Topological reaction sites--very strong chalcogen bonds.

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Topological reaction sites – very strong chalcogen bonds Esmail Alikhani,*ab Franck Fuster,c Bruno Madebeneab and Sławomir J. Grabowski*de The analysis of interactions in complexes of S(CN)2, Se(CN)2, SFCl and SeFCl with F and Cl anions is performed here. The sulphur and selenium atoms act in these complexes as Lewis acid centres interacting with fluorine and chlorine anions. The arrangement of sub-units in complexes is in agreement with the s-hole concept; particularly it is a result of contacts between positive and negative electrostatic potential sites. The interactions in complexes analyzed may be classified as very strong charge assisted chalcogen bonds and they possess numerous characteristics typical for covalent bonds. Even in the case of complexes of SFCl and SeFCl, i.e. SFCl2 and SeFCl2, the trivalency of the chalcogen atom is observed. The calculations were carried out at the MP2(full)/aug-cc-pVTZ level of approximation, the analyses were performed with the

Received 6th October 2013, Accepted 23rd November 2013 DOI: 10.1039/c3cp54208d

use of the Natural Bond Orbital (NBO) method, the Quantum Theory of ‘Atoms in Molecules’ (QTAIM) and the Electron Localization Function (ELF) approach. The results obtained by these methods are in agreement giving the consistent picture of the complexes’ configurations and their electron charge distribution. The QTAIM and ELF approaches allow us to predict for S(CN)2, Se(CN)2, SFCl and SeFCl molecules the directions of nucleophilic attack. They are in line with the prediction based on the s-hole concept. The

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Symmetry Adapted Perturbation Theory (SAPT) approach was also applied.

1 Introduction One can observe an increasing number of studies on so-called non-covalent interactions.1–3 In general, these are interactions between two centres; Lewis acid and Lewis base.4 However sometimes very weak interactions ruled mainly by the dispersive forces are also classified as non-covalent interactions;2 for example between noble atoms or between methane molecules. If we take into account only interactions where the Lewis acid and the Lewis base centres may be identified thus one can mention hydrogen,5–7 halogen,8,9 chalcogen,10,11 pnicogen,12–15 tetrel bonds16–19 and numerous others. The hydrogen bond is analyzed most often because of its importance in chemical, physical and biological processes,5–7 including life processes.20–22 However, other Lewis acid–Lewis base interactions are also important in numerous processes. a

UPMC Univ. Paris 06, UMR 7075, Laboratoire de Dynamique, Interactions et Reáctivite´ (LADIR), F-75005, Paris, France. E-mail: [email protected] b CNRS, UMR 7075, Laboratoire de Dynamique, Interactions et Reáctivite´ (LADIR), F-75005, Paris, France c Sorbonne Universite´s, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Theórique (LCT), F-75005, Paris, France d Faculty of Chemistry, University of the Basque Country UPV/EHU and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Spain. E-mail: [email protected] e IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

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The great number of such interactions is formed owing to the opposite values of the electrostatic potential between centres being in contact.23,24 And the s-hole concept is useful to indicate where the areas of the positive and negative electrostatic potential are located for the molecular surfaces considered.3,25–29 For example, the halogen atom, X, such as Cl, Br, or I, usually connected with the carbon, is characterized by the positive electrostatic potential in the extension of the C–X bond owing to the depletion of the electronic charge in this region, i.e. owing to the existence of the s-hole. This is why it interacts, similarly as the H-atom in the case of the hydrogen bond, with the Lewis base centre, B, forming the C–X B link named as the halogen bond.25,26 In general the halogen bond may be designated as A–X B, where A is covalently bonded to X. However the same halogen atom possesses the region of the negative electrostatic potential due to the electron charge density belt around the X-atom being perpendicular to the A–X bond and formed by free electron pair orbitals.25,26 In the latter case the X-atom may act as the Lewis base centre interacting with electrophiles. In other words the X-atom possesses the dual character since it may act as the Lewis acid and as the Lewis base. The halogen bond being the case of the former situation is similar in nature to the hydrogen bond.28,30,31 The properties of atoms of groups VI, V and IV may also be explained with the use of the s-hole concept.28,29,32,33 In the case of the group V, such atoms as for example P or As may act

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as the Lewis acid centres owing to the regions of the positive electrostatic potential.33 Such interactions are often named as the pnicogen bonds. In the case of the group VI, for example for sulphur and selenium centres, there are also s-holes characterized by the positive electrostatic potentials and hence the interactions of these atoms with the Lewis bases are possible34 and they are known as the chalcogen bonds. Even in the case of the group IV the s-holes are observed16–19 and the corresponding interactions were named recently the tetrel bonds18,19 while if the carbon atom is considered the term carbon bond may be applied.17 We put emphasis on the chalcogen bonds in this study since there are interesting findings on them; also their role in biological systems was reported. One can mention early studies on thiazole and selenazole nucleosides where calculations on S O and Se O interactions were performed up to the RHF/6-31G(d) level.35 There is the experimental study on hexagonal L-cystine where S S interactions were detected and also the Cambridge Structural Database search of C(sp3)–S–S–C(sp3) cystine fragments was performed;36 among 166 entries found only in 40 cases the S S intermolecular distance was smaller than the sum of the corresponding van der Waals radii. The directionality of S O interactions was analyzed theoretically for the sample of small complexes and also in that study the CSD search was performed for intra- and intermolecular S O contacts.37 DFT calculations were carried out on b-chalcogenvinylaldehydes38 and on b-chalcogenvinyl(thio)aldehydes39 where intramolecular chalcogen bonds were analyzed. There are other theoretical studies of Scheiner where chalcogen–chalcogen, chalcogen–pnictogen bonds were analyzed40 and where different non-covalent interactions were compared.41,42 Also very recently halogen, chalcogen and pnictogen bonds were compared from the theoretical and experimental point of view.43 High level calculations were performed on simple complexes linked through interactions such as O O, S S, Se Se and Te Te.44 The interactions in the 1,2,5-chalcogenadiazole dimers were studied by ab initio calculations and the CCSD(T) binding energies for the thia-, selena- and tellura-diazole dimers are equal to 3.1, 5.3, and 12.4 kcal mol1, respectively.45 This is in line with the s-hole concept which leads to the conclusion that the positive electrostatic potential connected with the s-hole increases within the same group of elements with the increase of the atomic number.27–29 There are other studies on interactions of the group VI atoms acting as the Lewis acids. For example, the properties of the divalent sulphur atom were described recently in detail.46 The study on interactions of H2CS, F2CS, OCS and SCS with chlorine anions should be mentioned here since such interactions may be classified as the charge assisted chalcogen bonds.11 Interactions assisted by charge are characterized by the enhanced strength in comparison with the neutral complexes. This was observed for the hydrogen bonds and the dihydrogen bonds47,48 as well as for the halogen bonds.49 In the case of the above mentioned chalcogen complexes of chloride anion calculated at the MP2/aug-cc-pVTZ level the binding energies do not exceed 10 kcal mol1; except for the SCS Cl complex where the binding energy is equal to 10.6 kcal mol1.11 This means that


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the above mentioned charge assisted chalcogen bonds are rather strong. Note that the binding energy for the water dimer amounts B5 kcal mol1 and the corresponding O–H O hydrogen bond is classified as medium in strength.6 This short review of studies on the chalcogen bond, the sub-class of the s-hole bond, shows its importance; particularly this interaction influences the arrangement of molecules in crystals. However the other types of the s-hole bond were also analyzed3 and their importance in the crystal engineering, molecular biology and in pharmacology was discussed.3 It was claimed that in the case of the chalcogen bond the hypervalent nature of a sulphur atom is observed since the lone pair of the ligand may be coordinated during the reaction with the sulphur centre to obtain the pseudo trigonal bipyramidal valence state.46 It means that such a reaction may be classified as the nucleophilic attack where the lone pairs of the sulphur do not participate in the reaction. If one refers to the s-hole concept such an attack should be directed to the sulphur s-hole characterized by the positive electrostatic potential. Hence the goal of this study is to analyze the above mentioned process to refer it to the s-hole concept as well as to analyze the electron charge distribution in the corresponding complexes. The complexes linked through very strong chalcogen bonds and being close to the transition state of the SN2 reaction were not analyzed before.

2 Computational methods The optimizations of all systems considered here were performed with the Gaussian09 set of codes50 leading to energetic minima since no imaginary frequencies were observed. MP2(full)/aug-ccpVTZ calculations were performed for sulphur dicyanide, S(CN)2, and selenium dicyanide, Se(CN)2, molecules and for their complexes with F and Cl ions. S(CN)2 and Se(CN)2 molecules were analyzed before and the meaningful positive electrostatic potential was found for them in extension of the C–S and C–Se bonds.33,34 The binding energies for the H3N S(CN)2 and H3N Se(CN)2 complexes calculated at the MP2/6-311++G(3df,2p)//B3PW91/6-311G(3df,2p) level amount to 8.0 and 9.7 kcal mol1, respectively.34 The complexes of SFCl and SeFCl molecules with Cl anions optimized at the same MP2(full)/aug-cc-pVTZ level are also analyzed here. The choice of the SFCl and SeFCl species is connected with the asymmetry of the electrostatic potential of S and Se atoms in comparison with the symmetrical electrostatic potential in S(CN)2 and Se(CN)2 moieties. In the case of latter species there are two equivalent areas of the positive electrostatic potential being the extension of C–S or C–Se bonds while for the former case the situation is slightly different. There are also two areas of the positive electrostatic potential but because of the more electronegative F-substituent in comparison with the Cl one, the s-hole being the extension of the F–S(Se) bond is more positive than the second s-hole. In general for both cases: S(Se)(CN)2 and S(Se)FCl, two directions of the nucleophilic attack may be predicted (Scheme 1). The binding energies (Ebin’s) for the complexes analyzed were calculated as differences between the energy of the complex and


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Scheme 1 The possible directions of the nucleophilic attack for the S(CN)2 and SFCl molecules. The picture is the same for analogous selenium complexes.

the sum of energies of monomers51 and corrected for the basis set superposition error (BSSE) by the counterpoise method.52 The monomers were optimized separately thus the effect of the deformation of the sub-units of the complex as a result of the complex formation is taken into account.51 Ebin for the stabilized systems is negative; it means that more negative values correspond to stronger interaction. Thus for the convenience of discussion Ebin positive values are presented here in the text while Ebin negative values are presented in tables. The Quantum Theory of ‘Atoms in Molecules’ (QTAIM) was applied.53,54 The QTAIM calculations were carried out with the use of the AIMAll program.55 The characteristics of bond critical points (BCPs) were analyzed: the electron density at BCP (rBCP), its Laplacian (r2rBCP), the total electron energy density at BCP (HBCP), and the components of the latter one, the potential electron energy density (VBCP) and the kinetic electron energy density (GBCP). The following relations between these characteristics are known (eqn (1), in atomic units). 1/4 r2rBCP = 2GBCP + VBCP and HBCP = GBCP + VBCP

(1)

The ELF method is also applied. The electron localization function (ELF) was introduced by Becke and Edgecombe56 and it is a local function describing how much the Pauli repulsion is efficient at a given point of the molecular space. This function was derived originally from the Laplacian of the conditional probability. An alternative interpretation of ELF in terms of the local excess kinetic energy density due to the Pauli repulsion principle has been given by Savin and co-workers.57 The latter approach allows us to generalize ELF to any wave function and in particular to the exact one. The gradient field of ELF was proposed to be used in order to carry out the topological analysis of the molecular space in a similar way as has been done for the Quantum Theory of ‘Atoms in Molecules’(QTAIM).58 The topological analysis based on the electron localization function (ELF) was applied to describe the structure of numerous molecules and complexes and also to describe various interactions.59–63 The ELF calculations and the part of QTAIM ones have been carried out with the TopMoD package.64,65 The ELF function was calculated over a rectangular box using a cubic grid of a step size smaller than 0.1 Bohr. From this box, the ELF isosurfaces have been visualized with the Amira 3.0 software.66 The accuracy of the integrated densities is of the order of 0.02e.


The Natural Bond Orbitals (NBO) method was applied here.67,68 For the A–H B hydrogen bond, the nB - sAH* is often considered as its characteristic interaction which expresses the maximum nB - sAH* overlapping,67–70 nB designates the lone electron pair of the proton acceptor and sAH* designates an antibonding orbital of the A–H proton donating bond. The nB - sAH* interaction is calculated as the second-order perturbation theory energy.67–70 For the complex linked through the chalcogen bond the nB - sZX* interaction is considered. Z designates the chalcogen atom (S or Se for complexes analyzed here), X is the substituent; there is the nucleophilic attack in the direction of the Z–X bond. The bond polarizations are discussed in this study. They are calculated as the percentage of the electron density on the atom considered (designated later as Pol%).67 The Symmetry Adapted Perturbation Theory (SAPT) approach was applied to deepen the understanding of the nature of interactions71 for S(CN)2 and Se(CN)2 complexes and the SAPT2012 program72 was used to perform calculations. SAPT is a well established approach to calculate the interaction energy of two closed-shell moieties where the interaction energy is obtained directly here as a sum of defined contributions. Thus it is different from the commonly applied approaches where the binding energy is calculated as a difference between the energy of the complex and the sum of energies of monomers. In the SAPT approach the interaction energy consists of the following terms: the first-order electrostatics (E(1) elst), second-order induction (2) (E(2) ) and dispersion (E ) energies, and their exchange counterind disp parts: first-order exchange (E(1) ), second-order exchange-induction exch (2) (E(2) ) and exchange-dispersion (E ). exch-ind exch-disp The SAPT method up to the second order gives the main part of the interaction energy. To estimate the higher-order induction and exchangeinduction energies, the Hartree–Fock ‘‘delta’’ correction term dEHF is applied. The SAPT2 interaction energy is calculated according to eqn (2). (2) (2) (1) (2) (2) ESAPT2 = E(1) int elst + Eind + Edisp + Eexch + Eexch-ind + Eexch-disp + dEHF (2)

3 Results and discussion 3.1 Analysis of electrostatic potentials and the formation of chalcogen bonds One of the aims of this study is to analyze the reaction sides for the sulphur and selenium compounds since the areas of the positive electrostatic potential are often attributed to the nucleophilic attack sites while the negative potential areas to the electrophilic attack. Table 1 presents the maximum and minimum electrostatic potential values for S(CN)2, Se(CN)2, SFCl and SeFCl moieties. The isosurface of the electron density of 0.001 au was chosen here according to the suggestion of Bader.73 For all compounds the maximum and positive electrostatic potential is located on sulphur or selenium atoms (see Fig. 1 and 2). This is in line with the s-hole concept since for the divalent Z-atoms in ZX2 molecules considered here (Z = S, Se; X = CN, Cl, F) there are the positive electrostatic potentials in the extension of the XZ bond,


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Table 1 Maximum and minimum electrostatic potentials (in au) for the Z(CN)2 and ZFCl (Z = S, Se) molecules analyzed here as the Lewis acid units for the 0.001 au electron density isosurface. The QTAIM charges of Z, N and F atoms are presented (in au)

Compound

Max (S, Se)

Charge

Min (N, F)

Charge

S(CN)2 Se(CN)2 SFCla SeFCla

0.0721 0.0781 0.0500 0.0643

0.834 0.818 0.919 0.981

0.0403 0.0423 0.0153 0.0219

1.010 1.023 0.683 0.641

a The charge for chlorine amounts 0.235 and 0.341 au for SFCl and SeFCl, respectively.

Fig. 2 Computed electrostatic potential on the 0.001 au molecular surface of SFCl; three projections corresponding to schemes at the right side are given; the positive electrostatic potential area in the extension of S–Cl bond is visible (the bottom picture). The pictures for the selenium moiety is analogous. Blue colour corresponds to maximum electrostatic potential, red to the minimum one (see Table 1).

Fig. 1 Computed electrostatic potential on the 0.001 au molecular surface of S(CN)2; three projections corresponding to schemes presented at the right side are given. The picture for the selenium moiety is analogous. Blue colour corresponds to maximum electrostatic potential, red to the minimum one (see Table 1).

at the edge of Z-atom. The electronegative X substituents enhance the positive s-holes. This was observed earlier for the dicyanide compounds.33,34 The minimum values of the electrostatic potential are located on substituents; for the S(CN)2 and Se(CN)2 species on N-atoms while for the SeFCl and SFCl on fluorine atoms (Fig. 1 and 2). This is interesting that for two last cases the local maxima of the positive electrostatic potential are observed for Cl-atoms in the extension of S–Cl and Se–Cl bonds. Thus, similarly as the S and Se centers, the Cl-atoms may act as the Lewis acids in the extension of S–Cl and Se–Cl bonds forming halogen bonds. The chlorine atom in the SFCl and SeFCl molecules exhibits also a large equatorial belt of the negative electrostatic potential. Table 1 also presents the QTAIM atomic charges for the atoms where the maximum or minimum electrostatic potential was observed. Additionally the footnote of the table presents the Cl-atom charge in SFCl and SeFCl molecules. One can see that the charges, as it was discussed in earlier studies,27–29,74


are not the proper descriptors of the Lewis acid–Lewis base properties and they are only presented here to confirm the previous conclusions. For example, chlorine atoms are characterized by the negative charges which do not explain the dual character of Cl-atoms which may act as the Lewis acids in the extension of S–Cl and Se–Cl bonds as well as they act as the Lewis bases in the direction perpendicular (or nearly so) to these bonds. Note that the maximum positive electrostatic potentials are greater for the selenium species than for sulphur ones (Table 1), which may suggest the stronger interactions for the former complexes than for the latter ones. Fig. 3 shows the molecular graphs of the selected complexes analyzed in this study. Only the sulphur complexes are presented since the selenium ones are analogous. For the SFCl2 complex there are two configurations (Fig. 3), one being the result of the nucleophilic attack in the F–S direction (Fig. 3b) and the second configuration is the result of this attack in the Cl–S direction (Fig. 3c). Hence the linear arrangement of F–S–Cl and Cl–S–Cl atoms is observed, respectively. Consequently there are two local energetic minima for the SFCl2 complex. For the [S(CN)2Cl] complex there is one energetic minimum since two sulphur s-holes are equivalent. The analogous situation as for the sulphur complexes exists for the selenium complexes. It is worth mentioning that for the ZFCl2 complexes the linear Cl–Z–Cl configurations (Fig. 3c) are more stable than the liner Cl–Z–F configurations (Fig. 3b) by 2.1 and 1.7 kcal mol1 for Z = S and Z = Se, respectively. The arrangement of sub-units after the process of complexation presented here is in line with the experimental observations. The chalcogen bonds were observed


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Paper Table 2 Results for the [Z(CN)2X] and ZFCl2 complexes (Z = S, Se), QTAIM parameters (in au) are presented, Dis (in Å) designates the distance between the Lewis base center (F, Cl) and the Z-atom of the Lewis acid, Pol% is also givena,b

Complex


[S(CN)2F] [S(CN)2Cl] [Se(CN)2F] [Se(CN)2Cl] [(SFCl)Cl],1c [(SFCl)Cl],2c [(SFCl)Cl],3c [(SFCl)Cl],1d [(SFCl)Cl],2d [(SFCl)Cl],3d [(SeFCl)Cl],1c [(SeFCl)Cl],2c [(SeFCl)Cl],3c [(SeFCl)Cl],1d [(SeFCl)Cl],2d [(SeFCl)Cl],3d SFCl, S–F SFCl, S–Cl SeFCl, Se–F SeFCl, Se–Cl

rBCP

r2rBCP

HBCP

Dis

Pol%

0.0995 0.0450 0.0976 0.0526 0.1407 0.1442 0.0709 0.1810 0.0866 0.0865 0.1198 0.1176 0.0677 0.1568 0.0778 0.0774 0.1873 0.1596 0.1639 0.1307

0.1401 0.0808 0.2052 0.0752 0.0123 0.1007 0.0692 0.1849 0.0520 0.0521 0.2488 0.0110 0.0683 0.4060 0.0579 0.0581 0.2714 0.1439 0.4516 0.0231

0.0459 0.0075 0.0403 0.0118 0.1115 0.0877 0.0210 0.1996 0.0311 0.0310 0.0637 0.0640 0.0210 0.1061 0.0277 0.0274 0.2072 0.1073 0.1141 0.0780

1.951 2.620 1.985 2.588 1.780 2.049 2.394 1.635 2.302 2.302 1.884 2.179 2.454 1.756 2.388 2.391 1.617 2.000 1.736 2.125

— — — — 13.51 38.21 14.62 22.41 17.94 17.92 11.17 33.27 13.18 20.02 15.39 15.33 24.33 40.26 22.09 35.92

a

The numeration of BCPs is given in the first left column according to the designations of Fig. 3. b The last four lines of the table correspond to the monomeric systems. c The configuration corresponding to Fig. 3b. d The configuration corresponding to Fig. 3c.

Fig. 3 The molecular graphs of the following complexes; (a) [S(CN)2Cl], (b) and (c) two configurations of the SFCl2 complex, big circles correspond to attractors while small circles to bond critical points. Bond paths and the electron density isolines are presented. The numeration of BCPs is introduced for the convenience of the further discussion.

in crystal structures of sulfur,75 selenium76 and tellurium77 dicyanides. For these crystal structures the similar arrangement of molecules was observed with the C–Z N angle (Z = S, Se, Te) close to 1801, where Z N is the chalcogen bond between dicyanide molecules. For example, for the tellurium dicyanide structure this angle is equal to 163.2(5)1.77 Table 2 shows that all interactions analyzed may be classified as strong ones since for all the total electron energy density at the corresponding bond critical point, HBCP, is negative. This also means that those interactions may be treated as covalent bonds or at least as interactions possessing partly covalent character. In a few cases the Laplacian of the electron density at BCP is negative, it means that such interactions are classified without any doubt as covalent bonds according to the QTAIM approach. It seems that for complexes of dicyanides the Z F(Cl) interactions may be classified as very strong chalcogen bonds. For the ZFCl2 complexes there are interactions which may be classified as covalent bonds thus the sulphur and selenium


atoms are trivalent and the latter species may be treated as single ions. It is confirmed by numerous results presented here. For example, the Z F(Cl) distances for complexes of dicyanides are greater than such distances in ZFCl2 ions (Table 2). The similar is observed for the electron density at BCP, rBCP, the lowest values are observed for the complexes of dicyanides. The latter values, B0.05–0.1 au, are large in comparison with other weak or medium in strength interactions, but smaller than rBCP’s for remaining species collected in Table 2. Fig. 4 shows dependencies between the distance and the electron density at BCP (the results of Table 2 are considered).

Fig. 4 The relationships between the distance (in Å) and the electron density at the corresponding BCP (in au); the following interactions are considered: S F (full circles), Se F (full squares), S Cl (open circles) and Se Cl (open squares).


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PCCP Table 3 Binding energy (corrected for BSSE), Ebin, BSSE correction, EBSSE, and the deformation energy, Edef (in kcal mol1), for complexes analyzed here

Complex


[S(CN)2Cl] [Se(CN)2Cl] [S(CN)2F] [Se(CN)2F] SFCl2 a SFCl2 b SeFCl2 a SeFCl2 b Scheme 2 The n(F) - sSC* interaction for the linear arrangement of F– S–C atoms. The similar situation is observed for all other dicyanide complexes.

Four classes of interactions are presented, S F, Se F, S Cl and Se Cl. One can see that the linear correlations are excellent and that the difference between interactions is greater if different kinds of the Lewis bases are considered (F or Cl anion) while for the same kind of anion the differences between S and Se species are not significant. For each linear relationship presented in Fig. 4 the point of the greatest distance and the smallest rBCP corresponds to the dicyanide complex. The NBO method indicates that for S and Se atoms in the ZFCl2 species there are three Z–F(Cl) s-bond orbitals, each with the electron occupancy close to 2. For the dicyanide complexes there is the n(F/Cl) - sZ–C* orbital–orbital interaction corresponding to the chalcogen bond (Scheme 2). The energies of those interactions for [S(CN)2F], [S(CN)2Cl], [Se(CN)2F] and [Se(CN)2Cl] complexes amount 48.5, 22.6, 62.8 and 40.7 kcal mol1, respectively. Thus these interactions, according to the NBO approach, may be classified as strong ones but not as covalent bonds. These interactions concern the linear arrangement (or close to linearity) of the C–Z F(Cl) atoms. The other n(F/Cl) - sZ–C* interactions corresponding to nonlinear arrangements in dicyanide complexes are negligible or even are not detectable (Scheme 2). Table 2 shows also the bond polarizations for the complexes of SFCl and SeFCl. They were calculated as the percentage of the electron density on the S or Se atom. All values in complexes, and it concerns Z–F and Z–Cl bonds, are smaller than the corresponding ones in monomers (see Table 2). It means that there is withdrawal of the electron charge from S and Se atoms to the terminal more electronegative parts (F and Cl atoms) as a result of the complex formation. It also means that the bonds in ZFCl2 species possess the strong ionic character. This is discussed in the next section. 3.2 The energy dependencies and the redistribution of the electronic charge Table 3 presents binding energies for the complexes analyzed here. These energies refer to the monomers optimized separately (see Computational methods section) thus they contain the deformation energy term.51 The binding energies contain also the BSSE correction term. All interactions analyzed are very


a

Ebin

EBSSE

Edef

27.7 33.5 46.8 54.7 22.7 24.4 30.9 32.6

2.5 3.2 2.9 4.1 2.6 3.0 3.9 3.9

2.4 4.3 5.6 7.5 8.7 15.5 7.3 12.0

Symmetric case (see Fig. 3c).

b

Asymmetric case (Fig. 3b).

strong since the binding energy range is from 27.7 to 54.7 kcal mol1. The strongest interactions are observed for the dicyanide complexes with fluorine anion, i.e. 46.8 and 54.7 kcal mol1 for sulphur and selenium moieties, respectively. It might be surprising since the results presented in the previous sections indicate the trivalency of S and Se atoms for SFCl2 and SeFCl2 moieties while for dicyanide complexes the interactions are detected. However other results should be discussed. The greatest deformation energies are observed for the SFCl2 and SeFCl2 moieties, even up to +15.5 kcal mol1. It coincides usually with the covalency of interaction connected with the meaningful electron charge redistribution being the result of complexation.48,78 The SAPT applied here seems to be the proper approach to analyze the closed-shell interactions.72 It was mentioned previously here that the nucleophilic attack of Cl anions on the ZFCl molecule leads to the formation of single ions since S or Se atoms become trivalent. This is why the SAPT approach was applied only for complexes of dicyanides. Table 4 shows the SAPT2 interaction energy as well as the interaction energy terms (eqn (2)). The Hartree–Fock EHF int energy for all four complexes analyzed here is always more than 20% ‘‘less attractive’’ than the SAPT2 energy, which shows the role of the dispersive contribution, E(2) disp. If one considers the attractive (negative) terms of the interaction energy thus the induction one, E(2) ind, seems to be the most important, followed by the electrostatic term, E(1) el and the above mentioned dispersive term. However the induction and dispersive terms are strongly damped (2) by their exchange counterparts, E(2) exch-ind and Eexch-disp, respectively.

Table 4

SAPT interaction energy terms (in kcal mol1)a

Energy term

[S(CN)2Cl]

[Se(CN)2Cl]

[S(CN)2F]

[Se(CN)2F]

E(1) elst E(1) exch E(2) ind E(2) disp E(2) exch-ind E(2) exch-disp dEHF EHF int ESAPT2 itt

50.6 59.4 98.2 17.3 78.0 5.0 8.2 21.4 31.8

66.8 77.4 196.0 18.2 159.8 5.2 2.7 28.9 41.3

104.4 135.9 205.7 26.6 144.2 7.9 15.0 49.5 63.8

123.2 148.0 352.7 25.3 265.6 7.7 0.2 61.3 80.2

a

See eqn (2), EHF int is the Hartree–Fock interaction energy.


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In the case of the induction interaction energy, it is reduced by 70–82% while for the dispersive energy its reduction is of 29–30%. On the other hand, the first order electrostatic energy is outweighed by the first order exchange energy. Hence it shows the role of the induction energy in spite of the fact that the latter one is strongly reduced by its counterpart. It may be explained in terms of the s-hole concept that the formation of complexes of dicyanides is steered by the electrostatic potentials, in consequence by the electrostatic interactions, but the other effects connected with the shift of the electron density are very important. There are other observations; the absolute values of the dispersive energy are greater for complexes of F than for complexes of Cl, even if the exchange counterpart of the dispersion energy is taken into account. However all interaction energy terms are interrelated thus for the stronger interaction and consequently the shorter intermolecular distance the absolute values of all interaction energy terms increase. If one compares the dispersive energies with the total SAPT2 ones, thus the dispersion contributes more to the stabilization energy for Cl complexes than for F ones. One can see the difference between the binding energies (Table 3) and the SAPT2 interaction energies (Table 4). However these terms are defined in different ways. The binding energy contains the deformation energy term being the result of complexation while SAPT2 energy considers the geometry of sub-units in the complex thus such deformation is not taken into account there. If one excludes the positive deformation energy from the binding energy thus the results are more ‘‘negative’’ and closer to the SAPT2 values. Additionally SAPT results are free from the basis set superposition error while the counterpoise method overestimates positive BSSE values included in the binding energies, especially for the MP2 method applied here.79 This leads to the results which suggest that the interactions analyzed are less attractive than they should be. The electronic shift related to the induction interaction energy term may be roughly evaluated if the QTAIM integrated charges are considered. It was mentioned earlier here that the charges are not the proper terms to predict the Lewis acid–Lewis base properties of the centers analyzed. However they may be applied to consider the processes connected with the electronic charge shift being the result of complexation. The QTAIM charges seem to be the proper ones for such a consideration since they are derived from the well performed electron charge space decomposition into the atomic basins.53,54 Besides it was claimed before that the charges derived from any population analysis are not measurable, it means that they do not have their experimental counterparts; except of QTAIM charges which may be determined from the crystal structure analysis.80 In the case of F or Cl ions interacting with dicyanides the negative charge of anions decreases approximately by 0.1–0.2e. It shows approximately how important is the electronic charge shift being the result of complexation for dicyanide complexes. This is worth mentioning that for the water dimer such electronic charge shift from the proton accepting molecule to the donating


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Fig. 5 The QTAIM charge distribution for the [S(CN)2Cl] complex; such distribution for isolated S(CN)2 and Cl is given in parentheses.

one amounts B0.02e (this depends on the level of calculations).81 Fig. 5 shows the distribution of QTAIM integrated charges for the [S(CN)2Cl] complex. The charges for non-interacting sub-units, i.e. S(CN)2 molecules and Cl ions are given in parentheses. This is interesting that the complexation leads to the decrease of the positive charge of sulphur and the increase of the negative charge of nitrogen atoms; the positive charge of carbon atoms increases. In other words the complexation leads to the accumulation of the negative charge on sulphur and nitrogen electronegative atoms and to its withdrawing from carbon atoms. The same qualitative picture is observed for the other dicyanide complexes analyzed here; the electron charge transfer from fluorine and chlorine anions to dicyanide moieties, the accumulation of electronic charge on nitrogens and sulfur or selenium and the depletion of the electronic charge on carbon atoms. For complexes of SFCl and SeFCl with Cl anions there is the electron charge transfer from the anion and the complexation leads to the decrease of the charge (increase of the electron density) for all atoms of the SFCl or the SeFCl moiety. It seems that the qualitative picture of the complexation is similar for all complexes considered since the electronic charge shift is observed, from the Cl or F to the Z-atom and next to the remaining parts of the Z(CN)2 or the ZFCl molecule. In the case of dicyanides, due to the difference in electronegativity between carbon and nitrogen atoms, the shift of the electron density to the nitrogen atoms is observed resulting in the increase of the positive charge of carbon atoms. 3.3

The ELF topological changes from reactants to products

As displayed in Fig. 6, the S(CN)2 unit is characterized by eight valence basins in both the S(CN)2 monomer and [S(CN)2Cl] complex. In other words, the formation of the [S(CN)2Cl] complex resulting from the S(CN)2 + Cl reaction corresponds to a process indicating the electrostatic character of the interaction between the chlorine anion and the sulphur site of the S(CN)2 unit. In contrast, for the SFCl + Cl reaction the decrease from seven valence basins in reactants to six ones in the final product is observed (Fig. 7). This reduction concerns a


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Table 5 ELF populations (in electrons) for S(CN)2 and SFCl monomers as well as for corresponding complexes

Basin

Without Cl

With Cl symmetric

S(CN)2 V(S)1 V(S)2 V(S, C1) V(C1, N1) V(N1) V(S, C2) V(C2, N2) V(N2) V(Cl)a

1.98 1.98 2.18 4.53 3.09 2.18 4.53 3.09 8.00

2.07 2.07 2.21 4.18 3.36 2.20 4.25 3.38 7.84

(+0.09) (+0.09) (+0.03) (0.35) (+0.27) (+0.02) (0.28) (+0.29) (0.16)

SFCl V(S)1 V(S)2 V(S, Cl) V(Cl) V(S, F) V(F) V(Cl)a

2.25 2.25 1.11 6.52 0.60 7.00 8.00

2.48 2.48 0.00 7.54 0.62 7.07 7.54

(+0.23) (+0.23) (1.11) (+1.02) (+0.02) (+0.07) (0.46)

a

With Cl asymmetric

2.40 2.40 1.11 6.56 0.00 7.63 7.63

(+0.15) (+0.15) (0.00) (+0.04) (0.60) (+0.63) (0.37)

Added chlorine anions.

Fig. 6 Isosurface of ELF function for S(CN)2 monomers (a) and the [S(CN)2Cl] complex (b) for Z(r) = 0.80.

Fig. 7 Isosurface of ELF function for SFCl monomers (a), the SFCl2 symmetrical complex (b) and the SFCl2 asymmetric complex (c) for Z(r) = 0.75.

disynaptic basin, namely V(S, Cl), in the symmetric product and V(S, F) in the asymmetric one. It is worth noting the lack of any disynaptic basin in the direction of the s-hole on both sides of the sulphur atom. In other words, two directional interactions (initially one of them is the S–F or S–Cl bond in the monomer)


should be characterized, similar to the previous case, as electrostatic ones from the ELF topological point of view. The ELF valence basin populations are gathered in Table 5. In the case of the [S(CN)2Cl] complex, we note a small charge transfer from chlorine anions to the S(CN)2 subunit when we compare the basin population of the S(CN)2 subunit to those of free S(CN)2. It amounts nearly 0.2 electrons coming from chlorine anions and borne equally by the sulphur monosynaptic basins. It is striking also to underline a charge redistribution within the S(CN)2 unit due to the interaction of Cl with S(CN)2. Accordingly, the population of both V(C1, N1) and V(C2, N2) decreases unequally (0.35 and 0.28e), while the population of two V(N1) and V(N2) monosynaptic basins increases unevenly (0.27 and 0.29e). The V(S, C1) and V(S, C2) populations are left almost unchanged upon the interaction. It is also interesting to note that the largest change occurs on the basin which is situated in the s-hole bond direction, namely the V(C1, N1) basin. The V(C2, N2) population increases but lesser than that of the V(C1, N1) one. An enhancement of charge transfer has been found in both SFCl2 species (0.46 and 0.37e for the symmetric and asymmetric compounds, respectively). We primarily found the transferred electrons equally on both monosynaptic basins of sulphur atoms. The ELF integrated population of two halogen atoms bonded to sulphur on the s-hole direction is the same within the symmetric (7.54e) and asymmetric (7.63e) compounds. It is interesting to note that the third halogen atom is bonded to the sulphur atom by a disynaptic basin oriented perpendicular to the s-hole direction. The population of this basin remains utterly unchanged when going from the SFCl monomer to the final SFCl2 product. It is worth noting that the observation of the reduction of the disynaptic basin, V(S, Cl), in the symmetric configuration and V(S, F) in the asymmetric one of the SFCl2 moiety is in line with the results presented in the former sections. For example,


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the polarization (the percentage of the electron density at the Satom) of the S–F and S–Cl bonds in the s-hole direction amounts 13.5% and 14.6%, respectively, while this value for the remaining C–Cl bond is equal to 38.2% (see Table 2). In the case of a symmetric moiety the polarization for both C–Cl bonds is equal to 17.9% and for the C–F bond 22.4%. Thus a concentration of the electronic density at the terminal atoms is observed for both configurations, greater in the direction of the nucleophilic attack. That is why the reduction of the disynaptic basis is observed in this direction. The similar picture of the electron density concentration is observed for the SeFCl2 configurations. 3.4

A topological description of the r-hole concept

In order to effect deeper analysis of the s-hole concept across two topological approaches, we now continue our study on the spatial distribution of the charge concentration (CC) and depletion (CD) within the studied molecular species. As a matter of fact, it is interesting to emphasize that the s-hole concept links the structural properties of halogen bonded systems as well as of other noncovalent interactions and the electrostatic potential providing a nice visual explanation. On the other hand, as it has been numerously underlined by Bader82,83 the topology of the Laplacian of a scalar function, such as electron density or electron localization functions, in real space is a consequence of the electron pairing determined by the conditional pair density and enables us to distinguish between CC and CD. A local CC corresponds actually to a Lewis base or a nucleophilic site, while a local CD to a Lewis acid or an electrophilic site on the molecular surface. The topology of the Laplacian of the electron density for the S(CN)2 molecule in three and in two dimensions is displayed in Fig. 8a and b, respectively. We note that the opening on the both sides of the sulphur atom is found for the Laplacian isosurfaces of r2r = 0.253 au. At this value, a clear separation occurs between the CC domain corresponding to the nonbonded electron pair of sulphur and those of two S–C bonds. The conical opening having its centre at the sulphur atom enables us to define two types of spatial gates: an electrophilic gate (VSCC = Valence Shell Charge Concentration) and a nucleophilic gate (VSCD = Valence Shell Charge Depletion). The analogous results for the S(CN)2 molecule obtained with the use of the topology of ELF function are presented in Fig. 9. Both kinds of gates are actually obtained with the ELF value equal to 0.759. In Fig. 10 and 11 the topology of the charge density and of the ELF function for the [S(CN)2Cl] complex are shown, for r2r(r) = 0.221 au and Z(r) = 0.754 au, respectively. As it could be expected that a second nucleophilic gate is still free and can accommodate another halogen anion or a Lewis base. A perfect isomorphic mapping between two topological approaches is shown in Fig. 12 for the S(CN)2 molecule. The VSCD gates provide a striking visual display of the chalcogen bonding region and explain nicely the geometrical parameters. It is interesting to note that the boundary angles of the VSCD gate not only fully cover the s-hole direction, but also provide a


Fig. 8 (a) Isosurfaces of the Laplacian of electron density (r2r = 0.253 au) of the S(CN)2 monomer. Isolines of r2r are included – black and red contours correspond to negative and positive Laplacian values, respectively (range set to 0.2 au with step equal to 4 102 au); (b) isolines for a unique value of r2r = 0.253 au are presented in the plane of S(CN)2 molecules. For r2r o 0.253, the isosurface splitting begins.

Fig. 9 (a) ELF function isosurfaces (Z(r) = 0.759) and contours (step equal to 0.1) for S(CN)2 monomers, (b) ELF function isolines given for an unique value of Z(r) equal to 0.759 in the plane of S(CN)2 molecules. For Z(r) > 0.759, the isosurface splitting begins.


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Fig. 12 ELF gate vs. QTAIM gate for the S(CN)2 monomer. Isosurface of ELF function (wired) and of Laplacian (shaded) is shown.

Fig. 10 (a) Isosurfaces of the Laplacian of electron density (r2r = 0.221 au) of the [S(CN)2Cl] complex. Isolines of r2r are included – black and red contours correspond to negative and positive Laplacian values, respectively (range set to 0.2 au with step equal to 4 102 au); (b) isolines for a unique value of r2r = 0.221 au are presented in the plane of the [S(CN)2Cl] complex.

Fig. 11 (a) ELF function isosurfaces (Z(r) = 0.754) and contours (step equal to 0.1) for the [S(CN)2Cl] complex, (b) ELF function isolines given for a unique value of Z(r) equal to 0.754 in the plane of the [S(CN)2Cl] complex.

region for the nucleophilic attack. The topology of the Laplacian of the electron density is in this sense more flexible than the s-hole direction.


This consideration is in agreement with the optimized geometrical parameters since the chlorine anion attacks indeed the sulphur atom in forming a Cl–S–C angle lesser than 1801, i.e. 174.21 for the [S(CN)2Cl] complex while for SFCl2 the Cl–S–Cl and F–S–Cl angles are equal to 176.41 and 177.01 for symmetric and asymmetric species, respectively. This is also in agreement with the experimental results for the crystal structures of dicyanides mentioned earlier here where the analogous angle for the chalcogen bonds was lesser than 1801. Finally, the results presented here are in line with studies of Politzer and coworkers27–29 where it was pointed out that the atomic charges do not allow us to predict the halogen bond formation and the other s-hole bonds, whereas as has been shown clearly here the topology of the Laplacian exhibited by a local function does it nicely. The topological analysis to describe the reaction paths and particularly the reaction sites was applied in numerous studies before. For example, Kraka and Cremer, in one of the first studies of this type,84 applied Bader’s theory to describe simple chemical reactions by the analysis of the changes in molecular graphs and the electron density during the reaction processes. The protonation of CN to give the HCN or HNC product was described and the contour-line diagrams of the Laplace concentration, defined as r2r(r), were considered.84 The authors have stated that the electrophilic attack of the proton at the nitrogen and carbon sides of CN is possible but the HNC product is less stable than HCN one. Similarly, the ELF method was applied to describe chemical reactions,85 particularly the ozone addition on benzene,86 or the SN2 reactions for the simple derivatives of methane;87 one can mention the other studies.88 However the analysis of the nucleophilic attack sites with the use of both QTAIM and ELF methods as well as the use of the latter topological approaches to explain the s-hole phenomenon were not performed before; particularly the deeper analysis of the geometrical dependencies for the nucleophilic attack derived from topological methods was not analyzed before.

4 Conclusions The chalcogen bonds analyzed here are classified as the s-hole bonds and the electrostatic potentials of monomers allow us to


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predict the arrangement of sub-units in complexes. For example, for all monomers analyzed here, i.e. S(CN)2, Se(CN)2, SFCl and SeFCl, there are two s-holes resulting in the corresponding positive electrostatic potential areas on molecular surfaces for S or Se atoms. Such areas indicate the possible nucleophilic attack sites of the Lewis base moiety. And really the geometry of the complexes formed confirms the s-hole concept predictions; the nucleophilic attack follows according to the s-hole direction since the arrangements close to linearity are observed for those complexes, i.e. the Cl Z–X angle is close to 1801, where Z = S or Se and X = C, Cl or F. The charge assisted chalcogen bonds analyzed here may be classified as extremely strong interactions. For complexes of dicyanides the Z Cl(F) contacts are characterized by the bond critical point possessing the negative value of the total electron energy density. This means that such interactions are partly covalent in nature or they may be even classified as covalent bonds. According to the NBO results the S and Se atoms are trivalent in the SFCl2 and SeFCl2 complexes. These species are characterized by the pseudo trigonal bipyramidal structure, which is typical for the nucleophilic attack in the case of sulphur compounds.46 The SAPT approach was also applied to analyze interactions in the complexes of dicyanides. It was found that the induction energy is the most important attractive interaction energy term for those complexes followed by the electrostatic and dispersive terms. It means that for such strong interactions the electron density shift is very important for the process of complexation but also that the electrostatic interactions steer the arrangement of sub-units in complexes. The topological approaches, QTAIM and ELF, allow us to analyze the electron charge distribution in species analyzed, which is the most important to predict the nucleophilic and electrophilic attack sites, named in this study nucleophilic and electrophilic gates. For all monomers considered: S(CN)2, Se(CN)2, SFCl and SeFCl, there are two nucleophilic gates and the interaction with chlorine or fluorine ions leads to the formation of complexes (or single ions as for SFCl2 and SeFCl2).

Acknowledgements Financial support comes from Eusko Jaurlaritza (GIC 07/85 IT330-07) and the Spanish Office for Scientific Research (CTQ2011-27374) (SJG). Technical and human support provided by Informatikako Zerbitzu Orokora – Servicio General de Informatica de la Universidad del Pais Vasco (SGI/IZO-SGIker UPV/ ń (MICINN), Gobierno EHU), Ministerio de Ciencia e Innovacio Vasco Eusko Jaurlanitza (GV/EJ), European Social Fund (ESF) is gratefully acknowledged (SJG).

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Notes and references 1 H.-J. Schneider, Angew. Chem., Int. Ed., 2009, 48, 3924–3977. ¨ller-Dethlefs, Non-Covalent Inter2 P. Hobza and K. Mu actions, Theory and Experiment, Royal Society of Chemistry,


28 29

Thomas Graham House, Science Park, Milton Road, Cambridge, 2010. J. S. Murray, K. E. Riley, P. Politzer and T. Clark, Aust. J. Chem., 2010, 63, 1598–1607. P. Lipkowski, S. J. Grabowski and J. Leszczynski, J. Phys. Chem. A, 2006, 110, 10296–10302. G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. S. Scheiner, Hydrogen Bonding: A Theoretical Perspective, Oxford University Press, New York, 1997. S. J. Grabowski, Hydrogen Bonding – New Insights, in Challenges and Advances in Computational Chemistry and Physics, ed. J. Leszczynski, Springer, 2006, vol. 3. P. Metrangolo and G. Resnati, Chem.–Eur. J., 2001, 7, 2511–2519. G. Cavallo, P. Metrangolo, T. Pilati, G. Resnati, M. Sansotera and G. Terraneo, Chem. Soc. Rev., 2010, 39, 3772–3783. ´ and M. Yan ˜ ez, J. Phys. Chem. A, 2002, 106, P. Sanz, O. Mo 4661–4668. W. Wang, B. Ji and Y. Zhang, J. Phys. Chem. A, 2009, 113, 8132–8135. ãs, F. Teixidor, S. Paavola M. R. Sundberg, R. Uggla, C. Vin ¨s, Inorg. Chem. Commun., 2007, 10, 713–716. and R. Kiveka ¨nnecke and E. Hey-Hawkins, Dalton (a) S. Tschirschwitz, P. Lo Trans., 2007, 1377–1382; (b) S. Bauer, S. Tschirschwitz, ¨nnecke, R. Franck, B. Kirchner, M. L. Clark and P. Lo E. Hey-Hawkins, Eur. J. Inorg. Chem., 2009, 2776–2788. J. E. Del Bene, I. Alkorta, G. Sanchez-Sanz and J. Elguero, J. Phys. Chem. A, 2011, 115, 13724–13731. S. Scheiner, Chem. Phys. Lett., 2011, 514, 32–35. A. Bundhun, P. Ramasami, J. S. Murray and P. Politzer, J. Mol. Model., 2013, 19, 2739–2746. D. Mani and E. Arunan, Phys. Chem. Chem. Phys., 2013, 15, 14377–14383. S. J. Grabowski, Phys. Chem. Chem. Phys., DOI: 10.1039/ C3CP53369G. ´, T. J. Mooibroek and A. Frontera, Angew. Chem., Int. A. Bauza Ed., 2013, 52, 12317–12321. J.-M. Lehn, Angew. Chem., Int. Ed. Engl., 1988, 27, 89–112. J.-M. Lehn, Angew. Chem., Int. Ed. Engl., 1990, 29, 1304–1319. J.-M. Lehn, Supramolecular Chemistry, Verlag-Chemie, Weinheim, 1995. T. Brinck, J. S. Murray and P. Politzer, Int. J. Quantum Chem., 1992, 44(suppl. 19), 57–64. T. Brinck, J. S. Murray and P. Politzer, Int. J. Quantum Chem., 1993, 48(suppl. 20), 73–88. T. Clark, M. Hennemann, J. S. Murray and P. Politzer, J. Mol. Model., 2007, 13, 291–296. J. S. Murray, P. Lane and P. Politzer, J. Mol. Model., 2009, 15, 723–729. P. Politzer, J. S. Murray and T. Clark, Phys. Chem. Chem. Phys., 2010, 12, 7748–7757. P. Politzer and J. S. Murray, ChemPhysChem, 2013, 14, 278–294. P. Politzer, J. S. Murray and T. Clark, Phys. Chem. Chem. Phys., 2013, 15, 11178–11189.


View Article Online


Paper

30 S. J. Grabowski, Phys. Chem. Chem. Phys., 2013, 15, 7249–7259. 31 Z. P. Shields, J. S. Murray and P. Politzer, Int. J. Quantum Chem., 2010, 110, 2823–2832. 32 P. Politzer, K. E. Riley, F. A. Bulat and J. S. Murray, Comput. Theor. Chem., 2012, 998, 2–8. 33 P. Politzer, J. S. Murray and J. S. Concha, J. Mol. Model., 2008, 14, 659–665. 34 J. S. Murray, P. Lane, T. Clark and P. Politzer, J. Mol. Model., 2007, 13, 1033–1038. 35 F. T. Burling and B. M. Goldstein, J. Am. Chem. Soc., 1992, 114, 2313–2320. 36 S. Dahaoui, V. Pichon-Pesme, J. A. K. Howard and C. Lecomte, J. Phys. Chem. A, 1999, 103, 6240–6250. 37 M. Iwaoka, S. Takemoto and S. Tomoda, J. Am. Chem. Soc., 2002, 124, 10613–10620. ´ and M. Ya ń ˜ez, Phys. Chem. Chem. Phys., 2003, 38 P. Sanz, O. Mo 5, 2942–2947. ń ˜ ez and O. Mo ´, Chem.–Eur. J., 2002, 8, 39 P. Sanz, M. Ya 3999–4007. 40 U. Adhikari and S. Scheiner, Chem. Phys. Lett., 2012, 532, 31–35. 41 S. Scheiner, Int. J. Quantum Chem., 2013, 113, 1609–1620. 42 S. Scheiner, CrystEngComm, 2013, 15, 3119–3124. ´, D. Quin õnero, P. M. Deya ` and A. Frontera, Crys43 A. Bauza tEngComm, 2013, 15, 3137–3144. ¨ppel and R. Gleiter, J. Am. 44 C. Bleiholder, D. B. Werz, H. Ko Chem. Soc., 2006, 128, 2666–2674. 45 S. Tsuzuki and N. Sato, J. Phys. Chem. B, 2013, 117, 6849–6855. 46 M. Iwaoka and N. Isozumi, Molecules, 2012, 17, 7266–7283. 47 S. J. Grabowski, W. A. Sokalski, E. Dyguda and J. Leszczynski, J. Phys. Chem. B, 2006, 110, 6444–6445. 48 S. J. Grabowski, Chem. Rev., 2011, 11, 2597–2625. 49 S. J. Grabowski, J. Phys. Chem. A, 2011, 115, 12340–12347. 50 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. Montgomery, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, revision A.1, Gaussian Inc., Wallingford CT, 2009. 51 (a) S. J. Grabowski, Annu. Rep. Prog. Chem., Sect. C, 2006, 102, 131–165; (b) S. J. Grabowski, A. J. Sadlej, W. A. Sokalski and J. Leszczynski, Chem. Phys., 2006, 327, 151–158.


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52 S. F. Boys and F. Bernardi, Mol. Phys., 1970, 19, 553–566. 53 R. F. W. Bader, Atoms in Molecules, A Quantum Theory; Oxford University Press, Oxford, 1990. 54 Quantum Theory of Atoms in Molecules: Recent Progress in Theory and Application, ed. C. Matta and R. J. Boyd, WileyVCH, 2007. 55 T. A. Keith, AIMAll (Version 11.08.23), TK Gristmill Software, Overland Park KS, USA, 2011 (aim.tkgristmill.com). 56 A. Becke and K. E. Edgecombe, J. Chem. Phys., 1990, 92, 5397. 57 A. Savin, O. Jepsen, J. Flad, O. K. Andersen, H. Preuss and H. G. von Schnerring, Angew. Chem., Int. Ed. Engl., 1992, 31, 323. 58 B. Silvi and A. Savin, Nature, 1994, 371, 683. 59 F. Fuster and B. Silvi, Theor. Chem. Acc., 2000, 104, 13–21. 60 S. Berski and Z. Latajka, Int. J. Quantum Chem., 2002, 90, 1108. 61 M. E. Alikhani, F. Fuster and B. Silvi, Struct. Chem., 2005, 16, 203–210. 62 X. Krokidis, V. Goncalves, A. Savin and B. Silvi, J. Phys. Chem. A, 1998, 102, 5065. 63 F. Fuster and S. J. Grabowski, J. Phys. Chem. A, 2011, 115, 10078–10086. 64 S. Noury, F. Fuster and B. Silvi, TopMod package, 1997. 65 S. Noury, X. Krokidis, F. Fuster and B. Silvi, Comput. Chem., 1999, 23, 597. 66 Amira 3.0, TGS, Template Graphics Software, Inc., San Diego, CA, 2002. 67 F. Weinhold and C. Landis, Valency and Bonding, A Natural Bond Orbital Donor – Acceptor Perspective, Cambridge University Press, 2005. 68 A. E. Reed, L. A. Curtiss and F. Weinhold, Chem. Rev., 1988, 88, 899–926. 69 F. Weinhold, THEOCHEM, 1997, 398–399, 181–197. 70 F. Weinhold and R. Klein, Mol. Phys., 2012, 110, 565–579. ´ ski and K. Szalewicz, Chem. Rev., 71 B. Jeziorski, R. Moszyn 1994, 94, 1887–1930. 72 R. Bukowski, W. Cencek, P. Jankowski, M. Jeziorska, B. Jeziorski, S. A. Kucharski, V. F. Lotrich, A. J. Misquitta, ´ ski, K. Patkowski, R. Podeszwa, F. Rob, S. Rybak, R. Moszyn K. Szalewicz, H. L. Williams, R. J. Wheatley, P. E. S. Wormer ˙uchowski, SAPT2012: An Ab Initio Program and P. S. Z for Symmetry-Adapted Perturbation Theory Calculations of Intermolecular Interaction Energies. Sequential and parallel versions. User’s Guide. Revision SAPT2012.1, Department of Physics and Astronomy, University of Deleware, Newark, Deleware, USA and Department of Chemistry, University of Warsaw, Warsaw, Poland, 2012. 73 R. F. W. Bader, M. T. Carrol, J. R. Cheeseman and C. Chang, J. Am. Chem. Soc., 1987, 109, 7968–7979. 74 T. Clark, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2013, 3, 13–20. 75 K. Emerson, Acta Crystallogr., 1966, 21, 970–974. ¨tke, B. Krumm and M. Scherr, Inorg. Chem., 76 T. M. Klapo 2008, 47, 7025–7028. ¨tke, B. Krumm, J. C. Ga ´lves-Ruiz, H. No ¨th and 77 T. M. Klapo I. Schwab, Eur. J. Inorg. Chem., 2004, 4764–4769.


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78 S. J. Grabowski and W. A. Sokalski, J. Phys. Org. Chem., 2005, 18, 779–784. 79 B. Paizs and S. Suhai, J. Comput. Chem., 1998, 19, 575–584. 80 (a) V. G. Tsirelson and R. P. Ozerov, Electron Density and Bonding in Crystals, Institute of Physics, Bristol, Philadelphia, 1996; (b) P. Coppens, X-ray Charge Densities and Chemical Bonding, IUCr, Oxford University Press, 1997; (c) T. S. Koritszansky and P. Coppens, Chem. Rev., 2001, 101, 1583–1638. 81 Y. Gu, T. Kar and S. Scheiner, J. Am. Chem. Soc., 1999, 121, 9411–9422. ´s-Guzma ń, Organo82 R. F. W. Bader, C. Matta and F. Corte metallics, 2004, 23, 6253.


Paper

´s-Guzma ń and R. F. W. Bader, Coord. Chem. Rev., 83 F. Corte 2005, 249, 633. 84 E. Kraka and D. Cremer, THEOCHEM, 1992, 255, 189–206. 85 V. Polo, J. Andres, S. Berski, L. R. Domingo and B. Silvi, J. Phys. Chem. A, 2008, 112, 7128–7136. 86 I. M. Ndassa, B. Silvi and F. Volatron, J. Phys. Chem. A, 2010, 114, 12900–12906. 87 V. Polo, P. Gonzalez-Navarrete and B. Silvi, Theor. Chem. Acc., 2008, 120, 341–349. ´s-Guzma ń, R. M. Go ´mez, T. Rocha-Rinza, M. A. 88 F. Corte ńchez-Obrego ń and J. M. Guevara-Vela, J. Phys. Chem. A, Sa 2011, 115, 12924–12932.


S···π Chalcogen Bonds between SF2 or SF4 and C-C Multiple Bonds.

Disordered weak and strong topological insulators.

Mechanical bonds and topological effects in radical dimer stabilization.

Cooperativity of halogen, chalcogen, and pnictogen bonds in infinite molecular chains by electronic structure theory.

Changing weak halogen bonds into strong ones through cooperativity with beryllium bonds.

Strong, low-barrier hydrogen bonds may be available to enzymes.

Strong interband Faraday rotation in 3D topological insulator Bi2Se3.

Unusually short chalcogen bonds involving organoselenium: insights into the Se-N bond cleavage mechanism of the antioxidant ebselen and analogues.

Topological Properties of Chemical Bonds from Static and Dynamic Electron Densities.

Switching the BZ reaction with a strong-acid-free gel.

Strong-field ionization of flash pyrolysis reaction products.

Strong magneto-optical effects due to surface states in three-dimensional topological insulators.

Catalytic Ring-Opening of Cyclic Alcohols Enabled by PCET Activation of Strong O-H Bonds.

Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator.

Combined topological and Landau order from strong correlations in Chern bands.

Transition between strong and weak topological insulator in ZrTe5 and HfTe5.

Responses to social and environmental stress are attenuated by strong male bonds in wild macaques.

Unusual crystal structure of N-substituted maleamic acid - very strong effect of intramolecular hydrogen bonds.

Superconductivity in HfTe5 across weak to strong topological insulator transition induced via pressures.

Bond-weakening catalysis: conjugate aminations enabled by the soft homolysis of strong N-H bonds.

Copper-catalyzed dehydrogenative cross-coupling reaction between allylic C-H bonds and α-C-H bonds of ketones or aldehydes.

Tetrel, chalcogen, and CH⋅⋅O hydrogen bonds in complexes pairing carbonyl-containing molecules with 1, 2, and 3 molecules of CO2.

Topological ring-current and bond-current properties of the altans of certain K-factorizable conjugated systems containing "fixed" single-bonds.

Regenerable antioxidants-introduction of chalcogen substituents into tocopherols.