClNH3
H2C¼
¼CHBrOH2
¼CHBrOCH2
H2C¼
CHBCBrOH2
CHBCBrOCH2
CH2¼CHBrNH3
CHBCBrNH3
CH2¼CHIOH2
CHBCIOH2
21.55
22.12
22.44
20.91
22.72
21.37
22.30
23.07
23.55
21.96
24.26
22.57
24.47
0.06
0.04
0.10
0.02
0.07
0.01
0.14
0.07
0.18
0.09
0.14
0.06
0.09
21.49
22.08
22.34
20.89
22.65
21.36
22.16
23.00
23.37
21.87
24.12
22.51
24.38
ng
Complexes
All energies are given in kcal/mol.
DECCSD(T) are the most accurate values.
b
Angles, and Energies for the 12 Complexes.a
Methods
PW91
PBEPBE
PBEKCIS
PBEKCISb
B97-1
B97-1b
PBE1PBE
B3LYP
B3P86
BHandHLYP
BLYP
BP86
B98
MPWPW91
MPWPBE
MPWLYP
MPWLYPb
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Table 4. Average Absolute deviations of Halogen Bonding Distances,
d(XO)
ff (C
XO)
DE
0.070
0.064
0.051
0.112
0.049
0.100
0.052
0.064
0.059
0.050
0.090
0.066
0.056
0.079
0.082
0.046
0.101
1.2
1.2
1.3
2.8
1.1
2.6
1.1
1.6
1.3
1.3
1.8
1.8
1.0
2.1
2.1
1.2
2.3
0.51
0.46
0.37
0.46
0.40
0.52
0.50
0.86
0.80
0.64
1.12
1.14
0.51
0.82
0.85
0.42
0.54
a
Distances are in angstroms, angles in degrees, and energies in kcal/mol.
Distance and angle deviations relative to MP2/aVDZ, while binding
energy deviations relative to the CCSD(T) CBS limits.
b
Values obtained with 6–31111G(2df,2p) basis set for comparison
purpose.
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eter function B3LYP does not perform well for halogen bonding
interactions, since the average absolute deviations amount to
0.064 Å and 0.86 kcal/mol for halogen bonding distance and
energy, respectively. The poor performance of B3LYP is
encountered in hydrogen-bonded systems as well.95 From Table
4, it is also observed that the best result of halogen bonding contacts is obtained by MPWLYP with an average deviation of
0.046 Å, while the best result of interaction energies is 0.37
kcal/mol as gained by PBEKCIS. The hybrid functionals generally yield deviations that are smaller than the corresponding
pure ones. Note that the PBE1PBE and B98 functionals perform
fairly well, with the average deviation of 0.05 Å for the contacts
and 0.5 kcal/mol for the binding energies. Overall, the PBEKCIS, B97-1, and MPWLYP methods provide accuracies similar
to the more computationally expensive ab initio approach. In
addition, good performance of 6-31111G(d,p) and Lanl2DZ*,
relatively small basis sets used here, is inspiring, since one of
the attractive features of DFT is its application to large systems
for which larger basis sets can be very demanding in routine
calculations.
To evaluate the dependence on basis set, geometry optimizations, and binding energies of the systems containing chlorine
and bromine are also calculated by using the three best functionals, i.e. PBEKCIS, B97-1, and MPWLYP, with the
6-31111G(2df,2p) basis set. Average absolute deviations of
halogen bonding distances, angles, and energies for these methods are also presented in Table 4. As can be seen, when the basis set size increases from 6-31111G(d,p) to 631111G(2df,2p), average absolute deviations increase significantly in all cases. Especially, average absolute deviations of
intermolecular distances enlarge by over 100%, while average
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Journal of Computational Chemistry
On
bonded interactions.89,90 Nevertheless, the correlated methods,
which have to be used to make an accurate description, are computationally very demanding even for small systems. Hence, it is
significant to explore strategies that are computationally less
demanding but describe these interactions with a similar accuracy as MP2 or higher levels of theory. A reasonable alternative
is offered by DFT methods, albeit the DFT approaches are less
reliable due to the lack of an appropriate description of the dispersion effect. Several previous studies have pointed out that the
DFT methods are able to provide the best compromise between
the accuracy of calculations and computational costs.91–94 Moreover, considering the vital significance of halogen bonding in
biomacromolecules, it would be significant for making large biologically relevant systems associated with halogen bonding interactions tractable at a relatively reliable quantum chemical level.
In light of the database for halogen bonding described earlier,
we have assessed the ability of many DFT methods for an accurate description of halogen-bonded complexes. The binding energies of the complexes are calculated by the 14 DFT methods
mentioned with the 6-31111G(d,p) and Lanl2DZ* basis sets at
respective optimized geometries. To analyze the performance of
each DFT method in detail, the average absolute deviations of
halogen bonding distances, angles, and energies are obtained
and displayed in Table 4. It should be pointed out that, for the
dimer H2C¼
¼CHClOCH2, a geometry optimization starting
with the halogen bond arrangement always converged to the
hydrogen bond conformation at the BLYP, BP86, MPWPW91,
and MPWPBE levels. Furthermore, the other DFT methods yield
extremely longer ClO contact relative to that of MP2/aVDZ,
which may be due to the fact that the DFT functionals fail to
account for important dispersion components. The results of this
complex are thus excluded from the statistical deviation analysis.
The data listed in Table 4 show that all the DFT functionals
reproduce halogen bonding angles very well (the greatest average deviation is only 2.18 as obtained by MPWPW91 and
MPWPBE). Not surprisingly, the more widely used three-param-
DOI 10.1002/jcc
Calculations on Halogen-Bonded Complexes and Comparison with DFT Methods
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absolute deviations of binding energies magnify by about 30%.
Therefore, medium-size basis set is recommended to study halogen-bonded systems when using DFT functionals.
Conclusions
ng
In this work, we report a systematic theoretical study on several
dimeric complexes of halocarbon molecules with water, formaldehyde, and ammonia. All complex structures are fully optimized
by using the MP2 method in conjunction with the aug-cc-pVDZ
basis set. Binding energies are extrapolated to the CBS limit in
terms of two commonly used extrapolation schemes and the hierarchy of Dunning’s correlation-consistent polarization basis set,
aug-cc-pVXZ (X 5 D, T, Q). Through this approach, binding
energies are predicted to be within a range of 20.91 to 24.47
kcal/mol for the systems considered here. Calculations also show
that halogen bonding interactions are fairly sensitive to the inclusion of higher-order electron correlation effects that lead to a repulsive correlation with respect to those at the MP2 level. The
performance of several DFT methods has been assessed on the
basis of the database obtained with ab initio calculations. It is
shown that while the more widely used three-parameter functional
B3LYP does not perform well for halogen bonding, PBEKCIS,
B97-1, and MPWLYP give the best performance. This work
would at least provide some reference bases for future DFT studies on complex halogen-bonded systems of interest.
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-F
16. Zordan, F.; Espallargas, G. M.; Brammer, L. Cryst Eng Comm
2006, 8, 425.
17. Reddy, C. M.; Kirchner, M. T.; Gundakaram, R. C.; Padmanabhan,
K. A.; Desiraju, G. R. Chem Eur J 2006, 12, 2222.
18. Padgett, C. M.; Walsh, R. D.; Drake, G. W.; Hanks, T. W.; Pennington, W. T. Cryst Growth Des 2005, 5, 745.
19. Zordan, F.; Purver, S. L.; Adams, H.; Brammer, L. Cryst Eng
Comm 2005, 7, 350.
20. Imakubo, T.; Miyake, A.; Sawa, H.; Kato, R. Synth Met 2001, 120,
927.
21. Boubekeur, K.; Syaas-Mayele, J. L.; Palvadeau, P. Tetrahedron Lett
2006, 47, 1249.
22. Bilewicz, E.; Rybarczyk-Pirek, A. J.; Dubis, A. T.; Grabowski, S. J.
J Mol Struct 2007, 829, 208.
23. Saha, B. K.; Nangia, A. Heteroatom Chem 2007, 18, 18.
24. Lucassen, A. C. B.; Karton, A.; Leitus, G.; Shimon, L. J. W.; Martin, J. M. L.; ver der Boom, M. E. Cryst Growth Des 2007, 7, 386.
25. Bertani, R.; Chaux, F.; Gleria, M.; Metrangolo, P.; Milani, R.; Pilati,
T.; Resnati, G.; Sansotera, M.; Venzo, A. Inorg Chimca Acta 2007,
360, 1191.
26. Aakeroy, C. B.; Schultheiss N.; Desper, J.; Moore, C. Cryst Eng
Comm 2007, 9, 420.
27. Wasilewska, A.; Gdaniec, M.; Polonski, T. Cryst Eng Comm 2007,
9, 203.
28. Chopra, D.; Thiruvenkatam, V.; Manjunath, S. G.; Row, T. N. G.
Cryst Growth Des 2007, 7, 868.
29. Auffinger, P.; Hays, F. A.; Westhof, E.; Ho, P. S. Proc Natl Acad
Sci USA 2004, 101, 16789.
30. Ghosh, M.; Meerts, I. A. T. M.; Cook, A.; Bergman, A.; Brouwer,
A.; Johnson, L. N. Acta Crystallogr Sec D 2001, 56, 1085.
31. Jiang, Y.; Alcaraz, A. A.; Chem, J. M.; Kobayashi, H.; Lu, Y. J.;
Snyder, J. P. J Med Chem 2006, 49, 1891.
32. Gopalakrishnan, B.; Aparna, V.; Ravi, J. J. M.; Desiraju, G. R.
J Chem Inf Model 2005, 45, 1101.
33. Himmel, D. M.; Das, K.; Clark, A. D.; Hughes, S. H.; Benjahad, A.;
Oumouch, S.; Guillemont, J.; Coupa, S.; Poncelet, A.; Csoka, I.;
Meyer, C.; Andries, K.; Nguyen, C. H.; Grierson, D. S.; Arnold, E.
J Med Chem 2005, 48, 7582.
34. Voth, A. R.; Hays, F. A.; Ho, P. S. Proc Natl Acad Sci USA 2007,
104, 6188.
35. Voth, A. R.; Ho, P. S. Current Topics Med Chem 2007, 7, 1336.
36. Brinck, T.; Murray, J. S.; Politer, P. Inter J Quantum Chem. Quantum Biol Symp 1992, 19, 57.
37. Trogden, G.; Murray, J. S.; Concha, M. C. J Mol Model 2007, 13,
313.
38. Politzer, P.; Lane, P.; Concha, M. C.; Ma, Y.; Murray, J. S. J Mol
Model 2007, 13, 305.
39. Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. J Mol Model
2007, 13, 291.
40. Murray, J. S.; Lane, P.; Clark, T.; Politzer, P. J Mol Model 2007,
13, 1033.
41. Murray, J. S.; Lane, P.; Politzer, P. Inter J Quantum Chem 2007,
107, 2286.
42. Lommerse, J. P. M.; Stone, A. J.; Taylor, R.; Allen, F. H. J Am
Chem Soc 1996, 118, 3108.
43. Brammer, L.; Bruton, E. A.; Sherwood, P. Cryst Growth Des 2001,
1, 277.
44. Banerjee, R.; Desiraju, G. R.; Mondal, R.; Howard, J. A. K. Chem
Eur J 2004, 10, 3373.
45. Zhao, Y.; Truhlar, D. G. J Chem Theor Comput 2006, 2, 1009.
46. Valerio, G.; Raos, G.; Meille, S. V.; Metrangolo, P. Resnati, G.
J Phys Chem A 2000, 104, 1617.
47. Karpfen, A. J Phys Chem A 2000, 104 6871.
ly
On
ot
-N
lic
ub
rP
fo
io
at
1. Metrangolo, P.; Resnati, G. Halogen Bonding: Fundamentals and
Applications, Springer: Berlin, 2008.
2. Metrangolo, P.; Resnati, G. Chem Eur J 2001, 7, 2511.
3. Corradi, E.; Meille, S. V.; Messina, M. T.; Metrangolo, P.; Resnati,
G. Angew Chem Int Ed 2000, 39, 1782.
4. Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Acc Chem Res
2005, 38, 386 and references therein.
5. Zordan, F.; Brammer, L.; Sherwood, P. J Am Chem Soc 2005, 127,
5979.
6. Espallargas, G.; Brammer, L.; Sherwood, P. Angew Chem Int Ed
2006, 45, 435.
7. Rosokha, S. V.; Neretin, I. S.; Rosokha, J. Y.; Hecht, J.; Kochi, K.
K. Heteroatom Chem 2006, 17, 449.
8. Awwadi, F. F.; Willett, R. D.; Haddad, S. F.; Twamley, B. Cryst
Growth Des 2006, 6, 1833.
9. Ranganathan, A.; El-Ghayoury, A.; Meziere, C.; Harte, E.; Clerac,
R.; Batail, P. Chem Commun 2006, 2878.
10. Metrangolo, P.; Resnati, G.; Pilati, T.; Liantonio, R.; Meyer, F.
J Polym Sci Part A: Polym Chem 2007, 45, 1. and references therein.
11. Metrangolo, P.; Resnati, G.; Pilati, T. Cryst Eng Comm 2006, 8,
946.
12. Liang, W. I.; Wang, Y.; Feng, F.; Jin, W. J. Analytica Chimica Acta
2006, 572, 295.
13. Marras, G.; Metrangolo, P.; Meyer, F.; Pilati, T.; Resnati, G. Vij, A.
New J Chem 2006, 30, 1397.
14. Metrangolo, P.; Prasang, C.; Resnati, G.; Liantonio, R.; Whitewood,
A. C.; Bruce, D. W. Chem Commun 2006, 3290.
15. Xu, J. W.; Liu, X. M.; Ng, J. K. P.; Lin, T.; He, C. B. J Mater
Chem 2006, 16, 3540.
ew
vi
Re
References
7
n
Journal of Computational Chemistry
DOI 10.1002/jcc
Lu et al. • Vol. 00, No. 00 • Journal of Computational Chemistry
8
ti
or
pp
Su
69.
70.
71.
72.
ng
73.
74.
at
rm
fo
In
75.
76.
77.
n
io
78.
79.
80.
81.
-F
or
82.
83.
84.
85.
vi
Re
86.
87.
Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J.
L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03,
Gaussian: Wallingford, CT, 2003.
Moller, C.; Plesset, M. S. Phys Rev 1934, 46, 618.
Boys, S. F.; Bernardi, F. Mol Phys 1970, 19, 553.
Peterson, K. A.; Woon, D. E.; Dunning, T. H. J Chem Phys 1994,
100, 7410.
Helgaker, T.; Klopper, W.; Koch, H.; Nago, J. J Chem Phys 1996,
106, 9639.
Perdew, J. P.; Wang, Y. Phys Rev B 1993, 45, 13244.
Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys Rev Lett 1996, 77,
3865.
Rey, J.; Savin, A. Inter J Quantum Chem 1998, 69, 581.
Toulouse, J.; Savin, A.; Adamo, C. J Chem Phys 2002, 117, 10465.
Hamprecht, F. A.; Cohen, A. J.; Tozer, D. J.; Handy, N. C. J Chem
Phys 1998, 109, 6264.
Becke, A. D. Phys Rev A 1988, 38, 3098.
Lee, C.; Yang, W.; Parr, R. G. Phys Rev B 1998, 37, 785.
Perdew, J. P. Phys Rev B 1986, 33, 8822.
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari,
K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees,
D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT,
Revision F. 2; Gaussian: Pittsburgh, PA, 1993.
Schmider, H. L.; Becke, A. D. J Chem Phys 1998, 108, 9624.
Adamo, C.; Barone, V. J Chem Phys 1998, 108, 664.
Bondi, A. J Phys Chem 1964, 68, 441.
Wu, D.; Li, Z. R.; Hao, X. Y.; Jalbout, A. F.; Adamowicz, L.; Li,
R. J.; Sun, C. C. J Chem Phys 2004, 120, 1330.
Hobza, P.; Havlas, Z. Theor Chem Acc 1998, 99, 372.
Frey, J. A.; Leist, R.; Leutwyler, S. J Phys Chem A 2006, 110,
4188.
Frey, J. A.; Leutwyler, S. J Phys Chem A 2006, 110, 12512.
Rappe, A. K.; Berstein, E. R. J Phys Chem A 2000, 104, 6117.
Del Bene, J. E.; Jordan, M. J. T. J Mol Struct Theochem 2001, 573,
11.
Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J Chem Theor Comput
2006, 2, 364.
Riley, K. E.; Op’t Holt, B. T.; Merz, K. M., Jr. J Chem Theor Comput 2007, 3, 407.
Cybulski, S. M.; Seversen, C. E. J Chem Phys 2005, 122, 014117.
Dahlke, E. E.; Truhlar, D. G. J Phys Chem B 2005, 109, 15677.
Zhao, Y.; Truhlar, D. G. J Chem Theor Comput 2005, 1, 415.
ew
88.
89.
90.
91.
92.
ly
ot
-N
93.
94.
95.
On
48. Ananthavel, S. P.; Manoharan, M. Chem Phys 2001, 269, 49.
49. Davey, J. B.; Legon, A. C.; Thumwood, J. M. A. J Chem Phys
2001, 114, 6190.
50. Alkorta, I.; Rozas, J.; Elguero, J. J Phys Chem A 1998, 102, 9278.
51. Wang, W. Z.; Wong, N.-B.; Zheng, W. X.; Tian, A. M. J Phys
Chem A 2004, 108, 1799.
52. Wang, Y. H.; Zou, J. W.; Lu, Y. X.; Yu, Q. S. J Theor Comput
Chem 2006, 4, 719.
53. Zou, J. W.; Jiang, Y. J.; Guo, M.; Hu, G. X.; Zhang, B.; Liu, H. C.;
Yu, Q. S. Chem Eur J 2005, 11, 740.
54. Lu, Y. X.; Zou, J. W.; Wang, H. Q.; Yu, Q. S.; Zhang, H. X.; Jiang,
Y. J. J Phys Chem A 2005, 109, 11956.
55. Wang, Y. H.; Zou, J. W.; Lu, Y. X.; Yu, Q. S. Xu, H. Y. Inter J
Quantum Chem 2007, 107, 501.
56. Riley, K. E.; Hobza, P. J Chem Theor Comput 2008, 4, 232.
57. Bilewicz, E.; Grabowski, S. J. Chem Phys Lett 2006, 427, 51.
58. Awwadi, F. F.; Willett, R. D.; Peterson, K. A.; Twamley, B. Chem
Eur J 2006, 12, 8152.
59. Politzer, P.; Murray, J. S.; Concha, M. C. J Mol Model 2007, 13,
643.
60. Riley, K. E.; Merz, K. M. J Phys Chem A 2007, 111, 1688.
61. Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A.
Chem Phys Lett 1989, 157, 479.
62. Dunning, T. H.; Peterson, K. A.; Woon, D. E.; In Encyclopedia of
Computational Chemistry; Schleyer, P. v. R., Ed.; Wiley: New
York, 1998; p. 88.
63. Jurecka, P.; Hobza, P. Chem Phys Lett 2002, 365, 89.
64. Klopper, W.; Luthi, H. P. Mol Phys 1999, 96, 559.
65. Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K.
J Phys Chem A 1999, 103, 8265.
66. Tsuzuki, S.; Luthi, H. J. Chem Phys 2001, 114, 3949.
67. Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K.
J Am Chem Soc 2002, 124, 104.
68. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.,
Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.;
Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.;
Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.;
Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala,
P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.;
Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;
Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M.
A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
lic
ub
rP
fo
io
at
n
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