Nature of a Hydride–Halogen Bond. A SAPT-, QTAIM-, and NBO

Article pubs.acs.org/JPCA

Nature of a Hydride−Halogen Bond. A SAPT-, QTAIM-, and NBO-Based Study§ Mirosław Jabłoński*,† and Marcin Palusiak‡ †

Department of Quantum Chemistry, Nicolaus Copernicus University, 7-Gagarina St., PL.87 100 Toruń, Poland Department of Theoretical and Structural Chemistry, University of Łódź, 163/165 Pomorska St., PL.90 236 Łódź, Poland

‡

S Supporting Information *

ABSTRACT: The nature of a hydride−halogen bond is investigated by means of high-level quantum mechanical calculations expended with symmetry-adapted perturbation theory (SAPT), quantum theory of atoms in molecules (QTAIM), and natural bond orbital (NBO) methods. As model hydride−halogen bonded systems complexes between either LiH or HBeH and either XCF3 or XCCH (X = F, Cl, Br, I) are used. It is shown that the formation of a hydride−halogen bond leads to the elongation of the Rδ+−Hδ− hydride bond, which is accompanied by the blue shift of the νR−H stretching vibration frequency and the increase of the IR intensity of this mode. All these effects, although untypical in the case of, e.g., hydrogen bonds, can be considered as rather typical for hydride−halogen bonded systems. The decomposition of the interaction energy based on the SAPT method clearly indicates the dominant role of the induction term, thus the inductive nature of a hydride−halogen bond in opposition to previous findings. NBO-based analysis indicates the charge transfer from the hydride molecule to the more remote parts of the halogen donor and that the elongation of the R−H bond is caused by the charge outflow from the σRH bonding orbital.

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INTRODUCTION In the plethora of inter- and intramolecular interactions the socalled halogen bonds have recently found a great interest.1−30 These are defined as interactions between a halogen atom (X) and an atom with an excess of electron charge density, most often being an atom with the electron lone-pair (Y). Thus they may be denoted by the RX−X···Y−RY formula. At first, the interaction of this type may seem to be surprising because the halogen atom, being highly electronegative, should accumulate the negative charge and then, as a result, lead to the repulsive interaction while acting on Y. Thus any stabilizing interaction of the RX−X···Y−RY type should not exist if one considers an atom in a molecule as a center bearing entirely positive or entirely negative charge only. The explication is in the anisotropy of the electron density distribution around the halogen atom.4,5,13,14,24,31 Namely, it is accepted that the electron density distribution around the halogen atom accepts ellipsoidal shape with longer radius being perpendicular to the direction of the RX−X halogen bond.4,5,13,14,24,31 As a result a region of the positive electrostatic potential (the so-called σ-hole) is formed on the outermost portion of the halogen’s surface along the RX−X bond’s direction. More precisely, the term σ-hole was originally referred to the electron-deficient outer lobe of the p (or nearly p) orbital involved in the formation of the RX−X covalent bond.4,5,13,14 This σ-hole is then encompassed by the negative electrostatic potential that forms an areola-like belt around the central part of X.4,5,13,14,24 In this way the halogen bond is a consequence of the interaction between Y and the σ-hole region of X and is believed to be mainly of the electrostatic nature.6,11,17,27 However, the dominant role of other energy contributions was also indicated.11,17,28 Riley and Hobza have © 2012 American Chemical Society

found that the dispersive interaction may be dominant in the interaction energy of H3CX···OCH2 (X = Cl, Br) systems.17 However, this finding relates to rather untypical halogen bonded systems where RX = H3C and the halogen atom is small. Otherwise, the electrostatic contribution prevails the interaction energy17 of a halogen bond. On the other hand, the significantly covalent nature of halogen bonds due to the dominant HOMO/ LUMO charge transfer has very recently been shown.28 In reverse to what was claimed by Riley and Hobza, the electrostatic contribution is to be systematically overbalanced by the exchange repulsion.28 Furthermore Zou et al.11 have found the dominant role of charge transfer in dihalogen···NH3 type systems, whereas the dominance of electrostatic term has been found if the halogen was bound to a carbon. Investigating the halogen bond as resulting mainly due to the electrostatic interaction between the σ-hole of a halogen atom and an atom with an excess of electron density, e.g., the electron lonepair, the interaction between partially negatively charged hydrogen atom and halogen, R−Hδ−···X−RX, should also exist. Indeed, this hydride−halogen bond is known and has already been investigated earlier for a small group of representative model systems.32,33 Very recently it has also been shown that a partially negatively charged hydrogen atom can readily interact with an atom with the electron lone-pair vacancy, leading to the so-called charge-inverted hydrogen bonds.34−36 Both these examples show that Hδ− behaves as a good Lewis base. Received: December 2, 2011 Revised: January 24, 2012 Published: January 30, 2012 2322

dx.doi.org/10.1021/jp211606t | J. Phys. Chem. A 2012, 116, 2322−2332

The Journal of Physical Chemistry A

Article

Thus, ΔEBSSE converges to ΔE as the basis set approaches the complete basis set (CBS) limit.60 To give more light in the nature of the hydride−halogen bond, we also performed decomposition of the interaction energy by means of the SAPT method37,38 with the use of the GAMESS package61,62 that was interfaced to the SAPT2008.2 code.63 The SAPT expansion was truncated and took account of the energy correction terms up to second order with respect to the intermolecular interaction operator.

In the present paper we investigate the nature of the hydride− halogen bond by means of high-level quantum mechanical calculations expanded with symmetry-adapted perturbation theory (SAPT), 37−39 quantum theory of atoms in molecules (QTAIM),40,41 and natural bond orbital (NBO)42,43 analysis. All these techniques of theoretical chemistry are among the most often used in investigations of the nature and properties of a wide range of molecular interactions, particularly their strength. A brief description of all these techniques is given in the Methodology.

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(20) (10) (10) (20) ESAPT = Eelst + Eexch + E ind,resp + Eexch ‐ind,resp

METHODOLOGY In the present article we investigated a group of model complexes possessing a hydride−halogen bond as resulting from the interaction between either Li−H or HBe−H acting as donors of Hδ− and either XCF3 or XCCH (X = F, Cl, Br, I) being the source of the halogen atom. Although it is accepted that the fluorine atom is not a good host of a σ-hole, we also investigated fluorinated species to put a consistency of the interaction strength. Moreover, in some cases the σ-hole on F can be created by the presence of highly electronegative atoms in the closest proximity of the X−RX bond. Properties under study in these systems were also compared to those calculated for a few halogen- and hydrogen-bonded complexes. In the former group we investigated H3N···ClCF3, ClCCH and H2O···ClCF3, and ClCCH (N···Cl−C and O···Cl−C halogen bonds, respectively) complexes, whereas in the latter we investigated F−H···ClCF3, ClCCH, and the water dimer (F−H···Cl and O−H···O hydrogen bonds, respectively). All geometry parameters for the investigated complexes and the isolated monomers were optimized at the level of the second-order Møller−Plesset perturbation theory (MP2)44−50 with the aug-ccpVTZ basis set51,52 for all atoms except iodine, for which the Sadlej pVTZ basis set was used.53−57 Calculations were performed with the use of the Gaussian 03 set of codes.58 The frequency analysis was used to verify that the optimized geometries correspond to the ground state stationary points. No imaginary frequencies were found. Shifts of the R−Hδ− (F−H and O−H in the case of hydrogen-bonded complexes) and the X−C stretching vibration frequencies upon the complex formation were also analyzed, thus the deuterium substitution for the hydrogen atom pointing into the halogen atom was used in the case of the HBe−H molecule to avoid couplings. Geometrical and spectroscopical properties of investigated systems are analyzed in the first part of the next section. The interaction energy is computed in several ways. In the supermolecular approach it is given by the difference between the total energy of the complex (AB) and the sum of total energies of the isolated monomers (A and B): ΔE = EAB({AB},AB) − [EA ({A},A) + EB({B},B)]

(12) (20) t (22) + Eelst,resp + tE(22) ind + Eexch‐ind + Edisp (20) (13) (1) + Eexch ‐disp + Eelst,resp + εexch(CCSD) HF + ε(2) disp(2) + δE int,resp

The right side of the above equation is a sum of perturbative energy correction terms that are the consequences of various physical interaction forces.37,38,63 These energy correction terms, except for the very last one, were collected into four fundamental physical components: electrostatic (Eelst), exchange (Eexch), induction (Eind), and dispersion (Edisp) as follows: (5)

(20) E ind = E ind,resp + tE(22) ind

(6)

(20) Edisp = Edisp + ε(2) disp(2)

(7)

+ ε(1) exch(CCSD)

(8)

We use the above grouping scheme in SAPT analysis because it was demonstrated that such a scheme is more appropriate and easier to interpret than other possible schemes.64 We are aware, however, that this is not the only grouping scheme possible for SAPT energy components. Recently, one of us tested65 this scheme against the other one proposed by Thanthiriwatte et al.66 It was found there that for this other scheme the results are qualitatively the same, whereas small quantitative differences do not change conclusions made on the basis of SAPT analysis. The interaction energy derived by means of the SAPT decomposition method can be thus written as follows:

(1)

HF ESAPT = Eelst + Eind + Edisp + Eexch + δE int,resp

(9)

Interaction energies obtained by means of aforementioned formulas are presented and discussed in the second part of the next section. For the optimized complexes, a detailed analysis of the electron distribution function was made according to the concept of the “Quantum Theory of Atoms in Molecules” (QTAIM) proposed by Bader,40,41 using the AIM2000 program.67,68 Properties of electron density calculated at the bond critical point (BCP) of the investigated interactions were characterized. The electron density at BCP, ρBCP, its Laplacian, ∇2ρBCP, and the electronic total energy density, HBCP, were

ΔECP = EAB({AB},AB) − [EA ({AB},AB) (2)

ΔE BSSE = ΔE + [EA ({A},AB) − EA ({AB},AB)] + [EB({B},AB) − EB({AB},AB)]

(10) (12) (13) Eelst = Eelst + Eelst,resp + Eelst,resp

(10) (20) (20) t (22) Eexch = Eexch + Eexch − ind,resp + Eexch‐ind + Eexch‐disp

where in the notation ES({B},G) S denotes the system, B the basis set, and G the geometry source used in calculations for the system S in geometry G. Then interaction energies that take into account either the counterpoise correction59 (ΔECP) or the counterpoise correction and the deformation energy (ΔEBSSE) were also computed:

+ EB({AB},AB)]

(4)

(3) 2323



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Table 1. Selected Geometrical and Spectroscopical Parameters of Investigated Complexesa system

dR−H

LiH···FCF3 LiH···ClCF3 LiH···BrCF3 LiH···ICF3 LiH···FCCH LiH···ClCCH LiH···BrCCH LiH···ICCH HBeD···FCF3 HBeD···ClCF3 HBeD···BrCF3 HBeD···ICF3 HBeD···FCCH HBeD···ClCCH HBeD···BrCCH HBeD···ICCH system

1.6050 1.6048 1.6065 1.6132 1.6049 1.6042 1.6046 1.6067 1.3293 1.3299 1.3304 1.3318 1.3291 1.3297 1.3299 1.3304 dR−H

H3N···ClCF3 H3N···ClCCH H2O···ClCF3 H2O···ClCCH system FH···ClCF3 FH···ClCCH HOD···OH2

ΔdR−H 0.0007 0.0005 0.0022 0.0089 0.0006 −0.0001 0.0003 0.0024 0.0000 0.0006 0.0011 0.0025 −0.0002 0.0004 0.0006 0.0011 ΔdR−H

dH···X

νR−H

ΔνR−H

com IR−H

3.20 2.66 2.47 2.28 3.15 2.69 2.51 2.34 2.94 2.85 2.75 2.65 2.91 2.84 2.74 2.64

1419 1444 1453 1472 1418 1447 1462 1493 1586 1587 1589 1591 1586 1589 1593 1601

2 28 37 56 2 31 46 77 3 5 7 9 4 6 10 19

195 400 695 1347 263 420 639 1129 36 59 79 129 40 62 82 122

νR−H

dY···Cl

dR−H

ΔdR−H

dH···X

3.06 3.06 2.98 2.96 ∠R−H−Y

0.9251 0.9252 0.9687

0.0033 0.0034 0.0073

2.39 2.41 1.95

176.8 176.7 171.1

ΔνR−H

com mon IR−H /IR−H

0.8 1.7 2.9 5.7 1.1 1.8 2.7 4.7 0.9 1.5 2.0 3.3 1.0 1.6 2.1 3.1 com mon IR−H /IR−H

com IR−H

∠H−Cl−C

νR−H

ΔνR−H

com IR−H

com mon IR−H /IR−H

97.2 94.8

4043 4043 2724

−80 −81 −106

403 414 193

3.3 3.4 9.8

a Bond distances in Å, angles in degrees, frequencies in cm−1, IR intensities in km/mol. Results obtained by means of the MP2/aug-cc-pVTZ method (Sadlej pVTZ basis set for I).

It should be remarked that only four systems investigated by us in this article have already been studied by other authors.32,33 These are Li−H···ClCF3 and HBe−H···ClCF3 analyzed by Grabowski et al.32 and HBeH···ClCCH and HBeH···BrCCH analyzed by Li et al.33 Thus the present studies are to widen the already known set of hydride−halogen bonded systems. Geometric and Spectroscopic Properties. For a system possessing the hydride−halogen bond, the geometrical as well as spectroscopical parameters characterizing both the hydride (R−H) and the hydride−halogen (H···X) bond are shown in Table 1, whereas those for the halogen covalent bond (X−C) are shown in Table 2. Hydride−halogen bonds are linear, similarly as standard halogen bonds. This characteristic property results from the axial position of the σ-hole relative to the X−RX bond. This is in contrast to the F−H···Cl−C hydrogen bond where, in spite of the F−H−Cl angle being close to 180°, H, Cl, and C atoms form almost the right angle (see values of ∠H−Cl−C at the bottom of Table 1). This is a demonstration of the anisotropy of a halogen atom that can act as the Lewis acid or as a Lewis base.27 Positive values of ΔdR−H as shown in the third column of Table 1 indicate the elongation of the Rδ+−Hδ− (R = Li, Be) bond upon interaction with a halogen atom. Thus this effect is the same as for typical hydrogen bonds, although in general much weaker (see for example ΔdR−H for the water dimer, which amounts to 0.0073 Å). The rather general elongation (however, rather small in many cases) of the hydride bond is in line with previous findings by Grabowski et al.32 and by Li et al.33 It is seen, however, that negligible shortenings of the hydride bond may also be obtained for less representative hydride−halogen bonded systems.

discussed because they are QTAIM parameters that are the most often used in studies on various intermolecular interactions.69−84 The use of a very large aug-cc-pVTZ basis set in this project is also advisible because this basis set leads to reliable values of QTAIM parameters calculated at BCPs.77,78 Results of QTAIM analysis are presented in the third part of the next section. MOs that result from quantum mechanical calculations are in general considerably delocalized. This may be taken as a disadvantage because their delocalized form may make the analysis of molecular properties difficult. NBO analysis, on the other hand, is based on a method thought to transform a given wave function into a localized form. Thus NBOs correspond to the one-center (electron lone-pairs, nonbonding orbitals) and two-center (bonds) elements of the Lewis structure of a molecule. As a consequence, this helps their interpretation.42,43 NBO-based analysis is presented in the fourth part of the Results and Discussion.

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RESULTS AND DISCUSSION

In confrontation with halogen bonds1−30 hydride−halogen bonds are being studied only sporadically.32,33 Recent studies32−36 have shown, however, that the hydrogen atom with the partial negative charge can readily interact with halogen atoms32,33 or atoms possessing a lone-pair vacancy.34−36 Thus Hδ− should be investigated as a good Lewis base. In this section we present characteristics of the hydride−halogen bond found in a series of complexes between either Li−H or HBe−H and either XCF3 or XCCH (X = F, Cl, Br, I). Presented characteristics are then compared to that found for several model halogen- or hydrogen-bonded species described in the Methodology in more detail. 2324



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Table 2. Selected Geometrical and Spectroscopical Parameters Concerning the X−C Bond in Investigated Complexesa system

dX−C

ΔdX−C

νX−C

ΔνX−C

com IX−C

com mon IX−C /IX−C

LiH···FCF3 LiH···ClCF3 LiH···BrCF3 LiH···ICF3 LiH···FCCH LiH···ClCCH LiH···BrCCH LiH···ICCH HBeD···FCF3 HBeD···ClCF3 HBeD···BrCF3 HBeD···ICF3 HBeD···FCCH HBeD···ClCCH HBeD···BrCCH HBeD···ICCH FH···ClCF3 FH···ClCCH H3N···ClCF3 H3N···ClCCH H2O···ClCF3 H2O···ClCCH

1.3123 1.7416 1.9137 2.1509 1.2763 1.6425 1.8000 2.0256 1.3188 1.7485 1.9102 2.1199 1.2796 1.6391 1.7849 1.9831 1.7650 1.6418 1.7442 1.6412 1.7439 1.6392

−0.0088 −0.0097 0.0025 0.0341 −0.0041 0.0041 0.0181 0.0527 −0.0023 −0.0028 −0.0010 0.0031 −0.0008 0.0007 0.0030 0.0102 0.0137 0.0034 −0.0071 0.0028 −0.0074 0.0008

1314 1130 1117 1117 1078 747 581 472 1296 1120 1107 1108 1073 761 614 533 1105 760 1128 754 1126 761

24 13 15 15 6 −17 −39 −74 6 4 5 5 1 −3 −6 −13 −11 −4 12 −10 10 −3

515 541 548 573 76 0 12 69 455 523 552 599 79 6 0 6 474 8 461 3 490 5

1.3 1.2 1.1 1.0 1.0 0.0 9.9 84.3 1.1 1.1 1.1 1.1 1.1 0.7 0.0 7.5 1.0 0.9 1.0 0.4 1.0 0.6

a Bond distances in Å, frequencies in cm−1, IR intensities in km/mol. Results obtained by means of the MP2/aug-cc-pVTZ method (Sadlej pVTZ basis set for I).

much longer than the hydrogen bond in the water dimer (dH···O = 1.95 Å). On the other hand, hydride−halogen bonds studied here are significantly shorter than representative halogen bonds, which are as long as 3 Å (see the lower part of Table 1). Finally, let us discuss changes of the X−C bond distance and both the frequency shift of its stretching vibration frequency and the change of its IR intensity upon the hydride−halogen bond formation. These data are given in Table 2. As indicated by the third column of this table, the X−C halogen bond that points toward the hydride hydrogen atom sometimes shortens, sometimes it lengthens, but taking into account that the strength of the hydride−halogen bond increases in the order F < Cl < Br < I, it is clearly seen that one obtains a shift from the shortening to the elongation of the X−C bond as the hydride−halogen bond strengthens. Thus one may conclude that this is the elongation of the X−C halogen bond instead of its shortening, which should be considered a typical effect of a hydride−halogen bond. Nevertheless, both effects may be obtained.32,33 Taking into account that LiH leads to stronger hydride−halogen bonds than BeH2 (vide infra), it is interesting to note that, for the same Lewis acid, LiH leads to both the larger shortening and the larger elongation of the X−C bond than BeH2. It should be mentioned that either shortening or the elongation of Cl−C bond can also result from the halogen bond formation. Consider, e.g., H3N···ClCF3 and H3N···ClCCH halogen-bonded systems listed in the lower part of Table 2. Though the shortening of the Cl−C bond is observed in the former complex (ΔdCl−C = −7.1 mÅ), the elongation of Cl−C takes place in the latter (ΔdCl−C = 2.8 mÅ). This is an interesting result if one considers that both complexes have almost the same interaction energies (vide infra). The same finding holds for systems with water instead of ammonia (see the last two rows in Table 2). It is also seen from Table 2 that, for the same hydride molecule, the XCF3 tends to

Interestingly enough, although both hydride−halogen and hydrogen bonds are characterized by the elongation of the R−H bond,a the blue shift of the νR−H stretching vibration frequency is observed in the former, whereas a typical red shift is found in the latter. This is a rather untypical effect if one recalls that the elongation of a bond and thus its weakening is often considered as being consolidated with the red shift of its stretching vibration frequency as it is for the (typical) hydrogen bonds. Blue shifts of the Be−H and Mg−H stretching vibration frequencies were also found by Li et al.33 for YRH···XCCY (X = Cl, Br; R = Be, Mg; Y = H, F, CH3) systems on the same level of theory (MP2/aug-cc-pVTZ). Thus, the blue shift of the R−H stretching vibration frequency upon the hydride−halogen bond formation seems to be a general finding, at least for the most representative systems. Interestingly enough, the larger the elongation of the R−H bond is the more evident is the blue shift of its stretching vibration frequency. Also it is interesting to note that the blue shift of the νR−H stretching vibration frequency is accompanied by the increase of the IR intensity of this mode. The same effect has been obtained for all systems investigated earlier by Li et al.33 A small decrease of the IR intensity of the R−H mode has only been obtained in the case where FCF3 is the halogen donor molecule. This, however, is not regarded as the representative one. Thus, the increase of the IR intensity of the R−H mode upon the hydride− halogen bond formation seems to be a general effect. If the amounts of the elongation of the R−H bond, of the blue shift of its stretching vibration frequency, and of the IR intensity increase are to indicate the strength of the Rδ+− Hδ−···X interaction, then the iodine-containing molecules are the best potential entities leading to the strong hydride− halogen bond. This seems to be particularly valid if LiH acts as a donor of Hδ−. This finding is also supported by values of the H···X distance (see column four in Table 1). Importantly, even though H···X contacts are the shortest if X = I, they are still 2325



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energies for all systems are calculated using three different approaches given by eqs 1−3. ΔECP takes into account the counterpoise correction,59 whereas ΔEBSSE contains both the counterpoise correction and the deformation energy. The latter can be given as the difference between ΔEBSSE and ΔECP. Let us analyze plain BSSE-uncorrected interaction energies first (ΔE). These are given in the second column of Table 3. It is evident that for a given hydride and for a given type of a halogencontaining molecule the strength of the hydride−halogen bond increases in the F < Cl < Br < I order. The same sequence is valid for halogen bonds and is explained by the increase of the positive value of the electrostatic potential of a σ-hole of a relevant halogen atom.4,5,13,14,24 In general, the same result is obtained if one considers BSSE-corrected interaction energies, although for dimers with HBeH, the F < Cl < I < Br order is obtained. This seems to be an effect of a large percentage of the BSSE in HBeH···ICF3 and HBeH···ICCH dimers (2.38 kcal/mol = 69% and 2.31 kcal/mol = 65%, respectively). The BSSE for bromine-containing counterparts are significantly smaller (0.87 kcal/mol = 41% and 0.81 kcal/mol = 37% for HBeH···BrCF3 and HBeH···BrCCH dimers, respectively). If X ≠ I, then the BSSE is lower than 1 kcal/mol, which, however, may constitute even up to 70% of the interaction energy if the dimer is very weak (see, e.g., HBeH···FCF3). It is interesting to note that the BSSE is much more significant for hydride−halogen bonded systems than for both hydrogen-bonded and particularly halogen-bonded systems. If one compares interaction energies of systems with the same halogen-containing molecules but with different hydrides, then it is immediately seen that LiH is a better Hδ− donor than HBeH and thus LiH leads to stronger hydride− halogen bonds. On the other hand, XCF3 is a better Lewis acid than XCCH, at least when the LiH molecule is a Lewis base.

the larger shortening or to the smaller elongation of the X−C bond than XCCH (for the same X). Results shown in Table 2 indicate that the stretching vibration frequency of the X−C mode can be shifted in both directions, i.e., the blue shift as well as the red shift can be obtained depending on the system. However, it is rather noticeable that νX−C in XCF3 is blue-shifted, whereas νX−C in XCCH (X ≠ F) is red-shifted. Similar frequency changes have also been obtained in the case of halogen-bonded complexes, whereas the red shift of νCl−C has been obtained in the case of hydrogen-bonded complexes. The discrepancy of effects also holds in the case of the change of the IR intensity of the X−C mode. All these results indicate that the origin of changes relating to the X−C bond is different in XCF3 than in XCCH. In other words, the remote part of the halogen-containing molecule may have a significant influence on the X−C bond. Interaction Energies and SAPT-Based Decomposition. As already mentioned in the Introduction, the halogen bond is most often believed to be of the electrostatic nature,6,11,17,27 although the relevance of other energy contributions was also shown.11,17,28 The nature of the hydride−halogen bond was investigated even more seldomly.30,32,33 Although decompositions of the interaction energy have already been investigated,30,32,33 none of these decompositions has been done by means of the SAPT method,37,38 which, however, belongs to the most often used in studies of interaction energy components. Thus, for all complexes investigated in this article we have performed the interaction energy decomposition based on the SAPT method. The result of this energy decomposition is given in Table 3. A short description of all energy terms used in this table is given in the Methodology. Because the basis set superposition error (BSSE) may be significant with the MP2 method, interaction Table 3. Interaction Energies (kcal/mol)a system

ΔE

ΔECP

ΔEBSSE

ΔEelst

ΔEind

ΔEdisp

ΔEexch

SAPT ΔEint

LiH···FCF3 LiH···ClCF3 LiH···BrCF3 LiH···ICF3 LiH···FCCH LiH···ClCCH LiH···BrCCH LiH···ICCH HBeH···FCF3 HBeH···ClCF3 HBeH···BrCF3 HBeH···ICF3 HBeH···FCCH HBeH···ClCCH HBeH···BrCCH HBeH···ICCH FH···ClCF3 FH···ClCCH HOH···OH2 H3N···ClCF3 H3N···ClCCH H2O···ClCF3 H2O···ClCCH

−0.28 −3.64 −6.23 −11.16 −0.19 −3.39 −5.95 −10.06 −0.30 −1.24 −2.11 −3.47 −0.30 −1.27 −2.19 −3.53 −1.74 −1.92 −5.18 −2.73 −2.73 −2.18 −2.19

−0.23 −3.50 −5.58 −8.71 −0.10 −3.17 −5.30 −7.87 −0.09 −0.94 −1.25 −1.12 −0.11 −0.99 −1.39 −1.25 −1.19 −1.43 −4.75 −2.52 −2.51 −1.97 −1.96

−0.17 −3.36 −5.31 −7.81 −0.09 −3.16 −5.18 −7.12 −0.09 −0.93 −1.24 −1.09 −0.11 −0.98 −1.38 −1.22 −1.10 −1.42 −4.71 −2.46 −2.50 −1.93 −1.96

−0.20 −6.57 −13.81 −32.66 0.05 −5.76 −12.13 −28.11 −0.09 −1.32 −2.43 n/cb −0.07 −1.32 −2.48 −5.20 −1.08 −1.16 −7.50 −4.49 −4.37 −2.71 −2.61

−0.70 −12.15 −45.59 −173.29 −0.81 −11.45 −40.28 −147.32 −0.20 −1.39 −4.33 n/cb −0.23 −1.48 −4.62 −14.67 −2.40 −2.24 −2.88 −4.86 −4.95 −1.61 −1.67

−0.55 −3.48 −6.24 −11.45 −0.61 −3.34 −5.71 −10.24 −0.49 −1.46 −2.31 n/cb −0.52 −1.50 −2.33 −3.91 −2.02 −1.87 −2.77 −2.68 −2.70 −1.94 −1.98

1.26 19.62 61.30 167.32 1.39 18.29 54.08 171.69 0.64 3.32 8.06 n/cb 0.71 3.45 8.36 23.05 4.79 4.05 8.91 9.85 9.93 4.31 4.40

−0.28 −3.77 −6.16 −43.47 −0.07 −3.23 −5.44 −9.34 −0.16 −1.07 −1.48 n/cb −0.15 −1.05 −1.49 −1.59 −1.19 −1.68 −5.05c −2.75 −2.61 −2.22 −2.12

a

Results obtained by means of the MP2/aug-cc-pVTZ method (Sadlej pVTZ basis set for I). bIn the case of the HBeH···ICF3 system the systematic convergence failure occurred during SAPT calculations. Most likely it resulted from the use of combined Sadlej-type and Dunning-type basis sets. SAPT values seem to be Therefore, the reliability of SAPT results obtained for other systems with iodine atoms may be relatively lower, although ΔEint c well fitted to the rest of results. SAPT results taken from ref 39. 2326



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systems, and their values are roughly twice as large as the electrostatic term. However, if the more classic water dimer is considered, then the electrostatic term clearly dominates in the interaction energy. This may lead to the conclusion that the domination of the inductive term in the case of hydride−halogen bonded systems arises due the close proximity of partially negatively charge hydrogen atom and a bulky and easily polarizable halogen atom. If the former determinant is replaced with Hδ+ (hydrogen bonds to halogens) or Y (e.g., N, O, thus halogen bonds), then the relative importance of the dispersive or electrostatic term increases. QTAIM-Based Analysis. Results concerning relevant QTAIM parameters calculated at the bond critical point of R−H, H···X, and X−C bonds are given in Table 4. The hydride−halogen bond is analyzed first. It is clearly seen that the value of ρH···X increases in the F < Cl < Br < I order. Thus it might seem that ρH···X should correlate well with the strength of the hydride−halogen bond. Dependences between ρH···X and SAPT are shown for all hydride−halogen ΔE, ΔEBSSE, and ΔEint bonded systems in Figure 1. Similar dependences plotted for all types of hydride−halogen bonded systems separately, i.e., for LiH···XCF3, LiH···XCCH, HBeH···XCF3, and HBeH···XCCH are given in the Supporting Information to mark the somewhat different point distributions depending on the type of a system (Figure S1,Supporting Information). First of all, the dissimilar distributions of points can be seen (Figure S1, Supporting Information) if one compares results for LiH with those for HBeH. Although the dependence between ρH···X and ΔE seems to be roughly linear for all four types of complexes, dependences between ρH···X and either ΔEBSSE or ΔESAPT are clearly different, depending on the hydride molecule. Namely, whereas for the case of LiH the clear deviation from linearity of points indicating the relation between ρH···X and EBSSE is only small, it is much more noticeable in the case of HBeH. Similar distributions of points are found for ESAPT; however, the deviation from linearity is less exposed (Figure S1). Because these differences between point distributions if one considers relations of ρH···X vs EBSSE and to a lesser extent ρH···X vs ESAPT seem to depend on the type of a hydride molecule, it is rather pointless to produce any correlations based on data for systems with diverse hydride molecules. It is clearly seen from Figure 1. It is also clear that if any linear correlation between ρH···X and the interaction energy is to be found, it is the plain ΔE, which should be used instead. Nevertheless, the linear correlation should not be good. We were also analyzing (for graphic representation and short comments see Supporting Information) relations between ρH···X and dH···X (Figure S2), LH···X and the interaction energy of a hydride− halogen bond (Figure S3), and LH···X vs ρH···X (Figure S4). The range of ρH···X values of the hydride−halogen bonded systems studied here is rather wide and amounts to 0.0023 au for LiH···FCF3 to as much as 0.0337 au for LiH···ICCH (Table 4). If one considers the water dimer with ρH···O = 0.0232 au, then only systems with the LiH···Br interaction have ρH···Br values slighty below, whereas only systems with the LiH···I interaction have larger values of ρH···I (0.0293 and 0.0337 au for LiH···ICF3 and LiH···ICCH, respectively). Values of ρY···Cl (Y = N, O) are close to 0.01 au in the case of all halogen-bonded systems studied here. These values are thus similar to those in the bond critical point of the LiH···Cl hydride−halogen bond, whereas ρH···Y are significantly greater for FH···Cl hydrogen bonds (ca. 0.014 au) even though they have lower energy values (Table 3). This supports the conlusion that the general relation between the amount of the electron density in the bond critial

The situation is reversed for HBeH; however, differences in interaction energies are very small in this case. Although decompositions of the interaction energy for a hydride−halogen bond have been already investigated,30,32,33 none of them was based on the SAPT method. Thus it is tempting enough to investigate the nature of a hydride−halogen bond by means of the SAPT method as well. The brief description of all energy components listed in Table 3 is given in the Methodology. It is clearly seen that for the hydride−halogen bond the induction term (ΔEind) is larger (i.e., more negative) than the electrostatic term (ΔEelst). It is the most evident for complexes with the LiH molecule; however, even for a complex with HBeH, the induction term can be ca. 2−3 times larger than the electrostatic term if X = Br or I (see HBeH···BrCCH and HBeH···ICCH). For the weakest hydride−halogen bonded systems studied here (i.e., those with X = F), the dispersive term (ΔEdisp) either has only a somewhat lower value than ΔEind or is even clearly dominant among all attractive terms (see HBeH···FCF3 or HBeH···FCCH). SAPTbased interaction energies reproduce the F < Cl < Br < I order of SAPT the increasing strength of a hydride−halogen bond (see ΔEint in the last column of Table 3). These energies are in general larger (i.e., more negative) than ΔEBSSE and ΔECP. It should be underlined that the inductive nature of a hydride−halogen bond as resulting from the SAPT method is in opposition to previous results by other authors.32,33 The decomposition of the interaction energy based on the ADF85 program led to the conclusion that a hydride−halogen bond is rather electrostatic in nature with only minor importance of charge transfer and polarization.33 The dominance of the electrostatic interaction in the interaction energy of a hydride− halogen bond was also indicated by Grabowski et al.32 where the variation-perturbation approach86 was used. The significant importance of the dispersion energy was indicated for very weakly bounded systems as for instance HBeH···ClSiF3 and FBeH···ClSiF3.32 Very recently, Grabowski30 has performed the natural energy decomposition analysis (NEDA)87−89 for a group of complexes where the chlorine atom behaves as either the Lewis acid or the Lewis base. One of those systems was the HMgH···ClCF3 dimer possessing a hydride−halogen bond. It was found that for interactions where ClCF3 acts as the Lewis acid (i.e., the halogen bond but the hydride−halogen bond as well) the polarization is the most important attractive interaction term.30 This result is in line with that found in the present study of the nature of a hydride−halogen bond, although it must be kept in mind that energy terms obtained by means of various energy decomposition schemes can hardly be compared. Thus we would like to underline that the result of studies of “a nature” of a given interaction that are based on the decomposition of the interaction energy may lead to opposite conclusions. This for instance happens in the case of a halogen bond where, despite the fact that they are commonly investigated as being electrostatic in nature,6,11,17,27 the dominance of, e.g., the charge transfer term may also be obtained.28 It should be mentioned that the large importance of the inductive term in the interaction energy for a halogen-bonded systems (see H3N···ClCF3 and H3N···ClCCH systems in the lower part of Table 3) has also been obtained in the present article. If H2O is taken instead of H3N, then it is the electrostatic term that becomes the most attractive and the induction energy is slightly lower than the dispersion energy (see the two last rows in Table 3). Both inductive and dispersive terms are almost equally important in the interaction energy of FH···ClCF3 and FH···ClCCH hydrogen-bonded 2327



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Table 4. QTAIM Parameters at BCPs of R−H, H···X, and X−C Bondsa system

ρR−H

ΔρR−H

LR−H

HR−H

ρH···X

LiH···FCF3 LiH···ClCF3 LiH···BrCF3 LiH···ICF3 LiH···FCCH LiH···ClCCH LiH···BrCCH LiH···ICCH HBeH···FCF3 HBeH···ClCF3 HBeH···BrCF3 HBeH···ICF3 HBeH···FCCH HBeH···ClCCH HBeH···BrCCH HBeH···ICCH system

0.0388 0.0386 0.0382 0.0471 0.0388 0.0387 0.0384 0.0376 0.0975 0.0977 0.0963 0.0955 0.0975 0.0977 0.0964 0.0958 ρR−H

−0.0001 −0.0003 −0.0007 0.0082 −0.0001 −0.0002 −0.0005 −0.0012 0.0002 0.0004 −0.0010 −0.0018 0.0002 0.0004 −0.0009 −0.0016 ΔρR−H

0.1663 0.1660 0.1646 0.0640 0.1664 0.1663 0.1657 0.1642 0.2022 0.2035 0.2054 0.2068 0.2022 0.2034 0.2060 0.2081 LR−H

−0.0001 0.0000 0.0001 −0.0181 −0.0001 0.0000 0.0001 0.0003 −0.0474 −0.0475 −0.0461 −0.0453 −0.0474 −0.0474 −0.0462 −0.0454 HR−H

0.0023 0.0120 0.0211 0.0293 0.0025 0.0113 0.0190 0.0337 0.0027 0.0066 0.0100 0.0163 0.0029 0.0066 0.0100 0.0163 ρH···X

FH···ClCF3 FH···ClCCH HOH···OH2 system H3N···ClCF3 H3N···ClCCH H2O···ClCF3 H2O···ClCCH a

0.3611 0.3609 0.3612 ρR−H

−0.0049 −0.0051 −0.0028 ΔρR−H

LH···X

ρX−C

HH···X

0.0079 0.0331 0.0458 0.0147 0.0087 0.0324 0.0438 0.0550 0.0112 0.0227 0.0301 0.0387 0.0121 0.0238 0.0314 0.0404 LH···X

0.0004 0.0008 −0.0007 −0.0051 0.0005 0.0009 −0.0003 −0.0044 0.0006 0.0011 0.0009 −0.0001 0.0007 0.0012 0.0010 0.0000 HH···X

−3.0580 −0.8629 0.0148 0.0439 −3.0562 −0.8621 0.0140 0.0425 −2.8050 −0.7658 0.0232 0.0857 LR−H HR−H ρH···X LH···X

0.0004 0.0005 0.0004

0.0111 0.0111 0.0095 0.0097

0.0416 0.0426 0.0446 0.0464

0.3117 0.2194 0.1721 0.1230 0.3079 0.2455 0.1918 0.1349 0.3058 0.2152 0.1731 0.1311 0.3038 0.2463 0.1976 0.1460 ρX−C 0.2074 0.2442

ΔρX−C 0.0081 0.0060 −0.0002 −0.0086 0.0053 −0.0005 −0.0065 −0.0133 0.0022 0.0018 0.0008 −0.0004 0.0013 0.0003 −0.0007 −0.0022 ΔρX−C −0.0060 −0.0019

LX−C

HX−C

−0.3716 −0.3399 −0.1656 0.0127 0.4081 −0.4742 −0.1877 0.1024 −0.3634 −0.3387 −0.1852 −0.0192 0.4312 −0.4945 −0.2222 0.1024 LX−C

−0.5147 −0.1665 −0.1129 −0.0665 −0.4835 −0.2255 −0.1509 −0.0760 −0.5007 −0.1624 −0.1132 −0.0743 −0.4740 −0.2299 −0.1592 −0.0869 HX−C

−0.3172 −0.4938

−0.1524 −0.2279

HH···X

ρX−C

ΔρX−C

LX−C

HX−C

0.0019 0.0020 0.0024 0.0025

0.2180 0.2460 0.2177 0.2466

0.0046 −0.0001 0.0043 0.0006

−0.3426 −0.4842 −0.3444 −0.4910

−0.1652 −0.2274 −0.1653 −0.2294

Results obtained by means of the MP2/aug-cc-pVTZ method (Sadlej pVTZ basis set for I).

If one compares values of ρR−H in hydrides with those in FH or H2O molecules (second column in Table 4), then it is clearly seen that the former are much lower, particularly in the case of the LiH molecule. This results from the significantly ionic character of the Li−H bond. This is supported by both clearly positive values of LR−H and either close to zero or slightly negative (for HBeH) values of HR−H comparing to considerably negative values of LR−H and HR−H for F−H and O−H in hydrogen donors. The changeb of the electron density value in the bond critical point of R−H upon the hydride−halogen bond formation is very small, being smaller than 0.001 au if X ≠ I. Interestingly, however, in spite of a rather typical decrease of the ρR−H value, its increase may also be observed for weak hydride−halogen bonded systems. This effect leads to the fact that hydride bonds can either elongate or shorten due to the hydride−halogen bond formation. However, the decrease of the electron density value is more typical and results in the elongation of the hydride bond, which is in line with ref 33. Taking into account that the value of ρR−H also decreases in the case of R−Hδ+ bond, it may be concluded that the decrease of the ρR−H value is a rather typical effect irrespective of the sign of the polarization of the R−H bond, i.e., irrespective of whether the hydrogen atom in R−H is positively or negatively charged. Relevant values of QTAIM parameters for the X−C bond critical point are also given in Table 4. Interestingly enough, it is seen that the increase of the strength of a hydride−halogen bond by the change of F toward I leads to the change of the sign and the magnitude of the ΔρX−C value, namely the change from the significant increase of ρX−C to the significant decrease of ρX−C can be noticed. It is in line with the switch of the change of a X−C bond length, namely from its shortening to its elongation.

SAPT Figure 1. Dependence between ρH···X and ΔE, ΔEBSSE, and ΔEint for all hydride−halogen bonded systems.

point of the intermolecular bond (e.g., hydrogen, halogen, hydride−halogen, etc.) and its energy does not exist if diverse types of complexes are considered together. For all systems studied here the Laplacian of the electron density in the bond critical point of H···X (LH···X) is positive, which is characteristic for so-called closed-shell interactions. Its value increases in the F < Cl < Br < I order, similarly as for the interaction energy. Although the HH···X is positive for most hydride−halogen bonded systems studied here, its value is negative for all systems with the LiH···X (X = Br, I) interaction, indicating a significantly partially covalent nature.40 2328



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Table 5. Changes of NBO Populations and of spm Characters of the Halogen’s LPz upon the Hydride−Halogen Bond Formation system

CT

LiH···FCF3 LiH···ClCF3 LiH···BrCF3 LiH···ICF3 LiH···FCCH LiH···ClCCH LiH···BrCCH LiH···ICCH HBeH···FCF3 HBeH···ClCF3 HBeH···BrCF3 HBeH···ICF3 HBeH···FCCH HBeH···ClCCH HBeH···BrCCH HBeH···ICCH system

0.0040 0.0191 0.0449 0.1214 0.0059 0.0175 0.0381 0.0991 0.0001 0.0017 0.0041 0.0111 0.0009 0.0026 0.0056 0.0123 CT

FH···ClCF3 FH···ClCCH HOH···OH2 system

−0.0094 −0.0077 −0.0090 CT

H3N···ClCF3 H3N···ClCCH H2O···ClCF3 H2O···ClCCH

0.0047 0.0044 0.0020 0.0024

Δn(σRH)

Δn(σRH * )

Δn(LPz)

Δn (ΣLP)

Δm(LPz)

Δm (%)

−0.0049 −0.0204 −0.0479 −0.1289 −0.0074 −0.0187 −0.0400 a −0.0009 0.0016 0.0009 −0.0035 −0.0023 0.0005 −0.0002 −0.0042 Δn(σRH)

0.0001 0.0007 0.0019 0.0058 0.0001 0.0005 0.0013 b 0.0001 0.0004 0.0008 0.0023 0.0004 0.0005 0.0009 0.0022 Δn(σ*RH)

−0.0009 −0.0013 −0.0023 −0.0055 −0.0010 −0.0023 −0.0034 −0.0074 −0.0005 −0.0007 −0.0013 −0.0023 −0.0006 −0.0009 −0.0016 −0.0037 Δn(LPz)

−0.0093 −0.0114 −0.0071 −0.0184 −0.0083 −0.0139 −0.0080 0.0049 −0.0035 −0.0028 −0.0023 −0.0024 −0.0025 −0.0036 −0.0027 −0.0009 Δn (∑LP)

sp0.33 sp0.12 sp0.07 sp0.03 sp0.44 sp0.21 sp0.14 sp0.08 sp0.33 sp0.14 sp0.10 sp0.07 sp0.44 sp0.23 sp0.17 sp0.13 m sp (LPz)

0.00 −0.02 −0.04 −0.06 −0.01 −0.03 −0.04 −0.07 0.00 0.00 0.01 −0.02 −0.01 −0.01 −0.01 −0.02 Δm(LPz)

0.00 −1.44 −2.69 −5.10 −0.49 −1.92 −3.26 −6.16 −0.02 −0.32 −0.62 −1.36 −0.22 −0.47 −0.81 −1.72 Δm (%)

−0.0003 −0.0003 −0.0002 Δn(σRH)

0.0075 0.0068 0.0091 Δn(σ*RH)

−0.0002 −0.0001

sp0.14 sp0.24 c spm(LPz)

0.00 0.00 d Δm(LPz)

+0.15 +0.04

Δn(LPz)

−0.0003 −0.0032 −0.0080 Δn (∑LP)

Δm (%)

−0.0006 −0.0014 −0.0007 −0.0013

−0.0066 −0.0076 −0.0065 −0.0078

sp0.13 sp0.22 sp0.13 sp0.22

−0.01 −0.02 −0.01 −0.02

−0.91 −1.34 −0.62 −0.97

spm(LPz)

a NBO analysis gives LP on H with n = 1.8019 e. bNBO analysis gives LP* on Li with n = 0.0981 e. cNBO analysis gives two unequivalent LPs with sp2.49 and sp3.25 characters. dsp1.59 (+24.08%) and sp2.25 (−23.38%).

NBO-Based Analysis. During the formation of a hydride− halogen bond the negative charge on the hydride hydrogen atom may either decrease or increase and there is the charge outflow from the halogen atom (for NBO atomic charges and their changes; see Table S1, Supporting Information). Similar changes of qH and qX have recently been also found by Li et al.33 The positive value of the charge transfer (CT) upon the complex formation (Table 5) indicates a charge flow from the hydride molecule to the halogen donor. The same direction of the charge flow upon the complex formation is valid for halogen-bonded systems, whereas it is opposite in the case of hydrogen bonds. Li et al.33 have shown that the linear correlation between CT and the interaction energy is rather poor (R = 0.89). Dependences between CT and ΔE, ΔEBSSE, SAPT , and ΔEind are shown in Figure 2 (the shorter range of ΔEint energy values from 0 to −15 kcal/mol is taken for better clarity). It is clearly seen that point distributions are antagonistic to linear correlations between CT and the interaction energy. Even if the induction energy is considered, the linear correlation is not very good (R2 = 0.967). It is important to note that the amount of the charge transfer in the case of LiH···XCF3 (X ≠ F) is larger than in the case of hydrogen-bonded systems (e.g., for water dimer CT = −0.009 e). It indicates that, particularly for these systems, the inductive term should be much more important in the interaction energy. This is supported by the results of SAPT analysis shown in Table 3. Changes of orbital populations may give deeper insight into the direction of the charge flow and thus the nature of a hydride−halogen bond. Changes of NBO populations of σRH and σRH * orbitals of a hydride molecule as well as of the electron lone pair in the direction of the X−C bond (LPz) and of the sum of populations of all electron lone pairs localized on

Figure 2. Dependence between charge transfer and ΔE, ΔEBSSE, SAPT , and ΔEind. ΔEint

the halogen atom pointing toward the hydride hydrogen (ΣLP) are shown in Table 5. Both the spm character of LPz and its change during the complex formation are also shown in the last three columns of Table 5. In general, a large charge outflow from the σRH orbital can be observed. Only a small part of this charge flow is directed to the σRH * antibonding orbital, thus the elongation of the R−H bond is rather caused by the charge outflow from the σRH bonding orbital than by the charge inflow to the σRH * antibonding orbital. The situation is thus completely different from that in the case of hydrogen bonds, where the elongation of the R−H bond is caused by the charge inflow to * antibonding orbital. This is supported by the data the σRH 2329



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systems of the FH···X type. In the latter case, however, the dispersive term becomes almost equally important. The formation of a hydride−halogen bond leads to the charge transfer from the hydride to the halogen-donor molecule. NBO-based analysis of the change of orbital populations indicates that the elongation of the R−H bond is caused by the charge outflow from the σRH bonding orbital rather than by the charge inflow to the σRH * antibonding orbital. The simultaneous charge transfer from the hydride molecule to the halogen-containing partner and the charge outflow from all electron lone pairs of the halogen atom indicate that the transferred charge is directed to the more remote parts of the latter.

presented for the three hydrogen-bonded systems in Table 5. The formation of a hydride−halogen bonded system leads to the charge outflow from the halogen’s electron lone pairs. Interestingly enough, only a small part comes from LPz, which is directed toward H. A similar finding holds for halogenbonded systems and for FH···ClCCH. However, in the latter case the FH···Cl interaction is not linear. The p character of LPz decreases (or its s character increases) on going from F to I and decreases even more upon the hydride− halogen complex formation. The decrease of the p character of LPz is also in force in the case of halogen-bonded systems, whereas its negligible increase is found in the case of hydrogen-bonded systems analyzed here (see the last column of Table 5). A scrutiny analysis of the change of the s (p) character of the Cl−C orbital has been recently performed by Grabowski30 and related to Bent’s rule.90 The decrease of the s-character on the Cl atom and its increase on the C atom was found during the HMgH···ClCF3 complex formation.30 Using Bent’s rule, one could suggest that the decrease of the p-character (or the increase of the s-character) of LPz during the hydride−halogen complex formation is caused by the increase of the electropositive character of the hydride halogen atom. Recalling the fact that this interaction leads to the charge outflow from the relevant hydride hydrogen atom this explanation may be acceptable; however, such changes of the hydride hydrogen’s charge are not observed for all systems investgated here. Any interactions between orbitals of hydride- and halogencontaining molecules are not dominant (as indicated by the rather low value of E(2)); however, the principal delocalizations for the σRX bonding orbital show that the charge that corresponds to this orbital is directed to the σXC * and Ry*(X) orbitals of the X-donor molecule. The former interaction, which dominates in the case of the most representative systems with X = Br, I, may nicely explain the elongation of the X−C bond upon the hydride−halogen bond formation.

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ASSOCIATED CONTENT

S Supporting Information *

Plots showing dependences between ρH···X and ΔE, ΔEBSSE, and SAPT ΔEint , commented plots and linear and exponential fits of ρH···X vs dH···X for all types of complexes separately, commented plot showing dependence between LH···X and ΔE, ΔEBSSE, and SAPT ΔEint , commented plots and fits showing the LH···X vs ρH···X dependence, commented table with NBO charges and their changes upon the hydride−halogen bond formation. This information is avaliable free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +48 (56) 6114695. Fax: +48 (56) 6542477. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Calculations have been carried out on the multiprocessor cluster at the Information and Communication Technology Center of Nicolaus Copernicus University, Toruń (http:// www.ucu.umk.pl). M.J. acknowledges University Grant No. 427-Ch. M.P. acknowledges computational grant in Wrocław Center for Networking and Supercomputing (http://www. wcss.wroclaw.pl).

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CONCLUSIONS It was shown that the hydride−halogen bond formation leads to the rather general elongation, however, small in many cases, of the Rδ+−Hδ− bond. The elongation of the R−H bond is accompanied by the blue shift of the νR−H stretching vibration frequency. This blue shift of νR−H is accompanied by the increase of the IR intensity of this mode. All these effects regarding the R−H bond seem to be rather typical for hydride−halogen bonded systems. It has also been shown that for the X−C bond one obtains a shift from its shortening to its elongation as the hydride−halogen bond strengthens. The stretching vibration frequency of the X−C bond can either increase or decrease depending on the system, a similar discrepancy is obtained in the case of the change of its IR intensity. However, νX−C is blue-shifted in XCF3, whereas it is rather redshifted in the case of XCCH (if X ≠ F). Thus the halogen atom behaves as a hydrogen atom in HCF3 and in HCCH, respectively, if it is built in hydrogen bond of the Y···H−C type. As indicated by the computed interaction energies, LiH leads to stronger hydride−halogen bonds than BeH2 and XCF3 is a better Lewis acid than XCCH (X = F, Cl, Br, I), at least when the LiH molecule is a Lewis base. Decomposition of the interaction energy based on the SAPT method clearly indicates the dominance of the inductive term, whereas the electrostatic term is only minor, which demonstrates the inductive nature of a hydride−halogen bond. The large importance of the inductive term is also found for halogen-bonded systems if ammonia acts as the Lewis base as well as in the case of hydrogen bonded

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DEDICATION Dedicated to the memory of Prof. Richard F. W. Bader.

§

ADDITIONAL NOTES We neglect the rather untypical shortening of the R−H bond in the so-called improper, blue-shifting hydrogen bonds. b Changes of relevant QTAIM parameters in the bond critical point of LiH in the LiH···ICF3 complex are not taken into account because the nonatomic attractor was found for LiH. a

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REFERENCES

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