Chemical Physics 415 (2013) 207–213

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Chemical Physics

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The halogen� � �oxygen interaction in 3-halogenopropenal revisited – Thedimer model vs. QTAIM indications

0301-0104/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.chemphys.2013.01.009

⇑ Corresponding author. Tel.: +48 (56) 6114695; fax: +48 (56) 654 24 77.E-mail address: teojab@chem.uni.torun.pl (M. Jabłonski).URL: http://www.chem.uni.torun.pl/zchk/jab/jab.html (M. Jabłonski).

Mirosław Jabłonski a,⇑, Marcin Palusiak b

a Department of Quantum Chemistry, Faculty of Chemistry, Nicolaus Copernicus University, Gagarina 7, PL-87 100 Torun, Polandb Department of Theoretical and Structural Chemistry, Pomorska 163/165, PL-90 236 Łódz, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 December 2012In final form 9 January 2013Available online 20 January 2013

Keywords:Intramolecular interactionInteraction energyRepulsive interactionHalogen bondBond pathBond critical pointAtoms in molecules

Even though a bond path and the corresponding bond critical point were found for the intramolecularX� � �O (X = Cl,Br) interaction in 3-halogenopropenal, thus according to QTAIM suggesting the stabilizingnature of this interaction, it was shown that this contact is repulsive. In order to utilize the well-definedenergy of the intermolecular interaction, a dimer model was used. The C–X� � �O@C fragment from the ZZconformer of 3-halogenopropenal was preserved with its original geometrical arrangement. Suchapproach leads to the conclusion according to which the presence of a bond path and the correspondingbond critical point do not necessarily indicate a stabilizing interaction between a pair of atoms, but ratheris a direct consequence of a large accumulation of the electron density between atoms. Values of QTAIMparameters characterizing both BCP of X� � �O and RCP remain rather unchanged if the C–X� � �O@C frag-ment with its preserved geometry is embedded in a dimer. It was also shown that atoms X and O areinteracting by negative surfaces of the molecular electrostatic potential. Also the charge transfer betweeninteracting fragments is opposite to expected.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

According to the Quantum Theory of Atoms in Molecules(QTAIM) of Bader [1,2] the existence of a bond path (BP) and a cor-responding bond critical point (BCP) between any two atoms is anecessary and sufficient condition for the existence of the attrac-tive interaction linking these atoms [3]. Thus the detailed analysisof the electron density distribution provides a rigorous tool foruncovering predominant interactions between atoms in molecularsystems. In a decisive majority of instances this pair of topologicalfeatures indeed accompany connections between atoms which arecomprehended as chemical bonds by a wide community of chem-ists. Nevertheless, a rich collection of theoretical data [4-15] showsthat such a pair of a bond path and the corresponding bond criticalpoint can also be found between atoms that normally would not beconsidered to form a chemical bond in a specific moleculararrangement. The most basic example may be the H� � �H contact.For instance, in the case of kekulene, the unique arrangement ofsix hydrogen atoms inside the inner molecular cavity yields highlycurved H� � �H bond paths forming a hexagonal ring [4]. The otherelementary instances may be the flattened biphenyl [5,6], phenan-threne, and other planar benzenoid hydrocarbons possessing the

phenanthrene moiety where BPs and BCPs corresponding toH� � �H contacts between hydrogen atoms in positions 4 and 5 areobserved [6].

By no means is such an unexpected presence of a bond pathlimited to H� � �H contacts only. It has also been found for such pairsof atoms as Ng� � �C [8–12], O� � �O [4,13], N� � �N [4], X� � �X (X = halo-gen) [7,14,15], and X� � �O [14]. In the case of CðNO2Þ�3 three pairs ofBPs and corresponding BCPs were found [4] between oxygen atomsof the adjacent nitro groups. Calculation based on QTAIM also re-vealed bond paths between oxygen atoms in open conformers ofenol forms of cis-b-diketones [13]. The intramolecular F� � �F bondpath was found in 1,8-difluoronaphtalene and then profoundlystudied by Matta et al. [15]. Bond paths indicating X� � �X interac-tions can also be found, for example, in perhalogenated cyclohex-anes, dodecahedranes and fullerenes [7]. The repulsive nature ofX� � �X interaction within all these systems was marked by comput-ing the energy of the transhalogenation reaction and by the signif-icant expansion of the C–C bond while hydrogens in C60H60 arereplaced by fluorines and then by chlorines [7]. Similar expansionof a cage has been found in the case of He@adamantane [8] wherethe antibonding nature of the He� � �tC interaction has been judgedbased on the negative value of the dissociation energy [8,9]. Nega-tive value of the dissociation energy has also been announced forthe He@cubane endohedral complex [11]. Atomic interaction lineof the He� � �C type has also been found in the case of much smallerHe� � �CH4 system even that positive, i.e. nonbonding, interaction

208 M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213

energies have been obtained for a wide range of He� � �C distances[8].

According to Cioslowski et al. [4–7], the presence of BP (or theso-called interaction line [1]) delineate major interactions in amolecular system which, however, do not have to be bonding. In-stead, it may indicate a significant nonbonding, i.e. repulsive inter-action [5–7]. Then the bond critical point corresponding to suchan unexpected bond path (or interaction line) is characterized bylow values of the electron density and its Laplacian. The corre-sponding bond paths (or attractor interaction lines) are usuallyconsiderably curved [5,6]. The repulsive nature of the H� � �H inter-action between ortho-hydrogen atoms in planar biphenyl has alsobeen shown by Poater, Solà and Bickelhaupt [16]. These Authorsconcluded that BP and BCP are not indicators of a stabilizing inter-action [17]. Haaland et al. [8,9] have shown that the interaction be-tween a helium atom and the adamantane cage is antibonding inspite of bond paths that link this helium atom with carbon atomsof the cage. Similar result has also been obtained for other endohe-dral complexes [10,11]. Based on the energy decomposition analy-sis [18], Cerpa et al. [12] have found that the overall interactionbetween the He2 fragment and the dodecahedrane (C20H20) cageis repulsive and results from the Pauli repulsion term. They havealso shown that the large value of the electron density in BCPmay result from the close proximity of atoms which, however,can be forced and does not necessarily indicate a bonding interac-tion between them, thus a short distance between a pair of atomsdoes not necessarily imply the existence of a chemical bond – con-clusion that is similar to that previously found by Cioslowski et al.[4–7]. Moreover, in this case, the He–He bond order is close to zero[12] as indicated by means of Wiberg Bond Index [19]. A multitudeof BPs and BCPs can also be present as a consequence of a largesymmetry of a system [11]. In this case, as Cerpa et al. [11] stress‘‘it is risky to make the one-to-one analogy between a bond pathand a chemical bond in the usual chemical sense of the word’’.

Nevertheless, it should be pointed out that the concept of BPand related BCP as a tight criterion for the existence of the bondingbetween the linked atoms was defended in a very convincing wayby Bader and his co-workers [20–26]. Thus, a dichotomy in under-standing and interpretation of the electron density topology attrib-uted to the atomic interaction exists in minds of chemists and theconsensus in the discussion probably had not been reached yet.This paper contributes to this discussion. The earlier-investigatedcontact between Cl and O in 3-chloropropenal is revisited. Recentlythe 3-chloropropenal molecule was supposed to be a system withthe intramolecular halogen bond of the Cl� � �O type [27]. Here thenature of the Cl� � �O contact in 3-chloropropenal is studied bymeans of a dimer model – a model which allows to estimate theinteraction energy directly from the supermolecular approach.

The intramolecular interaction of the Cl� � �O type in 3-chloro-propenal and its fluoro-derivatives was studied [27] by means ofa theoretical approach. Based on total energies and geometricalparameters of open and closed forms of 3-chloropropenal it wasconcluded that the closure of the five-membered pseudo-ringthrough the Cl� � �O contact does not lead to the electron densityredistribution and that it has a meaningless influence on boththe geometrical parameters and the energetic characteristics. Thus,if the Cl� � �O contact stabilizes the considered structure of 3-chloro-propenal and its derivatives, this stabilization is only weak. Inter-estingly, the Cl� � �O contact was indicated by the bond path andits corresponding bond critical point. Based on this finding as wellas on the value of ca. 0.01 au of the electron density in the BCP ofthis interaction it was then concluded that the Cl� � �O contact in 3-chloropropenal is a stabilizing interaction. However, it was alsoshown [27] that the closed form of 3-chloropropenal is less stablethan the open form. It leads to the conclusion that the Cl� � �O inter-action in this system is in fact repulsive if the open form is treated

as a reference system [28]. This conclusion was then supported[28] by positive (thus repulsive) estimates of the interaction energyof the Cl� � �O contact obtained by means of several methods.

Because of the indefiniteness of the interaction energy of anintramolecular interaction, many different methods can be pro-posed. As a consequence they may, in general, lead to a wide rangeof estimated values [29–34]. Thus it seems advisable to obtain anestimate of the intramolecular interaction energy based on fewmethods. To estimate the interaction energy of the X� � �O(X = F,Cl,Br, I) contact in 3-halogenopropenal (5X) one of us had re-cently used [28] the open-closed method [35,36], its recently mod-ified version termed as Method A [33,37], and the so-calledisodesmic reactions [38–40]. In this article we use another onemethod that is aimed for the estimation of the interaction energyof the X� � �O (X = F,Cl,Br) contact in 3-halogenopropenal (5X). Thismethod is, however, based on referring to a properly built dimer.From this reason, this method will be henceforth termed as the di-mer model. Details regarding the usage of this method and thecomprehensive discussion of its reliability can be found in the Re-sults and discussion section.

It should be underlined that due to the almost parallel ratherthan coaxial arrangement of C–X and C@O bonds, the X� � �O inter-action studied here will not be termed as an intramolecular halo-gen bond, but rather as the X� � �O interaction or contact.Moreover, in our opinion the intramolecular halogen bond shouldclearly be stabilizing and, as such, should be characterized by neg-ative estimate of the interaction energy (by definition its negativevalue means the attractive, i.e. bonding character of thisinteraction).

2. Methodology

All calculations have been performed by means of Gaussian 03set of codes [41] at the level of the second-order Møller–Plessetperturbation theory (MP2) [42] with aug-cc-pVTZ basis set[43,44]. For the geometry fully optimized 3-halogenopropenal(5X) molecules (X = F,Cl, Br) the frequency analysis has been usedto verify that the optimized structures correspond to the groundstate stationary points. No imaginary frequencies were found inthese cases. The QTAIM based analysis of the electron densitytopology has been obtained by means of the AIMAll program[45]. To support our final conclusions we have also computed themolecular electrostatic potential (MEP) which was mapped onthe electron density isosurface of 0.01 au. Plots have been obtainedby means of Molekel 4.3 program [46,47]. Cube files generated byGaussian 03 [41] were used for electron potential mapping.

3. Results and discussion

3.1. Structure of 3-halogenopropenal

All four conformers of 3-halogenopropenal (X = F,Cl,Br) areshown in Fig. 1. The cis-s-cis (ZZ) conformer possesses the intra-molecular X� � �O interaction whose energy is to be estimated basedon the dimer model. The influence of the presence of this interac-tion to the geometry of the ZZ form can be studied by means ofother conformers which are treated as references. Although inthe case of 3-halogenopropenal (5X) its EZ conformer seems tobe the most reasonable reference [28], all conformers are used asreferences to investigate changes of geometrical parameters whilethe X� � �O contact is formed. The most important geometricalparameters are listed in Tables 1 and 2.

The formation of the X� � �O contact leads to the elongation of theC@C bond, while C–C and C–X bonds are shortened. The length ofthe C@O bond is almost unchanged upon the formation of the

Fig. 1. Schematic presentation of four conformers of 3-halogenopropenal, X = F,Cl,and Br.

M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213 209

X� � �O contact (see Table 1). These geometrical changes are thesame as those resulting from the increase of steric effects as a con-sequence of molecular flattening [37] or external pressure exertedon a molecule [48].

Data presented in Table 2 indicate the swell of the 5X system ifa transition from one of the references to the ZZ form takes place.This effect is independent of the conformer that is used as a refer-ence and increases in the F < Cl < Br order as seen e.g. on the basis

Table 2Values of plane angles and their differences with respect to the closed ZZ conformer of 3-

System Form aXCC DaXCC aCCC

5F ZZ 123.6 – 126.0ZE 122.3 1.3 123.6EZ 121.9 1.7 119.6EE 122.6 1.0 118.3

5Cl ZZ 125.8 – 127.3ZE 124.6 1.2 125.1EZ 123.2 2.6 119.7EE 123.7 2.1 118.7

5Br ZZ 126.2 – 127.4ZE 124.9 1.3 125.2EZ 123.4 2.9 119.7EE 123.8 2.4 118.8

Table 1Values of bond distances and their differences with respect to the closed ZZ conformer of

System Form dX���O dC@C DdC@C dC—C

5F ZZ 2.829 1.338 – 1.471ZE – 1.335 0.003 1.466EZ – 1.334 0.004 1.472EE – 1.334 0.004 1.462

5Cl ZZ 3.024 1.343 – 1.472ZE – 1.340 0.003 1.467EZ – 1.338 0.005 1.477EE – 1.338 0.004 1.466

5Br ZZ 3.086 1.342 – 1.472ZE – 1.340 0.003 1.467EZ – 1.338 0.005 1.478EE – 1.339 0.004 1.467

of values ofP

Da compared for different halogens but for the samereference. It should be noted that the value of aCCC is the best indi-cator of the tension in the molecular skeleton since all three carbonatoms are present in the 5-membered quasi-ring in all conformersof 3-halogenopropenal. In other words, this is the only angle thatdoes not change its orientation upon conformational changes of5X. Indeed, the increase of aCCC upon the EZ ? ZZ step is the mostmarked.

The increase of bond distances and values of bond angles whilethe F ? Cl ? Br substitution is considered indicates the increase ofthe repulsive interaction in the X� � �O region. This effect is particu-larly marked if F is substituted by either Cl or Br [28]. The othergeometrical evidence of the local repulsion in the X� � �O regionmay be the twisted instead of flat structures of XCH2–C(@CH2)–CHO molecules. In this case the @CHX group in 5X (see Fig. 1) issubstituted by the –CH2X group which can rotate almost freelyaround the C–C bond and thus facilitate the halogen atom to es-cape from the molecular plane [28]. As it has been shown, the flat-tening of the former molecules leads to a significant opening of themolecular skeleton. This can be interpreted in terms of the repul-sive instead of attractive character of the X� � �O interaction [28].Thus, based on analyzed changes of geometrical parameters thattake place upon the X� � �O contact formation, we conclude that thisinteraction is in fact of the repulsive instead of the attractivenature.

3.2. The energy of X� � �O

Since the bonding/non-bonding character of an interaction isdetermined by the interaction (or bond) energy, this is the param-eter that should be considered when discussing about either bond-ing or non-bonding character of the relevant interaction [28].

halogenopropenal (X = F,Cl, Br).

DaCCC aCCO DaCCOP

Da a(av.)

– 125.2 – – 124.92.4 122.7 2.6 6.3 122.86.4 124.6 0.7 8.8 122.07.7 124.0 1.3 10.0 121.6

– 125.5 – – 126.22.2 122.4 3.0 6.4 124.07.6 124.4 1.1 11.2 122.46.4 123.8 1.7 10.1 122.1

– 125.3 – – 126.32.2 122.6 2.8 6.2 124.27.7 124.3 1.0 11.6 122.48.6 123.8 1.6 12.6 122.1

3-halogenopropenal (X = F,Cl, Br).

DdC—C dC—X DdC—X dC@O DdC@O

– 1.326 – 1.219 –0.005 1.338 �0.013 1.221 �0.002�0.001 1.333 �0.007 1.221 �0.001

0.009 1.332 �0.006 1.219 0.000

– 1.707 – 1.220 –0.005 1.722 �0.015 1.222 �0.002�0.005 1.713 �0.006 1.220 0.000

0.006 1.713 �0.006 1.219 0.001

– 1.855 – 1.220 –0.005 1.871 �0.016 1.221 �0.001�0.006 1.859 �0.003 1.220 0.000

0.005 1.859 �0.004 1.219 0.001

Table 3Interaction energies (in kcal/mol) of the X� � �O contact in the 3-halogenopropenalestimated by means of several methods (see text).

Method Systems

5F 5Cl 5Br

DEZE 3.04 2.95 2.94

DEEZ 2.56 2.62 2.40

DEEE 4.18 4.27 4.11

DEA 2.06 1.66 1.43

DEiso 2.92 2.64 2.22

DEZE���EZCP

1.82 2.98 3.49

DEZE���EECP

1.97 3.34 3.95

DEXMe���FaCP

0.52 1.06 1.08

DEXAc���FaCP

0.44 0.38 0.19

2 The new C–H bonds in XMe� � �Fa were inbuilt with the length of 1 Å and bond

210 M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213

Unfortunately, in the case of intramolecular interaction, the exactdefinition of the interaction (bond) energy cannot be established[29–34]. Nevertheless, one can propose [33-40] a method thatleads to a number which is to be understood as the energy of a (lo-cal) intramolecular interaction of interest. Since one can proposeseveral different methods and since, in general, they may lead todifferent estimates, the usage of few of them is highly recom-mended [34,28].

Based on the open-closed method [35,36], method A [33,37],and isodesmic reactions [38–40] it has very recently been shown[28] that the X� � �O (X = F,Cl,Br) contact in the 3-halogenopropenalis in fact repulsive as indicated by positive values of estimatedenergies of this contact (see Table 3). To confirm this result andto take advantage of the fact that, unlike the intramolecular case,the energy of the intermolecular interaction is a well-defined prop-erty, we are at present using an estimate based on the dimer mod-el. This model has already been used to estimate the interactionenergy of the intramolecular p � � �p interaction in 1,3,5,7-cyclo-octatetraene [49].

3.2.1. The dimer modelIn the dimer model one computes the interaction energy of a

reasonably chosen dimer on the basis of the very well-knownequation from the supermolecular approach

DE ¼ EA[BAB ðABÞ � EA

AðAÞ � EBBðBÞ; ð1Þ

where in the notation EBG(S) S denotes the system, B the basis set,

and G the geometry source used in calculations for the system S.The basis set superposition error (BSSE) was taken into accountby means of standard counterpoise method [50]

DECP ¼ EA[BAB ðABÞ � EA[B

AB ðAÞ � EA[BAB ðBÞ; ð2Þ

meaning that for isolated monomers both the geometry and the ba-sis set from the complex were used. According to Eq. (2) the inter-action energy of the X� � �O contact is well-defined.

Now the appropriate dimer was built in such a way that the C–X� � �O@CH fragment from the ZZ conformer of the 5X system wasinbuilt in either ZE� � �EZ or ZE� � �EE dimer of 5X (see Fig. 2). The veryshort intermolecular C–H� � �H–C contact was taken into account1

by considering the ‘rotated’ form of each dimer (Fig. 2). Then, theinteraction energy of the X� � �O contact in the dimer (whose arrange-ment is planned on that in 5X) has been obtained by means of thefollowing formula

DECPðX � � �OÞ ¼ DECPðdimerÞ � DECPðrotated dimerÞ: ð3Þ

1 The lengths of both these C–H bonds were taken as 1 Å to somewhat increase theH� � �H distance. However, the estimated value of DECP(X� � �O) is almost unchanged ifshorter H� � �H contact is conserved.

Since both DECP(dimer) and DECP(rotated dimer) were computedwith the correction for the basis superposition error and BSSE is al-most the same for both forms of a dimer, DECP(X� � �O) is almostequal to its BSSE-uncorrected counterpart (the latter energies notshown). More importantly, it should be stressed that the relativearrangement of all atoms in the C–H� � �H–C contact is conservedupon considering the rotated counterpart dimer (see Fig. 2).

As seen from Table 3 the estimated values of the X� � �O interac-tion in both dimers are clearly positive, thus, as a consequence ofassumptions of the dimer model, indicating also the repulsive nat-ure of the X� � �O contact in 5X systems. Meaningfully, the repulsionenergy of the X� � �O contact is to increase with increasing the size ofthe halogen atom X. It is also seen that the estimated values ofeither DEZE���EZ

CP or DEZE���EECP are similar to each other if X = Cl,Br

(2.98 and 3.49 kcal/mol or 3.34 and 3.95 kcal/mol, respectively)while these values are protruding (1.82 or 1.97 kcal/mol, respec-tively) if X = F. Thus, this trend in interaction energy values agreeswith that found on analyzing the influence of the halogen atom togeometrical changes in the ZZ conformer of 5X.

From nine (ZZ form must be excluded due to the intramolecularX� � �O interaction) possible dimers of different conformers of 5X wehave used only ZE� � �EZ and ZE� � �EE to avoid some new interactions(other than the already discussed H� � �H close contact) in the ‘nor-mal’ or ‘rotated’ form. However, even in both these cases the ‘ro-tated’ form is somewhat contaminated with a new H� � �Ointeraction with a distance of ca. 2.44 Å. Thus, it seems to be desir-able to simplify the dimer model. As a result we have also consid-ered halogenomethane� � �formaldehyde and halogenoacetylene� � �formaldehyde dimers. Hereafter they will be denoted as XMe� � �Faand XAc� � �Fa, respectively. Geometries of these dimers as well astheir ‘rotated’ counterparts are shown in Fig. 2. Again, the relativeorientation of both monomers was fixed to preserve theC–X� � �O@CH fragment from the ZZ form of 5X unaltered.2 The pres-ence of some new interactions in the dimer was, again, taken intoaccount by considering the rotated counterpart system with possiblyhigh conservation of atomic positions (see Fig. 2 for better visualiza-tion of model dimers used in these cases).

The estimated values of DECP(X� � �O) (see DEXMe���FaCP and DEXAc���Fa

CP

in Table 3) are much smaller than either DEZE���EZCP or DEZE���EE

CP , butare still positive, indicating the repulsive nature of X� � �O in 5X.The previously obtained (for DEZE���EZ

CP and DEZE���EECP ) trend of energy

values, i.e. DECP(F� � �O) < DECP(Cl� � �O) 6DECP(Br� � �O) is still pre-served if DEXMe���Fa

CP values are considered, however this trend is vio-lated if XAc� � �Fa dimer is used. Importantly, all estimationmethods proposed in this and the earlier article [28] clearly showthat the X� � �O interaction in the 3-halogenopropenal molecule israther repulsive, although a bond path and a corresponding bondcritical point were found in 5Cl [27] and 5Br [28]. It would be inter-esting to see whether values of QTAIM parameters computed inboth the bond critical point of X� � �O and in the ring critical point(RCP) of 5X are preserved or at least similar to those found in mod-el dimer systems possessing the conserved arrangement of the C–X� � �O@C–H contact. This issue is considered in the followingsection.

3.3. Topological characteristics of BCPX� � �O

Values of the QTAIM-based parameters computed for BCPX� � �O in5X (X = Cl,Br) and all dimer model systems (with X = Cl,Br) are

angles corresponding to either the sp3 or sp2 hybridisation. In the case of the XAc� � �Fasystem, the (non-existent in 5X) CCH fragment was firstly optimized in isolated XCCHand then used in calculations for the dimer, while the C–H bond in Fa pointingtowards XCCH was again fixed with its length of 1 Å and the aHCO bond angle wasgiven a value of 120�.

Table 4Values of QTAIM parameters for BCPX� � �O.

System q r2q V G H k1 k2 k3 e DIX;O CT

5Cl 0.013 0.050 �0.009 0.011 0.002 �0.010 �0.008 0.068 0.329 0.084 –Cl (ZE� � �EZ) 0.012 0.053 �0.009 0.011 0.002 �0.009 �0.008 0.070 0.193 0.080 0.010Cl (ZE� � �EE) 0.013 0.051 �0.009 0.011 0.002 �0.010 �0.007 0.068 0.398 0.083 0.019ClMe� � �Fa 0.013 0.051 �0.009 0.011 0.002 �0.010 �0.008 0.069 0.288 0.080 0.033ClAc� � �Fa 0.013 0.050 �0.009 0.011 0.002 �0.010 �0.007 0.068 0.390 0.079 0.064

5Br 0.013 0.048 �0.009 0.010 0.002 �0.010 �0.008 0.066 0.206 0.096 –Br (ZE� � �EZ) 0.014 0.049 �0.009 0.011 0.002 �0.010 �0.008 0.067 0.289 0.095 0.014Br (ZE� � �EE) 0.014 0.049 �0.009 0.011 0.002 �0.010 �0.008 0.067 0.291 0.095 0.017BrMe� � �Fa 0.014 0.049 �0.009 0.011 0.002 �0.010 �0.008 0.068 0.216 0.091 0.034BrAc� � �Fa 0.014 0.048 �0.009 0.010 0.002 �0.010 �0.008 0.066 0.284 0.091 0.067

Fig. 2. Geometries of model dimers.

M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213 211

listed in Table 4. These results are also completed with delocaliza-tion index estimated for X and O atomic basins (DIX;O) and the va-lue of charge transfer in a dimer (CT). In the case of systems withX = F, no BCP was found for the F� � �O contact. According to QTAIM,the X� � �O interaction is characterized as of the closed-shell type asindicated by low values of the electron density (q) and positive val-ues of both its Laplacian (r2q) and the electronic total energy den-sity (H).

More importantly for the present discussion, values of allQTAIM parameters characterizing BCPX� � �O (Table 4) remain ratherthe same if the C–X� � �O@CH fragment from the ZZ form of 5X istransposed to any of the model dimer system. Thus, one may con-clude that values of QTAIM parameters computed in the bond crit-ical point of an interaction depend on the type of atoms, thedistance between them, but also on the molecular fragment theyare built-in. The presence of a bond path and the correspondingbond critical point results rather from the close proximity of a pairof atoms, particularly those large and highly polarizable, and, as aconsequence, the mutual interpenetration of their electron densitycontributions [4–7,11,12,28], instead of from the necessarily stabi-lizing interaction between them [3]. The close proximity of highlypolarizable atoms that results in the presence of a pair of BP andBCP occurs, for example, in perhalogenated fullerenes [7], 1,8-dif-luoronaphtalene [15], 1,8-naphthalenediol [13], the CðNO2Þ�3 ion[4], and ZE conformers of enol forms of cis-b-diketones [13]. Letus mention again that all estimates, used in the earlier article[28] as well as the dimer model utilized at present, show the repul-sive instead of the attractive nature of the X� � �O interaction in 5X(X = F,Cl,Br). This conclusion is supported by geometrical data.

The positive value of CT (see the last column in Table 4) showsthat the electron density is transferred from the halogen-contain-ing molecule to the oxygen-containing molecule (XMe� � �Fa andXAc� � �Fa), thus the X� � �O interaction in dimers, that is to modelX� � �O in 5X, is not a halogen bond, where the opposite direction

of CT occurs [51,52], i.e. from the halogen-acceptor atom (O, N,etc.) to the halogen.

Somewhat surprisingly, values of QTAIM parameters are alsopreserved if ring critical points (RCP) in 5X and model dimers areconsidered (see Table 5). This finding is even valid for r2q thatis very sensitive to the distribution of the electron density, as beingits 2nd-order derivative. The preservation of values of QTAIMparameters in RCPs of investigated systems most likely resultsfrom the fact that the C–X� � �O@C fragment consisting of heavyatoms is kept unchanged on switching from 5X to any of the dimermodel systems, even though the central carbon atom of the molec-ular skeleton is absent (see Figs. 1 and 2).

3.4. MEP-based analysis

Plots that represent the molecular electrostatic potential (MEP)mapped onto the electron density isosurface are easy and veryhelpful tool to display the likely preferred interactions betweenatoms of a molecular system [53–57], yet not only bonding [28].This results from the fact that some atoms are represented by po-sitive sites of MEP, while others possess negative sites. One canthus visualize sites of X and O atoms in investigated systems withthe X� � �O contact [28]. Such plots for 5X and all model dimers areshown in Fig. 3. For the electron density isosurface the value of0.01 au was used to avoid the fusion of atomic surfaces of X andO atoms. As seen from Fig. 3, atoms X and O are stitched up withnegative surfaces of MEP, thus suggesting the repulsive nature ofthe X� � �O contact. It is also seen that the mutual orientation ofthe halogen atom and the electron lone pairs on oxygen (indicatedby the dark blue color in Fig. 3) are not conducive to the interactionbetween the electron lone pair and the r-hole [58] on halogen as inthe case of halogen bonds [55].

Table 5Values of QTAIM parameters for RCP.

System q r2q V G H k1 k2 k3

5Cl 0.012 0.059 �0.010 0.012 0.002 �0.009 0.012 0.056Cl (ZE� � �EZ) 0.011 0.059 �0.010 0.012 0.003 �0.008 0.012 0.055Cl (ZE� � �EE) 0.012 0.057 �0.010 0.012 0.002 �0.009 0.011 0.055ClMe� � �Fa 0.012 0.057 �0.010 0.012 0.002 �0.008 0.011 0.054ClAc� � �Fa 0.012 0.056 �0.010 0.012 0.002 �0.009 0.010 0.055

5Br 0.012 0.057 �0.010 0.012 0.002 �0.009 0.014 0.052Br (ZE� � �EZ) 0.012 0.055 �0.010 0.012 0.002 �0.009 0.012 0.052Br (ZE� � �EE) 0.012 0.055 �0.010 0.012 0.002 �0.009 0.012 0.052BrMe� � �Fa 0.012 0.056 �0.010 0.012 0.002 �0.008 0.012 0.051BrAc� � �Fa 0.012 0.054 �0.010 0.012 0.002 �0.009 0.011 0.052

Fig. 3. Molecular electrostatic potential mapped onto the electron density isosurface of 0.01 au. The scale if from dark blue, the most negative (�0.07 au), to red, the mostpositive (0.13 au). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

212 M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213

4. Conclusions

Although the bond path and the corresponding bond criticalpoint were found for the intramolecular X� � �O (X = Cl,Br) interac-tion in 3-halogenopropenal [27], thus, according to the QuantumTheory of Atoms in Molecules of Bader [1,2], suggesting the stabi-lizing nature of this interaction [3], it was shown that this contactis repulsive in fact as indicated by various estimating methodsbased on a properly chosen reference form of 3-halogenopropenal[28]. This conclusion is now supported by other estimates of theinteraction energy of X� � �O in 3-halogenopropenal based on the di-mer model which takes advantage of the fact that the energy of the

intermolecular interaction is a well-defined property. To use thedimer model, a properly build dimer was used where the C–X� � �O@CH fragment from the ZZ conformer of the 3-halogenopro-penal was preserved with the same geometrical arrangement. Theusage of this model supports that the X� � �O interaction in the ZZform of 3-halogenopropenal is rather repulsive thus indicating thatthe presence of a bond path and a corresponding bond criticalpoint do not necessarily indicate a stabilizing interaction betweenany pair of atoms [4–7,11,12]. This rather results from the closeproximity of atoms, highly polarizable in particular, thus, as a con-sequence, leading to a large accumulation of electron charge be-tween atoms.

M. Jabłonski, M. Palusiak / Chemical Physics 415 (2013) 207–213 213

It was shown that values of QTAIM parameters in both the bondcritical point of the X� � �O interaction and in the ring critical pointare preserved on switching from the 5X molecule to any of themodel dimer system. Most likely the antibonding nature of theX� � �O contact in 3-halogenopropenal is also supported by mapsdisplaying the molecular electrostatic potential (MEP) mappedonto the electron density isosurface. Atoms X and O are interactingby negative surfaces of MEP.

Acknowledgment

Computational grants at the Interdisciplinary Centre for Mathe-matical and Computational Modelling (ICM) of the University ofWarsaw (<http://www.icm.edu.pl/web/guest/home>) and theWroclaw Center for Networking and Supercomputing (<http://www.wcss.wroc.pl>) are gratefully acknowledged.

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