Directionality of Halogen Bonds: An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study

Nasim Orangi [a], Kiamars Eskandari [a], *, Joseph C. R. Thacker[b] and Paul L. A.

Popelier[b]

[a] Department of Chemistry, Isfahan University of Technology, Isfahan, 84156-83111, Iran.

[b] Manchester Institute of Biotechnology (MIB), 131 Princess Street, M1 7DN, Great Britain, and

School of Chemistry, University of Manchester, Oxford Road, Manchester, M13 9PL Great Britain

1

Abstract

Interacting Quantum Atoms (IQA) and Interacting Quantum Fragments (IQF)

analyses are used to study F3C−X ⋯ N H 3 (X= Cl and Br) model complexes in order to

determine the origin of halogen bond directionality. IQA allows for the calculation of intra-

and interatomic classical and exchange-correlation energies, which can be used to determine

the energetic nature of the changes that occur when deviating from the preferred halogen

bond approach. The Relative Energy Gradient (REG) method is also applied to rank the IQA

energies and reveal which energy contributions best describe the total behavior of the system.

Indeed, all the pairwise interactions and atomic self-energies are angularly dependent; some

terms favor the linear structure and some tend toward nonlinear arrangements. For instance,

when the C−X … N angle is altered, the halogen-nitrogen interaction energy behaves like the

total energy of the system while the carbon-nitrogen interaction works against the total

energy profile. Furthermore, the REG values reveal that the contribution of the halogen-

nitrogen interaction to the total behavior of the system is small. Instead, the secondary

interactions (e.g., fluorine-nitrogen and carbon-hydrogen interactions) and atomic self-

energies are mainly responsible for the angular preference of these halogen bonds. Finally,

IQF calculations followed by REG analysis reveal the importance of the self-energy of the

fragments.

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1. Introduction

A halogen bond (indicated by R−X ⋯Y ) is a non-covalent interaction in which a

covalently bonded halogen atom (X) in a molecule (R−X) acts as an electrophile and

interacts with a nucleophilic site (Y) in the same or another molecule. [1, 2] Indeed, the

formation of halogen bonds is the result of an anisotropic electron distribution around the

halogen atom. The electron density around a covalently bonded halogen atom is not

spherically symmetric but is flattened. This anisotropic distribution of electron density around

these halogen atoms is mirrored in the molecular electrostatic potential (ESP) maps[3, 4], and in

plots of the Laplacian of the electron density, ∇2 ρ.[5]

One of the most important features of halogen bonds is their tendency toward

linearity. The halogen bonds are highly directional and the R−X−Y angle, θ, tends toward

180°.[6] This propensity is usually attributed to one or more of the following factors: an

enhancement in the orbital interactions, a reduction in the lone-pair repulsion and an increase

in the electrostatic attractions as θ approaches 180°.[6] Murray et al.[7] and Tsuzuki et al.[8]

ascribed the linearity of halogen bonds to the electrostatic interactions. However, using

symmetry adapted perturbation theory (SAPT)[9, 10], Adhockery and Scheiner[11] showed that

the exchange-repulsion energy component is mainly responsible for directionality of halogen

bonds and the electrostatic term is insensitive to angular distortion. In addition, SAPT(DFT)

analyses of Stone[12] indicated that the linearity of R−X−Y is not due to electrostatics but is

a consequence of exchange-repulsion. Huber and co-workers, used natural energy

decomposition analysis (NEDA)[13-16] to show that the directionality of halogen bonds is

mostly due to charge transfer and Pauli repulsion terms, while the electrostatic components

favor the perpendicular R−X−Y arrangement.[6] From their block localized wavefunction

3

(BLW) method, Mo et al.[17] showed that the linearity of halogen bonds is largely governed by

charge transfer interactions.

Amongst the many methods that have been used to partition the interaction energy,

the method called Interacting Quantum Atoms (IQA) provides an appealing approach to

study molecular systems at the atomistic level.[18] The (IQA) framework, developed by

Blanco and coworkers,[19-22] establishes a tool to decompose the total energy of the system

into intra-atomic and interatomic contributions. Indeed, IQA uses quantum topological atoms

and hence is a part of Quantum Chemical Topology (QCT), which is a collection of methods

that use a (gradient) vector field to partition chemical systems.[23, 24]

In the present work, the IQA scheme is applied to investigate the orientational

preference and directional features of the halogen bonds in the F3C−X ⋯ N H 3 (X= Cl and

Br) model complexes. Since IQA offers a large number of energy terms contributing to the

total energy of the complex, we used the Relative Energy Gradient (REG) method to rank

these components and find the term(s) that best describe the total behavior of the system.

Recently, the REG method has been successfully used to detect the most important energy

terms that describe the hydrogen bond in the water dimer[25], the cause of the fluorine gauche

effect[26], some SN2 model reactions[18], and catalytic effects in the peptide hydrolysis in HIV-

1 Protease[27]. Here the REG method will be used to analyze the angular behavior of IQA

terms and find those that control the directionality of halogen bonded complexes.

2. Theoretical Background

2.1. Interacting Quantum Atoms

The IQA approach partitions the total energy of a system into intra-atomic (self-

energy) and interatomic energy terms:[19, 20]

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Etotal=∑A

EIQA (A)=∑A

E selfIQA ( A )+ 1

2∑A∑A ≠ B

E∫ ¿IQA ( A ,B )(1)¿

Here, E selfIQA ( A ) is the internal atomic energy of atom A and contains all of the monoatomic

energy contributions. The self-energy can be partitioned as:

E selfIQA ( A )=T ( A)+V en (A )+V ee ( A )(2)

where T(A), V en( A), and V ee ( A ) are, respectively, the kinetic energy of the electrons, the

electron-nuclear and electron-electron potential energies in the atomic basin A. It is also

possible to define the atomic deformation energy as:

E¿ ( A )=[E selfIQA ( A )]complex−[ E self

IQA ( A ) ]fragment(3)

where E¿¿) is the change in the IQA self-energy of atom A when comparing the energy

between the atom in the complex and in its relevant isolated state.

E∫ ¿IQA ( A , B) ¿ is the interatomic interactions energy between atoms A and B and can be further

partitioned as:

E∫ ¿IQA ( A , B)=V nn (A , B)+V en( A, B)+V en(B, A)+V ee( A, B) ( A ≠ B) (4)¿

where V nn( A , B) characterizes the inter-nuclear repulsion between the nuclei of A and B,

V en( A ,B) and V en(B , A ) indicate the electron-nuclear interactions between the topological

atoms A and B, and finally, V ee( A , B) characterizes the interatomic electron–electron

potential energy. The V ee( A , B) energy component can be further partitioned as:

V ee( A , B)=V eeCoul( A , B)+V ee

xc(A , B)(5)

in which V eeCoul( A , B) and V ee

xc(A ,B) represent, respectively, the Coulombic and exchange-

correlation interaction energies between the electrons in atoms A and B. Einter ( A ,B) can also

be rewritten as a sum of classical, V cl( A , B) , and non-classical, V xc(A ,B), terms:

E∫ ¿IQA ( A , B)=V cl( A , B )+V xc(A ,B )(6)¿

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Here, V cl( A , B) is the sum of all the classical electrostatic energy terms between the atoms A

and B.

V cl ( A , B )=V nn ( A , B ) +V en ( A , B )+V en(B , A)+V eeCoul ( A , B )(7)

From a different point of view, V cl( A ,B) term can be divided into charge-transfer, V ct (A , B),

and polarization, V pol (A , B), with terms defined as[26]

V ct (A , B)=Q00( A)Q00(B)

r AB(8)

V pol(A ,B)=V cl( A , B)−V ct( A ,B)(9)

where Q00( A) and Q00(B) are the monopole moments of atoms A and B, respectively.

3. Computational Details

In the current work, we studied the halogen bonds in the complexes F3C−Br⋯ N H 3

and F3C−Cl⋯ N H3. Full geometry optimizations of these complexes at the MP2/aug-cc-

pVDZ level of theory indicated that the C−X−N angle, denoted θ, is 180° in the most

energetically stable structures. To investigate the origin of X-bond directionality in these

molecules, the θ angle has been chosen as the control coordinate and changed from θ=180°

(in the linear structure) to θ=90° in steps of 10 degrees. In all structures, the X ⋯ N distances

have been fixed at the optimized value of the linear geometries (2.97 and 3.04 Å for the

Br⋯ N and Cl⋯ N bonds, respectively), while all other geometric parameters were optimized.

All the geometries have been partially optimized at the MP2/aug-cc-pVDZ level. For the IQA

calculations, the wavefunctions were generated by B3LYP single-point calculations at the

MP2 geometries. The compatibility[28] between IQA and B3LYP ensures that the total

molecular energy obtained with the IQA terms (using equation 1) is very close to the original

energy calculated with GAUSSIAN09[29]. In the current work, the difference between IQA

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total energies and the original total energies, were smaller than 1.7 and 2.7 kJ mol -1 for

F3C−Br⋯ N H 3 and F3C−Cl⋯ N H3, respectively. These differences are due to the atomic

integration errors. All IQA terms were calculated by the AIMALL program.[30] The REG

analysis was performed by the ANANKE program on all V cl and V xc components and on

self-energy terms (E selfIQA ( A )). The variation in geometry is essential for the REG method to

work as it extracts chemical insight from a dynamic rather than static analysis.

4. Result and Discussion

4.1. IQA Analysis

As stated, halogen bonds are highly directional and the C−X−N angles tend toward

linearity. This is also the case for the molecules in the current work (i.e. F3C−Br⋯ N H 3 and

F3C−Cl⋯ N H3). The linear structures (with θ=180°) are energetically the most stable

geometries and the complexes become less stable as the C−X−N angle deviates from

linearity. To reveal the nature of halogen bonding at atomistic level, we first consider

interatomic and deformation energies in the global minimum (linear structure) of the

complexes. Pairwise atomic interactions between the atoms of F3C−X and the atoms of

N H3, in the global minimum of the complexes have been collected in the last columns of

Tables 1, 2 and Tables S1 and S2 of the Supporting Information. As indicated, bromine and

chlorine atoms show different behavior in their interactions with the hydrogens of ammonia:

Cl-H interactions are negative while Br-H ones are positive (Tables S1 and S2). It is also

worth noting that the interaction energies between the main interacting atoms (i.e., halogen

and nitrogen that are directly connected to each other to form a halogen bond) are not the

largest contributors. Instead, the largest attractive interactions correspond to the carbon-

nitrogen pair. Nonetheless, in both complexes the sum of interatomic interactions is negative

and plays a stabilizing role in the complex formation; the attractive terms (i.e. E∫ ¿IQA (C , N ) ¿,

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E¿ tIQA ( X , N ), E∫ ¿IQA ( F , H )¿ and also E∫ ¿IQ A (Cl, H )¿ in F3C−Cl⋯ N H3)) are large enough to

overcome the repulsive components (henceforth, we will use attractive and repulsive terms

respectively for negative and positive values of interatomic energies). The classical and

exchange-correlation parts of these interatomic interactions have also been summarized in

the last columns of Tables 1, 2, S1 and S2. As indicated, all the interatomic interactions (with

the exception of E∫ ¿IQA ( X , N )¿) are mainly classical in nature; about 99% of them come from the

classical components.

The situations for halogen-nitrogen interactions are different. In the bromine-nitrogen

interaction in the F3C−Br⋯ N H 3 complex, both the classical, V cl(Br ,N ), and exchange-

correlation, V xc(B r , N ) terms are negative and have almost equal contributions to E∫ ¿IQA ( Br , N )¿

. Dividing V cl(Br ,N ) into charge transfer and polarization terms (Eq 9), shows that this

interaction is dominated by the charge transfer. In contrast to the Br⋯ N bond, in the Cl⋯ N

interatomic interaction (in the F3C−Cl⋯ N H3) the classical term is repulsive (+10.7 kJ/mol)

and V xc (Cl , N ) is the only stabilizing component (-50.2 kJ/mol) in E∫ ¿IQA (Cl , N )¿. Indeed, the

repulsive nature of the classical component in the chlorine-nitrogen interaction arises from

the charge transfer term. Both chlorine and nitrogen atoms are negatively charged (-0.08e and

-1.16e for Cl and N, respectively) and hence the charge transfer term is positive.

Atomic self-energies also play a non-negligible role in the stabilization or

destabilization of a complex. When two fragments interact, the shapes of the interacting

atoms undergo a series of changes that may alter their self-energies. Using the atoms of the

isolated optimized fragments as references in equation 3, the intra-atomic deformation

energies of atoms in the complexes have been calculated. The atomic deformation energies

for the linear structure of F3C−Br⋯ N H 3 and F3C−Cl⋯ N H3 complexes are reported in

the last row of Table 3. The positive values of deformation energies of bromine, chlorine,

nitrogen and hydrogen atoms demonstrate that these atoms are destabilized when F3C−Br

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and F3C−Cl participate in a halogen bonding interaction with ammonia. Carbon and fluorine

atoms are stabilized during complex formation.

To find the origin of the directionality in the studied halogen bonds, the angular

dependence of IQA terms was considered. To this end, we performed a scan of θ from 180° to

90° in steps of 10°

. IQA analysis was then carried out on the resulting set of wave functions.

The interatomic interaction energies are summarized in Tables 1 and S1 (for F3C−Br⋯ N H 3

), 2 and S2 (for F3C−Cl⋯ N H 3). The results show that, for all θ angles, the interaction

energies between halogen-nitrogen, E∫ ¿IQA ( X , N )¿, carbon-nitrogen, E∫ ¿IQA (C , N ) ¿, and fluorine-

hydrogen(s), E∫ ¿IQA ( F , H )¿, are attractive. In all orientations, the largest attractive contribution

corresponds to the carbon-nitrogen pair and, interestingly, the contribution of the main pair

(i.e. the halogen-nitrogen interaction) is significantly smaller and plays a secondary role in

the stabilization of the structures.

In both complexes, E∫ ¿IQA ( X , N )¿ becomes less negative as the C−X−N angle deviates

from linearity. In other words, the interatomic Br−N and Cl−N interactions are more

favorable in the linear arrangements of their complexes. Figure 2 shows the variation of

V cl ( Br , N ) and V xc(Br , N) during angular distortion in the F3C−Br⋯ N H 3 complex. As

indicated, both V cl ( Br , N ) and V xc(Br , N) terms of E∫ ¿IQA ( Br , N )¿ favor the linear complex but

the classical term is more sensitive to this angular distortion. The variation of V ct (Br , N ) and

V pol (Br , N) with θ has also been depicted in Fig. 2. Both terms become less favorable as θ

distorts from linearity. However, since the atomic charge of Br and N remain almost constant,

the charge transfer is less sensitive to the angular distortion (the charges of the Br and N

atoms change from 0.098e and -1.160e in the linear structure to, respectively, 0.090e and -

1.140e in the perpendicular arrangement. Topological charges of all atoms have been

collected in Tables S3 and S4 of Supporting Information). Accordingly, the angular

9

dependence of V cl ( Br , N ) is mainly controlled by the polarization term, which changes from -

33.0 kJ/mol in θ=180° to -18.0 kJ/mol in θ=90°

.

The situation for chlorine-nitrogen interaction in the F3C−Cl⋯ N H3 complex is

different. In contrast to the bromine complex, the classical interaction between chlorine and

nitrogen is repulsive for all θ angles (Table 2). Since both chlorine and nitrogen atoms are

negatively charged, their charge transfer energy (that is, monopole-monopole interaction) is

positive. This term is large enough to overcome the stabilizing effect of the attractive

polarization component and make V cl (Cl , N ) positive. Nevertheless, the absolute value of the

exchange-correlation term, V xc (Cl , N ), is larger than V cl (Cl , N ), which makes E∫ ¿IQA (Cl , N )¿

negative. The angular dependence of E∫ ¿IQA (Cl , N )¿ and also its V cl (Cl , N ), V xc (Cl , N ),

V ct (Cl , N ) and V pol(Cl , N ) components are depicted in Figure 3. As indicated, the strongest

chlorine-nitrogen interaction corresponds to the linear arrangement and as θ decreases so

does the absolute value of E∫ ¿IQA (Cl , N )¿. Indeed, both V cl (Cl , N ) and V xc (Cl , N ) terms become

less favorable as θ decreases but the classical term (and its polarization component) is more

sensitive to the angular distortion.

From a comparison between Fig. 2 and 3 it is evident that the interatomic bromine-

nitrogen interaction is significantly stronger than that of chlorine-nitrogen. However, the

angular profile of E∫ ¿IQA ( Br , N )¿ is slightly shallower than that of E∫ ¿IQA (Cl , N ). ¿ In other words, the

chlorine-nitrogen interatomic interaction is more angularly dependent than that of bromine-

nitrogen. This is also the case for the classical part of these interatomic interactions and

V cl (Cl , N ) is more sensitive to the angular distortion than V cl ( Br , N ). As stated, the V xc

component of bromine-nitrogen and chlorine-nitrogen interactions are almost angle-

independent and the angular dependences of E∫ ¿IQA ( Br , N )¿ and E∫ ¿IQA (Cl , N )¿ are determined largely

by their classical components. It seems that the angular behavior of bromine-nitrogen and

chlorine-nitrogen interactions are in line with the trends in their halogen σ -hole (the region of

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positive electrostatic potentials on the surfaces of halogens[31, 32]) size and magnitude. As

indicated by Kolar and co-workers[33, 34], both the σ -hole size (i.e. the spatial range of positive

ESP) and magnitude (i.e. the maximum of ESP) increase with the increasing atomic number

of the halogen. Our results also show that the chlorine σ -hole size is smaller than that of

bromine (that is, the sign of ESP on the chlorine surface changes at smaller angles in

comparison to bromine). This means that the bromine-nitrogen interaction is favorable in a

much broader angular region and is hence less sensitive to the angular changes (in

comparison to the chlorine-nitrogen interaction). On the other hand, there is a relation

between the magnitude of the σ -hole and halogen-nitrogen interaction energy; the σ -hole

magnitude in the bromine complex is greater than in the chlorine one, and the bromine-

nitrogen interaction is stronger than the chlorine-nitrogen. Nonetheless, it should be

emphasized that the σ -hole concept does not provide a complete explanation for these

interatomic interactions. For instance, in spite of the opposite sign of ESP on the surfaces of

nitrogen and chlorine, the V cl (Cl , N ) interaction is repulsive. It is also worth noting that the

bond directionalities in the complexes cannot be explained merely by the interatomic

halogen-nitrogen interactions. Although the interatomic chlorine-nitrogen interaction is more

sensitive to the angle than the bromine-nitrogen one, the tendency toward linearity is higher

for bromine-containing molecules than chlorine ones (see reference [34] and references

therein).

Unlike the halogen-nitrogen interatomic interactions, other attractive interactions (i.e.

E∫ ¿IQA (C , N ) ¿ and E∫ ¿IQA ( F , H )¿ in both complexes and also the chlorine-hydrogens interaction,

E∫ ¿IQA (Cl , H ) ¿, in the F3C−Cl⋯ N H3 complex) favor the non-linear arrangement. When the

geometry of halogen-bonded complexes varies from linear to perpendicular, the absolute

values of E∫ ¿IQA (C , N ) ¿, E∫ ¿IQA ( F , H )¿ and E∫ ¿IQA (Cl , H ) ¿ increase (see Tables 1, 2, S1 and S2). These

interactions are negative for all the C−X−N angles and mainly classical in nature (about

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99% of E∫ ¿IQA (C , N ) ¿, E∫ ¿IQA ( F , H )¿ and E∫ ¿IQA (Cl , H ) ¿ comes from their classical components). On the

other hand, most of the repulsive interatomic interactions (i.e. carbon-hydrogen(s) and

nitrogen-fluorine(s) interactions) favor the linear arrangement of the complexes. As indicated

in Tables S1 and S2, the repulsion in these pairs increases as θ decreases. The bromine-

hydrogen(s) interaction in the F3C−Br⋯ N H 3 complex is also repulsive; however, it favors

the nonlinear structures (Table S1).

Atomic self-energies are also affected by the angular distortions. In both complexes,

as the θ angle changes from 180° to 90°

, the carbon, fluorine and nitrogen atoms become less

stable while the hydrogens become more stable. In other words, E selfIQA (C ), E self

IQA ( F ), E selfIQA ( N )

favor the linear arrangements. The largest destabilization corresponds to E selfIQA (C ). Bromine

and chlorine self-energies show different behaviors: Br is destabilized while Cl is stabilized

as θ deviates from linearity. In spite of that, in both complexes the total atomic self-energies

(i.e. ∑AE self

IQA ( A ), sums over all atoms in the complexes) favor the near-linear arrangements

(Figure 4).

Finally, it should be noted that although the secondary interatomic interactions are

highly angularly dependent, they work in opposite ways and, to a large extent, cancel each

other out. For instance, one can obtain the total interactions between CF3 group and NH3

molecule by adding the fluorines-nitrogen, fluorines-hydrogens, carbon-nitrogen, and carbon-

hydrogens interatomic energies together. Due to the opposite signs of these interactions, the

total CF3-NH3 interaction energy is small. Furthermore, unlike the individual interatomic

interactions, the total interaction between CF3 and NH3 groups is almost angularly

independent. For example, in the F3CBr-NH3 complex, the total classical CF3-NH3 interaction

changes from -1.4 kJ mol−1in the linear structure to -2.9 kJ mol−1 in the perpendicular (θ=90°

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) structure. This change amounts to only 1.5 kJ mol−1, and is significantly smaller than the

corresponding difference in the Br-NH3 complex, where it is about 11.6 kJ mol−1.

The IQA scheme can be generalized by aggregation of atoms into groups or

fragments. This generalization is usually referred to as the Interacting Quantum Fragment

(IQF) analysis. [35, 36] Equations (1) – (9) are still valid, but A and B now indicate fragments

instead of atoms. Here, we used IQF analysis to obtain the total interactions between the

F3CX and NH3 fragments. The values of the inter-fragment interactions, their classical and

exchange-correlation components, and deformation energies of the fragments have been

summarized in Tables S5 and S6 of the Supporting Information. As indicated, the inter-

fragment interaction and their components play secondary roles in the bond directionalities.

Indeed, the most considerable angular changes correspond to the self-energies of the

fragments that favor the linear geometry.

4.2. The REG Analysis

As indicated in the previous section, there are different IQA energetic terms that

affect the total energy profiles and directional features of the complexes. The REG method

(explained in detail elsewhere[25]) proposed a systematic procedure to find the relative

importance of each energy term. Indeed, REG compares the behavior of the total energy

changes of the complex with IQA energy contributions and ranks them.

Figure 5 shows the total energy profiles of C F3 Br …N H 3 and C F3Cl …N H 3

complexes as a function of the C−X−N angle θ, which varies from 90° to 270°

. In both

complexes, the energy curve is symmetric around the minimum point that appears at θ=180°.

Therefore, it is possible to dissect these energy profiles into two segments or barriers:

barrier 1 at the left of the energy minimum and barrier 2 at the right of it. In addition, in the

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C F3 Br⋯ N H 3 profile, two maxima appeared at θ=100° and θ=260°

, and hence two extra

barriers (barrier 3 and barrier 4 in Figure 5) are observed, one from θ=100° to θ=90°

and

the other from θ=260° to θ=270°

. Since the energy curves are symmetric, we only focus on

the barriers at the left of the minimum (i.e. barrier 1 and barrier 3)

Let us consider all possible point along a barrier and label them with the control

coordinate s. Since the IQA terms are additive, the total energy of the system at s, Etotal (s ), is

recovered by:[25]

Etotal (s )=∑i=1

N

E i ( s )(10)

where the subscript i indicates the IQA energy term and N is the total number of energy

contributions. When the relationship between Etotal and Ei is linear, one can write:

Ei (s )=mREG ,i ∙ Etotal (s )+c i(11)

for every energy term i. Here, mREG , i is the REG value, which can be estimated using the

ordinary least-squares linear regression analysis.[25] Finally, the linear relationship between

Etotal and Ei, which is essential to obtain valid REG values, can be evaluated by the estimation

of Pearson correlation coefficients, Ri, one for each energy contribution.

The REG and Ri values for barrier 1 (100° ≤ θ ≤180° ) in the C F3 Br⋯ N H3 complex

have been summarized in Table 4. The IQA terms with positive and negative REG values

contribute, respectively, to stabilizing and destabilizing the linear structure with respect to the

energy of barrier 1. The largest positive REG corresponds to the classical interaction

between F3 and N6 atoms (see Figure 1 for atom numbering). This means that the

V cl(F 3 , N 6) term (with REG value of 2.14) is the term that most contributes to the barrier 1

behavior. The positive value of REG shows that V cl(F 3 , N 6) and the total energy have the

same sign. In other words, V cl(F 3 , N 6) works in the same direction as barrier 1 and thus

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favors the linear structure of C F3 Br⋯ N H 3. It should be also noted that the REG of the

polarization part of V cl(F 3 , N 6) is negative and works against the barrier but is compensated

by the charge transfer energy that stabilizes the linear structure (i.e. its REG is positive). The

second, third and fourth largest contributors in barrier 1 are E selfIQA (C ), V cl (C 1 , H 7 ),

V cl (C 1 , H 8 ) with REG values of 1.49, 1.20 and 1.17, respectively. It is also worth noting

that, although the V cl ( Br , N ) and V xc (Br , N) terms of E∫ ¿IQA ( Br , N )¿ favor the linear structure,

their REG values are very small and hence, have a negligible contribution in the formation of

barrier 1. On the other hand, V cl(C 1 , N 6), V cl ( F 3 , H 7 ), V cl ( F 3 , H 8 ) and V c l (F 3 , H 9 ) with

the largest negative REG value of -3.30, -0.79, -0.74 and -0.42, respectively, work against the

barrier 1 and most favor the non-linear arrangements (Table 4). The REG values of the

charge transfer part of these interatomic interactions are negative while those of their

polarization terms (with the exception of V cl ( F 3 , H 9 )) are positive and stabilize the linear

structures.

Table 5 shows the REG values for the barrier 3 (θ ≤ 100° ) in the C F3 Br …N H 3

complex. As indicated, the classical carbon-nitrogen interaction,V cl (C 1 , N6 ) , with a REG

value of 77.06 most contributes to this barrier. The second, third and fourth largest

contributors to this barrier are V cl(F4 , H 7), V cl(F4 , H 8) and V cl(F4 , H 9) with REG values of

33.42, 26.26 and 19.83, respectively. These highest ranked IQA terms behave in the same

direction as this barrier and prefer perpendicular arrangements. In all these terms, the charge-

transfer contributions play a dominant role and the polarization terms have smaller positive

REG values. Entries at the bottom end of Table 5 represent energy terms that work in the

opposite direction to the total energy. The V cl(F4 , N6) component has the largest negative

REG with a value of -84.21 and favors the structure of 100° over the perpendicular one.

15

Table 6 indicates the REG values of the energetic terms of barrier 1 (90°≤ θ ≤180°) in

the C F3Cl⋯ N H 3 complex. The classical part of the fluorine-nitrogen interaction

, V cl ( F 9 , N 3 ) , with the highest REG value (4.62) is the strongest contributor to the barrier 1,

followed by V cl(C 1 , H 4 ), V c l(C 1 , H 5) and V c l(C 1 , H 6) components. Indeed, these

repulsion interactions work in the same direction as barrier 1 and favor the linear

arrangement. The REG values of the polarization and charge transfer parts of the relevant

interactions (with the exception of the polarization part of V cl ( F 9 , N 3 ) are positive and work

in the same direction as barrier 1 but the charge transfer REG values are larger and play a

dominant role. The REG of V cl(Cl , N ), and V xc(Cl , N) terms are positive and favor the linear

arrangement but they are very small. Indeed, although Cl−N interaction is the primary

interaction in this complex, it plays a small role in the stabilization of the linear structure.

Also, at the bottom of Table 6, there are a number of terms with the largest negative values

including V cl(C 1 , N 3), V cl(F 9 , H 4), V c l(F 9 , H 5) and V c l(F 9 , H 6) components that

work against the barrier 1 and favor the non-linear form of the complex. The charge transfer

contributions are found as the dominant destabilizing terms (with the largest negative REG

values) in these interatomic interactions.

We also performed a REG analysis on the IQF energy components of barrier 1 in the

C F3 Br …N H 3 and C F3Cl …N H 3 complexes. The REG values for the classical and

exchange-correlation inter-fragment interactions, and for the self-energies of the fragments,

are, respectively, 0.23, 0.06, and 0.86 in the C F3 Br …N H 3 complex and 0.29, -0.51, and

1.46 in the C F3Cl …N H3 complex. These values show that the self-energy of the fragments

plays the dominant role in the stabilization of the linear structure, followed by the classical

inter-fragment interactions. The exchange-correlation inter-fragment interaction favors the

non-linear structure of C F3Cl …N H 3, while it plays a minor role in the stabilization of

linear C F3 Br …N H 3.

16

5. Conclusion

To find the origin of halogen bond directionality at atomic level, the IQA method was

used to decompose the energy profile of halogen bonded complexes into intra-atomic and

interatomic energy contributions. We also used the REG method to rank the IQA energy

terms and find the ones that best describe the behavior of the total system. Although the total

electrostatic interaction is almost insensitive to angular distortion, the interatomic

electrostatic interactions are angularly dependent. The REG analyses of IQA energy

components show that the interatomic electrostatic interactions play important roles in the

bond directionality of halogen bonds. However, they are hidden in the different interatomic

interactions that change in opposite ways, and cancel each other out as the halogen bond

angle varies. Some interatomic interactions (e.g. carbon-hydrogen(s) and fluorine(s)-nitrogen

interactions) favor the linear arrangement of the complexes, while others (e.g., carbon-

nitrogen and fluorine-hydrogen(s) interactions) are more favorable in the non-linear

arrangements. A remarkable point here is that the exchange-correlation components of these

interatomic interactions are almost angularly independent and classical electrostatic

interactions determine the angular behavior of these interatomic interactions. It is also worth

noting that the interaction between halogen and nitrogen (that are connected directly to form

a halogen bond) play a minor role in the directionality of halogen bonds. Instead, the

secondary interactions (e.g., fluorine-nitrogen, carbon-hydrogen interactions) and also atomic

self-energies are the most important participants. Furthermore, an analysis at the level of

atomic groups rather than individual atoms (called IQF) indicates that the classical

electrostatic and exchange-correlation inter-fragment interactions play small roles in the bond

directionality. According to the IQF point of view, the self-energy of the fragments is mainly

responsible for the directionality of halogen bonds.

17

References

[1] M. H. Kolar, P. Hobza, Chem. Rev. 2016, 116, 5155-5187.[2] P. Metrangolo, G. Resnati, Halogen bonding: fundamentals and applications, Springer, Berlin, 2008.[3] T. Clark, M. Hennemann, J. S. Murray, P. Politzer, J. Mol. Model. 2007, 13, 291-296.[4] T. Clark, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2013, 3, 13-20.[5] K. Eskandari, H. Zariny, Chem. Phys. Lett. 2010, 492, 9-13.[6] S. M. Huber, J. D. Scanlon, E. Jimenez-Izal, J. M. Ugalde, I. Infante, Phys. Chem. Chem. Phys. 2013, 15, 10350-10357.[7] Z. P. Shields, J. S. Murray, P. Politzer, Int. J. Quantum Chem. 2010, 110, 2823-2832.[8] S. Tsuzuki, A. Wakisaka, T. Ono, T. Sonoda, Chem. Eur. J. 2012, 18, 951-960.[9] R. Moszynski, P. E. Wormer, B. Jeziorski, A. van der Avoird, J. Chem. Phys. 1995, 103, 8058-8074.[10] S. Scheiner, Molecular interactions. From van der Waals to strongly bound complexes, Wiley Press, 1997.[11] U. Adhikari, S. Scheiner, Chem. Phys. Lett. 2012, 532, 31-35.[12] A. J. Stone, J. Am. Chem. Soc. 2013, 135, 7005-7009.[13] E. D. Glendening, A. Streitwieser, J. Chem. Phys. 1994, 100, 2900-2909.[14] E. D. Glendening, J. Am. Chem. Soc. 1996, 118, 2473-2482.[15] G. K. Schenter, E. D. Glendening, J. Phys. Chem. 1996, 100, 17152-17156.[16] E. D. Glendening, J. Phys. Chem. A. 2005, 109, 11936-11940.[17] C. Wang, L. Guan, D. Danovich, S. Shaik, Y. Mo, J. Comput. Chem. 2016, 37, 34-45.[18] I. Alkorta, J. C. R. Thacker, P. L. A. Popelier, J. Comput. Chem. 2018, 39, 546-556.[19] A. Martín Pendas, E. Francisco, M. Blanco, J. Comput. Chem. 2005, 26, 344-351.[20] M. Blanco, A. Martín Pendas, E. Francisco, J. Chem. Theory Comput. 2005, 1, 1096-1109.[21] E. Francisco, A. Martín Pendas, M. Blanco, J. Chem. Theory Comput. 2006, 2, 90-102.[22] D. Tiana, E. Francisco, M. Blanco, P. Macchi, A. Sironi, A. Martín Pendas, J. Chem. Theory Comput. 2010, 6, 1064-1074.[23] P. L. A. Popelier in Quantum chemical topology: on bonds and potentials,Vol. 115, Springer, 2005,pp.1-56.[24] B. Silvi, M. E. Alikhani, C. Lepetit, R. Chauvin in Topological Approaches of the Bonding in Conceptual Chemistry,Vol. 22, Springer, 2016,pp.1-20.[25] J. C. R. Thacker, P. L. A. Popelier, Theor. Chem. Acc. 2017, 136, 86.[26] J. C. R. Thacker, P. L. A. Popelier, J. Phys. Chem. A. 2018, 122, 1439-1450.[27] J. C. R. Thacker, M. Vincent, P. L. A. Popelier, Chem. Eur. J. 2018, 24, 11200–11210.[28] P. I. Maxwell, Á. Martín Pendas, P. L. A. Popelier, Phys. Chem. Chem. Phys. 2016, 18, 20986-21000.[29] Gaussian 09, revision A. 2, M. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. Petersson, Gaussian. Inc, Wallingford CT, 2009.[30] AIMAll (Version 14.11. 23), T. A. Keith, 2014.[31] J. S. Murray, P. Lane, P. Politzer, J. Mol. Model. 2009, 15, 723-729.[32] P. Politzer, P. Lane, M. C. Concha, Y. Ma, J. S. Murray, J. Mol. Model. 2007, 13, 305-311.[33] M. Kolar, J. Hostaš, P. Hobza, Phys. Chem. Chem. Phys. 2014, 16, 9987-9996.[34] M. Kolar, J. Hostaš, P. Hobza, Phys. Chem. Chem. Phys. 2015, 17, 23279-23280.[35] A. M. Pendas, E. Francisco, M. Blanco, Faraday Discuss. 2007, 135, 423-438.[36] A. M. Pendas, M. A. Blanco, E. Francisco, J. Comput. Chem. 2007, 28, 161-184.

18

Figure 1. Two views of the configuration of the (a) C F3 Br …N H 3 and (b) C F3Cl …N H3 complexes, with atoms marked by numerical labels used throughout this article.

19

Figure 2. The variation of E∫ ¿IQA ( Br , N )¿ and its classical and quantum contributions with θ (in degrees) in F3C−Br⋯ N H 3 complex.

20

Fig3. The variation of E∫ ¿IQA (Cl , N )¿ and its classical and quantum contributions with θ (in degrees) in F3C−Cl⋯ N H3 complex.

21

Fig 4. The variation of total atomic self-energy of a) F3C−Br⋯ N H 3 and b) F3C−Cl⋯ N H3 with C−X−N angle, θ. Energy values are in atomic units.

22

Fig 5. Total energy profile of the C F3 Br …N H 3 and C F3Cl …N H 3 complexes as the C−X−N angle changes. The translated energy is defined as ETotal

translated (θ j )=ETotal (θ j )−Etotal, where j = 1, 2, …, M.

23

Table 1. Bromine-nitrogen and carbon-nitrogen interatomic interaction energies and their components (in kJ/mol) in different θ angles (in degree) in the complex of F3C−Br⋯ N H 3. The IQA values in bold correspond to the global minimum structure

F3C−Br⋯ N H 3 90 100 110 120 130 140 150 160 170 180(global)

E∫ ¿IQA (Br , N)¿

-135.25

-133.99

-137.54

-138.09

-139.73

-144.67

-149.64

-155.02

-159.62 -159.05

V xc -69.43 -69.10 -69.67 -69.98 -70.45 -70.92 -71.49 -72.02 -72.58 -72.90

V cl -65.82 -64.90 -67.87 -68.11 -69.28 -73.76 -78.15 -83.00 -87.04 -86.16

V ct -47.85 -48.15 -49.74 -50.67 -51.42 -52.07 -52.11 -52.92 -53.05 -53.10

V pol -17.97 -16.75 -18.14 -17.44 -17.86 -21.69 -26.04 -30.08 -33.99 -32.97

E∫ ¿IQA (C , N )¿

-710.36

-652.52

-611.65

-579.04

-553.83

-535.24

-522.64

-513.55

-509.59 -508.81

V xc -1.56 -0.90 -0.99 -1.36 -1.88 -2.38 -2.81 -3.13 -3.34 -3.43

V cl -709.2 -651.6 -610.7 -577.7 -551.9 -532.9 -519.8 -510.4 -506.2 -505.4

V ct

-740.29

-684.40

-642.19

-609.33

-582.91

-563.62

-549.94

-539.97

-535.50 -535.33

V pol 31.09 32.78 31.53 31.65 30.97 30.75 30.11 29.55 29.26 29.95

Table 2. Chlorine-nitrogen and carbon-nitrogen interatomic interaction energies and their components (in kJ/mol) in different θ angles (in degree) in the F3C−Cl⋯ N H 3 complex. The IQA values in bold correspond to the global minimum structure.

F3C−Cl⋯ N H3 90 100 110 120 130 140 150 160 170 180

E∫ ¿IQA (Cl , N)¿ -8.83 -14.82 -17.41 -21.85 -24.62 -29.45 -32.43 -36.19 -39.12 -39.48

V xc -48.13 -50.52 -50.23 -50.40 -50.19 -50.05 -50.10 -50.09 -50.13 -50.19

V cl 39.30 35.70 32.82 28.55 25.56 20.59 17.67 13.90 11.00 10.70

V ct 46.94 45.03 44.08 43.12 42.29 41.90 41.90 41.82 41.83 41.86

V pol -7.65 -9.33 -11.26 -14.58 -16.73 -21.30 -24.23 -27.92 -30.83 -31.16

E∫ ¿IQA (C , N )¿

-798.77 -750.09

-704.95 -668.92

-639.55 -618.71 -605.74

-595.62 -590.19 -587.99

V xc -0.90 -0.68 -0.60 -0.75 -1.00 -1.28 -1.55 -1.75 -1.88 -1.93

V cl - -749.41 - -668.16 - -617.42 -604.19 - -588.31 -586.05

24

797.87 704.36 638.54 593.87

V ct

-819.42 -768.56

-723.19 -686.87

-657.98 -637.05 -623.05

-612.48 -606.75 -605.37

V pol 21.56 19.15 18.84 18.71 19.44 19.63 18.86 18.62 18.44 19.31

Table 3. The atomic deformation energy (E¿ ( A )) in all orientation of F3C−X ⋯ N H3complexes. (Energy values and angles are in kJ/mol and degree, respectively). The IQA values in bold correspond to the global minimum structure.

F3C−Cl⋯ N H 3 F3C−Br⋯ N H 3

E¿ (H )bE¿ (N )E¿ (F)aE¿ (C)E¿ (Cl)E¿ (H )bE¿ (N )E¿ (F)aE¿ (C)E¿ ( Br )

-9.3436.866.73-59.8250.62-9.1249.23-13.13-75.3185.5990

-8.5330.90-14.38-68.5057.54-14.0542.53-11.72-71.0384.12100

-7.9129.75-14.25-77.3558.63-13.5841.30-15.19-82.0484.82110

-6.8128.73-17.73-87.2259.36-11.1540.08-16.43-83.6582.67120

-6.5625.69-17.48-85.8059.08-6.6639.35-17.17-95.7080.95130

-3.0426.08-17.29-87.9058.03-0.1340.92-20.77-104.3079.20140

2.7129.05-18.36-97.0257.536.1342.17-19.27-110.7777.15150

6.1129.89-18.83-103.1256.5211.9443.90-22.68-125.3578.02160

8.7231.11-19.05-105.2755.7817.6146.84-22.72-131.7677.94170

10.2931.92-19.05-103.1455.6920.7049.04-22.60-128.1877.57180

a) Sum of deformation energies of all fluorines.

b) Sum of deformation energies of all hydrogens.

25

Table 4. REGs with the largest absolute magnitude calculated for barrier 1 in C F3 Br …N H 3 (100° ≤ θ ≤180° ¿

Energy terms REG R V ct REG R V pol REG R

V cl(F 3 , N 6) 2.14 0.93 V ct (F 3 , N 6) 2.26 0.93 V pol(F 3 , N 6) -0.12 -0.88

E selfIQA (C 1 ) 1.49 0.99 −¿ −¿ −¿ −¿ −¿ −¿

V cl (C 1 , H 7 ) 1.20 0.97 V ct (C 1, H 7 ) 1.13 0.97 V pol (C 1 , H 7 ) 0.07 0.77

V cl (C 1 , H 8 ) 1.17 0.91 V ct (C 1, H 8 ) 1.09 0.90 V pol (C 1 , H 8 ) 0.08 0.96

V cl ( N 6 , H 9 ) 0.89 0.98 V ct (N 6 , H 9 ) 1.21 0.97 V pol ( N 6 , H 9 ) -0.32 -0.94

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl ( Br 5 , N 6 ) 0.57 0.98 V ct (Br 5 ,N 6 ) 0.11 0.94 V pol ( Br 5 , N 6 ) 0.46 0.96

V XC ( Br 5 , N 6 ) 0.09 0.99 −¿ −¿ −¿ −¿ −¿ −¿

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl ( F 2 , C 1 ) -0.37 -0.94 V ct (F 2, C 1 ) -0.35 -0.98 V pol ( F 2 , C 1 ) -0.02 -0.23

V cl ( F 3 , H 9 ) -0.42 -0.89 V ct (F 3 , H 9 ) -0.37 -0.88 V pol ( F 3 , H 9 ) -0.05 -0.98

V cl ( F 3 , H 8 ) -0.74 -0.90 V ct (F 3 , H 8 ) -0.76 -0.89 V pol ( F 3 , H 8 ) 0.02 0.48

V cl ( F 3 , H 7 ) -0.79 -0.95 V ct (F 3 , H 7 ) -0.83 -0.95 V pol ( F 3 , H 7 ) 0.04 0.68

V cl (C 1 , N 6 ) -3.30 -0.94 V ct (C 1, N 6 ) -3.37 -0.94 V pol (C 1 , N 6 ) 0.08 0.96

26

Table 5. REGs with the largest absolute magnitude calculated for energy barrier 3 in C F3 Br …N H 3 . (θ ≤ 100° ¿

Energy terms REG R V ct REG R V pol REG R

V cl (C 1 , N 6 ) 77.06 1.00 V ct (C 1 , N 6) 75.46 1.00 V pol(C 1 , N 6) 1.60 1.00

V cl ( F 4 , H 7 ) 33.42 1.00 V ct (F 4 ,H 7 ) 35.29 1.00 V pol ( F 4 , H 7 ) -1.87 -1.00

V cl ( F 4 , H 8 ) 26.26 1.00 V ct (F 4 , H 8 ) 25.08 1.00 V pol ( F 4 , H 8 ) 1.18 1.00

V cl ( F 4 , H 9 ) 19.83 1.00 V ct (F 4 , H 9 ) 18.28 1.00 V pol ( F 4 , H 9 ) 1.55 1.00

V cl ( N 6 , H 7 ) 7.48 1.00 V ct (N 6 , H 7 ) 9.52 1.00 V pol ( N 6 , H 7 ) -2.04 -1.00

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

E selfIQA (C 1 ) 5.78 1.00 −¿ −¿ −¿ −¿ −¿ −¿

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl ( Br 5 , N 6 ) 1.25 1.00 V ct (Br 5 ,N 6 )-0.40 -1.00 V pol ( Br 5 , N 6 ) 1.65 1.00

V XC ( Br 5 , N 6 ) 0.45 1.00 −¿ −¿ −¿ −¿ −¿ −¿

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl (C 1 , F 4 ) -9.78 -1.00 V ct (C 1, F 4 ) -3.08 -1.00 V pol (C 1 , F 4 ) -6.70 -1.00

V cl (C 1 , H 9 ) -18.27 -1.00 V ct (C 1, H 9 ) -16.19 -1.00 V pol (C 1 , H 9 ) -2.08 -1.00

V cl (C 1 , H 8 ) -23.41 -1.00 V ct (C 1, H 8 ) -20.65 -1.00 V pol (C 1 , H 8 ) -2.76 -1.00

V cl (C 1 , H 7 ) -29.53 -1.00 V ct (C 1, H 7 ) -27.90 -1.00 V pol (C 1 , H 7 ) -1.62 -1.00

V cl ( F 4 , N 6 ) -84.21 -1.00 V ct (F 4 , N 6 ) -85.41 -1.00 V pol ( F 4 , N 6 ) 1.20 1.00

27

Table 6. REGs with the largest absolute magnitude calculated for barrier 1 in C F3Cl …N H 3(90°≤ θ ≤ 180°)

Energy

terms

REG R V ct REG R V pol REG R

V cl ( F 9 , N 3 ) 4.62 0.94 V ct (F 9 , N 3 ) 4.96 0.93 V pol ( F 9 , N 3 ) -0.34 -0.73

V cl (C 1 , H 4 ) 3.25 0.92 V ct (C 1, H 4 ) 3.12 0.92 V pol (C 1 , H 4 ) 0.13 0.74

V cl (C 1 , H 5 ) 2.14 0.89 V ct (C 1, H 5 ) 1.88 0.86 V pol (C 1 , H 5 ) 0.26 0.88

V cl (C 1 , H 6 ) 1.79 0.86 V ct (C 1, H 6 ) 1.47 0.84 V pol (C 1 , H 6 ) 0.32 0.96

V cl ( F 7 , N 3 ) 1.69 0.76 V ct (F 7 , N 3 ) 1.65 0.75 V pol ( F 7 ,N 3 ) 0.05 0.94

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

E selfIQA (C 1 ) 1.68 0.95 −¿ −¿ −¿ −¿ −¿ −¿

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl (Cl2 , N 3 ) 1.18 0.99 V ct (Cl 2, N 3 ) 0.17 0.84 V pol (Cl 2 , N 3 ) 1.01 1.00

V XC (Cl 2, N 3 ) 0.03 0.34 −¿ −¿ −¿ −¿ −¿ −¿

⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

V cl ( F 7 , H 4 ) -0.72 -0.85 V ct (F 7 ,H 4 ) -0.69 -0.85 V pol ( F 7 , H 4 ) -0.03 -0.57

V cl ( F 9 , H 6 ) -1.14 -0.90 V ct (F 9 , H 6 ) -1.07 -0.88 V pol ( F 9 , H 6 ) -0.07 -0.90

V cl ( F 9 , H 5 ) -1.26 -0.95 V ct (F 9 , H 5 ) -1.21 -0.95 V pol ( F 9 , H 5 ) -0.05 -0.73

V cl ( F 9 , H 4 ) -1.95 -0.92 V ct (F 9 , H 4 ) -2.16 -0.90 V pol ( F 9 , H 4 ) 0.21 0.75

28

V cl (C 1 , N 3 ) -7.82 -0.92 V ct (C 1, N 3 ) -7.88 -0.92 V pol (C 1 , N 3 ) 0.05 0.51

Table of Content Image

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