How Does Halogen Bonding Behave in Solution? A Theoretical Study

ARTICLE pubs.acs.org/JPCA

How Does Halogen Bonding Behave in Solution? A Theoretical Study Using Implicit Solvation Model Yunxiang Lu,*,† Haiying Li,† Xiang Zhu,† Weiliang Zhu,‡ and Honglai Liu† †

Key Laboratory for Advanced Material and Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China ‡ Drug Discovery and Design Center, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai 201203, China

bS Supporting Information ABSTRACT: A systematic study of halogen bonding interactions in gas phase and in solution was carried out by means of quantum chemical DFT/B3LYP method. Three solvents with different polarities (chloroform, acetone, and water) were selected, and solvation effects were considered using the polarized continuum model (PCM). For charged halogenbonded complexes, the strength of the interactions tends to significantly weaken in solution, with a concomitant elongation of intermolecular distances. For neutral systems, halogen bond distances are shown to shorten and the interaction energies change slightly. Computations also reveal that in the gas phase the binding affinities decrease in the order Cl
> Br
> I
, while in solution the energy gaps of binding appear limited for the three halide anions. According to free energy results, many systems under investigation are stable in solution. Particularly, calculated free energies of formation of the complexes correlate well with halogen-bonding association constants determined experimentally. The differences of the effects of solvent upon halogen and hydrogen bonding were also elucidated. This study can establish fundamental characteristics of halogen bonding in media, which would be very helpful for applying this noncovalent interaction in medicinal chemistry and material design.

’ INTRODUCTION Halogen bonding, a specific intermolecular interaction between a halogen atom and an electron-rich partner, has attracted widespread interest of chemists in recent years, due to its directionality and strength comparable to hydrogen bonding.1
15 It was well-documented that covalently bound halogens X display a region of positive electrostatic potential (the so-called positive cap) on the outer side of X along the extension of the R
X bonds.10 An electron-rich molecule prefers to approach the positive cap, thereby giving rise to a linear interaction. Now the positive region on X has been rationalized via the concept of σ
hole: the electron-deficient outer portion of the half-filled bonding orbital of X when forming a covalent bond with R, known previously as “polar flattening”.16
19 Moreover, this concept has been extended to atoms of Groups IV
VI to explore their potential to form directional noncovalent interactions.20,21 Over the past decade, the group of Metrangolo and Resnati has applied halogen bonding as an alternative to hydrogen bonding and metal-ion coordination in such diverse fields as crystal engineering, supramolecular architecture, and molecular recognition.2
8,22
25 In particular, the research found that aliphatic or aromatic iodo-perfluorocarbons (I-PFCs) are generally robust tectons in halogen-bond-based supramolecular r 2011 American Chemical Society

chemistry.3
6,26 Another fruitful field for halogen bonding is the development of solid-state materials with electronics applications, such as organic semiconductors, metals, and superconductors.27
30 Halogen bonding also holds vast potential for novel biomedical applications.3,7,31
40 For example, in 2007 Ho and co-workers reported that the conformational isomer of a four-stranded DNA junction that contains a Br 3 3 3 O halogen bond was stabilized by 2
5 kcal/mol relative to the corresponding hydrogen-bond-containing isomer.32 More recently, the Cl/ Br 3 3 3 π interactions have been demonstrated as an important contribution to protein
ligand binding affinity.41 Despite the wide applications of halogen bonding in many fields noted above, this noncovalent interaction remains poorly understood to data in some important aspects. Currently, the use of solution-phase halogen bonding to control and facilitate anion recognition has been reported,42
44 and a number of binding constants for the interaction in the solute phases were determined.45
48 More Importantly, Taylor et al. have investigated the thermodynamics of halogen bonding in organic Received: December 7, 2010 Revised: March 16, 2011 Published: April 05, 2011 4467

dx.doi.org/10.1021/jp111616x | J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

Table 1. Calculated Geometrical Parameters in Vacuum for the Complexes at Various Levels of Theorya B3LYP

MP2

d(I 3 3 3 Y)

— (C
I 3 3 3 Y)

μ

d(I 3 3 3 Y)

— (C
I 3 3 3 Y)

d(I 3 3 3 Y)

— (C
I 3 3 3 Y)

2.819

178.0

8.51

2.786

177.9

2.864

178.6

2.989

178.4

6.86

2.948

178.4

3.029

178.6


3I

3.232

178.3

5.89

3.178

178.3

3.278

178.5

3 NH3

2.922

177.8

5.06

2.845

177.8

2.947

178.1

3 OH2

3.030

177.5

4.05

2.968

176.6

3.004

179.0

2.794

179.8

10.73

2.754

179.8

2.824

179.8


3 Br

2.965

179.8

9.00

2.915

179.8

2.982

179.8

3I 3 NH3

3.207 2.928

179.8 179.9

7.94 5.13

3.141 2.836

179.8 179.9

3.220 2.929

179.8 179.9

C6F5I 3 3 3 OH2

3.022

179.7

4.12

2.950

178.9

2.986

179.6

complexes C2F3I 3 3 C2F3I 3 3 C2F3I 3 3 C2F3I 3 3 C2F3I 3 3 C6F5I 3 3 C6F5I 3 3 C6F5I 3 3 C6F5I 3 3 a

PBE




3 Cl
3 Br


3 Cl


Distances are given in angstroms, angles in degrees, and dipole moments in debye.

solution and established linear free energy relationships for the halogen bond donor ability of substituted iodo-perfluoroarenes.49 However, knowledge of halogen bonding in solution has lagged far behind other intermolecular forces such as hydrogen bonding50 and interactions involving aromatic systems.51 Halogen bonding in small model molecules has been intensively studied by means of ab initio calculations at post Hartree
Fock and density functional levels.52
77 The key geometrical and energetic features of the interaction were wellestablished. For example, the attractive nature of the interaction results in intermolecular distances shorter than the sums of van der Waals (vdW) radii of the involved atoms; the interaction strength decreases in the following order: I > Br > Cl. In a recent article, we have used a two-layer QM/MM ONIOM methodology to investigate halogen bonding interactions in several protein complexes with halogenated ligands.78 Nevertheless, most of the theoretical studies available by far focused mainly on accurate descriptions of isolated halogen-bonded complexes in vacuum and totally ignored the environmental effects. Also these studies usually reported gas-phase interaction energies rather than free energy results that should be more meaningful for describing halogen bonding in real systems. Considering the increasing importance of halogen bonding in solute phases as well as in proteins, it is necessary to understand general characteristics of this interaction in media from a theoretical viewpoint. In this paper, the effects of solvents on a series of halogenbonded systems were systematically studied through density functional theory (DFT) method and the self-consistent reaction field (SCRF) theory. Given that iodo-perfluoroalkenes and arenes, very good halogen bond donors, have been commonly used in the recognition of halide anions and in the study of thermodynamics of halogen bonding in solution,43,49 iodo-perfluorobenzene (C6F5I) and -ethane (C2F3I) were chosen here as model donors of halogen bonding. Three halide ions (Cl
, Br
, I
), ammonia (NH3), and water (H2O) were selected as electron donors. To model various experimental situations, three solvents with a wide range of dielectric constants ε, namely, chloroform, acetone, and water, were chosen. The main purpose of this work was to establish structural and energetic properties of halogen bonding in solution and, in particular, to compare with those determined experimentally. This study would be of great

importance for the applications of halogen bonding in molecular recognition and biological design.

’ COMPUTATIONAL METHODS The geometries of all the monomers and complexes were fully optimized in vacuum by means of the B3LYP,79,80 PBE,81 and MP282 methods. The aug-cc-pVDZ-PP basis set, which uses pseudopotentials to describe the inner core orbitals, was employed for bromine and iodine, while for all other atoms aug-cc-pVDZ was applied.83 These basis sets have been demonstrated potent in the description of various halogen-bonded systems.56,57,59,63 All of the gas-phase structures were characterized as potential energy minima at the same theoretical levels by verifying that all vibrational frequencies are real. The interaction energy (ΔE) was estimated as the difference between the total energy of the complex and the sum of total energies of the two monomers. The basis set superposition error (BSSE) was eliminated by the standard counterpoise method of Boys and Bernardi.84 Atomic charges were computed by using natural population analysis (NPA) at the B3LYP level of theory. Calculations in solution were performed via the standard polarizable continuum model (PCM)85
87 at the B3LYP level of theory. The molecular cavity was constructed through the united atom topological model (UAO) employing default radii.85 This implicit solvation approach has been widely used in the studies of the effects of solvent on hydrogen bonding.88
92 The optimized geometries in gas phase were utilized as starting points for the optimizations in three continuous media: chloroform, acetone, and water with dielectric constants of 4.90, 20.70, and 78.39, respectively. Free energy of formation of the complex in solution (ΔGsoln) at 298.15 K was attained in terms of90,93
95 ΔGsoln ¼ ΔGgas þ ΔΔGsolv þ RT lnð1=22:4Þ

ð1Þ

where ΔGgas is free energy of the interaction in the gas phase and ΔΔGsolv is the difference of free energy of solvation (ΔGsolv) between the complex and its subunits; the third expression is a correction with regard to the reference state changing from ideal gas to solution.96 Here it has to be pointed out that thermal contributions derived from gas-phase calculations may result in certain errors in the estimation of ΔGsoln.97 All of these calculations were carried out with the help of the Gaussian 03 suite of programs.98 4468

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

Table 2. Calculated Energetic Data in Gas Phase for the Dimers at Various Levels of Theorya B3LYP dimers C2F3I 3 3 C2F3I 3 3 C2F3I 3 3 C2F3I 3 3

a




3 Cl
3 Br
3I

3 NH3

C2F3I 3 3 C6F5I 3 3

3 OH2

C6F5I 3 3 C6F5I 3 3 C6F5I 3 3

3 Br
3I 3 NH3


3 Cl


C6F5I 3 3 3 OH2

PBE

MP2

ΔE

BSSE

ΔECP

ΔE

BSSE

ΔECP

ΔE

BSSE

ΔECP


26.49

0.31


26.18


30.02

0.33


29.69


25.07

1.88


23.19


23.68

0.24


23.44


27.38

0.26


27.12


23.27

2.87


20.40


20.32

0.22


20.10


24.17

0.22


23.95


19.87

2.76


17.11


6.06

0.48


5.58


7.56

0.49


7.07


7.49

1.91


5.58


3.36

0.26


3.10


4.07

0.25


3.82


4.92

1.34


3.58


26.64

0.30


26.34


31.30

0.32


30.98


25.79

1.99


23.80


23.77

0.26


23.51


28.60

0.28


28.32


24.07

3.07


21.00


20.31
5.90

0.24 0.49


20.07
5.41


25.24
7.63

0.23 0.49


25.01
7.14


20.67
7.63

3.01 1.94


17.66
5.69


3.36

0.26


3.10


4.20

0.25


3.95


5.00

1.35


3.65

All values are in kilocalories per molel.

Figure 1. Optimized structures of the halogen-bonded complexes under study in vacuum at the B3LYP level of theory. Distances in angstroms and angles in degrees.

’ RESULTS AND DISCUSSION Gas-Phase Calculation. The key geometrical parameters and energetic data in gas phase for the dimeric complexes calculated at the levels of B3LYP, PBE, and MP2 are summarized in Tables 1 and 2. The B3LYP-optimized structures of the dimers under investigation are displayed in Figure 1. It can be seen from Table 1 and Figure 1 that the optimized equilibrium C
X 3 3 3 Y contacts at the three theoretical levels are essentially linear (≈180), clearly indicating the electrostatically driven noncovalent interaction of halogen bonding which has been

well-validated in previous articles.10,56,60 All the predicted intermolecular distances are much less than the sums of vdW radii of the interacting atoms.99 Among the systems considered, the dimer C6F5I 3 3 3 Cl
exhibits the shortest intermolecular separations (about 2.8 Å), a reduction of approximately 25% of the sum of vdW radii of the I and Cl atoms, which suggests the strongest halogen bond in this dimer (vide infra). When compared to PBE, the hybrid functional B3LYP yields halogen bond lengths more close to MP2, especially for neutral systems. Taking the MP2 results as a reference, the average absolute deviations of the distances amount to 0.028 and 0.074 Å, respectively, for B3LYP and PBE. Notably, relative to C6F5I-containing systems, slightly longer intermolecular distances are observed for the complexes containing C2F3I. Moreover, the departure from the linearity of the contacts in the latter complexes appears larger. These indicate relatively stronger halogen bonds in the dimers of C6F5I. From Table 2, it is seen that BSSE-corrected interaction energies are computed to be within a range of
3.58 to
23.80 kcal/mol for MP2,
3.10 to
26.34 kcal/mol for B3LYP, and
3.82 to
30.98 kcal/mol for PBE. Evidently, the energetic data calculated with B3LYP appear more close to those of MP2; the mean absolute deviations of the corrected energies amount to 2.00 and 4.65 kcal/mol, respectively, for B3LYP and PBE. Table 2 also shows that the values of BSSE calculated with the two DFT functionals are much smaller than that with MP2. This is not surprising in view of the overcorrection of the counterpoint approach when using MP2 in the calculations of noncovalent interactions.56,63 In fact, the average absolute deviations of the uncorrected energies for B3LYP and PBE reduce to 0.80 and 2.86 kcal/mol, respectively. However, the strength order of halogen bonds in the examined complexes predicted with the three different methods remains unaltered. Moreover, both the B3LYP and PBE interaction energies correlate well with those of MP2; the linear correlation coefficients (R2) are all as high as 0.99. On the basis of these results, the B3LYP method, the most popular DFT functional at present for studying hydrogen bonding in gas and liquid phases,90
92 was utilized in the following calculations. Nevertheless, it should be noticed that, in comparison with B3LYP, the PBE functional performs better on the neutral halogen-bonded systems. For example, the uncorrected interaction energies of C2F3I 3 3 3 NH3 calculated with PBE and MP2 are approximately the same in magnitude (
7.56 kcal/mol vs
7.49 kcal/mol), while B3LYP produces a 4469

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

Table 3. Interaction Enthalpies and Free Energies in Gas Phase for the Dimers at B3LYP and MP2 Levels of Theorya B3LYP complexes

ΔH

ΔG

ΔH

ΔG

C2F3I 3 3 3 Cl
C2F3I 3 3 3 Br
C2F3I 3 3 3 I
C2F3I 3 3 3 NH3


26.60


19.71


25.06


18.08


23.80


17.11


23.28


16.45


20.44
4.66


13.99 2.65


19.88
6.16


13.27 0.36

C2F3I 3 3 3 OH2 C6F5I 3 3 3 Cl
C6F5I 3 3 3 Br


a

MP2

C6F5I 3 3 3 I
C6F5I 3 3 3 NH3 C6F5I 3 3 3 OH2


2.11

4.13


3.72

1.36


26.64


20.25


25.72


19.13


23.80


17.54


24.00


17.53


20.35


14.33


20.60


14.35


4.43

2.29


6.28


0.50


2.07

3.37


3.79

1.19

All values are in kilocalories per mole.

much smaller value of
6.06 kcal/mol. As indicated by the energetic data in Table 2, the interactions in charged systems belong to strong halogen bonds, whereas in neutral complexes the interactions should be classified as medium halogen bonds in which a larger dispersion contribution to the stability occurs. Namely, PBE gives better performance on moderate and weak halogen bonds, which has been substantiated in a recent benchmark study of neutral (weak) halogen bonding interactions.63 As expected, the strongest halogen bond is found in the system of C6F5I 3 3 3 Cl
, consistent with the shortest intermolecular distance in this case (vide supra). The strength of charged interactions decreases in the order Cl
> Br
> I
, which agrees with our previous calculated results of halogen bonds between bromobenzene and halide ions.57 By performing B3LYP/aug-ccpVDZ computations, the interaction energies of charged systems vary from
20.07 to
26.34 kcal/mol, while for neutral complexes the interaction energies are predicted to be within a range of
3.10 to
5.58 kcal/mol. Apparently, halogen bonds in these systems are comparable in strength to strong hydrogen bonds, reflecting very good halogen bond donors of iodo-perfluoroalkenes and -arenes. In fact, the chief breakthrough in the application of halogen bonding in solid-state supramolecular chemistry was based on the specific synthons involving I-PFCs,3,4 because of their effectiveness in producing strong halogen bonds as theoretically disclosed here. Table 3 collects calculated enthalpies and free energies of formation of the complexes in the gas phase at the B3LYP and MP2 levels of theory. As can be seen, the values of ΔH calculated with B3LYP are almost equal to corresponding interaction energies for charged systems, whereas the differences between ΔH and ΔE for neutral complexes amount to almost 1 kcal/mol. Particularly, the entropy contribution to the interaction energies appears to be substantial; at both theoretical levels the values of TΔS are estimated to be about
7 kcal/mol in all cases. Clearly, the entropy term disfavors the formation of halogen-bonded complexes. Similar to hydrogen bonding,90 the huge loss of entropy can be related to the transition of translational and rotational degrees of freedom of the monomers into vibrational ones when forming the dimers. All charged complexes are predicted to be stable at room temperature in the gas phase due to the negative ΔG values, while the neutral systems are unstable according to the positive ΔG values. This implies that most moderate and weak halogen bonds seem to be unfavorable

in the gas phase at room temperature. From Table 3, it is also seen that for charged systems the B3LYP-calculated enthalpies and free energies are close to those of MP2, while more negative values of ΔH and ΔG are predicted at the MP2 level for neutral complexes. This is not unexpected, because the interactions in charged complexes belong to strong halogen bonds in which the charge-transfer (CT) force plays an important role. In these systems the amount of CT from halide anions to I-PFCs is calculated to be in the 224
261 me range, considerably larger than that in neutral systems (see Table S1 of the Supporting Information). In fact, it has been generally recognized that the B3LYP method performs well on strong hydrogen bonds but describes weak dispersion interactions poorly.90,100 Results in Solution. As a result of the major contribution of electrostatic and charge-transfer interactions to halogen bonding,56,60 the polarity of the solvent should have a pronounced effect on the properties of this interaction. The key geometrical parameters optimized in the three solvents with different polarities (chloroform, acetone, and water) are summarized in Table 4. It is evident that halogen bonds in solution remain highly linear ( — (C
I 3 3 3 Y) ≈ 180), thus indicating the electrostatic nature of these interactions in mediums. The directionality of halogen bonding was frequently discovered in solid-state supramolecules and biomolecules such as proteins and nucleic acids.3,31,78 For all charged systems, halogen bond distances are elongated by about 0.13
0.36 Å under solvent effects, as graphically illustrated in Figure 2a. Therefore, these bonds are destabilized with the increase of the polarity of the solvent. As compared to the C2F3I-containing complexes, a greater elongation of intermolecular distances is observed for the systems of C6F5I, which mirrors the larger dipole moments of the latter dimers. However, opposite trends are encountered in the neutral dimers: halogen bond distances tend to shorten by 0.12
0.21 Å under solvent effects, so that the interactions are stabilized with the increasing polarity of the solvent (see Figure 2b). The neutral systems containing C2F3I (instead of C6F5I) undergo a more pronounced effect, as also reflected in the larger values of dipole moment of these dimers in solution. Thus, in solvent environments neutral and charged halogen bonds behave in a quite different way, which was also found in diverse hydrogen-bonded systems.90 Notably, relative to the distance changes from gas to chloroform and then to acetone, the corresponding changes from acetone to water are quite limited (see Figure 2). Therefore, very polar solvents should affect the geometry of halogen-bonded complexes marginally, as also disclosed in the strength of halogen bonds in solution (vide infra). It should be noticed that the shortening of neutral halogen bonds in solution is always accompanied by the concomitant increase of the C
X bond, while the elongation of charged ones is always associated with the decrease of the C
X bond. Such tendencies were also discovered for hydrogen bonds with various strength in solution.90 Consequently, the shortening of neutral halogen bonds may be attributable to nonadditivity/polarization effects as well in PCM calculations. To validate these findings, we also perform B3LYP computations in vacuum on the complexes of C2F5I with the addition of solvent molecules. The optimized geometries of neutral and charged systems are displayed in Figures S1 and S2 of the Supporting Information, respectively. It can be seen from Figure S1 that the presence of solvent molecules (acetone and water) causes shorter I 3 3 3 N/O intermolecular 4470

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

Table 4. Geometrical Parameters and Dipole Moments in Three Solvents for the Complexes Calculated with B3LYP/ aug-cc-pVDZ a chloroform

a

acetone

water

complexes

d(I 3 3 3 Y)

θ

μ

d(I 3 3 3 Y)

θ

μ

d(I 3 3 3 Y)

θ

μ

C2F3I 3 3 3 Cl
C2F3I 3 3 3 Br
C2F3I 3 3 3 I
C2F3I 3 3 3 NH3

2.978

178.0

12.31

3.052

178.0

13.71

3.077

178.0

14.14

3.136

178.4

10.44

3.200

178.3

11.73

3.224

178.3

12.13

3.363 2.777

178.3 178.0

9.20 6.67

3.421 2.725

178.3 178.1

10.41 7.29

3.448 2.715

178.3 178.1

10.83 7.43

C2F3I 3 3 3 OH2 C6F5I 3 3 3 Cl
C6F5I 3 3 3 Br


2.896

178.2

4.91

2.862

178.2

5.19

2.857

178.1

5.25

3.015

179.9

16.66

3.117

179.9

18.70

3.157

179.9

19.33

3.177

179.9

14.78

3.272

179.9

16.72

3.304

179.9

17.27

3.412

179.9

13.56

3.505

179.9

15.44

3.534

179.9

15.96

2.805

179.9

6.38

2.773

179.9

6.75

2.773

179.9

6.78

2.927

179.3

4.66

2.906

179.1

4.78

2.903

178.8

4.80

C6F5I 3 3 3 I
C6F5I 3 3 3 NH3 C6F5I 3 3 3 OH2

Distances are given in angstroms, angles in degrees, and dipole moments in Debye.

Figure 2. Intermolecular distances for charged complexes (a) and neutral complexes (b) in gas and liquid phases.

distances, which can be ascribed to the cooperative effects between halogen bonding and hydrogen bonding. For example, the I 3 3 3 N distances for C2F5I
NH3, C2F5I
NH3
H2O, and C2F5I
NH3
2H2O are computed to be 2.922, 2.835, and 2.755 Å, respectively, while in trimers and tetramers the H2O molecules are involved in hydrogen bonds (O
H 3 3 3 N) with the halogen bond accept NH3. Moreover, our NPA calculations also show that the magnitude of CT from electron donors to I-PFCs tends to increase with the addition of solvent molecules (see Table S1), which may account for the stability of halogen bonds in trimers and tetramers. However, the intermolecular I 3 3 3 X separations become larger for charged systems with the presence of solvent molecules (chloroform and water), as shown in Figure S2. In trimers and tetramers the CHCl3 and H2O molecules form halogen bonds (C
I 3 3 3 X) and hydrogen bonds (O
H 3 3 3 X) with halide ions, respectively. Particularly, CT from halide anions to solvent molecules also happens, and the amount of CT from the anions to I-PFCs decreases in trimers and tetramers, as suggested by the NPA analysis. This may lead to the destabilization of charged halogen bonds in solution. From Figures S1 and S2, it is also clear that all the I 3 3 3 Y contacts remain highly linear with the presence of solvent molecules ( — (C
I 3 3 3 Y) > 175), very compatible with the PCM results.

Table 5. Corrected Interaction Energies ΔEcp in Gas and Liquid Phases for the Dimers Calculated with B3LYP/aug-ccpVDZa dimers

gas

chloroform

acetone

water

C2F3I 3 3 3 Cl
C2F3I 3 3 3 Br
C2F3I 3 3 3 I



26.18


6.90


3.80


3.16


23.44


6.64


3.85


3.24


20.10


6.13


3.72


3.16


5.58


6.02


6.10


6.07


3.10


2.72


2.56


2.50


26.34
23.51


5.59
5.33


2.74
2.77


2.26
2.29


20.07


4.83


2.65


2.20


5.41


5.26


5.07


4.96


3.10


2.49


2.22


2.14

C2F3I 3 3 C2F3I 3 3 C6F5I 3 3 C6F5I 3 3

a

3 NH3 3 OH2
3 Cl
3 Br

C6F5I 3 3 3 I
C6F5I 3 3 3 NH3 C6F5I 3 3 3 OH2

All values are in kilocalories per mole. Interaction energies in different solvents are corrected by BSSE obtained in vacuum.

Calculated interaction energies for the systems under study in the three solvents are presented in Table 5 and shown graphically in Figure 3. As can be seen, the strength of charged interactions tends to significantly weaken under solvent effects, in agreement with the elongation of intermolecular distances as mentioned 4471

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

Table 7. Free Interaction Energies ΔG in Gas and Liquid Phases for the Studied Systems Calculated with B3LYP/augcc-pVDZ a complexes


C2F3I 3 3 3 Cl C2F3I 3 3 3 Br
C2F3I 3 3 3 I


Figure 3. Interaction energies for the complexes of C2F3I in gas and liquid phases.

Table 6. Solvation Free Energies ΔGsolv for the Studied Molecules in Different Solvents Calculated at the B3LYP Level of Theorya systems

chloroform

acetone

water

C2F3I 3 3 3 Cl
C2F3I 3 3 3 Br
C2F3I 3 3 3 I



36.88


47.43


46.52


34.84


44.68


43.46


32.99


42.12


40.68


0.81


3.53


0.56


2.29


5.43


2.73


36.64


48.65


47.52

3 Br C6F5I 3 3 3 I
C6F5I 3 3 3 NH3 C6F5I 3 3 3 OH2


34.63


45.88


44.31


32.84
0.71


43.32
3.76


41.48
0.08


2.58


6.34


3.04

Cl



56.90


68.71


70.41

Br



52.78


63.78


65.23

I



48.69


58.73


60.03

NH3


1.21


2.44


1.45

H2O


3.85


5.94


5.41

1.51 0.85

0.43
1.02

2.89 2.00

C2F3I 3 3 C2F3I 3 3 C6F5I 3 3 C6F5I 3 3

C2F3I C6F5I a

3 NH3 3 OH2
3 Cl


All values are in kilocalories per mole.

above. When comparing the results in gas phase and in water, the reduction of interaction energies of charged complexes amounts to more than 20 kcal/mol. The strength order (Cl
> Br
> I
) observed in the gas phase only reproduces in chloroform with much smaller energy gaps, whereas in acetone and water environments charged interactions becomes almost identical in strength (see Figure 3). Hence, very polar solvents have little influence on the interaction energies of halogen-bonded complexes, similar to the geometries of these systems in solution. It is worth mentioning that a more pronounced attenuation of charged halogen bonds is found for the complexes of C6F5I compared to C2F3I, which coincides with the trend of intermolecular distances of these charged systems in solution (vide supra). However, the neutral dimers behave somewhat complicated as shown in Figure 3: the interaction in C2F3I 3 3 3 NH3 becomes slightly stronger in solution, while halogen bonds in

a

gas

chloroform

acetone

water


19.71


3.04


0.70


0.55


17.11


2.52


0.28


0.07


13.99


1.64

0.35

0.63

C2F3I 3 3 C2F3I 3 3 C6F5I 3 3

3 NH3

2.65


0.30


0.71


1.19

3 OH2
3 Cl

4.13
20.25

2.34
2.68

2.37
1.01

2.08
1.20

C6F5I 3 3 C6F5I 3 3

3 Br
3I


17.54


2.08


0.46


0.46


14.33


1.17

0.26

0.38

C6F5I 3 3 C6F5I 3 3

3 NH3

2.29

0.10

0.15


0.18

3 OH2

3.37

1.95

2.15

1.90




All values are in kilocalories per mole.

other three systems appreciably weaken with the increase of the solvent polarity. The differences of interaction energies in gas and liquid phases for neutral systems are less than 1 kcal/mol. Previous study of halobenzene
formaldehyde complexes also revealed that the introduction of solvents (ether and water) destabilizes the systems by 0.2
0.9 kcal/mol and halogen bonds in the dimers appear comparable in strength in solution.59 In summary, solvents have a general destabilization effect on halogen-bonded systems; strong halogen bonds tend to significantly weaken in solution in contrast to moderate and weak ones; more polar solvents should affect halogen bond strength to a much less degree. The solvation free energies computed for the three solvents using the B3LYP/aug-cc-pVDZ method are reported in Table 6. It is evident that, for charged systems, the solvation energy enlarges (more negative) as the dielectric constant of the solvent increases. However, changes of the solvation energy are quite limited from acetone to water in relation to those from chloroform to acetone, consistent with the results of geometries and interaction energies of these dimers in solution (see above). Notably, the differences between the solvation energy of the charged complex on one hand and the sum of its subunits on the other are positive, ranging from 14 to 21 kcal/mol, which suggests that interaction energies of these systems are considerably smaller in solution compared to those in vacuum as demonstrated above. Here the positive contribution of ΔΔGsolv can be ascribed to the much larger solvation energies of halide anions since they are charged. Nonetheless, different behaviors are observed for neutral systems: the differences of the solvation energies between the complexes and the sum of respective monomers are negative for C2F3I 3 3 3 NH3 and C6F5I 3 3 3 NH3, within a range of
0.30 to
2.00 kcal/mol, while for C2F3I 3 3 3 OH2 and C6F5I 3 3 3 OH2 the corresponding differences are positive but less than 0.6 kcal/mol. As a consequence, slightly stabilizing effects of ΔΔGsolv occur in the formation of former two complexes in solution. It is noteworthy that, on account of the large size of the iodine atom and hydrophobic groups of PFCs, repulsive solvation effects are mostly found for C2F3I and C6F5I. This may lead to the negative contribution of ΔΔGsolv in the two systems. In Table 7 the ΔG values calculated in terms of eq 1 for the dimeric complexes under investigation in the three solvents are collected. It can be readily appreciated that the dimers containing 4472

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A Cl
and Br
as well as C2F3I 3 3 3 NH3 display negative ΔG values in three solvents, thus indicating that these systems are stable in solution. The two complexes of I
also show negative values in chloroform, but positive ΔG values are attained in acetone and water. In general, free energies of the formation of charged systems become progressively more positive with the polarity of the solvents, consistent with the weakening of halogen bonds in these systems. In all charged cases, the values of ΔGsoln decrease in the order Cl
> Br
> I
, which accords with the order of binding constants Ka (1.9  104, 3.8  103, and 7.6  102 M
1, respectively, for Cl
, Br
, and I
) measured by 19F NMR titrations in acetone.43 Particularly, calculated free energies of formation of the complexes of iodo-perfluorobenzene with the three anions in acetone correlate well with the experimentally determined log Ka (R2 = 0.99). However, it must be mentioned that the receptor used in experiments for binding of halide anions displays tridentate halogen bond donors.43 Free energies of binding calculated from the associate constants amount to
5.83,
4.88, and
3.93 kcal/mol, respectively, which are much larger (at least over three times) than the values of ΔG in acetone obtained according to eq 1. Clearly, cooperative effects of multiple halogen bond donors play a important role in achieving high-affinity binding of halide ions in solution. The associate constant of the receptor (2,3,4,5-tetrafluoro-6-iodobenzoic acid) that possesses monohalogen bond donor in binding of Cl
was measured to be 70 M
1 in acetone, and the free energy of binding was computed to be
2.52 kcal/mol.43 This value deviates to some extent from our calculated ΔG of
1.01 kcal/mol but compares well with that in chloroform (
2.68 kcal/mol), although different substituents are presented at the ortho position of the iodine atom (in our work iodo-pentafluorobenzene was selected as halogen bond donor). In addition, experimentally available binding constants for the complexes of iodo-perfluoroalkenes and -arenes with triethylamine appeared less than 3 M
1 in different organic solvents, and free energies of binding were evaluated to be very small ( Br
> I
) observed in the gas phase only reproduces in chloroform, whereas in more polar environments the charged interactions are almost identical in strength. On the basis of free energy results, several systems under study appear to be stable in solution. Particularly, calculated free energies of formation of the complexes correlate well with the experimentally measured log Ka. The solvation energies of charged complexes are always smaller than the sums of their corresponding subunits, thus indicating positive contribution of ΔΔGsolv to ΔG in solution. Nonetheless, slightly stabilizing effects of ΔΔGsolv occur in two neutral systems of C2F3I 3 3 3 NH3 and C6F5I 3 3 3 NH3. This behavior is quite different in relation to hydrogen bonding in which the ΔΔGsolv contribution to ΔG in solution is always positive and independent of the interaction strength.90,91 It must be pointed out that in this work the solvent effects were considered in an implicit way. In fact, the solvent molecules can influence the formation of halogen-bonded complexes to a large degree. Recently, concentration-dependent Br 3 3 3 O halogen bonds between carbon tetrabromide and several oxygen-containing organic solvents have been analyzed via UV
vis spectra and DFT calculations.101 Clearly, more detailed studies of the solvent effect on large systems containing halogen bonds with various strength should be performed explicitly, which are currently underway in our laboratory. ’ ASSOCIATED CONTENT

bS

Supporting Information. Figures showing optimized structures of the studied complexes of C2F5I with the presence of solvent molecules and a table listing the charge shifts in these systems. This material is available free of charge via the Internet at http://pubs.acs.org.

4473

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was financially supported by the Natural Science Foundation of Shanghai (Grant 11ZR1408700), the National Natural Science Foundation of China (Grant 20736002), the Program for Changjiang Scholars and Innovative Research Team in the University of China (Grant IRT0721), and the 111 Project of China (Grant B08021). ’ REFERENCES (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) Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Acc. Chem. Res. 2005, 38, 386. (4) Metrangolo, P.; Resnati, G.; Pilati, T.; Liantonio, R.; Meyer, F. J. Polym. Sci., Part A: Polym. Chem. 2007, 45, 1. (5) Metrangolo, P.; Meyer, F.; Pilati, T.; Resnati, G.; Terraneo, G. Angew. Chem., Int. Ed. 2008, 47, 6114. (6) Cavallo, G.; Metrangolo, P.; Pilati, T.; Resnati, G.; Sansotera, M.; Terraneo, G. Chem. Soc. Rev. 2010, 39, 3772. (7) Metrangolo, P.; Resnati, G. Science 2008, 321, 918. (8) Bertani, R.; Sgarbossa, P.; Venzo, A.; Lelj, F.; Amati, M.; Resnati, G.; Pilati, T.; Metrangolo, P.; Terraneo, G. Coord. Chem. Rev. 2010, 254, 677. (9) Legon, A. C. Phys. Chem. Chem. Phys. 2010, 12, 7736. (10) Politzer, P.; Murray, J. S.; Clark, T. Phys. Chem. Chem. Phys. 2010, 12, 7748. (11) Shirman, T.; Arad, T.; van der Boom, M. E. Angew. Chem., Int. Ed. 2009, 48, 1. (12) Laguna, A.; Lasanta, T.; Lopez-de-Luzuriage, J. M.; Monge, M.; Naumov, P.; Olmos, M. E. J. Am. Chem. Soc. 2009, 132, 1646. (13) Fourmigue, M. Curr. Opin. Solid State Mater. Sci. 2009, 13, 36. (14) Rissanen, K. CrystEngComm 2008, 10, 1107. (15) Brammer, L.; Espallargas, G. M.; Libri, S. CrystEngComm 2008, 10, 1712. (16) Politzer, P.; Lane, P.; Concha, M. C.; Ma, Y.; Murray, J. S. J. Mol. Model. 2007, 13, 305. (17) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. J. Mol. Model. 2007, 13, 291. (18) Murray, J. S.; Lane, P.; Politzer, P. J. Mol. Model. 2009, 15, 723. (19) Politzer, P.; Murray, J. S.; Concha, M. C. J. Mol. Model. 2007, 13, 643. (20) Murray, J. S.; Lane, P.; Clark, T.; Politzer, P. J. Mol. Model. 2007, 13, 1033. (21) Murray, J. S.; Lane, P.; Politzer, P. Int. J. Quantum Chem. 2007, 107, 2286. (22) Dey, A.; Metrangolo, P.; Pilati, T.; Resnati, G.; Terraneo, G.; Wlassics, I. J. Fluorine Chem. 2009, 130, 816. (23) Abate, A.; Biella, S.; Cavallo, G.; Meyer, F.; Neukirch, H.; Metrangolo, P.; Pilati, T.; Resnati, G.; Terraneo, G. J. Fluorine Chem. 2009, 130, 1171. (24) Casnati, A.; Cavallo, G.; Metrangolo, P.; Resnati, G.; Ugozzoli, F.; Ungoro, R. Chem.—Eur. J. 2009, 15, 7903. (25) Casnati, A.; Liantonio, R.; Metrangolo, P.; Resnati, G.; Ugozzoli, F.; Ungoro, R. Angew. Chem., Int. Ed. 2006, 45, 1915. (26) Metrangolo, P.; Carcenac, Y.; Lahtinen, M.; Pilati, T.; Rissanen, K.; Vij, A.; Resnati, G. Science 2009, 323, 1461. (27) Kato, R.; Imakubo, T.; Yamamoto, H.; Maeda, R.; Fujiwara, M.; Sawa, H. Mol. Cryst. Liq. Cryst. 2002, 380, 61. (28) Imakubo, T.; Sawa, H.; Kato, R. Synth. Met. 1997, 86, 1847.

ARTICLE

(29) Imakubo, T.; Miyake, A.; Sawa, H.; Kato, R. Synth. Met. 2001, 120, 927. (30) Imakubo, T.; Sawa, H.; Kato, R. Synth. Met. 1995, 73, 117. (31) Auffinger, P.; Hays, F. A.; Westhof, E.; Ho, P. S. Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 16789. (32) Voth, A. R.; Hays, F. A.; Ho., P. S. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 6188. (33) Voth, A. R.; Ho., P. S. Curr. Top. Med. Chem. 2007, 7, 1336. (34) Jiang, Y.; Alcaraz, A. A.; Chem, J. M.; Kobayashi, H.; Lu, Y. J.; Snyder, J. P. J. Med. Chem. 2006, 49, 1891. (35) Kraut, D. A.; Churchill, M. J.; Dawson, P. E.; Herschlag, D. ACS Chem. Biol. 2009, 4, 269. (36) Voth, A. R.; Khuu, P.; Oishi, K.; Ho, P. S. Nat. Chem. 2009, 1, 74. (37) Valadares, N. F.; Salum, L. B.; Polikarpov, I.; Andricopulo, A. D.; Garratt, R. C. J. Chem. Inf. Model. 2009, 49, 2606. (38) Lu, Y. X.; Wang, Y.; Zhu, W. L. Phys. Chem. Chem. Phys. 2010, 12, 4543. (39) Wasik, R.; Lebska, M.; Felczak, K.; Poznanski, J.; Shugar, D. J. Phys. Chem. B 2010, 114, 10601. (40) Hernandes, M. Z.; Cavalcanti, S. M. T.; Moreira, D. R. M.; de Azevedo, W. F.; Leite, A. C. L. Curr. Drug Targets 2010, 11, 303. (41) Matter, H.; Nazare, M.; Gussregen, S.; Will, D. W.; Schreuder, H.; Bauer, A.; Urmann, M.; Ritter, K.; Wagner, M.; Wehner, V. Angew. Chem., Int. Ed. 2009, 48, 2911. (42) Serpell, C. J.; Kilah, N. L.; Costa, P. J.; Felix, V.; Beer, P. D. Angew. Chem., Int. Ed. 2010, 49, 5322. (43) Sarwar, M. G.; Dragisic, B.; Sagoo, S.; Taylor, M. S. Angew. Chem., Int. Ed. 2010, 49, 1674. (44) Kilah, N. L.; Wise, M. D.; Serpell, C. J.; Thompson, A. L.; White, N. G.; Christensen, K. E.; Beer, P. D. J. Am. Chem. Soc. 2010, 132, 11893. (45) Cabot., R.; Hunter, C. A. Chem. Commun. (Cambridge, U. K.) 2009, 2005. (46) Libri, S.; Jasim, N. A.; Perutz, R. N.; Brammer, L. J. Am. Chem. Soc. 2008, 130, 7842. (47) Dimitrijevic, E.; Kvak, O.; Tayor, M. S. Chem. Commun. (Cambridge, U. K.) 2010, 9025. (48) Metrangolo, P.; Panzeri, W.; Recupero, F.; Resnati, G. J. Fluorine Chem. 2002, 114, 27. (49) Sarwar, M. G.; Dragisic, B.; Salsberg, L. J.; Gouliaras, C.; Taylor, M. S. J. Am. Chem. Soc. 2010, 132, 1646. (50) Cook, J. L.; Hunter, C. A.; Low, C. M. R.; Perez-Velasco, A.; Vinter, J. G. Angew. Chem., Int. Ed. 2007, 46, 3706. (51) Meyer, E. A.; Castellano, R. K.; Diederich, F. Angew. Chem., Int. Ed. 2003, 42, 1201. (52) Valerio, G.; Raos, G.; Meille, S. V.; Metrangolo, P.; Resnati, G. J. Phys. Chem A 2000, 104, 1617. (53) Karpfen, A. J. Phys. Chem. A 2000, 104, 6871. (54) Alkorta, I.; Rozas, J.; Elguero, J. J. Phys. Chem. A 1998, 102, 9278. (55) Wang, W. Z.; Wong, N.-B.; Zheng, W. X.; Tian, A. M. J. Phys. Chem. A 2004, 108, 1799. (56) 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. (57) Lu, Y. X.; Zou, J. W.; Wang, H. Q.; Yu, Q. S.; Zhang, H. X.; Jiang, Y. J. J. Phys. Chem. A 2007, 111, 10781. (58) Awwadi, F. F.; Willett, R. D.; Peterson, K. A.; Twamley, B. Chem.—Eur. J. 2006, 12, 8152. (59) Riley, K. E.; Merz, K. M. J. Phys. Chem. A 2007, 111,, 1688. (60) Riley, K. E.; Hobza, P. J. Chem. Theory Comput. 2008, 4, 232. (61) Wang, W. Z.; Hobza, P. J. Phys. Chem. A 2008, 112, 4114. (62) Shishkin, O. V. Chem. Phys. Lett. 2008, 458, 96. (63) Lu, Y. X.; Zou, J. W.; Fan, J. C.; Zhao, W. N.; Jiang, Y. J.; Yu, Q. S. J. Comput. Chem. 2009, 30, 725. (64) Hauchecorne, D.; Szostak, R.; Herrebout, W. A.; van der Veken, B. J. ChemPhysChem 2009, 10, 2105. (65) Li, Q. Z.; Wang, Y. L.; Liu, Z. B.; Li, W. Z.; Cheng, J. B.; Gong, B. A.; Sun, J. Z. Chem. Phys. Lett. 2009, 469, 48. 4474

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475

The Journal of Physical Chemistry A

ARTICLE

(66) Riley, K. E.; Murray, J. S.; Politer, P.; Concha, M. C.; Hobza, P. J. Chem. Theory Comput 2009, 5, 155. (67) Torii, H.; Yoshida, M. J. Comput. Chem. 2010, 31, 107. (68) Bilewicz, E.; Grabowski, S. J. Chem. Phys. Lett. 2006, 427, 51. (69) Bernal-Uruchurtu, M. I.; Hernandez-Lamoneda, R.; Janda, K. C. J. Phys. Chem. A 2009, 113, 5496. (70) Li, Q. Z.; Lin, Q. Q.; Li, W. Z.; Cheng, J. B.; Suo, J. Z. ChemPhysChem 2008, 9, 2265. (71) Alkorta, M.; Blanco, F.; Solimannejia, M.; Elguero, J. J. Phys. Chem. A 2008, 112, 10856. (72) Del Bene, J. E.; Alkorta, I.; Elguero, J. J. Phys. Chem. A 2010, 114, 8463. (73) An, X. L.; Jing, B.; Li, Q. Z. J. Phys. Chem. A 2010, 114, 6428. (74) Donald, K. J.; Wittmaack, B. K.; Crigger, C. J. Phys. Chem. A 2010, 114, 7213. (75) Wang, W. Z.; Zhang, Y.; Ji, B. M. J. Phys. Chem. A 2010, 114, 7257. (76) Amezaga, N. J. M.; Pamies, S. C.; Peruchena, N. M.; Sosa, G. L. J. Phys. Chem. A 2010, 114, 552. (77) Fan, H. Y.; Eliason, J. K.; Moliva, A. C. D.; Olson, J. L.; Flancher, S. M.; Gealy, M. W.; Ulness, D. J. J. Phys. Chem. A 2009, 113, 14052. (78) Lu, Y. X.; Shi, T.; Wang, Y.; Yang, H. Y.; Yan, Y. H.; Luo, X. M.; Jiang, H. L.; Zhu, W. L. J. Med. Chem. 2009, 52, 2854. (79) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (80) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (81) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (82) Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (83) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007. (84) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (85) Barone, V.; Cossi, M.; Tomasi, J. J. Chem. Phys. 1997, 107, 3210. (86) Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027. (87) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005, 105, 2999. (88) Abdalla, S.; Springborg, M. J. Phys. Chem. A 2010, 114, 5823. (89) Mammino, L.; Kabanda, M. M. J. Phys. Chem. A 2009, 113, 15064. (90) Aquino, A. J. A.; Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. J. Phys. Chem. A 2002, 106, 1862. (91) Scheiner, S.; Kar, T. J. Phys. Chem. B 2005, 109, 3681. (92) Lithoxoidou, A. T.; Bakalbassis, E. G. J. Phys. Chem. A 2005, 109, 366. (93) Tunega, D.; Haberhauer, G.; Gerzabek, M.; Lischka, H. J. Phys. Chem. 2000, 104, 6824. (94) Aquino, A. J. A.; Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. Phys. Chem. Chem. Phys. 2000, 2, 2845. (95) Aquino, A. J. A.; Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. Phys. Chem. Chem. Phys. 2001, 3, 1979. (96) Cieplak, P.; Kollman, P. A. J. Am. Chem. Soc. 1988, 110, 3734. (97) Pasalic, H.; Aquino, A. J. A.; Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Georg, H. C.; Moraes, T. F.; Coutinho, K.; Canuto, S.; Lischka, H. J. Comput. Chem. 2010, 31, 2046. (98) 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.; 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. (99) Bondi, A. J. Phys. Chem. 1964, 68, 441. (100) Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 415. (101) Zhou, W. S.; Han, J.; Jin, W. J. J. Phys. Chem. A 2009, 113, 10125. 4475

dx.doi.org/10.1021/jp111616x |J. Phys. Chem. A 2011, 115, 4467–4475