Hydrogen Bond versus Halogen Bond in HXO n ( X = F , Cl , Br , and I ) Complexes with Lewis Bases

We have theoretically studied the formation of hydrogen-bonded (HB) and halogen-bonded (XB) complexes of halogen oxoacids (HXOn) with Lewis bases (NH3 and Cl−) at the CCSD(T)/CBS//RIMP2/aug-cc-pVTZ level of theory. Minima structures have been found for all HB and XB systems. Proton transfer is generally observed in complexes with three or four oxygen atoms, namely, HXO4:NH3, HClO3:Cl, HBrO3:Cl, and HXO4:Cl. All XB complexes fall into the category of halogen-shared complexes, except for HClO4:NH3 and HClO4:Cl, which are traditional ones. The interaction energies generally increase with the number of O atoms. Comparison of the energetics of the complexes indicates that the only XB complexes that are more favored than those of HB are HIO:NH3, HIO:Cl−, HIO2:Cl, and HIO3:Cl. The atoms-in-molecules (AIM) theory is used to analyze the complexes and results in good correlations between electron density and its Laplacian values with intermolecular equilibrium distances. The natural bon orbital (NBO) is used to analyze the complexes in terms of charge-transfer energy contributions, which usually increase as the number of O atoms increases. The nature of the interactions has been analyzed using the symmetry-adapted perturbation theory (SAPT) method. The results indicate that the most important energy contribution comes from electrostatics, followed by induction.


Introduction
The comprehension of noncovalent forces lays the foundations for the interdisciplinary field of catalysis, supramolecular, biological, and atmospheric chemistry [1].The pathways of biological and chemical processes are frequently controlled by complex combinations of noncovalent interactions [2].Thus, an accurate description of the interactions between molecules is mandatory to comprehensively advance the fields of biology, physics, and chemistry.
In addition, apart from hydrogen bonding [3][4][5][6][7], there are other kinds of noncovalent interactions that have been attracting much attention from the scientific community, especially in the last few years, namely tetrel [8][9][10], pnictogen [11], chalcogen [12,13], halogen [14,15], and aerogen [16] bonds.There is a common pattern in all these noncovalent contacts: an interaction between an electron-density-rich region of a molecule, acting as a Lewis base, with an electron-density-deficient region (tetrel, pnictogen, chalcogen, halogen, or aerogen atoms) of another molecule, acting as a Lewis acid, the latter corresponding to a region of lower electron density associated with a portion of the surface electrostatic potential of a system, known as σ-hole.The formation of a covalent bond or bonds causes an anisotropy of the charge distribution of the atom giving rise to these σ-holes [17,18].Particularly, according to IUPAC [19], "A halogen bond occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity."Recently, halogen bonds have attracted considerable attention due to their having similar functions to hydrogen bonds.For instance, halogen bonds have been used in the recognition mechanism of chemical and biological molecules [20][21][22], drug design [23][24][25], organocatalysis [26][27][28], and material science [29][30][31].
Atmospheric reactive nitrogen compounds are of particular importance to the surface-atmosphere exchange over agricultural land.In this regard, NH 3 is the primary contributor to atmospheric reactive nitrogen dry deposition [58].The majority of NH 3 emissions originate from livestock excreta and, to a lesser extent, from agricultural sources from the application of N-containing fertilizers [59,60].As the primary basic gas in the atmosphere, NH 3 also reacts with trace acidic gases, such as hydrogen chloride (HCl).The product of this reaction gives rise to the aerosol ammonium chloride (NH 4 Cl), which acts as scattering aerosol that alters the Earth's total albedo and contributes significantly to regional and global climate [61].
Despite the extensive research on the comparison between hydrogen-and halogen-bonding interactions on hypohalous acid complexes, to the best of our knowledge, no theoretical and experimental studies involving interactions of hypohalous acids with a chloride ion and the rest of the halogen oxoacids with NH 3 and Cl − are available in the literature.In this article, we aim to account for the formation of binary complexes between halogen oxoacids and either NH 3 or Cl − by means of high-level ab initio calculations (CCSD(T)/CSB//RI-MP2/aug-cc-pVTZ).As two types of complexes can be formed (hydrogen-bonded or halogen-bonded), we analyze which one is more favored.The characterization of the interactions has been scrutinized by using the atoms-in-molecules (AIM) theory (electron density analysis, degree of covalency), the natural bon orbital (NBO) (charge transfer effects), and the symmetry-adapted perturbation theory (SAPT) method (energy partition).

Halogen Oxoacids
Initially, we compared our computed geometries of the halogen oxoacids with experimental evidence.However, the experimental gas phase geometries are only available for all hypohalous acids and perchloric acid.For the rest of the HXO n compounds, the comparison has been made with high-level ab initio calculations available in the literature.All of these geometrical data are gathered in Table 1.The inspection of the results revealed that our calculated geometries are in good to excellent agreement with both the experimental and theoretical ones from the literature.As far as we are concerned, high-level ab initio calculations are not available for HIO 3 , HBrO 4 , and HIO 4 .Therefore, this is the first time that such results are reported.We have computed the molecular electrostatic potential (MEP) surfaces of the halogen oxoacids, paying special attention to the regions where the hydrogen and the halogen atoms are located, i.e., where the hydrogen and halogen bonding can be established (Figure 1).The MEP values associated with these regions are gathered in Table 2.A positive electrostatic potential region is located at the outermost region of both the H and halogen atoms in all cases, except for F in HFO, implying favorable formation of the complexes of HXO n with electron-rich systems, such as NH 3 and Cl − .In this regard, the MEP values for the hydrogen bonding interaction are always larger than the corresponding MEP values for the halogen bonding for the same oxoacid, suggesting that, from the electrostatic point of view, the HB complex will be the preferred arrangement.For example, the difference between HB and XB MEP values oscillates between 6.2 and 47.9 kcal•mol −1 for HIO 3 and HClO 4 , respectively.In the HB region, for the HXO and HXO 2 series of compounds, the MEP values diminish on going from X = F to X = I.The opposite is observed for the HXO 4 compounds, with MEP values increasing from X = Cl to X = I.However, for the HXO 3 oxoacids, the MEP values increase from X = Cl to X = Br to then decrease for X = I.In the XB region, the MEP values increase on going from X = Cl to X = I, as expected.For each X, the HB and XB MEP values follow different trends: the former values are very similar, except for HXO 4 , which is sensibly larger, whereas the latter values increase from X = Cl to X = Br and decrease for X = I.In addition, we have compared the XB MEP values with the X-OH distances and found a good linear correlation (R 2 = 0.900, Figure S1 of the Supplementary Materials).However, no linear correlation is observed when comparing the O-H distances with the HB MEP values (R 2 = 0.248, Figure S2 of the Supplementary Materials).Thus the XB MEP results are able to reproduce the geometric results for the oxoacids, as opposed to the HB MEP results.

Geometrical Features and Energetics
We have considered two types of complexes between the halogen oxoacids and the Lewis bases, namely hydrogen-bonded (HB) complexes, formed through the interaction between either N atom (from ammonia) or Cl − and the hydrogen atom of the oxoacid, and halogen-bonded (XB) complexes, formed through the interaction between N or Cl − and the halogen atom of the oxoacid.At the RI-MP2/aug-cc-pVTZ level, both HB and XB complexes are local minima for all oxoacids, except for the fluorine derivative, for which the HB complex is the only one obtained, as expected from the abovementioned MEP results.In Tables 3 and 4 we have put together the interaction energies and equilibrium distances for the NH 3 and Cl − complexes, respectively.The structure of the complexes is essentially independent of the nature of the halogen atom.For example, the geometry of all HB and XB HBrO n complexes is reported in Figures 2 and 3, respectively.3), we observe that the N•••H equilibrium distances range between 1.776 and 1.057 Å for HIO and HBrO 4 complexes, respectively.These distances are much shorter than the sum of the van der Waals radii of N and H atoms (2.86 Å) [70].These results indicate that the interaction established in these HB complexes is strong, as reflected in their interaction energies (∆E) that range between −10.7 and −20.8 kcal•mol −1 for HBrO and HIO 4 complexes, respectively.For comparison purposes, the interaction energy of the H 3 N•••H 2 O complex, computed at the MP2/aug-cc-pVTZ level, is −6.70 kcal•mol −1 [32], much smaller than our reported values.In fact, for some of them (HXO 4 ), a proton transfer is observed; the largest ∆E values were observed for the HClO   The results for the chloride HB complexes (Table 4) follow the same trends that have just been mentioned for the NH 3 HB complexes.Thus, a good linear correlation (R 2 = 0.888, Figure S3 of the Supplementary Materials) is found when comparing ∆E values of NH 3 and Cl − HB complexes.Notwithstanding, this correlation is improved (R 2 = 0.960) when an outlier is removed (HIO 3 ).In this regard, ∆E values for HXO, on one hand, and for HXO 2 :Cl − complexes, on the other hand, are constant.In addition, the Cl•••H equilibrium distances range between 1.918 and 1.333 Å for HFO and HBrO 4 complexes, respectively, larger than the ones corresponding to the HB NH 3 complexes, because of the larger size of the Cl atom.Again, these distances are much shorter than the sum of the van der Waals radii of Cl and H atoms (3.02 Å) [70].The interaction is much stronger (∆E = −24.0 to −49.1 kcal•mol −1 for HBrO and HIO 4 complexes, respectively) than that found for the HB NH 3 complexes because of the anionic nature of the chloride.Now, proton transfer is not only observed for HXO 4 but for HXO 3 complexes as well.The interaction energy increases, the HB distances shorten (Cl• • • H distances from 1.333 to 1.491 Å) to values quite close to the RI-MP2/aug-cc-pVTZ computed distance in hydrogen chloride (1.275 Å), and the O-H distances lengthen (within 0.292-0.633Å range) with the number of oxygen atoms as found in the HB NH 3 complexes.Now, let us analyze the XB complexes, starting with the NH 3 ones.From the inspection of the results, gathered in Table 3, we observe that the N•••X equilibrium distances range from 3.240 to 2.340 Å for HClO 4 and HIO 4 complexes, respectively, which, at the same time, are the ones with the smallest and largest ∆E values (−2.2 and −20.2 kcal•mol −1 , respectively).All of these distances are much shorter than the sum of the van der Waals radii of either Cl, Br, or I and N atoms (3.48, 3.52, and 3.70 Å, respectively) [70].These results indicate that the interaction in these XB complexes is attractive, as can be interpreted from their negative ∆E values.Despite the size of the halogen atom increases on going from Cl to I, the shortest and largest XB equilibrium distances were observed for the HIO n and HClO n complexes, with the HBrO n complexes being intermediate between both.Another intimately related general trend was observed in the binding energies of all these complexes: their value decreases as the size of the halogen increases, a fact that can be related to the deeper σ-hole observed for the iodine derivatives (Figure 1), as predicted by our MEP calculations, which results in quite short N•••I distances.Thus, in each series of the HXO n complexes, the most and least stable complexes correspond to the iodine and chlorine derivatives, respectively, with the bromine complexes being intermediate between both.For example, in the HXO 2 :NH 3 series, the ∆E values are −4.4,−6.9, and −12.5 kcal•mol −1 , with N•••X distances of 2.888, 2.755, and 2.649 Å for X = Cl, Br, and I, respectively.On the other hand, in each series of complexes for a given n, the interaction energy increases from n = 1 to n = 3, i.e., as the number of oxygen atoms augments.For instance, in the HClO n :NH 3 series, the ∆E values are −4.3,−4.4, and −4.8 kcal•mol −1 for n = 1, 2, and 3, respectively.However, for n = 4, the interaction energy drops to −2.2 kcal•mol −1 .The same trend is also observed for the HBrO n :NH 3 series.Unlike HClO n and HBrO n , the ∆E values of the iodine oxoacids increase all the way from n = 1 to n = 4.These results can be explained in terms of the accessibility of the halogen atom by the Lewis base.In free HClO 4 and HBrO 4 , the O-X-OH bond angles are 103.7 • and 102.7 • , and the X=O bond lengths are 1.42 and 1.58 Å, whereas in HIO 4 that bond angle is a little bit smaller (101.5 • ) and, most importantly, the I=O bond length is much longer (1.76 Å), moving the three oxo oxygen atoms a little bit further away, resulting in less repulsion with the electron-rich N atom of NH 3 when approaching the HIO 4 molecule.To some extent, these interaction energy results are in agreement with the MEP results (the largest ∆E values are obtained for the molecules with the largest HB MEP values, Table 2), meaning that electrostatics plays an important role in the stabilization of the complexes.
Just as in the HB complexes, the results for the chloride XB complexes (Table 4) follow the same trends as the NH 3 XB complexes, with interaction energies that are substantially more negative with Cl − than NH 3 .As a matter of fact, the comparison of ∆E values of NH 3 and Cl − XB complexes yields a good linear correlation (R 2 = 0.953, Figure S4 of the Supplementary Materials).Therefore, in each series of the complexes, the most and least stable complexes in the HXO n series correspond to the iodine and chlorine derivatives, respectively.In addition, in each series of complexes for a given n, the interaction energy increases from n = 1 to n = 3, and then drops for n = 4, except for HIO n for which the ∆E values increase from n = 1 to n = 4.The Cl•••X equilibrium distances range between 3.313 and 2.476 Å for HClO 4 and HBrO 4 complexes, respectively.As expected from the large and negative ∆E values, these distances are much shorter than the sum of the van der Waals radii of either Cl, Br, or I and Cl atoms (3.64, 3.68, and 3.86 Å, respectively) [70].
Comparison of the energetics of the complexes indicates that the only XB complexes that are more favored than the HB ones are HIO:NH 3 , HIO:Cl − , HIO 2 :Cl − , and HXO 3 :Cl − .Therefore, as the number of the O atoms increases, the XB complexes with an anionic Lewis base are being more favored than the HB ones, especially those with X = I (the halogen atom with the deepest σ-hole), except for those formed with HXO 4 due to the accessibility of the X atom by the Lewis base.

Electron Density Analysis
The AIM methodology was applied to evaluate the properties of the charge density for our systems.The topological analysis of the electron density reveals the presence of a single intermolecular bond critical point (BCP) that connects the interacting atom of the Lewis base (N or Cl) with either the H or X atom of HXO n in HB and XB complexes, connected through the corresponding bond paths.For example, the molecular graphs of all HClO n :NH 3 complexes are shown in Figure 4.Moreover, for HXO 2 :NH 3 and HXO 4 :NH 3 HB complexes, an additional BCP is located between an H atom of NH 3 and an O atom of the oxoacid, giving rise to the formation of a ring critical point.At the intermolecular BCPs, the values of the electron densities, ρ, range between 0.299 and 0.047 a.u.for HXO n :NH 3 HB complexes, between 0.218 and 0.050 a.u.for HXO n :Cl − HB complexes, between 0.076 and 0.008 a.u.for HXO n :NH 3 XB complexes, and between 0.084 and 0.011 a.u.for HXO n :Cl − XB complexes (Tables 5 and 6).Moreover, very large and negative values of the Laplacian, ∇ 2 ρ, are obtained for the HB complexes where proton abstraction occurs (Table 5), namely all HXO 4 HB complexes and HXO 3 :Cl − HB ones, consistent with the existence of a covalent bond.For the rest of the HB complexes, HXO n :Cl − XB complexes (except that with HClO 4 ), HIO n :NH 3 complexes, and the HBrO:NH 3 complex, positive ∇ 2 ρ values are accompanied by negative values of the total electron density energy, (Table 5), which indicate a partial covalent nature of these interactions [71,72].For the rest of the XB complexes, the positive values accompanying ∇ 2 ρ and H, in addition to the low ρ values, are genuine descriptors of charge-depleted intermolecular regions at BCPs, expected of closed-shell interactions [73][74][75][76][77][78][79][80][81].
The graphical representations of the electron density at the intermolecular BCP versus the intermolecular equilibrium distance (Figure 5) have good second-order polynomial trendlines, with correlation coefficients R 2 = 0.950 for all HB complexes, and 0.946 and 0.823 for NH 3 and Cl − XB complexes, respectively.There is also an excellent second-order polynomial fitting for the representation of ρ at the intermolecular BCP in HB complexes, ρ HB , versus the O-H distance (R 2 = 0.999 and 1.0 for NH 3 and Cl − complexes, respectively, Figure S5 of the Supplementary Materials).A comparison of the binding energies with the properties of the intermolecular BCPs reveals an interesting trend: the higher the electron density at the BCP, the stronger the interaction.The same trend applies to the Laplacian.In fact, there is a very good polynomial correlation (Figures S6 and S7 of the Supplementary Materials) between the interaction energies and the values of either ∇ 2 ρ HB (R 2 = 0.837-0.975)or ρ XB (R 2 = 0.824-0.995).These results point out that the ρ XB and ∇ 2 ρ HB values can be used as a measure of bond order for this type of interaction.This is in line with other studies, especially on hydrogen-bonded systems, where it was found that the ρ value is a good descriptor of the strength of the interaction [75,82].

Natural Bond Orbital Analysis
A Natural Bond Orbital (NBO) analysis was carried out to further analyze the geometrical, energetical, and topological characteristics of these HB and XB interactions between the halogen oxoacid derivatives and the Lewis bases.We have examined all possible intermolecular interactions between occupied (donor) Lewis-type NBOs and vacant (acceptor) non-Lewis NBOs and estimated their energetic importance by the second-order perturbation theory.According to the NBO analysis, the interaction is primarily based on a charge donation from the lone pairs of either the N atom of NH 3 or chloride Cl to the vacant σ* antibonding orbital of the H-O bond in the HB complexes of HXO n [Lp(N) → σ*(H-O)], and to the vacant σ* antibonding orbital of the X-OH bond in the HXO n XB complexes, as derived from the calculated second-order orbital perturbation energies (E (2) ) listed in Table 7.In the case of the HB complexes, very large E (2)  HB values were obtained (between 56.8 and 29.2 kcal•mol −1 for the NH 3 complexes and between 80.8 and 49.8 kcal•mol −1 for the Cl − ones) due to the proximity of the interacting groups.Significant E (2)  XB values were also obtained for the XB complexes, with increasing values as we move from X = Cl to X = I.Thus, E (2)   XB is maximum for HIO n complexes, the ones with the deepest σ-holes, and minimum for HClO n complexes, the ones with the shallowest σ-holes.In fact, in nine of the HB complexes (where a proton transfer was observed) and two of the XB complexes, the NBO method is not able to properly recognize the constituent molecules (Table 7) most likely due to the proximity of the interacting groups.Consequently, a significant charge is transferred from either the NH 3 or Cl − unit to the oxoacid, even in the cases when no proton transfer complexes are considered (up to 0.105 e and 0.181 e in NH 3 and Cl − HB complexes, and up to 0.179 e and 0.437 e in NH 3 and Cl − XB complexes).In the case of the XB complexes, the E (2) values for the NH 3 complexes (between 28.4 and 0.3 kcal•mol −1 ) are smaller than the corresponding ones for their HB counterparts.This is not the case for Cl − XB complexes, with E (2)  XB values that are larger than their HB counterparts for HXO complexes.
The secondary intermolecular interaction found by means of the AIM analysis in HXO 2 :NH 3 HB complexes is also found in the NBO analysis [Lp(O) → σ*(H-N)], though they contribute with very small E (2) values (0.7, 1.0, and 1.5 kcal•mol −1 for X = Cl, Br, and I, respectively) compared to the ones that were obtained for the primary HB interaction.
In addition, we have also compared the charge transfer with the second-order orbital perturbation energies, obtaining a very good linear correlation for NH 3 and Cl − HB (R 2 = 0.995 and 0.951, respectively, Figure S8 of the Supplementary Materials) and XB (R 2 = 0.978 (excluding HIO 4 ) and 0.955, respectively, Figure S9 of the Supplementary Materials) complexes.Therefore, the larger the E (2) energy, the larger the charge transfer, irrespective of the nature of the complexes.

Energy Partition Scheme
The physical nature of these HB and XB interactions has been analyzed by means of SAPT calculations.The energy contributions obtained from the SAPT partitioning scheme are listed in Table S1 (HB) and Table S2 (XB) of the Supplementary Materials and the corresponding terms are represented in Figure 6 (HB) and Figure 7 (XB).Some complexes have been removed from the analysis (proton transfer complexes and HClO 3 , HBrO 4 , and HIO 4 XB complexes with Cl − ) because they yield misleading results, most likely due to the proximity of the interacting units.The SAPT analysis revealed that the electrostatic term, E el , is negative for all complexes, larger for anionic than for neutral complexes, with values ranging from −34.0 to −18.8 kcal•mol −1 and from −40.1 to −30.5 kcal•mol −1 for HXO n :NH 3 and HXO n :Cl − HB complexes, respectively.The same behavior is observed for XB complexes, with E el values between −76.4 and −4.2 kcal•mol −1 and between −77.3 and −9.4 kcal•mol −1 for HXO n :NH 3 and HXO n :Cl − complexes, respectively.
E el is the most important attractive contribution in all cases, with a relative weight within all attractive forces greater than 53.2% in HB complexes and greater than 47.3% in XB complexes.In addition, the electrostatic contribution becomes larger with the increasing number of O atoms in HB complexes.For instance, the E el values are −19.9,−25.1, and −29.1 kcal•mol −1 for HClO:NH 3 , HClO 2 :NH 3 , and HClO 3 :NH 3 HB complexes, respectively.In XB complexes, however, the E el values increase on going from X = Cl to X = I, due to the smallest and largest σ-holes for these atoms, respectively, as observed in HXO:NH 3 XB complexes (E el = −11.9,−22.0, and −30.4 kcal•mol −1 for X = Cl, Br, and I, respectively).In general, the induction term, E i , is the second most important attractive contribution.The E el term, E i , becomes larger with the number of oxygen atoms in HB complexes, as it usually increases with the size of the X atom in XB complexes.The smallest contribution, the dispersion energy, E d , is kept more or less constant within each HXO n HB series and, at the same time, it becomes larger within each HXO n XB series, as expected from the high polarizability of the heavier X atoms.

Theoretical Methods
All of the geometries of the systems were fully optimized at the resolution of the identity second-order Møller-Plesset perturbation theory (RI-MP2) with the aug-cc-pVTZ basis set [83,84].For iodine atoms [85], the aug-cc-pVTZ-PP pseudo potential basis set was used.Harmonic vibrational frequencies were computed at the same level used in order to verify that the structures obtained correspond to local minima.
The energies of the systems were refined by using the CCSD(T)/CBS method.The CCSD(T) technique provides reliable interaction energies only if they are combined with extended atomic orbital (AO) basis sets, and the larger the basis set, the better the interaction energies that result.Owing to the rather strong dependence of the interaction energy on the AO-basis-set size, it is recommended that the relevant calculations be performed at the complete basis-set (CBS) limit.Different extrapolation schemes have been introduced and the scheme of Helgaker et al. [86,87] has become most widely used.
Here, the Hartree-Fock (HF) and correlation (MP2) energies are extrapolated separately as shown in Equations ( 1) and (2), respectively: where E X and E CBS are the energies for the basis set with the largest angular momentum X and for the complete basis set, respectively.The CCSD(T)/CBS level can be attained via a separate extrapolation of the MP2 and higher-order correlation energies towards the basis-set limit (Equation ( 3)).
Here, each of the components is differently sensitive to the AO basis set: the MP2 correlation energy is the more slowly converging, and the larger the basis set used in the extrapolation, the better.In our case, we have used a two-point extrapolation scheme by using the aug-cc-pVTZ and the aug-cc-pVQZ basis sets.The third term, called the CCSD(T) correction term (E[CCSD(T)] − E[MP2)], is determined as the difference between the CCSD(T) and MP2 energies and converges much faster than the MP2 correlation energy, the second term.The use of such a term is possible because the MP2 and CCSD(T) energies converge with basis-set size in a very similar way; consequently, its difference is much less basis-set-dependent and much smaller basis sets can be applied.In our case, we have used the aug-cc-pVTZ (AVTZ) basis set to compute the CCSD(T) correction.All of the geometry optimizations described herein were carried out by using TURBOMOLE version 7.0 [88] and CBS calculations were computed by using the MOLPRO program [89].Binding energies were obtained as the difference between the energy of the complex and the energies of the optimized isolated monomers.
The bonding characteristics were analyzed by means of the Atoms-in-Molecules (AIM) theory [90,91].For this purpose, we have located the most relevant bond critical points (BCP), and evaluated the electron density at each of them, with the facilities of AIMALL programs [92].All of the interactions were characterized by the formation of a BCP between the atoms involved that are connected by the corresponding bond paths.
The Natural Bond Orbital (NBO) method [93] has been employed to evaluate atomic charges using the NBO-3.1 program, included within the Gaussian-09 program, and to analyze charge-transfer interactions between occupied and empty orbitals.Because MP2 orbitals are nonexistent, the charge-transfer interactions have been computed using the M06-2X functional with the aug-cc-pVTZ basis set at the MP2/aug-cc-pVTZ complex geometries, so that at least some electron correlation effects could be included.
The SAPT (Symmetry Adapted Perturbation Theory) [94] method allows for the decomposition of the interaction energy into different terms related to physically well-defined components, such as those arising from electrostatic, exchange, induction, and dispersion terms.The interaction energy can be expressed within the framework of the SAPT method as: where E el (1) is the electrostatic interaction energy of the monomers, each one with its unperturbed electron distribution; E exch (1) is the first-order exchange energy term; E i (2) denotes the second-order induction energy arising from the interaction of permanent multipoles with induced multipole moments and charge-transfer contributions, plus the change in the repulsion energy induced by the deformation of the electronic clouds of the monomers; and E D (2) is the second-order dispersion energy, which is related to the instantaneous multipole-induced multipole moment interactions plus the second-order correction for coupling between the exchange repulsion and the dispersion interactions.
The density fitting DFT-SAPT (DF-DFT-SAPT) formulation has been used to investigate interaction energies.In this approach, the energies of interacting monomers are expressed in terms of orbital energies obtained from the Kohn-Sham density functional theory [95,96].In addition to the terms listed in Equation ( 4), a Hartree-Fock correction term δ(HF), which takes into account higher-order induction and exchange corrections, has been included [97].The DF-DFT-SAPT calculations have been performed using the PBE0/aug-cc-pVTZ/aug-cc-pVTZ-PP computational method [98].As an auxiliary fitting basis set, the JK-fitting basis of Weigend [99] was employed.The cc-pVQZ JK-fitting basis was used for all atoms.For the intermolecular correlation terms, i.e., the dispersion and exchange-dispersion terms, the related aug-cc-pVTZ MP2-fitting basis of Weigend, Köhn, and Hättig [100] was employed.All SAPT calculations have been carried out with the MOLPRO program [89].

Conclusions
In the present manuscript, we have analyzed the formation of HB and XB complexes with two Lewis bases (NH 3 and Cl − ) and the halogen oxoacids, HXO n from a theoretical point of view.The geometry of the HB and XB complexes is very similar within each HXO n series and, therefore, it is independent of the X atom.The interaction is quite strong for both types of complexes, giving rise to large interaction energies and intermolecular equilibrium distances much shorter than the sum of the van der Waals radii of the atoms involved in the interaction.In fact, proton transfer was generally observed in complexes with three or four oxygen atoms, namely, HXO 4 :NH 3 , HClO 3 :Cl − , HBrO 3 :Cl − , and HXO 4 :Cl − .The interaction energies generally increase with the number of O atoms.Comparison of the energetics of the complexes indicates that the only XB complexes that are more favored than those of HB are HIO:NH 3 , HIO:Cl − , HIO 2 :Cl − , and HIO 3 :Cl − .The atoms-in-molecules analysis revealed the presence of a bond critical point between the atoms involved in the interaction.Moreover, good correlations were obtained between electron density and its Laplacian values with intermolecular equilibrium distances.The topological analysis indicates a partial covalent nature of the HB interactions, apart from the complexes where proton transfer was observed.The NBO calculations show the presence of large charge-transfer-stabilizing energies, E (2) , in both HB and XB complexes, that usually increase as the number of O atoms increases.The SAPT calculations show that the most important energy contribution comes from electrostatics, followed by induction and dispersion.Both E el and E i values increase with the number of O atoms for HB complexes and with the size of the X atom for XB complexes.

Supplementary Materials:
The following are available online at http://www.mdpi.com/2304-6740/7/1/9/s1, Figure S1: Graphical representation of d(X-OH) (in Å) versus XB MEP (in kcal/mol) in halogen oxoacids, Figure S2: Graphical representation of d(O-H) (in Å) versus HB MEP (in kcal/mol) in halogen oxoacids, Figure S3: Graphical representation of interaction energies of HB HXO n :NH 3 versus HB HXO n :Cl − (in kcal•mol −1 ), Figure S4: Graphical representation of interaction energies of XB HXO n :NH 3 versus XB HXO n :Cl − (in kcal•mol −1 ), Figure S5: Second-order polynomial relationship between the O-H distance (in Å) and the electron density for HB, ρ HB , complexes, Figure S6: Second-order polynomial relationship between the interaction energy, ∆E, (in kcal•mol −1 ) and the Laplacian of the electron density for HB, ∇ 2 ρ HB , complexes, Figure S7: Second-order polynomial relationship between the interaction energy, ∆E, (in kcal•mol −1 ) and the electron density for HB, ρ HB , complexes, Figure S8: Value of the charge of the Lewis base, in e, (NH 3 , up, Cl − , down) versus.E (2)  HB , in kcal•mol −1 , for all HB complexes with no proton transfer, Figure S9: Value of the charge of the Lewis base, in e, versus.E (2)  XB , in kcal•mol −1 , for all XB complexes.Table S1: SAPT electrostatic, exchange, dispersion, and induction energy contributions (E el , E ex , E d , and E i , respectively) of HB complexes.Energies in kcal•mol −1 , Table S2: SAPT electrostatic, exchange, dispersion, and induction energy contributions (E el , E ex , E d , and E i , respectively) of XB complexes.Energies in kcal•mol −1 .

Figure 2 .
Figure 2. The optimized structures of the HB complexes between HBrO n and NH 3 , and between HBrO n and Cl − .Let us first analyze the NH 3 HB complexes.From the inspection of the results (Table3), we observe that the N•••H equilibrium distances range between 1.776 and 1.057 Å for HIO and HBrO 4 complexes, respectively.These distances are much shorter than the sum of the van der Waals radii of N and H atoms (2.86 Å)[70].These results indicate that the interaction established in these HB complexes is strong, as reflected in their interaction energies (∆E) that range between −10.7 and −20.8 kcal•mol −1 for HBrO and HIO 4 complexes, respectively.For comparison purposes, the interaction energy of the H 3 N•••H 2 O complex, computed at the MP2/aug-cc-pVTZ level, is −6.70 kcal•mol −1[32], much smaller than our reported values.In fact, for some of them (HXO 4 ), a proton transfer is observed; the largest ∆E values were observed for the HClO 4 , HBrO 4 , and HIO 4 complexes with NH 3 (−17.7,−20.1, and −20.8 kcal•mol −1 , respectively), which have quite short interatomic N•••H distances (1.126, 1.057, and 1.061 Å, respectively) accompanied by the expected lengthening of the H-O distance by 0.429, 0.680, and 0.675 Å, respectively.The smallest ∆E values and the largest intermolecular HB distances were obtained for the HXO:NH 3 complexes, and are constant for every halogen atom (ca.−11 kcal•mol −1 and ca.1.77 Å, respectively).Nearly constant ∆E values were also observed for the HXO 2 complexes, though a little bit larger than for the HXO ones.In fact, the N•••H distances are the same for both HXO and HXO 2 complexes.Particularly, the HXO 2 complexes show an additional intermolecular interaction, an HB between the X=O oxygen atom, and an NH 3 hydrogen atom, with increasing O•••H distances (2.148, 2.191, and 2.259 Å for X = Cl, Br, and I, respectively) due to the concomitant lengthening of the X=O distance.Significant variations appear for the HXO 3 :NH 3 complexes, yielding larger ∆E values and shorter intermolecular HB distances than those for the HXO and HXO 2 complexes.Thus, the interaction energy increases, the N•••H distances shorten, and the O-H distances lengthen with the number of oxygen atoms because of the increasing electron-withdrawing character of the XO n moiety, making the H atom much more acidic.Moreover, for n = 3 and n = 4, the ∆E values of the HXO n complexes are not constant, unlike for n = 1 and n = 2, obtaining the largest

4 ,
HBrO 4 , and HIO 4 complexes with NH 3 (−17.7,−20.1, and −20.8 kcal•mol −1 , respectively), which have quite short interatomic N•••H distances (1.126, 1.057, and 1.061 Å, respectively) accompanied by the expected lengthening of the H-O distance by 0.429, 0.680, and 0.675 Å, respectively.The smallest ∆E values and the largest intermolecular HB distances were obtained for the HXO:NH 3 complexes, and are constant for every halogen atom (ca.−11 kcal•mol −1 and ca.1.77 Å, respectively).Nearly constant ∆E values were also observed for the HXO 2 complexes, though a little bit larger than for the HXO ones.In fact, the N•••H distances are the same for both HXO and HXO 2 complexes.Particularly, the HXO 2 complexes show an additional intermolecular interaction, an HB between the X=O oxygen atom, and an NH 3 hydrogen atom, with increasing O•••H distances (2.148, 2.191, and 2.259 Å for X = Cl, Br, and I, respectively) due to the concomitant lengthening of the X=O distance.Significant variations appear for the HXO 3 :NH 3 complexes, yielding larger ∆E values and shorter intermolecular HB distances than those for the HXO and HXO 2 complexes.Thus, the interaction energy increases, the N•••H distances shorten, and the O-H distances lengthen with the number of oxygen atoms because of the increasing electron-withdrawing character of the XO n moiety, making the H atom much more acidic.Moreover, for n = 3 and n = 4, the ∆E values of the HXO n complexes are not constant, unlike for n = 1 and n = 2, obtaining the largest values for X = I, most likely due to the increasing impact that the oxygen atoms have on the highly polarizable iodine atom.

Figure 4 .
Figure 4. Molecular graphs of HB and XB complexes of HClO n :NH 3 .The bond and ring critical points are represented by green and red dots, respectively.Only bond paths are depicted.

Figure 5 .
Figure 5.The second-order polynomial relationship between the intermolecular distance (in Å) and the electron density for HB, ρ HB , (up) and XB, ρ XB , (down) complexes.

Figure 7 .
Figure 7. SAPT electrostatic, exchange, dispersion, and induction energy contributions (E el , E ex , E d , and E i , respectively) of XB complexes.Energies in kcal•mol −1 .

Table 5 .
Electron density (ρ HB ), Laplacian (∇ 2 ρ HB ), and electron density total energy (H HB ) in a.u.for the intermolecular bond critical points for HB complexes.