Effects of Xenon Insertion into Hydrogen Bromide. Comparison of the

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Effects of Xenon Insertion into Hydrogen Bromide. Comparison of the Electronic Structure of the HBr···CO2 and HXeBr···CO2 Complexes Using Quantum Chemical Topology Methods: Electron Localization Function, Atoms in Molecules and Symmetry Adapted Perturbation Theory Emilia Makarewicz, Agnieszka J. Gordon, Krzysztof Mierzwicki, Zdzislaw Latajka, and Slawomir Berski* Faculty of Chemistry, University of Wroclaw, 14 F. Joliot-Curie, 50-383, Wroclaw, Poland S Supporting Information *

ABSTRACT: Quantum chemistry methods have been applied to study the influence of the Xe atom inserted into the hydrogen−bromine bond (HBr → HXeBr), particularly on the nature of atomic interactions in the HBr···CO2 and HXeBr···CO2 complexes. Detailed analysis of the nature of chemical bonds has been carried out using topological analysis of the electron localization function, while topological analysis of electron density was used to gain insight into the nature of weak nonbonding interactions. Symmetry-adapted perturbation theory within the orbital approach was applied for greater understanding of the physical contributions to the total interaction energy.

1. INTRODUCTION Properties of molecules containing rare-gas atoms (Rg) have been of interest to both experimental and theoretical scientists for many years. Molecules involving the Xe atom, XePtF6, XeF4, and XeF2, were synthesized in 1962.1−3 A very interesting molecule, HArF, was identified and characterized by Räsänen’s group in 20014through infrared spectroscopy experiments in low-temperature noble-gas matrices. Structurally similar systems containing the Xe atom, namely HXeCl, HXeBr, HXeI,5 HXeH,6 HXeOH,7 and HXeSH8 have also been identified. In addition to the single molecules,9 intermolecular complexes including rare-gas atoms have been investigated both experimentally and theoretically. For example, the results of experimental work on HXeH···H2O,10 HArF···N2, HKrF··· N2, and HKrCl···N2 complexes have been published.11 These complexes exhibit interesting spectroscopic properties associated with blue shift of the frequency of the Rg−H bond. On the other hand, Cukras and Sadlej12 reported the results of symmetry-adapted perturbation theory (SAPT) interaction energy decomposition for the HArF···N2 and HArF···P2 complexes. A similar study was carried out by Jankowska and Sadlej13for the HXeF···HF complex. For the intermolecular complexes containing any rare-gas atoms (ARgB···XY) two principal questions can be considered: (1) how does the presence of the Rg atom influence the electronic structure of the AB subunit (AB → ARgB) and (2) does the modification of the heteromonomer bound to significantly change the electronic structure of the whole © XXXX American Chemical Society

weakly bound complex ARgB···XY in comparison to that of AB···XY? In order to answer these questions, a comparative study on weakly bonded complexes, consisting of unsubstituted molecules (AB···XY) and rare-gas substituted molecules (ARgB···XY), was undertaken. It is worth emphasizing that the effects of insertion of the Rg atom on properties of the hydrogen halide molecule have already been investigated. For example, Avramopoulos et al.14 studied the effect of Ar insertion into the HF molecule. He examined the values of the dipole moment, polarizabilities, and first hyperpolarizabilities. The calculations showed that the values of μz, αzz, and βzzz are greatly modified and are much larger than those calculated for the HF molecule. Similarly, the insertion of the Xe atom in the Au−F molecule significantly modified the (hyper)polarizability of AuXeF, and the effect for AuXeF was greater than that for the XeAuF configuration.15 Theoretical studies on the effects of rare-gas atom insertion into molecules are usually carried out within Hilbert space, where the wave function is approximated by the set of the molecular orbitals (canonical, NBO, or localized in one of an infinite number of ways). Less frequently the real-space analysis is performed using the topological analysis of the electron density,16 electrostatic potential,17 or electron localization function (ELF).18−20 Received: March 5, 2014 Revised: May 6, 2014

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Figure 1. Geometrical structures of the planar (Cs) and linear (C∞v) complexes of HBr···CO2 and HXeBr···CO2 optimized at the CCSD(T)/Def2TZVPPD computational level. The bond lengths and differences calculated in relation to the optimized geometrical structures of the isolated monomers are given in angstroms.

with Def2-TZVPPD basis set32 obtained from the EMSL Basis Set Library using the Basis Set Exchange software33,34 has been applied. For the Xe atom, 28 electrons have been replaced by the pseudopotential. The minima on the potential energy surface (PES) have been confirmed through nonimaginary frequencies in a harmonic vibrational analysis. The single-point calculations including a generation of the molecular orbitals for the ELF analysis have been performed using the Gaussian0935 program. The interaction energy Eint, calculated using the supermolecular method, is defined as a difference between the total energy of the complex and HBr, CO2 (HXeBr, CO2) monomers with geometrical structures corresponding to the complex. The value of Eint has been corrected (EintCP) by the basis set superposition error (BSSE) using the counterpoise procedure.36 The dissociation energy D0 is defined as a difference between Etot for the complex and optimized geometrical structures (equilibrium geometry) of the HBr, CO2 (HXeBr, CO2) monomers corrected with the vibrational zero-point energy correction (ZPVE). The EintCP value has also been corrected for the vibrational zero-point energy difference (EintCP + ΔZPVE). The EintCPvalues at the CCSD(T) level have been calculated using the Gaussian0935 program. The topological analysis of electron density ρ(r) has been carried out using the AIMAll program37 with the CCSD wave function calculated for the geometrical structures, optimized at the CCSD(T)/Def2-TZVPPD computational level. Because the pseudopotential was used for the Xe atom, additional electron density function data in the wave function file was included in the form of a wfx file. The approximation based on

In the present paper, the effects of insertion of the Xe atom into hydrogen bromide (HBr HXeBr) are studied together with changes in the intermolecular properties after complex formation with the CO2 molecule. The HXeBr···CO2 complex has been studied by Tsuge et al.21 by experimental infrared spectroscopy in low-temperature noble-gas matrices. HXeBr in CO2 and Xe environments was recently studied by Cohen et al.22 with density functional theory (DFT) using the B3LYP-D functional. Geometrical structures of the HXeBr···CO2 and HBr···CO2 complexes were studied at the CCSD(T)/Def2-TZVPPD level of calculations. The CCSD(T) method is considered the “gold standard” of computational chemistry. Furthermore, several electron density functionals (M052x, M062x, B3LYP, ωB97XD, and B2PLYP) and those including dispersion-correction schemes DFT-D3 by Grimme23,24 were used together with three methods of quantum chemical topology (QCT), namely, the topological analysis of the electron density, ρ(r) as introduced by Bader;16,25 electron localization function, η(r) as proposed by Silvi and Savin;19,26,27 and combined analysis of both fields, ρ(r)/η(r) as described by Raub and Jansen.28 The physical components of the interaction energy Eint were calculated using symmetry adapted perturbation theory.29 The results enable comprehensive comparative analysis of the electronic structure of the HBr···CO2 and HXeBr···CO2 complexes.

2. COMPUTATIONAL DETAILS The optimization of the geometrical structures and calculation of vibrational frequencies has been carried out using the MOLPRO30 program. The CCSD(T) method31in conjunction B

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natural orbitals of the correlated first-order total density matrix was used in generation of wfx file. Topological analysis of electron localization function (ELF) η(r) has been performed using the TopMod09 package38 with the CCSD wave function calculated for the geometrical structures optimized at the CCSD(T)/Def2-TZVPPD computational level. The approximation adopted for CCSD and MP2 wave function is based on natural orbitals, and their occupancy and was proposed by Feixas et al.39 The parallelepipedic grid of points with step 0.05 bohr was used. SAPT analysis has been performed using the aug-cc-pVTZ basis set for the H, C, and O atoms40,41 and the all-electron basis set proposed by Ahlrichs for Xe.42 The geometrical structures, optimized at the CCSD(T)/Def2-TZVPPD computational level, have been used.

Table 1. Energy Parameters for the HBr···CO2 and HXeBr··· CO2 Complexes. Calculations were Performed at the CCSD(T)/Def2-TZVPPD Computational Levela HBr···CO2

HXeBr···CO2

parameter

C∞v

Cs

C∞v

Cs

ΔEb ΔE + ΔZPVEc D0d Einte BSSEf EintCPg EintCP + ΔZPVE

0.25 0.09 −1.22 −2.01 0.61 −1.40 −0.82

−2.49 −2.36 −1.13 −1.70 0.51 −1.19 −0.77

−1.48 −1.86 0.65 −1.22 −1.07

−3.84 −4.61 1.26 −3.34 −3.06

a

Calculations were performed at the CCSD(T)/Def2-TZVPPD computational level. bΔE: the difference between the total energy Etot of optimized geometrical structures of the Cs and linear (C∞v) complexes, Etot(Cs) − Etot(C∞v). cValue of ΔE corrected by vibrational zero-point energy difference ΔZPVE. dD0: the dissociation energy defined as the difference between Etot of optimized geometrical structures of the Cs and C∞v complexes and optimized geometrical structures of the monomers (HBr, HXeBr, CO2), corrected by vibrational zero-point energy difference (ΔZPVE). eE int: the interaction energy. fBSSE: the basis set superposition error calculated using the counterpoise correction (CP). gEintCP: the interaction energy corrected for the BSSE.

3. RESULTS AND DISCUSSION 3.1. Geometrical Structures and Energetic Parameters. Geometrical structures of the HXeBr···CO2 and HBr··· CO2 complexes have been optimized at the CCSD(T)/Def2TZVPPD computational level. The results are compared in Figure 1. The linear complexes (C∞v) are stabilized by the Br− H···O hydrogen bond (Br-(Xe)-H···O1CO2). Introduction of the Xe atom into the HBr molecule (HXeBr···CO2) results in elongation of the H···O1 distance by 0.190 Å. For the planar structures (Cs) of the complexes, the C···Br distance is shortened by 0.196 Å after introduction of the Xe atom (HXeBr···CO2). The O1···Br and O2···Br distances are elongated by 0.005 Å and shortened by 0.275 Å, respectively. The differences between the bond lengths calculated for isolated monomers (HBr, HXeBr, CO2) and the complexes are shown in Figure 1. Insertion of the Xe atom into the HBr···CO2 system with Cs symmetry results in a small change of the O1− C−Br angle and shortening of the distance between the Br atom and the C and the O2 atoms. Such a geometrical rearrangement is evidently associated with a changing nature of the intermolecular interactions between HBr···CO2 and HXeBr···CO2. Various energetic parameters calculated for the HBr···CO2 and HXeBr···CO2 complexes are gathered in Table 1. For the HBr···CO2 complex, the most stable structure is the C∞v form, stabilized by the Br−H···O hydrogen bond. The Cs form lies only 0.09 kcal/mol (ΔE + ΔZPVE) above the C∞v complex on the total energy scale. Both forms can be classed as isoenergetic. Introduction of the Xe atom into HBr changes the relative stability order. The Cs structure of the HXeBr···CO2 complex becomes more stable. The difference between total energies (ΔE + ΔZPVE) of the Cs and C∞v complexes is −2.36 kcal/ mol. It is apparent that introduction of Xe in HBr essentially modifies and strengthens intermolecular interactions with CO2. Dissociation energies D0 calculated for both HBr···CO2 and HXeBr···CO2 complexes are negative. The values obtained for the HBr···CO2 complex [−1.22 kcal/mol (C∞v) and −1.13 kcal/mol (Cs)] are essentially smaller than those for the HXeBr···CO2 complex [−1.48 kcal/mol (C∞v) and −3.84 kcal/ mol (Cs)]. The presence of the Xe atom inside the HBr molecule results in remarkable enhancements of interaction especially for the Cs structure of HXeBr···CO2. Such a system is expected to be stabilized not only by larger electrostatic interactions, caused by a very large change of the dipole moment [0.84D (HBr) to 5.76D (HXeBr)], but also by dispersive interactions due to the large polarizability of the Xe atom. Such an effect is less profound for the Br−H···O

hydrogen-bonded C∞v form, in which the dispersion energy contribution is expected to be much smaller. The interaction energy corrected for the BSSE (EintCP) and ΔZPVE (EintCP + ΔZPVE) for both complexes is negative; thus, their formation is accompanied by total energy lowering. The intermolecular interaction for the C∞v form of the HBr···CO2 complex is only 0.05 kcal/mol larger than that in the Cs complex, and both complexes can be considered isoenergetic. The insertion of the Xe atom into the HBr molecule causes intermolecular forces to change, leading to stronger interactions in the Cs form of the HXeBr···CO2 complex. The value of EintCP + ΔZPVE is 1.99 kcal/mol larger than that for the C∞v form. At this point it is worth comparing our results with those presented by Tsuge et al.21 The geometrical structures were optimized with the same computational method, CCSD(T), but using different basis sets. The Def2-TZVPPD basis set was used in this work, whereas Tsuge et al.21 used the aug-ccpVTZ-PP basis set. In both cases two minima on the potential energy surface of the HBr···CO2 and HXeBr···CO2 complexes have been found, corresponding to two geometrical structures (C∞v and Cs). Our calculations yield the ΔE + ΔZPVE value, a difference between total energies of the Cs and C∞v structures of HXeBr···CO2 complexes, only 0.16 kcal/mol smaller than those obtained using the aug-cc-pVTZ-PP basis set. Similarly small discrepancies are observed when the EintCP values for the Cs and C∞v HXeBr···CO2 complexes are calculated. The values obtained with the Def2-TZVPPD basis set are only 0.31 and 0.04 kcal/mol, respectively, smaller than those yielded by the aug-cc-pVTZ-PP basis set. This shows that both basis sets yield very similar values of the energetic parameters. Because of the weak character of the intermolecular interactions in the HBr···CO2 and HXeBr···CO2 complexes, it is interesting to examine the ability of a range of popular functionals (B3LYP,43 M062X,44 ωB97XD,45 and B2PLYP46) to correctly describe their energetics and geometrical structure. We have chosen only three representatives of the hybrid functionals (B3LYP, M062X, ωB97XD) from the fourth rung of “Jacob’s ladder” of density functional approximations C

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Table 2. Comparison of Energy Parameters for the HBr···CO2 and HXeBr···CO2 Complexes Calculated by Various Density Functionals HBr···CO2 Einta

Eint

CPb

Eint

HXeBr···CO2

CP

+ ΔZPVE

M062X M062X-D3 B3LYP B3LYP-D3 B2PLYP B2PLYP-D3 ωB97XD

−1.52 −1.56 − −1.77 − −1.78 −1.19

−1.45 −1.49 − −1.68 − −1.58 −1.13

−0.37 0.45 − −0.79 − −0.79 −0.14

M062X M062X-D3 B3LYP B3LYP-D3 B2PLYP B2PLYP-D3 ωB97XD

−1.28 −1.32 −0.98 −1.79 −1.44 −1.90 −1.21

−1.16 −1.20 −0.86 −1.70 −1.19 −1.65 −1.09

−0.17 −0.21 −0.31 −1.10 −0.61 −1.06 −0.55

ΔE

c

Cs structure 1.84 2.59 − 1.50 − 1.52 1.57 C∞v structure − − − − − − −

Eint

EintCP

EintCP + ΔZPVE

ΔE

−4.39 −2.28 −1.74 −3.97 −2.91 −4.27 −3.33

−4.30 −2.21 −1.68 −3.88 −2.51 −3.83 −3.23

−3.83 −1.44 −1.49 −3.6 −2.80 −2.22 −2.97

−2.49 −2.28 −0.81 −2.21 −1.23 −2.1 −4.39

−1.09 −1.14 −0.61 −1.22 −1.15 −1.55 −1.19

−0.98 −1.03 −0.53 −1.12 −0.91 −1.29 −1.09

−0.7 −0.77 −0.44 −0.93 −0.73 −1.08 −0.86

− − − − − − −

Eint: the interaction energy. bEintCP: the interaction energy corrected for BSSE. cΔE: the difference between the total energy of the optimized geometrical structures of both complexes (Etot(Cs)) − Etot(C∞v)) corrected for the vibrational zero-point energy difference (ΔZPVE). a

Figure 2. Critical points, bond paths, ring paths, and basin paths for the electron density field calculated for the planar (Cs) HBr···CO2 and HXeBr··· CO2 complexes using the AIM method. Calculations were performed at the CCSD/Def2-TZVPPD//CCSD(T)/Def2-TZVPPD computational level.

proposed be Perdew.47 The B2PLYP functional represents the last fifth rung because it incorporates the unoccupied orbitals; B3LYP is the density functional that dominated computational chemistry since 1993; and M062X is thought to be its successor. The ωB97XD functional is a long-range corrected hybrid functional that includes empirical atom−atom dispersion corrections (D2). Additionally, in the case of the B3LYP, M062X, and B2PLYP functionals, the newest Grimme’s dispersion scheme (D3) was used, B3LYP-D3, M062X-D3, B2PLYP-D3.48

In Table 2, the energetic parameters (Eint, EintCP, EintCP + ΔZPVE, and energy difference between the C∞v and Cs forms ΔE), calculated with seven different electron density functionals are presented. In Figure 2S of the Supporting Information, all the optimized intermolecular distances are shown. In the case of the weaker HBr···CO2 complex (Cs form), only two functionals, B3LYP and B2PLYP, fail to predict the stability yielding the postive values of Eint, EintCP, and EintCP + ΔZPVE. For the slightly stronger C∞v form, most of the functionals correctly describe the HBr···CO2 complex, except for the D

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introduction of Xe into HBr molecule increases its ability to form intermolecular interactions. The delocalization and bond indices for the Cs geometrical structures of the HBr···CO2 and HXeBr···CO2 complexes are showed in Table 3. The values of ρBCP(r) for weak interactions

B3LYP, which shows the lack of stability once the BSSE is removed from the interaction energy (EintCP > 0; EintCP + ΔZPVE > 0). It is worth emphasizing that the inclusion of the D3 correction (B3LYP-D3) improves the functional performance. In the case of the much stronger HXeBr···CO2 complex, with both the Cs and C∞v symmetry structures, all DFT functionals predicted the stability correctly. When using the DFT approach, the best results of EintCP + ΔZPVE for the Cs symmetry of the HBr···CO2 complex (as compared to the CCSD(T) value −0.77 kcal/mol) are obtained for the B3LYP-D3 (−0.79 kcal/mol) and B2PLYP-D3 (−0.79 kcal/mol) density functionals with the dispersion correction (D3). For the C∞v form, the B2PLYP functional yields the value −0.61 kcal/mol, which is close to the CCSD(T) value of −0.82 kcal/mol. In the case of the HXeBr···CO2 complex (C∞v symmetry), the B2PLYP-D3 density functional was found to give the best result: −1.08 kcal/mol (−1.07 kcal/mol obtained by the CCSD(T) method). Interestingly, for the most stable Cs form of the HXeBr···CO2 complex, the best result (−2.97 kcal/ mol) is obtained using the ωB97XD density functional (−3.06 kcal/mol at the CCSD(T) level). In all the cases, the best results were obtained with the density functionals that contained Grimme’s dispersion scheme (D3 or D2). 3.2. Topological Analysis of ρ(r). According to Bader,24 identification of the gradient path within the electron density field ρ(r) joining the bond critical point (BCP) with the nuclear attractors confirms the existence of atomic interactions between atoms.49 Such definition is based on strong physical arguments;50 however, it should not be confused with the phenomenon of the chemical bond.51 The topological analysis of ρ(r) field for HBr···CO2 and HXeBr···CO2 complexes was performed for the CCSD wave function, calculated for the geometrical structures optimized at the CCSD(T)/Def2TZVPPD computational level. Comparison of the topology of ρ(r) fields for the linear complexes of HBr···CO 2 and HXeBr···CO2 shows no qualitative differences; therefore, it will not be discussed here. Figure 2 compares the critical points (CPs) of ρ(r) for both HBr···CO2 and HXeBr···CO2 complexes with the Cs geometrical structures. There are nine CPs in the HBr···CO2 complex: four (3,−1) CPs and five nuclear attractors. Intermolecular interaction is characterized by the BCP localized on the gradient path joining the O1 atom with Br atom. Very small values of the electron density for BCP ρBCP(r) (0.007 e/ bohr3) as well as positive value of the Laplacian ∇2ρBCP(r) (0.024 e/bohr5) confirm the existence of noncovalent interaction between the HBr and CO2 molecules, most probably dominated by dispersion. Three other CPs describe the covalent bonds in HBr and CO2. After insertion of Xe into hydrogen bromide and the formation of the HXeBr···CO2 complex, the number of CPs increases from 9 to 13. Four (3,−1) CPs correspond to the covalent bonds in HXeBr and CO2 molecules; two (3,−1) CPs define the O1···Br and O1···Xe intermolecular interactions. Furthermore, one ring (3,+1) CP is found around the center of the complex. The appearance of two new CPs, (3,−1) and (3, +1), can be a consequence of the fold catastrophe when the CO2 molecule in the linear HXeBr···CO2 complex bends toward HXeBr and the O1 atom begins to interact with the Xe atom. It is worth emphasizing that modification of the HBr molecule by the Xe atom does not alter the O1···Br interaction in the parent HBr···CO2 complex but forms an additional one between the Xe and O1 atom. It is apparent that the

Table 3. Delocalization and Bond Indices (Atomic Units) for HXeBr···CO2 and HBr···CO2 Complexes with Cs Symmetrya A−B

δ(A,B)b

O1···Br H−Br C−O1 C−O2

0.035 0.922 1.095 1.107

O1···Xe O1···Br H−Xe Xe−Br C−O1 C−O2

0.048 0.047 0.757 0.530 1.078 1.110

ρBCP

∇2ρBCP

HBr···CO2 (Cs) 0.005 +0.022 0.205 −0.502 0.459 +0.240 0.461 +0.285 HXeBr···CO2 (Cs) 0.007 +0.028 0.007 +0.024 0.138 −0.172 0.050 +0.072 0.456 +0.213 0.463 +0.321

Hb

ε

0.001 −0.195 −0.864 −0.870

2.386