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Cooperativity between the hydrogen bonding andhalogen bonding in F3CX ··· NCH(CNH) ··· NCH(CNH)complexes (X=Cl, Br)Mohammad Solimannejad a , Masumeh Malekani a & Ibon Alkorta ba Quantum Chemistry Group, Department of Chemistry, Faculty of Sciences , ArakUniversity , Arak 38156-8-8349, Iranb Instituto de Química Médica (CSIC) , Juan de la Cierva 3, 28006 Madrid, SpainPublished online: 13 May 2011.

To cite this article: Mohammad Solimannejad , Masumeh Malekani & Ibon Alkorta (2011) Cooperativity between the hydrogenbonding and halogen bonding in F3CX ··· NCH(CNH) ··· NCH(CNH) complexes (X=Cl, Br), Molecular Physics: An InternationalJournal at the Interface Between Chemistry and Physics, 109:13, 1641-1648, DOI: 10.1080/00268976.2011.582050

To link to this article: http://dx.doi.org/10.1080/00268976.2011.582050

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Molecular PhysicsVol. 109, No. 13, 10 July 2011, 1641–1648

RESEARCH ARTICLE

Cooperativity between the hydrogen bonding and halogen bonding in

F3CX � � �NCH(CNH) � � �NCH(CNH) complexes (X^Cl, Br)

Mohammad Solimannejada*, Masumeh Malekania and Ibon Alkortab

aQuantum Chemistry Group, Department of Chemistry, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran;bInstituto de Quımica Medica (CSIC), Juan de la Cierva 3, 28006 Madrid, Spain

(Received 22 February 2011; final version received 4 April 2011)

MP2 calculations with the cc-pVTZ basis set were used to analyse the intermolecular interactions inF3CX � � �NCH(CNH) � � �NCH(CNH) triads (X¼Cl, Br), which are connected via hydrogen and halogen bonds.Molecular geometries, binding energies, and infrared spectra of the dyads and triads were investigated at theMP2/cc-pVTZ computational level. Particular attention was given to parameters such as the cooperativeenergies, cooperative dipole moments, and many-body interaction energies. All studied complexes, with thesimultaneous presence of a halogen bond and a hydrogen bond, show cooperativity with energy values rangingbetween �1.32 and �2.88 kJmol�1. The electronic properties of the complexes were analysed using the MolecularElectrostatic Potential (MEP), electron density shift maps and the parameters derived from the Atoms inMolecules (AIM) methodology.

Keywords: cooperativity; �-hole bonding; halogen bonding; hydrogen bonding

1. Introduction

Non-covalent interactions between molecules play a

very important role in supramolecular chemistry,

molecular biology, and materials science [1].

Although research has traditionally focused on the

most common hydrogen-bonded (HB) interactions,

more recently interest has grown in other types of

intermolecular interactions, such as halogen bonds,

and �-hole bonds.Halogen bonding describes a directional interaction

between covalently bound halogen atoms (X) and

Lewis bases (A). Several excellent reviews on halogen

bonding are now available [2,3] together with a recent

book [4].When a half-filled p orbital participates in the

formation of a covalent bond, its electron normally

tends to be localized in the internuclear region, thereby

diminishing the electronic density in the outer (non-

involved) lobe of that orbital. This electron-deficient

outer lobe of a half-filled p orbital involved in a

covalent bond is called a ‘�-hole’ [5]. Positive �-holeshave now been found computationally on the outer

surfaces of Group V, VI, and VII atoms in numerous

molecules [6–9]. Halogen bonding is a subset of �-holebonding. It has increasingly become recognized that

�-hole bonding, especially involving Group VII,

occurs widely in biological systems [6,7], and there isalso considerable interest in applying this concept incrystal engineering [10,11].

Recently, a few articles concerning the cooperativ-ity between hydrogen and halogen bonding and �-holebonds have been published [12–18]. In the presentwork, we study some simple structures that includehydrogen bonding and halogen bonding. We selectedtwo trifluoromethylhalo derivatives (F3CX, X¼Cl andBr) due to their implication in atmospheric chemistryand the greenhouse effect [19], and the HCN/HNCisomers, which are prototypes of linear hydrogen bonddonor/acceptors. We performed a theoretical study onthe eight F3CX� � �NCH(CNH)� � �NCH(CNH) triads(X¼Cl, Br) with the aim of investigating the effect ofhydrogen bonding on a halogen bond and thecooperativity between them. Additionally, to under-stand this cooperativity effect, we also performed amany-body interaction analysis of the title complexes.

2. Computational details

The structures of the monomers and the complexes wereoptimized and characterized by frequency computa-tions at the MP2/cc-pVTZ computational level. In avery recent paper, Riley et al. [20] pointed out that this

*Corresponding author. Email: m-solimannejad@araku.ac.ir

ISSN 0026–8976 print/ISSN 1362–3028 online

� 2011 Taylor & Francis

DOI: 10.1080/00268976.2011.582050

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method provides very good estimates of the geometriesand energies for non-covalent complexes. Calculationswere performed using the Gaussian 03 program [21].

The interaction energy was calculated as thedifference of the total energy of the complexes andthe sum of the isolated monomers in their minimaconfigurations. The full counterpoise (CP) method [22]was used to correct the interaction energy for theinherent basis set superposition error (BSSE).

The Atoms in Molecules (AIM) methodology [23]was used to analyse the electron density of the systemsconsidered at the MP2/cc-pVTZ computational level.Topological analysis was carried out with the AIMAllprogram [24]. The atomic charges were obtained byintegration of the electron density in the atomic basins.The value of the integrated Laplacian was used as ameasure of the quality of the integration. Values of thisparameter smaller than 1� 10�3 for all the atoms of asystem have been shown to provide a small averageerror in the total charge of the system [25].

The Molecular Electrostatic Potential (MEP) andtotal electron densities were evaluated with theGaussian 03 facilities. Electron density differencemaps were obtained as the difference of the electrondensity of the complex and the electron density of themonomers with their geometry within the complex.

3. Results and discussion

3.1. Geometries

The systems studied form stable triads with C3v

symmetry (Scheme 1). The bond angle between the

halogen, hydrogen and nitrogen (carbon) atomsinvolved in the interactions are 180�. The intermole-cular distances found for these systems are in the range3.07–3.23 A for X � � �C(N) halogen bonds and 1.91–2.31 A for hydrogen bonds (Table 1).

For the systems with halogen and hydrogen bonds,the X � � �C(N) and H � � �C(N) distances in the triadsare smaller than the corresponding values in the dyads,with differences in the range between 0.03–0.06 A and0.01–0.03 A, respectively. The values given are thedifferences in distances between trimers and dimers(Table 1). This trend can be interpreted as a cooper-ative effect of the hydrogen and halogen bonds.

3.2. Energies

The interaction energy of the dyads can be regarded asthe energy difference between the complex and themonomers, Ei(AB)¼EAB� (EAþEB), and the corre-sponding value for the triads (Ei(ABC)) is calculated ina similar way. Ei(AB, T) and Ei(BC, T) are theinteraction energies of the AB and BC dyads when theyare in the triad geometry. Table 2 presents theinteraction energy of the eight studied triads and therespective dyads. All results are corrected for BSSEusing the counterpoise method. As shown in Table 2,the binding energy of the title complexes ranges from�26.64 to �43.67 kJmol�1.

An energetic cooperativity parameter was calcu-lated using the following equation [26–28]:

ECoop ¼ Ei ABCð Þ � Ei ABð Þ � Ei BCð Þ, ð1Þ

where Ei(ABC) is the interaction energy of the trimer,and Ei(AB) and Ei(BC) are the interaction energies ofthe isolated dimers within their corresponding minimaconfiguration. In all cases studied, a favorablecooperativity is observed for the calculated triadswith values that range between �1.32 and�2.88 kJmol�1. The maximum and minimum energeticcooperativity values correspond to the most and leaststable complexes studied in the present work (Table 2).

Table 1. Intermolecular distances R of the investigated triads (T) and dyads. DR indicates the change relativeto the respective dyad.

Triad (A � � �B � � �C) R(AB, T) R(AB) DRAB R(BC, T) R(BC) DRBC

F3CBr � � �CNH � � �CNH 3.155 3.220 �0.065 2.025 2.051 �0.026F3CCl � � �CNH � � �CNH 3.232 3.286 �0.054 2.033 2.051 �0.018F3CBr � � �CNH � � �NCH 3.160 3.220 �0.060 1.916 1.939 �0.023F3CCl � � �CNH � � �NCH 3.234 3.286 �0.052 1.924 1.939 �0.015F3CBr � � �NCH � � �CNH 3.073 3.119 �0.046 2.304 2.330 �0.026F3CCl � � �NCH � � �CNH 3.097 3.140 �0.042 2.313 2.330 �0.016F3CBr � � �NCH � � �NCH 3.076 3.119 �0.043 2.171 2.197 �0.025F3CCl � � �NCH � � �NCH 3.104 3.140 �0.036 2.179 2.197 �0.017

X=Cl and Br

F3CX......NCH(CNH)......NCH(CNH)

RA–B RB–C

A B C

Scheme 1. Disposition of the monomers within thecomplexes.

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Linear correlations can be obtained between thecooperativity energy and the variation of the inter-molecular A–B distance from the dimer to the trimer(Figure 1). Thus, shortening of the intermoleculardistance provides the same physical information as theenergetic cooperativity.

Analysis of the energetic cooperativity indicatesthat the nature of the interacting halogen atommodulates the cooperativity effect and consequentlyan almost perfect linear correlation can be obtainedwhen the values of the energetic cooperativity arecompared for the triads of the same interactinghydrogen-bonded dimers (Figure 2).

3.3. Many-body interaction analysis

The two- and three-body contributions to thetotal binding energy are obtained by many-bodyanalysis [29,30]. The two-body terms (DEA–B, DEA–C

and DEB–C) can be calculated as the binding energies of

each molecular pair in the triad geometry minus the

energy sum of the monomers, all frozen in the triad

geometry. The three-body term DEA–B–C is calculated

as the total binding energy of the triad minus the

interaction energy of each pair of monomers, all frozen

in the triad geometry using the equation [31]

DEA�B�C ¼ Ei ABCð Þ � DEA�B � DEA�C � DEB�C:

ð2Þ

The total relaxation energy (ER) is defined as the

sum of the energies of the monomers frozen in the triad

geometry minus the sum of the energies of the

optimized monomers. Thus, the total binding energy

of the triad is obtained using the equation [31]

Ei ABCð Þ ¼DEA�BþDEA�CþDEB�CþDEA�B�CþER:

ð3Þ

y=32.87x–0.1005

R2=0.977

y=44.78x+0.0107

R2=0.9981

–3.5

–3

–2.5

–2

–1.5

–1

–0.5

0

–0.07 –0.065 –0.06 –0.055 –0.05 –0.045 –0.04 –0.035 –0.03

ECoop

Δ R

AB

Figure 1. Relationship between the cooperativity energy and the variation in the intermolecular A–B distance from the isolateddimer to the trimer. White and black squares represent the CF3Cl and CF3Br complexes, respectively.

Table 2. Interaction energies Ei (kJmol�1) of hydrogen and halogen bonding in the studied dyads (D) andtriads (T) at the MP2/cc-pVTZ level.

Triad (A � � �B � � �C) Ei(ABC) Ei(AB) Ei(BC) Ei(AB, T) Ei(BC, T) ECOOP

F3CBr � � �CNH � � �CNH �43.67 �9.40 �31.40 �8.31 �31.25 �2.88F3CCl � � �CNH � � �CNH �39.77 �6.46 �31.40 �5.58 �31.31 �1.91F3CBr � � �CNH � � �NCH �42.01 �9.40 �29.91 �8.59 �29.77 �2.70F3CCl � � �CNH � � �NCH �38.16 �6.46 �29.91 �5.82 �29.84 �1.79F3CBr � � �NCH � � �CNH �30.85 �9.09 �19.70 �8.74 �19.62 �2.06F3CCl � � �NCH � � �CNH �27.70 �6.57 �19.70 �6.32 �19.66 �1.43F3CBr � � �NCH � � �NCH �29.74 �9.09 �18.75 �8.80 �18.65 �1.90F3CCl � � �NCH � � �NCH �26.64 �6.57 �18.75 �6.39 �18.69 �1.32

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The results are presented in Table 3, where allenergies are corrected for BSSE. As seen from Table 3,the two-body interaction energy in some cases providesthe largest contribution (up to 80%) to the totalinteraction energy.

For all triads, the two-body and three-body inter-action energies DEA–B, DEB–C, and DEA–B–C areattractive, reinforcing the total interaction energy.For all triads, DEA–C is the smallest two-body inter-action term, which is consistent with the largestdistance between them. For all complexes, DEB–C islarger than DEA–B, which is consistent with the ideathat hydrogen bonding is more important than halogenbonding in the stability of the complexes studied.

The relaxation energy, ER, can be taken as ameasure of the degree of strain that drives thedistortion of the ternary system. As can be seen from

Table 3, the relaxation energy is positive, correspond-ing to the destabilization contribution to the totalinteraction energy of the triads. The relaxation energyis the largest for F3CBr � � �CNH � � �CNH and thesmallest for F3CCl � � �NCH � � �NCH, which is inagreement with the order of stability of these triads.

3.4. Vibrational analysis

Table 4 shows the frequency shift and intensity ratio ofthe HC(HN) stretching vibration of the triads anddyads relative to those of the isolated HCN(HNC)molecules. As expected, the formation of complexesresults in a red-shift and an intensity enhancement ofthe HC(HN) stretching vibration in the infraredspectra.

–3.00 –2.75 –2.50 –2.25 –2.00 –1.75–2.00

–1.75

–1.50

–1.25

F3CX···NCH···NCH

F3CX···NCH···CNH

F3CX···CNH···NCHE

Coo

p (F

3CC

l com

plex

es)

ECoop (F3CBr complexes)

Equation y=a+b*x

Adj. R–Square 0.99859

Value Standard error

D Intercept –0.20486 0.03104

D Slope 0.59021 0.01282 F3CX···CNH···CNH

Figure 2. Energetic cooperativity (kJmol�1) of the F3CBr triads versus the corresponding F3CCl triads.

Table 3. Decomposition of the interaction energy (kJmol�1) of the studied triads using thetriad geometry.

Triad (A � � �B � � �C) DEA–B DEB–C DEA–C DEA–B–C ER

F3CBr � � �CNH � � �CNH �9.60 �32.29 �0.68 �2.56 1.45F3CCl � � �CNH � � �CNH �6.69 �32.26 �0.48 �1.61 1.26F3CBr � � �CNH � � �NCH �9.63 �30.43 �0.61 �2.43 1.10F3CCl � � �CNH � � �NCH �6.67 �30.45 �0.42 �1.53 0.90F3CBr � � �NCH � � �CNH �9.22 �19.84 �0.60 �1.73 0.54F3CCl � � �NCH � � �CNH �6.73 �19.86 �0.43 �1.15 0.46F3CBr � � �NCH � � �NCH �9.23 �18.79 �0.54 �1.62 0.45F3CCl � � �NCH � � �NCH �6.74 �18.81 �0.39 �1.08 0.38

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In the present study, a cooperativity factor [32] isadopted to evaluate the cooperativity effect within thecomplexes studied. The cooperativity factor Ab iscalculated [13] as follows:

Ab ¼ D~�triad=D~�dyad: ð4Þ

The results for the HC(HN) stretching vibrationsare listed in Table 4. The cooperativity factor rangesfrom 1.09 to 1.21. The variation of the intensity of theH–X vibrations in the HB donor has been shown to berelated to the interaction energy of the complex [33].In the cases studied, the intensity ratio of theH–C(H–N) stretching vibration with respect to theisolated monomers, �triad and �dyad, shows large valuesfor all the triads and dyads considered. The differencebetween �triad and �dyad, D�, is greater than 1 for thebromine complexes and less that 1 for almost allchlorine complexes.

3.5. Dipole moments

Of the electronic properties considered, we havestudied the effect of triad formation on the dipolemoment value (Table 5). A cooperativity parameter

has been defined for dipole moment enhancement dueto complex formation,

Coop� dipole ¼ DDipole ABCð Þ � DDipole ABð Þ

� DDipole BCð Þ,ð5Þ

where the corresponding DDipole is calculated as thedifference between the dipole moment of the clusterand the vectorial sum of the isolated monomers in theirminimum-energy geometric configuration. The moduleof the variations of the dipole moments is shown inTable 5. Triads with large values of DDipole(ABC) arethose with energetic cooperativity. It should be notedthat the largest values of DDipole(ABC) are associatedwith the dipole moments of F3CX and HCN/HNC,pointing in the same direction within the triad. Thedipole cooperativity is in general small, between 0.30and 0.09Debye, being slightly larger for those systemsthat show more energetic cooperativity than for thosethat present less energetic cooperativity.

3.6. Electron density analysis

Table 6 shows the variation in electron density and theLaplacian of the electron density at two bond critical

Table 4. Frequency shifts D ~� (cm�1) and intensity ratios � of the H–C (H–N) stretching vibration in the studied triads and thecorresponding dyads relative to those in isolated HCN and HNC.a,b

Triad (A � � �B � � �C) D ~�triad D ~�dyad D ~� Ab �triad �dyad D�

F3CBr � � �CNH � � �CNH �352 �308 �43 1.14 6.65 5.19 1.46F3CCl � � �CNH � � �CNH �337 �308 �28 1.09 6.17 5.19 0.97F3CBr � � �CNH � � �NCH �284 �249 �35 1.14 5.76 4.57 1.18F3CCl � � �CNH � � �NCH �275 �249 �25 1.10 5.36 4.57 0.79F3CBr � � �NCH � � �CNH �133 �110 �22 1.21 6.68 5.16 1.52F3CCl � � �NCH � � �CNH �127 �110 �17 1.15 6.22 5.16 1.05F3CBr � � �NCH � � �NCH �108 �90 �18 1.20 6.51 5.08 1.42F3CCl � � �NCH � � �NCH �102 �90 �12 1.14 6.08 5.08 0.99

aD ~�¼D ~�triad�D ~�dyad, Ab¼D ~�triad/D ~�dyad and D�¼ �triad� �dyad.bThe ~� values of H–C and N–H in isolated HCN and HNC are 3476 and 3837 cm�1, respectively.

Table 5. Cooperativity of the dipole moments (Debye) in the investigated triads.

Triad (A � � �B � � �C) D(ABC) D(AB) D(BC) Coop-dipole

F3CBr � � �CNH � � �CNH 2.23 1.10 0.80 0.30F3CBr � � �CNH � � �NCH 1.87 1.10 0.55 0.22F3CBr � � �NCH � � �CNH 2.32 1.18 0.80 0.14F3CBr � � �NCH � � �NCH 1.95 1.18 0.55 0.12F3CCl � � �CNH � � �CNH 1.87 0.79 0.84 0.19F3CCl � � �CNH � � �NCH 1.57 0.79 0.60 0.15F3CCl � � �NCH � � �CNH 1.96 0.86 0.84 0.11F3CCl � � �NCH � � �NCH 1.65 0.86 0.60 0.09

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points located between molecules A, B, and C. An

enhancement in electron density and the Laplacian of

electron density at the bond critical point is observed

for all triads studied.

The calculated charges of the molecules in the

dyads and triads are shown in Table 7. In all cases, the

first electron donor molecule of the chain shows a

positive charge. For the triads, the central molecule

Figure 3. Electron density isosurfaces at �0.0005 a.u. Green and blue isosurfaces indicate a gain and a loss of electron density,respectively.

Table 7. Charge of the molecules (e) within the dyads and triads obtained using the AIM methodology.

Triad (A � � �B � � �C) A (ABC) B (ABC) C (ABC) A (AB) B (AB) B (BC) C (BC)

F3CBr � � �CNH � � �CNH �0.018 �0.021 0.039 �0.014 0.014 �0.036 0.036F3CBr � � �CNH � � �NCH �0.018 �0.010 0.028 �0.014 0.014 �0.026 0.026F3CBr � � �NCH � � �CNH �0.009 �0.013 0.021 �0.006 0.006 �0.020 0.020F3CBr � � �NCH � � �NCH �0.009 �0.006 0.015 �0.006 0.006 �0.014 0.014F3CCl � � �CNH � � �CNH �0.010 �0.028 0.038 �0.010 0.010 �0.036 0.036F3CCl � � �CNH � � �NCH �0.012 �0.015 0.027 �0.010 0.010 �0.026 0.026F3CCl � � �NCH � � �CNH �0.006 �0.015 0.021 �0.005 0.005 �0.020 0.020F3CCl � � �NCH � � �NCH �0.006 �0.008 0.014 �0.005 0.005 �0.014 0.014

Table 6. Changes in the AIM parameters of the triads relative to the respectivedyads.

Triad (A � � �B � � �C) D�AB Dr2AB D�BC Dr2

BC

F3CBr � � �CNH � � �CNH 0.0015 0.0047 0.0015 0.0010F3CCl � � �CNH � � �CNH 0.0010 0.0037 0.0011 0.0008F3CBr � � �CNH � � �NCH 0.0014 0.0043 0.0015 0.0022F3CCl � � �CNH � � �NCH 0.0009 0.0036 0.0009 0.0014F3CBr � � �NCH � � �CNH 0.0010 0.0042 0.0009 0.0016F3CCl � � �NCH � � �CNH 0.0007 0.0037 0.0005 0.0010F3CBr � � �NCH � � �NCH 0.0009 0.0039 0.0009 0.0026F3CCl � � �NCH � � �NCH 0.0006 0.0031 0.0006 0.0017

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of the cluster and the F3CX derivatives show a negative

charge, which, in six of the eight cases studied,

is more negative in the central molecule than

in F3CX. The two exceptions are the

F3CBr � � �CNH � � �NCH and F3CBr � � �NCH � � �NCH

clusters. A comparison of the charges of the dyads and

triads shows that the absolute values of the charge of

the molecules at both ends of the triads are larger than

the corresponding charge in the dyads, while the

central molecule shows a negative charge that is

smaller in absolute value than that observed for the

isolated BC dimer.The electron density difference maps (Figure 3)

of the triads show a loss of electron density at the

first electron donor end and a gain is observed for

F3CX, especially increasing the electron density of

the fluorine atoms. Along the linear complex, the

loss and gain of the electron density regions arealternated.

3.7. Molecular electrostatic potentials

The a priori analysis of the Molecular ElectrostaticPotential (MEP) of isolated molecules has long beenrecognized as a useful tool for elucidating the formationof weak complexes based on its sign andmagnitude [34].In fact, linear correlations have been found between theMEP and the binding energy for hydrogen-bondedcomplexes [35]. More recently, it has been used toexplain the cooperativity effect in hydrogen-bondedclusters [16].

The triads studied here can be considered as theinteraction of F3CX with electron donors. The value ofthe interacting negative MEP region of the electrondonor can provide clues as to the strength of theinteraction (Table 8, Figure 4). The values of theelectron donor regions of the dyads are always largerthan those of the corresponding monomers, whichindicates that the dyads are better electron donors and,as such, the interaction with F3CX should be stronger.

4. Conclusions

Ab initio calculations at the MP2/cc-pVTZ level havebeen used to explore the cooperativity inF3CX � � �NCH(CNH) � � �NCH(CNH) triads (X¼Cl,Br). The equilibrium structures, vibrational spectra,energetics, and cooperative effect on the properties ofthe complexes have been analysed.

Figure 4. Molecular electrostatic potential of the isolated monomers and some dimers. The red and green isocontourscorrespond to the �0.05 a.u. isosurfaces.

Table 8. Molecular electrostatic minima(a.u.) associated with the electron donormoiety of HCN and HNC and thecorresponding dyads.

System H extreme

HNC �0.075HCN �0.067HNC:HNC �0.097HCN:HNC �0.095HNC:HCN �0.085HCN:NCN �0.084

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All studied triads show energetic cooperativity.Linear correlations have been established between thecooperativity energy and the variation of the inter-molecular distance from the dimer to the trimer.In addition, linear correlations can be obtained whenthe values of the energetic cooperativity of the triadsare compared with the same interacting hydrogen-bonded dimers. These findings can help us to obtain abetter understanding of the cooperative role of halogenand hydrogen bonding in molecular recognition, crys-tal engineering and biological systems.

Supporting information

Cartesian coordination of optimized structures at theMP2/cc-pVTZ computational level.

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