The nature of inter- and intramolecular interactions in F2OXe…HX (X= F, Cl, Br, I) complexes

Electronic structure of the XeOF2 molecule and its two complexes with HX (X= F, Cl, Br, I) molecules have been studied in the gas phase using quantum chemical topology methods: topological analysis of electron localization function (ELF), electron density, ρ(r), reduced gradient of electron density |RDG(r)| in real space, and symmetry adapted perturbation theory (SAPT) in the Hilbert space. The wave function has been approximated by the MP2 and DFT methods, using APF-D, B3LYP, M062X, and B2PLYP functionals, with the dispersion correction as proposed by Grimme (GD3). For the Xe-F and Xe=O bonds in the isolated XeOF2 molecule, the bonding ELF-localization basins have not been observed. According to the ELF results, these interactions are not of covalent nature with shared electron density. There are two stable F2OXe…HF complexes. The first one is stabilized by the F-H…F and Xe…F interactions (type I) and the second by the F-H…O hydrogen bond (type II). The SAPT analysis confirms the electrostatic term, Eelst(1) and the induction energy, Eind(2) to be the major contributors to stabilizing both types of complexes.


Introduction
The XeOF 2 molecule, with the xenon atom formally in oxidation state +4, was first observed by Ogden and Turner [1] in 1966 and subsequently by Jacob and Opferkuch [2] in 1976. Intermolecular complexes of XeOF 2 with hydrogen fluoride (F 2 OXe … HF) have been synthesized and characterized by the Schrobilgen group [3], using vibrational spectroscopy and computational methods (Scheme 1). The most interesting result stemming from those experimental studies is stabilization of the F 2 OXe … HX complex with the weak F-H … O and F-H … F hydrogen bonds and weak Xe … F interactions. A detailed nature of the xenon-fluorine interaction is currently not entirely understood and the state-of-art electronic structure analysis is crucial to gain a deeper insight into this interaction.
Topological analysis of electron density field, ρ(r) proposed by Bader [4] and known as atoms in molecules theory (AIM), topographical analysis of localized electron detector (LED) [5,6] or the non-covalent index (NCI) [7], both based on the magnitude of the reduced gradient of electron density (|RDG(r)|), can fully characterize all bonding and nonbonding interactions, without a need to evoke the molecular orbital concept. On the other hand, topological analysis of electron localization function, η(r), (ELF) [8,9], serves best as a tool for covalent bonding analysis.
The current paper presents optimized geometrical structures of the F 2 OXe … HX (X= F, Cl, Br, I) complexes in the gas phase together with theoretical properties of intermolecular interactions. Non-covalent intermolecular interactions are described using topological analysis of electron density, ρ(r) and |RDG(r)|. Detailed analysis of the electronic structure of the isolated XeOF 2 molecule and its intermolecular complexes with hydrogen fluoride, HF, has been performed using topological analysis of ρ(r), and η(r) fields. Finally, the nature of non-covalent intermolecular interactions in the F 2 OXe … HF has been examined using the symmetry adapted perturbation theory (SAPT) [10].
The APF-D functional, based on the new hybrid density functional, APF, includes the empirical dispersion model (D) [14]. The functional uses a spherical atom model for the instantaneous dipole-induced dipole interactions. The functional correctly describes a large portion of the potential energy surface (PES) for noble gas complexes with various diatomic molecules [14]. The B2PLYP functional [20] combines the exact HF exchange with an MP2-like correlation in the DFT calculation, and belongs to the final fifth rung of the Jacob's ladder, introduced by Perdew [21]. It incorporates information about the unoccupied Kohn-Sham orbitals.
In the Def2-TZVPPD basis set [22] 28 electrons been replaced by the pseudopotential (ecp-28) for both Xe and I atoms. The minima on the potential energy surface (PES) have been confirmed through non-imaginary frequencies in the harmonic vibrational analysis.
Interaction energies, defined as a difference between the total energy of the complex and its monomers with geometrical structures corresponding to the complex (E int ), have been corrected using basis set superposition error (BSSE) (E int CP ) obtained with the counterpoise procedure proposed by Boys and Bernardi [23]. The differences between the E tot values for the complex and optimized geometrical structures (equilibrium geometry) for the isolated monomers, dissociation energy ΔE dis, have been corrected for the vibrational zero-point energy correction (ΔE dis + ΔZPVE). The final E int CP value also includes the vibrational zero-point energy correction, (E int CP + ΔZPVE). Topological analysis of electron density, ρ(r), has been carried out using the AIMAll program [24] with the DFT(M062X) wave function, calculated for the geometrical structures, optimized at the DFT(M062X)/Def2-TZVPPD computational level. The wfx files containing additional information for the atomic region, described by ecp-28, have been used.
Reduced gradients of the electron density have been calculated using the AIMAll program with the wave function approximated at the DFT(B3LYP)/TZP//DFT(M062X)/Def2-TZVPPD level.
Topological analysis of ELF has been performed using the TopMod09 package [25] with the wave function approximated using the DFT(B3LYP)/Def2-TZVPPD single-point calculations for geometrical structures optimized at the DFT(M062X)/Def2-TZVPPD computational level. The parallelepipedic grid of points with step 0.05 bohr has been used.
SAPT analysis has been performed using the MOLPRO (Version 2012.1) program [19] for the geometrical structures optimized at the B2PLYP + GD3/Def2-TZVPPD computational level.

Results and discussion
Geometrical structure and interaction energy Geometrical structures of the intermolecular F 2 OXe … HX (X= F, Cl, Br, I) complexes have been optimized using a variety of density functionals and the MP2 method. Optimized geometrical structures are shown in Fig. 1. For the F 2 OXe … HX (X= F, Cl, Br, I) complexes, two minima on the PES have been found. Structural differences between complexes (type I and type II) lie mainly in the orientation of the HX molecule with respect to the XeOF 2 molecule. The optimized geometrical parameters for all the F 2 OXe … HX complexes are shown in Table 1 (type I) and Table 2 (type II). The parameters obtained with the DFT(M062X + GD3) method have been omitted since the addition of the dispersion correction did not bring any changes. Only complexes with the HF molecule are discussed and compared to the existing experimental results [3]. Optimizations performed at the highest computational level, CCSD(T)/Def2-TZVPPD, yield the following results: The type I complex is stabilized by the F-H … F hydrogen bond and the Xe … F non-bonding interaction, confirmed by bond paths with the bond critical points (BCP) localized for the gradient field of ρ(r) (see Fig. 2a). The F-H … F hydrogen bond is topologically characterized by relatively large electron density for the BCP (ρ BCP (r) = 0.025 e/bohr 3 ) and positive value of the Laplacian electron density for the BCP (∇ 2 ρ BCP (r) = 0.122 e/bohr 5 ) (see Table 3). Supposedly weaker Xe … F interaction is characterized by smaller ρ BCP (r) (0.016 e/ bohr 3 ) and smaller and positive ∇ 2 ρ BCP (r) (0.070 e/bohr 5 ). The (3,-1) CP between Xe and F nuclear attractors is localized in a proximity of the (3,+1) CP. The type II complex is stabilized only by the F-H … O hydrogen bond (ρ BCP (r) = 0.033 e/ bohr 3 , ∇ 2 ρ BCP (r) = 0.107 e/bohr 5 ) and the BCP characterizing this interaction is shown in Fig. 2b. The ρ BCP (r) value is larger than that obtained for the F-H … F hydrogen bond in the type I. The difference can be caused by stronger intermolecular interaction.
The strength of intermolecular interaction has been evaluated using supermolecular approach with two parameters: the interaction energy, (E int CP , E int CP + ΔZPVE) and the dissociation energy (ΔE dis + ΔZPVE). Values for the F 2 OXe … HX (X= F, Cl) complexes have been presented in Table 4, and for the F 2 OXe … HX (X=Br, I) complexes in Table 5. During discussion we will concentrate on the values of E int CP + ΔZPVE only.
The E int CP + ΔZPVE values for all complexes (type I and II) are smaller than −7.39 kcal/mol at the DFT level (HF, B2PLYP + GD3) and smaller than −5.66 kcal/mol at the  HI complex, all three (M062X, B3LYP, APF-D) DFT functionals (also B3LYP + GD3 and M062X + GD3) and the MP2 method show the type I as more stable, due to the I-H … F and Xe … I interactions. The differences in the E int CP + ΔZPVE vary between 0.15 kcal/mol (B3LYP + GD3) and 0.69 kcal/mol (B3LYP). Only the B2PLYP and B2PLYP + GD3 functionals yield slightly larger stability for the type II complex. The  Fig. 2 The critical points of the ρ(r) field and 2D maps of the Laplacian of ρ(r) field for the F 2 OXe … HF complexes E int CP + ΔZPVE differences are 0.32 and 0.55 kcal/mol, respectively. The differences in energy are generally smaller than 1 kcal/mol, therefore calculations at a higher computational level, CCSD(T)/Def2-TZVPPD, has been used in order to establish the relative stability of both structures. The E int CP (E int CP + ΔZPVE) for the type I obtained this way is −6.32 (−4.67) kcal/mol and −6.16 (−4.32) kcal/mol for the type II, thus the complex stabilized with the F-H … F hydrogen bond and Xe … F interaction is slightly more stable (0.16 kcal/mol -ΔE int CP ). The CCSD(T) level yield similarly small value of he E int CP + ΔZPVE differences between both type complexes as the DFT (APFD, M062X, M062X + GD3, B3LYP, B3LYP + GD3) and MP2 method.
As the electrostatic energy is the largest contributor to the total interaction energy, the weakening of stabilization can be associated with a decreasing value of the dipole moment for hydrogen halides. Values of the dipole moment for XeOF 2 and HF, HCl, HBr and HI calculated using M062X functional are 2.735D and 1.839, 1.113, 0.881, 0.467D, respectively.

Infrared frequencies
Both computationally characterized structures depict a hydrogen-bonded complex, where the estimated H-X vibrational frequencies exhibit large shifts to lower wavenumbers (see Table 6). Shift magnitudes diminish going from smaller   Table 6). Such an effect can be caused by an interaction between the halogen atom of the HX moiety with the Xe atom, resulting in the strengthening of the Xe=O bond. Delocalized electron density between two complex subunits is observed, which also explains slightly smaller vibrational shifts when going from F to I, i.e. in the decreasing order of the halogen atom electronegativity.
Estimated vibrational shifts of the Xe-F bonds in XeOF 2 upon complexation are shown in Table 6. For both structures, the Xe-F vibrational modes display a downward shift as compared to the monomer values at all computational levels. The magnitudes of ν asym (Xe-F) vibrational shifts increase when going from F to I. All the calculated vibrational shifts indicate a hydrogen-bonded complex, in which an increased interaction between a positively charged hydrogen decides on the interaction direction and stretches the Xe-F bond via electron density delocalization to the space between the complex subunits. For the type I larger vibrational shifts are observed. Hydrogen bonded interaction is prevalent in the type I complexes, however the X … Xe interaction is also present. The latter does not appear in the type II complexes (according to AIM results), resulting in a deformation of the subunit structures.
All theoretically predicted vibrational shifts indicate the hydrogen-bonding interaction between the subunits as the main interaction channel, with existing interaction between a halogen atom of the HX moiety and the Xe atom of XeOF 2 . These features are also noticeable in the calculated structures of studied complexes, with the type II complexes more tilted from the HX halogen tail towards the XeOF 2 subunit. Analysis of the F 2 OXe … HF electron density confirms the interaction patterns above, showing the bond critical points (BCP) in the space between xenon and the halogen atom of the HX subunit.

Topological analysis of ρ(r), |RDG(r)| and η(r) fields
In the light of topological analysis of electron localization function, ELF, local electronic structures of the F 2 OXe … HX complexes, both types I and II, are represented by a set of core and valence attractors, constituting a sum of two attractor sets, localized separately for the XeOF 2 and HX (X= F, Cl, Br, I) molecules. Since topologies of η(r) field are similar for different hydrogen halides, interacting with XeOF 2 , only Electronic structure of the isolated XeOF 2 molecule is represented by four core attractors corresponding to oxygen, C(O), xenon, C(Xe) and fluorine, C(F) cores. In the valence space the disynaptic and monosynaptic non-bonding attractors are observed: two sets of V i=1,2 (Xe,F), V i=1,2 (Xe,O) and V i=1, 2 (Xe) localized below and above the molecular plane. All attractors and values of the basin populations () are shown in Fig. 3. The V i=1,2 (Xe) attractors characterize the non-bonding electron density in the valence shell of Xe. These attractors can be associated with classical Lewis lone pairs. The localization of the disynaptic attractors in space, V i=1,2 (Xe,F), V i=1, 2 (Xe,O), (far from bonding regions) suggests that those attractors characterize non-bonding electron density rather than the Xe-F and Xe=O chemical bonds. Combined analysis of the ρ(r) and η(r) fields, as proposed by Raub and Jansen [31], shows that the V i (Xe,F) and V i (Xe,O) basins contain electron density, coming exclusively from the fluorine (99 %) and oxygen (90 %) atoms. Atomic contributions to the V i (Xe,F) and V i (Xe,O) basins are shown in Fig. 3. Thus the V i (Xe,F) and V i (Xe,O) basins display the non-bonding characteristics of the V(F) and V(O) basins, respectively. It is worth emphasizing that the absence of shared electron density in the bonding basins, V i (Xe,F) and V i (Xe,O), unambiguously shows that the typical covalent Xe-F and Xe=O bonds as predicted by the Lewis formula, are not confirmed by topological analysis of ELF. It is evident that the electron densities of the xenon-fluorine and xenon-oxygen interactions are largely delocalized. Such characteristic suggests the chargeshift model of resonating electron density as a good explanation of its nature using the valence bond view of chemical bonding. Recent study on the bonding in the XeF 2 molecule by Braïda and Hiberty [32] has shown that the charge-shift bonding, characterized by the dominant large covalent-ionic interaction energy, is a major stabilizing factor.
The AIM analysis carried out for the type I complex shows that BCP localized for the H … F interaction displays the largest ellipticity, ε BCP, (0.310) for all the BCPs (see Table 3). Such high degree of electron density delocalization can be caused by close proximity of the (3,+1) CP (see Fig. 2). Total energy density, H BCP is 0.003 hartree/bohr 3 , thus kinetic energy is a slightly dominant factor for the BCP, confirming a closedshell interaction type, typical for hydrogen bonds. This conclusion is also supported by a very small average number of electron pairs delocalized (shared) between the F and H atoms (bond index, DI = 0.035). The non-covalent interaction, Xe … F, stabilizing the complex has similarly large value of ε BCP (0.227). Such high value of electron density delocalization can also be explained by the proximity of the (3,+1) CP. Non-covalent character of interaction is shown by a small average number of electron pairs delocalized between Xe and F atoms (0.087). The type II F 2 OXe … HF complex is bound only by a single F-H … O hydrogen bond. The BCP characteristics for the H … O interaction are totally different from that observed for the H … F interaction (type I). Electron density delocalization for the BCP is much smaller -the value of the ε BCP is 0.058 and the value of H BCP is slightly negative (−0.003 hartree/bohr 3 ). The non-covalent character of the interaction is associated with a relatively small average number Table 6 Vibrational stretching frequency shifts (in cm −1 ) for the ν(H-X), ν(Xe=O), ν asym (Xe-F) and ν asym (Xe-F) vibrations vib: ν (H-X)   molecule  HF  HCl  HBr  HI   Type: a  I  I I  I  I I  I  II  I  II I  I I  I  I I  I  II  I  II  MP2 12 In order to support our findings, we performed additional calculations using reduced density gradient. 2D plot and the relief map of reduced density gradient magnitude, |RDG(r)| for both structures are shown in Fig. 4. For the type I complex distinctive planar regions clearly exist and they are situated almost perpendicularly to the gradient paths of ρ(r) that join the attractor nuclei, F, H and Xe, F. Those regions are situated near the BCPs (ρ(r) field) characterizing the non-bonding H … F and Xe … F interactions. Thus both topological analysis of ρ(r) and topographical analysis of |RDG(r)| indicate the existence of both types of intermolecular interactions (I and II). A very similar picture has been obtained for the type II complex, with the planar region situated perpendicularly to the gradient path joining H and O nuclei attractors. However, this region also comprises interaction between the Xe and F atoms, where BCP of ρ(r) field is not observed. This suggests that the Xe … F interaction is also present in the type II complex, but is weaker than the H … F interaction. As reported by Contreras-Garcia et al. [33] sometimes there is no direct comparison between obtained BCPs of ρ(r) and the |RDG(r)| isosurfaces.

The SAPT analysis
Nature of the non-covalent interactions in the F 2 OXe … HX complexes has been investigated using the symmetryadapted intermolecular perturbation theory (SAPT). This approach calculates the total interaction energy between molecules as a sum of individual first and second order interactions with a clear physical interpretation. Selected components of total interaction energy are collected in Table 7. SAPT enables clear separation of electrostatic E elst (1) , induction E ind (2) and dispersion E disp (2) terms together with their respective exchange counterparts E exch (1) , E ind-exch (2) , E disp-exch (2) . The latter ones are sometimes denoted as Pauli repulsion due to electron exchange between monomers, when the molecules are close to each other. The SAPT0 and SAPT2 expressions discussed in this paper are defined as follows: For the F 2 OXe … HF complex, SAPT2 calculations using the Def2-TZVPPD basis set shows that the type I complex (F-H … F and Xe … F interactions) is more stable (−8.57 kcal/mol) than the type II complex (−7.08 kcal/mol). The interaction energies calculated at both SAPT0 and SAPT2 levels are similar to those obtained at the DFT and MP2 levels using the supramolecular approach (see Table 4). As can be seen, the δ int HF terms for these complexes are not very high (less than 19  ). Introduction of the exchange contribution at the first SAPT order for the type I structure shows higher stabilization of the complex (E elst (1) + E exch (1) = −2.06 kcal/mol). For the type II complex, the exchange contribution is slightly (0.55 kcal/mol) bigger than the electrostatic energy. This confirms the stability of the complex formed with the F-H … F and Xe … F interactions (type I), even without including the electron correlation correction. For the type II complex, stabilized only by the F-H … O hydrogen bond, the electron correlation needs to be included in order to obtain a reliable picture.
The electric polarization caused by nuclear and electron cloud charges largely influence intermolecular interactions. Thus, the induction energy, E ind (2) , is the biggest contributor to the total SAPT energy at the second-order for both complexes (type I and type II). It is, however, still smaller than the electrostatic effect. The E ind-exch (2) contribution is a compensation to the E ind (2) term, whereas the E ind-exch (2) values are roughly half of the E ind (2) absolute value for both complexes. Even if the differences between the E ind (2) absolute values for the type I and type II complexes are negligible (0.07 kcal/ mol), the total SAPT2 energy (E int SAPT2 ) for the type I complex is lower than for the type II. Thus E ind (2) contributes less to the type I E int SAPT2 than for the type II. Absolute values of the dispersion energy, E disp (2) for the type I and type II complexes -the attractive energy determined by mutual interactions of the induced multiple moments in both molecules -are almost equal, −3.66 and −3.69 kcal/mol, respectively. Contribution of the dispersion energy to the E int SAPT2 energy is about 43 % for the type I and 52 % for type II. The E dispexch (2) term, the compensation term to the E disp (2) , has quite significant influence on the total interaction energy, compensating E disp (2) by about 17 % (type I) and 16 % (type II). The E ind (2) / E disp (2) ratio is an effective measure of a relationship between induction and dispersion effects. Calculated ratios of E ind (2) / E disp (2) for the type I and type II F 2 OXe … HF complex are 1.86 and 1.81, respectively. The type I complex is therefore more favorable than the type II complex.

Conclusions
The nature of chemical bonds and intermolecular interactions formed by noble gases deserve special attention, due to group 18 relative unreactivity. New compounds and intermolecular complexes are being constantly researched for. Identification of the F 2 OXe … HF complex by Schrobilgen's group [3] constitutes a very interesting example in the area. This paper presents a detailed description of geometrical structures, energetics and infrared spectra of the intermolecular complexes of XeOF 2 with hydrogen halides, F 2 OXe … HX (X= F, Cl, Br, I). Our research shows that combined application of the quantum chemical topology methods, namely topological analysis of electron density, reduced density gradient and electron localization function (in real space) provide a complete description of the electronic structure of the F 2 OXe … HF complex. Topological studies have been complemented with the interaction energy decomposition analysis (SAPT), based on the molecular orbitals in the Hilbert space. Not only such an approach does offer a deeper insight into the nature of chemical Fig. 4 2D and relief maps of the reduced density gradients for the F 2 OXe … HF complexes. The bond paths of ρ(r) field are shown for the type II structure