Article pubs.acs.org/JPCA

Neutral Compounds with Xenon−Germanium Bonds: A Theoretical Investigation on FXeGeF and FXeGeF3 Stefano Borocci, Maria Giordani, and Felice Grandinetti* Dipartimento per la Innovazione nei sistemi Biologici, Agroalimentari e Forestali (DIBAF), Università della Tuscia, L.go dell’Università, s.n.c., 01100 Viterbo, Italy S Supporting Information *

ABSTRACT: The structure and stability of FXeGeF and FXeGeF3 were investigated by MP2, CCSD(T), and B3LYP calculations, and their bonding situation was examined by NBO and AIM analysis. These molecules are thermochemically stable with respect to dissociation into F + Xe + GeFn (n = 1, 3), and kinetically stable with respect to dissociation into Xe + GeFn+1, thus suggesting their conceivable existence as metastable species. FXeGeF and FXeGeF3 are best described by the resonance structures F−(Xe-GeF+) and F−(Xe-GeF3+), and feature essentially ionic xenon−fluorine interactions. The xenon−germanium bonds have instead a significant contribution of covalency. The comparison with XeGeF+ and XeGeF3+ suggests that the stability of FXeGeF and FXeGeF3 arises from the F−-induced stabilization of these ionic moieties. This structural motif resembles that encountered in other noble-gas neutral and ionic species.

1. INTRODUCTION The capability of xenon to combine with oxygen and fluorine was suggested by Pauling in 1933.1 This prediction, however, did not find immediate confirmation,2 and the inertness of the noble gases, including xenon, became an accepted paradigm. It was only in 1962 that Bartlett announced the preparation of “Xe+PtF6−”,3,4 and Hoppe et al.,5 and Claassen et al.6 achieved the fluorination of xenon. These pioneering reports opened the gate to xenon chemistry,7 which soon emerged as promisingly rich,8 and rapidly became a relevant chapter of the chemistry of main-group elements.9,10 A first xenon−carbon compound, Xe(CF3)2, was inferred in 1979 by infrared spectroscopy,11 but the first structural characterization of a compound with a Xe−C bond, the pentafluorophenylxenon(II) cation, was achieved in 1989.12−14 In the subsequent decade, the chemistry of organoxenon derivatives was considerably expanded,15−17 and new compounds and bonding motifs are continually being reported.18−20 A significant contribution to the field came also from studies performed in cold matrices, particularly in the past decade. Under cryogenic conditions, it is possible to obtain molecular species such as HXeCN,21 ClXeCN and BrXeCN,22 HXeCCH,23,24 and HXeCCXeH,23 HXeCCF,25 HXeC3N,26 and HXeC4H.27 Theoretical calculations have also disclosed novel xenon−carbon compounds,28−34 including somewhat unexpected species such as the highly coordinated Xe(CCH)n (n = 4, 6),35 and the polymeric H−(Xe−C2)n−Xe−H (n ≥ 1).36 The richness and variety of xenon−carbon chemistry stimulates interest for the capability of xenon to combine with the heaviest congeners of group 14. This subject is, however, only little explored. The gaseous trifluorosilylxenon, F3Si−Xe+, is the only recognized example of molecular species with a xenon−silicon bond.37 This cation was observed so far by mass © 2014 American Chemical Society

spectrometric techniques and investigated by theoretical calculations.38,39 Under proper conditions, it was possible to obtain also the high-energy isomers F2Si−Xe−F+ and FSi−F− Xe−F+.39 These “inserted” cations resemble FXeSiF, the only predicted example of neutral compound with a xenon−silicon bond.40 More recently, the gaseous trifluorogermylxenon cation F3Ge−Xe+, a molecular species with a xenon−germanium bond, was detected by mass spectrometric techniques.41 The alternative and theoretically less stable isomers F2Ge−Xe−F+ and FGe−F−Xe−F+ were not produced.41 Neutral compounds with xenon−germanium bonds are still unexplored, both experimentally and theoretically. We therefore decided to perform ab initio and density functional theory (DFT) calculations to investigate, in particular, the structure, stability, and bonding properties of FXeGeF (the analogous of FXeSiF40), and FXeGeF3. The latter species is suggested not only by the experimental detection of F3Ge−Xe+,41 but also by the previous theoretical investigation of FKrGeF3,42 the only predicted example of a krypton−germanium neutral compound. The results of our calculations will be discussed in the present article.

2. COMPUTATIONAL DETAILS The ab initio and DFT calculations were performed with Gaussian 03.43 The employed methods were the second-order Møller−Plesset (MP2),44 the coupled cluster with inclusion of single and double substitutions and an estimate of connected triples, CCSD(T),45 and the hybrid exchange-correlation Received: January 16, 2014 Revised: April 10, 2014 Published: April 10, 2014 3326

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species. The geometries obtained at the MP2 and B3LYP levels of theory with the aug-cc-pVTZ-PP basis set are listed in Table 1, and the parameters computed with the def2-TZVPP and augcc-pVDZ-PP basis sets are listed in Table S1 of the Supporting Information (SI). In general, while the bond angles of both FXeGeF and FXeGeF3 are only little affected by the theoretical level, the bond distances are more sensitive to the employed method and basis set. These effects are, however, quite regular (see the discussion in the SI), and well exemplified by the data reported in Table 1. The FXeGeF energy minimum has a planar structure of Cs symmetry. The F−Xe−Ge arrangement is nearly linear, and the Xe−Ge−F angle is predicted at around 95°−96°. The B3LYP distances are invariably longer than the MP2, with a largest difference of 0.085 Å for the Xe−Ge bond. In any case, even assuming the less compact structure, the comparison with the bond distances obtained by sum of the single-bond covalent radii60 of F, Ge, and Xe (Xe−F: 1.95 Å, Xe−Ge: 2.52 Å, and Ge−F: 1.85 Å) points to FXeGeF as a chemically bound species. The structure of the FXeGeF3 energy minimum (C3v symmetry) is even more compact than that of FXeGeF. At both the MP2 and B3LYP level, the bond distances are invariably shorter, with appreciable contractions of 0.12−0.15 Å for Xe−F and Xe−Ge, and lower changes of ca. 0.03 Å for Ge− F. These structural changes reflect also in the increased value of the Xe−Ge−F bond angle, which is predicted at around 112°. Not unexpectedly, the Xe−Ge bond distance is definitely longer than the Xe−C distance of FXeCF3, computed at around 2.2 Å at the MP2 level of theory.29,30 To investigate the bonding situation of FXeGeF and FXeGeF3, we performed NBO and AIM calculations. The data obtained at the MP2/aug-cc-pVTZ-PP level of theory are reported in Tables 2 and 3. The data obtained at the MP2 and B3LYP levels of theory with the other employed basis sets, listed in Tables S2−S4 of the SI, are fully in line with these estimates. Figure 2 shows the MP2/aug-cc-pVTZ-PP electron densities (a and b) and Laplacian of the electron densities (c and d). According to the NBO analysis, in both FXeGeF and FXeGeF3 the fluorine atoms bear high negative charges, predicted at around −0.7 e to −0.8 e for F(Xe), and −0.6 e to −0.7 e for F(Ge). The Ge and the Xe atoms bear instead positive charges, predicted, respectively, at around 1.0 e and 0.45 e in FXeGeF, and 2.0 e and 0.7 e in FXeGeF3. The relatively high positive charges on the Xe atoms suggest, in particular, the breaking of their closed-shell structures, and the participation to chemical bonds with the neighboring atoms. In this regard, the Wiberg bond indices (WBIs) of the Xe−Ge bonds, predicted at around 0.5 for FXeGeF and 0.6 for FXeGeF3, point to xenon−germanium interactions with a significant contribution of covalency. On the other hand, the WBIs of the Xe−F bonds (ca. 0.15 for FXeGeF and ca. 0.2 for FXeGeF3) are suggestive of essentially ionic xenon−fluorine interactions. Consistently, in both FXeGeF and FXeGeF3 the NBO analysis (see Table 2) reveals a σ(Xe−Ge) bond orbital, with an occupancy only slightly lower than 2 e. In FXeGeF, this bond involves nearly pure p orbitals of Xe (5p) and Ge (4p), and is polarized toward Xe (ca. 77%). In FXeGeF3, the bond involves a 5p orbital of Xe and a nearly pure sp3 orbital of Ge, and has a degree of polarization (ca. 64% on Xe) lower than that of FXeGeF. On the other hand, in both FXeGeF and FXeGeF3, the F atom bound to Xe is recognized as an

functional B3LYP, which combines the three-term exchange functional by Becke (B3)46,47 with the correlation functional by Lee, Yang and Parr (LYP).48 The Xe atom was treated by the small-core (28 electrons), scalar-relativistic effective core potential (ECP-28) developed by the Stuttgart/Cologne group.49 The employed basis sets were the def2-TZVPP designed by Weigend and Ahlrichs,50 and the aug-cc-pVnZ-PP (n = D, T), obtained combining the Dunning’s correlation consistent double- and triple-ζ basis sets for F and Ge, augmented with diffuse functions (aug-cc-pVnZ),51,52 with the (9s7p7d)/[5s4p3d] and (13s12p10d2f)/[6s5p4d2f ] basis sets designed for Xe in conjunction with the ECP-28.49 Both the MP2 and the CCSD(T) were employed within the frozen-core approximation (for the Xe atom, the frozen-core orbitals were 4s4p with the def2-TZVPP and 4s4p4d with the aug-cc-pVnZPP). The geometry optimizations performed at the MP2 and B3LYP levels of theory were based on analytical energy gradients, and any located critical point was characterized as an energy minimun or transition structure (TS) by calculating its harmonic frequencies, used also to evaluate the zero-point vibrational energy (ZPE). Any TS was also unambiguously related to its interconnected energy minima by intrinsic reaction coordinate (IRC) calculations.53 The natural bond orbital (NBO) analysis54 was performed with the GENNBO 5.0W program.55 The atoms-in-molecules (AIM)56 calculations were performed with the AIMAll program.57 We calculated in particular the charge density ρ, the Laplacian of the charge density ∇2ρ, the energy density H, and the kinetic energy density G at the bond critical points (bcp’s), intended as the points on the attractor interaction lines where ∇ρ = 0. The missing core electron density on Xe was modeled by a single stype Gaussian function, with exponent α = 4π and coefficient c = 8 × Nc (Nc = number of core electrons =28). As recently discussed,58 for small-core pseudopotentials, the inclusion of a single function is in general sufficient to avoid the interference of the spurious electron density critical points which arise from the absence of the core electron density.

3. RESULTS AND DISCUSSION A. Geometries and Bonding Situation. The connectivities of the presently investigated FXeGeF and FXeGeF3 are shown in Figure 1. The CCSD/aug-cc-pVTZ-PP T1 diagnostics59 resulted invariably below the recommended threshold of 0.02, thus suggesting the validity of singlereference methods to describe the electronic structure of these

Figure 1. Connectivities of the FXeGeF and FXeGeF3 energy minima and transition structures. 3327

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107.6 108.3

Xe−Ge−F1

96.3 97.2 109.5 109.1 1.681 1.696 FXeGeF3

Xe−Ge−F F−Xe−Ge

106.3 102.1 101.0 97.6 1.725 1.746 1.688 1.706 2.624 2.706 2.478 2.548

Xe−Ge Xe−F

2.360 2.405 2.371 2.404 95.1 96.4 111.7 112.0

Xe−Ge−F F−Xe−Ge

179.7 179.6 180.0 180.0 1.736 1.753 1.704 1.722

Ge−F Xe−Ge

2.695 2.780 2.584 2.653 2.228 2.269 2.105 2.123

Xe−F

independent unit with four lone pairs (F−). The NBO analysis predicts also the expected σ(Ge−F) bond(s), which have occupancies of nearly 2 e and are strongly polarized toward the F atom(s). Overall, FXeGeF and FXeGeF3 are best described by the Lewis structures F−(Xe−Ge−F+) and F−[Xe−Ge− (F)3+]. The AIM analysis is consistent with this description, and furnishes also further insights into the character of the various interactions. The obtained data (see Table 3 and Figure 2) are, in particular, best discussed taking into account a very recent study by Boggs et al.61 These authors examined a wide series of noble-gas molecules, and classified the interactions involving the Ng atoms into three types, namely, covalent bonds, weak bonding interactions with some covalent properties (Wc), and weak bonding interactions with some noncovalent properties (Wn). A bond is covalent if the bond length agrees with the sum of the covalent atomic radii (Rcov), and the AIM properties at the corresponding bcp fulfill at least one of the following criteria (derived by a critical survey of diatomic molecules that are covalently bound in the classical outlook of chemists): (a) ∇2ρ < 0 and large ρ (at least 0.1 au), (b) H < 0 and large ρ, (c) H < 0 and G/ρ < 1, (d) small |H| (less than 0.005 au) and G/ρ < 1. If one or more of these criteria are fulfilled, but the bond length is longer than Rcov, the bond is classified as Wc or Wn. Thus, based on the data of Table 1, the Xe−F bond distance of both FXeGeF and FXeGeF 3 appreciably exceeds the corresponding Rcov of 1.95 Å. In addition (see Table 3), even though these interactions could be in principle classified as covalent bonds of type c (H < 0 and G/ ρ < 1), the predicted values of G/ρ are quite close to the limiting value of 1, and the values of ∇2ρ are definitely positive. The essentially ionic character of the Xe−F interaction in both FXeGeF and FXeGeF3 is confirmed by the visual inspection of the Laplacian of the electron density (see Figure 2c,d). As typical for closed-shell interactions,56 the critical points on the Xe−F paths lie far from a nodal surface in the Laplacian of ρ, and in regions of charge depletion (∇2ρ > 0). On the other hand, for FXeGeF, the critical point on the Xe−Ge path is located close to a nodal surface in ∇2ρ, and the Xe and Ge atomic basins neighboring the interatomic surface exhibit opposite behavior with respect to the sign of the Laplacian of ρ. Thus, the Xe−Ge bond of FXeGeF must be viewed as transitional in character from closed-shell to shared type.56 Interestingly, the application of the criteria by Boggs et al.61 points to a bonding interaction with some covalent properties (Wc). In fact, the calculated bond distance (2.7−2.80 Å) exceeds the corresponding value of Rcov (2.52 Å), but the Xe− Ge bond can be definitely assigned as a covalent bond of type c (H < 0 and G/ρ < 1). The value of ∇2ρ is also slightly negative. Compared with FXeGeF, the Xe−Ge bond of FXeGeF3 possesses an even higher degree of covalency. In fact, from Table 3, the interaction is certainly classifiable as a covalent bond of type c. In addition, at the corresponding bcp, ∇2ρ is negative and the electron density, predicted as ca. 0.08 e a0−3, is close to the lower limit of 0.1 e a0−3, which would support the classification also as a covalent bond of type a. In addition, the calculated bond distance is shorter (2.6−2.7 Å) than that of FXeGeF, and approaches the value of Rcov (2.52 Å). Overall, these data suggest a xenon−germanium interaction with a high contribution of covalency. This interpretation is supported by the plotted Laplacian of the electron density of FXeGeF3 (see Figure 2d). As typical for shared-type interactions,56 the critical point on the Xe−Ge path is located in a region of charge concentration (∇2ρ < 0), and the Xe and Ge atomic basins

MP2 B3LYP MP2 B3LYP FXeGeF

Ge−F

Ge−F1

TS minimum

Table 1. Optimized Geometries (Å and Degrees) of FXeGeF and FXeGeF3 (see Figure 1) Obtained with the aug-cc-pVTZ-PP Basis Set

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109.5 109.5

F−Ge−F1

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Table 2. NBO Analysis of the FXeGeF and FXeGeF3 Energy Minima (See Figure 1) Performed at the MP2/aug-cc-pVTZ-PP Level of Theory NHOa FXeGeF

FXeGeF3

b

NBO

occ

σ(Xe−Ge)

1.936

σ(Ge−F)

1.963

σ(Xe−Ge)

1.867

σ(Ge−F)

1.951

Qe

atom

%s

%p

%d

%f

Xe Ge Ge F Xe Ge Ge F

0.8 2.9 8.8 22.9 0.2 25.2 25.1 23.9

97.9 95.3 89.8 76.6 98.4 73.1 73.6 75.7

1.3 1.7 1.1 0.5 1.3 1.6 0.9 0.4

0.1 0.1 0.3 0.0 0.1 0.1 0.3 0.0

c 0.879 0.476 0.307 0.952 0.799 0.601 0.366 0.931

c

d

WBI

F(Xe)

Xe

Ge

F(Ge)

(77.3) (22.7) (9.4) (90.6) (63.9) (36.1) (13.4) (86.6)

0.519

−0.823

0.447

1.072

−0.695

−0.733

0.689

1.934

−0.630

0.445 0.614 0.562

a Atomic natural hybrid orbitals that compose the two-centers natural bond orbitals (NBOs). bOccupancy (e) of the NBO. cCoefficient of the NHO. The percentage contribution of the NHO (c2 × 100) is given in parentheses. dWiberg bond index. eAtomic charge (e).

Table 3. AIM Analysisa of the FXeGeF and FXeGeF3 Energy Minima (See Figure 1) Performed at the MP2/aug-cc-pVTZPP Level of Theory FXeGeF

FXeGeF3

bond

ρ

∇2 ρ

H

G

G/ρ

Xe−F Xe−Ge Ge−F Xe−F Xe−Ge Ge−F

0.077 0.065 0.143 0.100 0.081 0.157

0.221 −0.003 0.819 0.232 −0.036 0.905

−0.018 −0.023 −0.065 −0.038 −0.033 −0.078

0.074 0.022 0.270 0.096 0.024 0.304

0.961 0.338 1.888 0.960 0.296 1.936

path (see Table 3), the Laplacian of ρ is positive, but the density is high (0.14−0.16 e a0−3), and H is definitely negative. Thus, according to Boggs et al.,61 likewise, for example, the diatomic CO, F2, and IF, these interactions can be classified as covalent bonds of type b. B. Thermohemistry and Stability. To investigate the stability of FXeGeF and FXeGeF3, we calculated the energy change at 0 K, ΔE0, of the dissociations described by eqs 1−4 (n = 1, 3): FXeGeFn → F + Xe + GeFn →XeF2 + GeF(n − 1)

The charge density ρ (e a0−3), the Laplacian of the charge density ∇2ρ (e a0−5), the energy density H (hartree a0−3), and the kinetic energy density G (hartree a0−3) are calculated at the bond critical point on the specified bond. a

(1) (2)

→F− + XeGeFn+ →Xe + GeF(n + 1)

(3) (4)

The data obtained at the B3LYP, MP2, and CCSD(T) levels of theory with the aug-cc-pVTZ-PP basis set are listed in Table 4. Table 4. Dissociation Energies at 0 K (kcal mol−1) of the FXeGeF and FXeGeF3 Energy Minima (see Figure 1) Calculated with the aug-cc-pVTZ-PP Basis Set FXeGeF

a

FXeGeF3a

Figure 2. Contour line diagrams showing the electron density ρ (a and b) and the Laplacian of the electron density ∇2ρ (c and d) in the molecular plane of FXeGeF and FXeGeF3 calculated at the MP2/augcc-pVTZ-PP level of theory. In c and d, solid lines indicate regions of charge depletion (∇2ρ > 0), and dashed lines indicate regions of charge concentration (∇2ρ < 0). Bond critical points are shown in black. The solid lines which connect the atomic nuclei are the bond paths, and the solid lines which cross the bond paths indicate the zeroflux surfaces in the molecular plane.

F + Xe + GeF XeF2 + Ge F− + XeGeF+ Xe + GeF2 E‡c F + Xe + GeF3 XeF2 + GeF2 F− + XeGeF3+ Xe + GeF4 E‡d

B3LYP

MP2

CCSD(T)b

37.6 97.7 118.1 −96.6 8.2 34.3 38.4 158.3 −97.1 37.6

41.8 99.4 115.2 −100.3 9.7 42.4 54.2 153.3 −108.0 33.3

33.7 (36.3) 97.6 (101.1) 116.7 (117.6) −100.1 (−100.4) 9.5 (9.4) 34.8 51.0 154.6 −108.4 33.7

a

Reference species. bAt the MP2/aug-cc-pVTZ-PP optimized geometries. The values in parentheses are calculated with the aug-ccpVQZ-PP basis set. cEnergy barrier of the reaction FXeGeF → Xe + GeF2. dEnergy barrier of the reaction FXeGeF3 → Xe + GeF4.

To check the convergence of the basis set in the single-point CCSD(T) calculations, the thermochemistry of the reactions involving FXeGeF was recalculated with the aug-cc-pVQZ-PP basis set. As shown in Table 4, the obtained values do not appreciably deviate from those obtained with the aug-cc-pVTZPP. To allow a direct comparison with FXeGeF3, the CCSD(T) data discussed below are those obtained with the aug-cc-pVTZPP basis set.

neighboring the interatomic surface exhibit homogeneous behavior with respect to the sign of ∇2ρ. Finally, for both FXeGeF and FXeGeF3, the predicted Ge−F distances are invariably even shorter than the corresponding value of Rcov (1.85 Å). In addition, at the critical point on the Ge−F bond 3329

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Table 5. Harmonic Vibrational Frequencies (cm−1) of the FXeGeF and FXeGeF3 Energy Minima (See Figure 1) Calculated at the MP2/aug-cc-pVTZ-PP Level of Theorya

a

ν(Xe−F)

ν (Xe−Ge)

ν (Ge−F)

δ (F−Xe−Ge)

δ (Xe−Ge−F)

FXeGeF

373 (343/a′)

210 (35/a′)

695 (117/a′)

149 (2/a′)

FXeGeF3

460 (267/a1)

165 (23/a1)

729 (125/a1) 769 (99/e)

73 (11/a″) 76 (12/a′) 80 (12/e)

159 (3/e)

δ (F−Ge−F)

umbrella (GeF3)

237 (11/e)

297 (121/a1)

IR intensities (km mol−1) and symmetries are given in parentheses.

degree of stabilization of XeGeF+ and XeGeF3+ by F− in the neutral FXeGeF and FXeGeF3 (vide inf ra). C. Harmonic Vibrational Frequencies. The harmonic vibrational frequencies of FXeGeF and FXeGeF3 obtained at the MP2/aug-cc-pVTZ-PP level of theory are listed in Table 5. The B3LYP/aug-cc-pVTZ-PP values (listed in Table S5) are, in general, lower than the MP2. However, the largest differences amount to only 30−40 cm−1, and the two methods furnish a strictly similar description of the vibrational motions and of their relative intensities. The most intense absorption of FXeGeF is the Xe−F stretching (343 km mol−1), predicted at 373 cm−1. The Ge−F stretching is relatively less intense (117 km mol−1), and predicted at 695 cm−1. This value is comparable, in particular, with the Ge−F stretching motions of GeF2, whose three fundamental absorptions are predicted, at the MP2/aug-ccPVTZ level of theory, at 697 cm−1 (vs), 674 cm−1 (vas), and 263 cm−1 (δ). These estimates are in very good agreement with the experimental values of 692 cm−1, 663 cm−1, and 263 cm−1 derived from gas-phase infrared measurements.64 The Xe−Ge stretching of FXeGeF lies at 210 cm−1, and is the least intense among the three stretching motions (35 km mol−1). The two F−Xe−Ge bending modes (in-plane and out-of-plane) are also less intense (ca. 10 km mol−1), and predicted at nearly identical wave numbers of 73 and 76 cm−1. For FXeGeF3, the Xe−F stretching (again predicted as the most intense absorption) lies at 460 cm−1, and the Ge−F stretchings lie at 729 cm−1 (a1 component), and 769 cm−1 (e component) (for comparison, the symmetric and asymmetric stretchings of GeF4 are predicted, respectively, at 740 and 810 cm−1). Thus, compared with FXeGeF, the wavenumbers of the Xe−F and Ge−F stretchings increase, respectively, by nearly 90 cm−1, and by nearly 30−70 cm−1. These blue shifts parallel the predicted shortening of the Xe−F and Ge−F distances passing from FXeGeF to FXeGeF3 (see Table 1). The Xe−Ge distance also decreases passing from FXeGeF to FXeGeF3, but the corresponding stretching frequency is red-shifted by 45 cm−1, and lies at 165 cm−1 for FXeGeF3. We ascertained that this variation reflects a force constant of the Xe−Ge vibration of FXeGeF that is actually higher than that of FXeGeF3 (1.1163 vs 0.5225 mdyn Å−1 at the MP2/aug-cc-pVTZ-PP level of theory). Thus, an increase of the covalent character of the Xe−Ge bond passing from FXeGeF to FXeGeF3 (vide supra) apparently results in a less steep shape of the corresponding harmonic curve. The wave numbers of the F−Xe−Ge and Xe−Ge−F bending motions of FXeGeF3 lie at 80 and 159 cm−1, respectively, and are strictly similar to the corresponding values of FXeGeF. We finally note the less intense F−Ge−F bending motion at 237 cm−1, and the more intense “umbrella” motion at 297 cm−1. D. Comparison between FXeGeFn and XeGeFn+ (n = 1, 3). The structural description of FXeGeF and FXeGeF3 as F−(XeGeF+) and F−(XeGeF3+) suggested by the NBO and

The ΔE0 of the three-body (3B) dissociation (1) is definitely positive and predicted, at the CCSD(T) level of theory, as 33.7 kcal mol−1 for FXeGeF and 34.8 kcal mol−1 for FXeGeF3. The B3LYP estimates are close to these values, but the MP2 estimates are higher by ca. 7−8 kcal mol−1. This discrepancy is, indeed, not unexpected. In fact, previous systematic investigations on the performance of MP2 and B3LYP in predicting the stability of noble-gas hydrides HNgY62,63 revealed that the MP2 method generally overestimates the bond energies, while the B3LYP furnishes substantially more realistic predictions. The dissociation into XeF2 and Ge or GeF2 by reaction 2 is more endothermic than reaction 1, and the products of the heterolytic dissociation into F− and XeGeFn+ (n = 1, 3) are even higher in energy. On the other hand, for both FXeGeF and FXeGeF3, the two-body (2B) dissociation into Xe and GeF2 or GeF4 according to eq 4 is largely exothermic (by ca. 100−110 kcal mol−1). The corresponding energy barrier is, however, positive and predicted, at the CCSD(T) level of theory, as 9.5 kcal mol−1 for FXeGeF, and 33.7 kcal mol−1 for FXeGeF3. The quantitative criteria for the kinetic stability of noble-gas molecules were so far assessed by Hu and coworkers.63 They found in particular that for an XNgY system (X, Y not hydrogen), in order to have a half-life of ca. 100 s in the gas phase at 100, 200, and 300 K, a 3B channel such as reaction 1 must have barriers, respectively, of 9, 17, and 25 kcal mol−1, and a 2B channel such as reaction 4 must have barriers, respectively, of 6, 13, and 21 kcal mol−1. Based on the data listed in Table 4, FXeGeF is predicted to be metastable up to at least 100 K, and FXeGeF3 up to 300 K and even higher. Reactions 4 occur through the TSs depicted in Figure 1. The geometries computed at the MP2 and B3LYP levels of theory with the aug-cc-pVTZ-PP basis set are listed in Table 1, and those obtained with the def2-TZVPP and aug-cc-pVDZ-PP basis sets are listed in Table S1. Depending on the employed computational level, the single imaginary frequency ranges between 77.0i cm−1 and 99.6i cm−1 for FXeGeF, and 125.1i cm−1 and 208.5i cm−1 for FXeGeF3. The reaction coordinate is invariably dominated by the bending of the F−Xe−Ge angle, which closes, with respect to the energy minimum, by nearly 73°−78° for FXeGeF, and by nearly 79°−82° for FXeGeF3 (see Table 1). This major structural change is accompanied by a contraction of ca. 0.07−0.10 Å of the Xe−Ge bond distance, and by an elongation of ca. 0.15−0.30 Å of the Xe−F bond distance. The Ge−F distance remains, instead, essentially unchanged. Finally, we note from Table 4 the large differences in the stability between FXeGeF and FXeGeF3 on both the 2B dissociation channels 2 and 4 and the charge separation reaction 3. As for the 2B channels, the difference likely reflects the different degree of fluorination of the GeFx product, whose stability increases by increasing the number of F atoms. As for reaction 3, the difference essentially measures the different 3330

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AIM analysis (vide supra) invites a comparison with the cationic XeGeF+ and XeGeF3+. As mentioned in the Introduction, the latter species was actually observed in the gas phase by mass spectrometric experiments.41 The forthcoming discussion is based, in particular, on the MP2/aug-cc-pVTZ-PP data reported in Figure 3 and in Tables 6 and 7.

investigation of this structural motif could reveal still uncovered neutral and ionic species containing noble gas atoms. E. Comparison between FXeSiF and FXeGeF. As mentioned in the Introduction, the neutral FXeSiF was so far explored by theoretical calculations.40 The geometry and vibrational spectrum were obtained at the MP2/LJ18/6-311+ +G(2d,2p) level of theory, and the bonding situation was assayed by analysis of the electron localization function (ELF). The energetics was evaluated by CCSD(T)//MP2/LJ18/6311++G(2d,2p) single-point calculations. FXeSiF has a planar connectivity strictly similar to that predicted for FXeGeF, and the bonding situation is also strictly analogous. FXeSiF is, in fact, described as F−(Xe−Si)2+F−, with a shared-electron type Xe−Si bond featuring a ELF bond order of 0.76.40 The Xe−F and Si−F bonds are, instead, prevalently ionic, even though, like the Ge−F bond of FXeGeF, the ELF analysis suggested some covalent contribution to the Si−F bond. The structural analogy between FXeSiF and FXeGeF emerges also from the comparison of their harmonic vibrational frequencies. The predicted patterns are, in fact, qualitatively strictly similar, and there are also quantitative analogies, particularly in the motions involving the Xe−F bonds. Thus, likewise FXeGeF, the most intense absorption of FXeSiF is the Xe−F stretching, predicted at 350 cm−140 (373 cm−1 in FXeGeF). The two F−Xe−Si bending modes (in-plane and out-of-plane) are also less intense and fall at 83 and 79 cm−140 (73 and 76 cm−1 in FXeGeF). This confirms the essentially ionic character of the Xe−F bonds, only marginally affected by the nature of X (X = Si, Ge). On the other hand, consistent with the atomic mass of Ge higher than that of Si, the Ge−F stretching (695 cm−1) and the Xe−Ge−F bending of FXeGeF (149 cm−1) are significantly red-shifted with respect to the Si−F stretching (862 cm−1), and the Xe− Si−F bending (299 cm−1) of FXeSiF.40 The Xe−Ge stretching of FXeGeF, 210 cm−1, is instead blue-shifted with respect to the Xe−Si stretching of FXeSiF, 175 cm−1,40 despite the Xe−Si bond distance of FXeSiF, 2.652 Å,40 is shorter than the Xe−Ge bond distance of FXeGeF, 2.695 Å (see Table 1). The Xe−F bond distance of FXeGeF, 2.228 Å, is also shorter than the value predicted for FXeSiF, 2.273 Å.40 Overall, these structural data suggest that FXeGeF is more stable than FXeSiF. As a matter of fact, at the CCSD(T)/MP2 level of theory, the 2B decomposition of FXeSiF into Xe + SiF2 resulted exothermic by 122 kcal mol−1, with an energy barrier of 11.1 kcal mol−1.40 This value is only slightly higher than that predicted for the analogous reaction involving FXeGeF, 9.5 kcal mol−1 (see Table 4). In addition, compared with the dissociation of

Figure 3. Bond distances (Å), bond angles (deg), and NBO atomic charges (e, italics) of XeGeF+ and XeGeF3+ calculated at the MP2/augcc-pVTZ-PP level of theory.

The NBO analysis of XeGeF+ and XeGeF3+ (see Table 6) still predicts the formation of σ(Xe−Ge) bonds. In addition, based on the AIM data (see Table 7), and using the criteria by Boggs et al.,61 these interactions can be still assigned as Wc. However, compared with FXeGeF and FXeGeF3, the covalent character of these bonds appears to be lower. Thus, at the corresponding bcp’s, the electron density is lower, the ∇2ρ is slightly positive, and the energy density is still negative but lower. In addition, passing from FXeGeFn to XeGeFn+ (n = 1, 3), the WBI decreases, and the degree of charge transfer from Xe to Ge becomes appreciably lower. These changes in the electronic structure reflect in the geometric structure of XeGeFn+, which is less compact than that predicted for FXeGeFn (the Xe−Ge distances are longer, and the Xe−Ge− F angles are smaller). Overall, the comparison between FXeGeFn and XeGeFn+ (n = 1, 3) suggests that the compactness of the neutral molecules essentially arises from the F−-induced stabilization of their constituting cationic moieties. Interestingly, this bonding situation resembles that of other Ng compounds such as (LiF)2(HeO),65 F(NgO)n− (Ng = He, Ar, Kr, Xe; n = 1−4),66,67 FNgS−,68 FNgSe−,69 and FNgBN−,70 which consist of intrinsically unstable or only marginally stable NgX (X = O, S, Se, BN), strongly stabilized by the fluoride anion up to the formation of covalent Ng−X bonds. All these species exemplify the concept of polarization of the Ng−element bond by a molecular dipole in a neutral molecule, highlighted in particular by Grochala.71 The further

Table 6. NBO Analysis of XeGeF+ and XeGeF3+ (See Figure 3), and Wiberg Bond Indices (WBIs) Calculated at the MP2/augcc-pVTZ-PP Level of Theory NHOa XeGeF+

XeGeF3+

b

NBO

occ

σ(Xe−Ge)

1.936

σ(Ge−F)

1.963

σ(Xe−Ge)

1.867

σ(Ge−F)

1.976

WBI

atom

%s

%p

%d

%f

Xe Ge Ge F Xe Ge Ge F

3.8 0.5 0.0 0.0 5.5 15.4 28.4 21.0

95.9 96.3 96.1 99.6 94.1 81.2 70.3 78.4

0.2 2.9 3.3 0.4 0.4 3.1 1.0 0.5

0.0 0.3 0.7 0.0 0.1 0.3 0.2 0.0

c 0.965 0.263 0.185 0.983 0.908 0.419 0.380 0.925

c

(93.1) (6.9) (3.4) (96.6) (82.5) (17.5) (14.5) (85.6)

Xe−Ge

Ge−F

0.277

0.458

0.479

0.627

a

Atomic natural hybrid orbitals that compose the two-center natural bond orbitals (NBOs). bOccupancy (e) of the NBO. cCoefficient of the NHO. The percentage contribution of the NHO (c2 × 100) is given in parentheses. 3331

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Table 7. AIM Analysisa and Harmonic Vibrational Frequencies (cm−1) of XeGeF+ and XeGeF3+ (See Figure 3) Calculated at the MP2/aug-cc-pVTZ-PP Level of Theorya XeGeF

+

XeGeF3+

bond

ρ

∇2 ρ

H

G

G/ρ

ν (Xe−Ge)

ν (Ge−F)

δ (Xe−Ge−F)

Xe−Ge Ge−F Xe−Ge

0.031 0.162 0.060

0.031 0.975 0.023

−0.005 −0.081 −0.023

0.013 0.324 0.028

0.419 2.000 0.467

137 (41/a′)

778 (89/a′)

93 (8/a′)

166 (2/a1)

765 (34/a1) 860 (74/e)

117 (1/e)

Ge−F

0.175

1.014

−0.095

0.035

0.200

δ (F−Ge−F)

umbrella (GeF3)

229 (20/e)

250 (149/a1)

The charge density ρ (e a0−3), the Laplacian of the charge density ∇2ρ (e a0−5), the energy density H (hartree a0−3), and the kinetic energy density G (hartree a0−3) are calculated at the bond critical point on the specified bond. aIR intensities (km mol−1) and symmetries are given in parentheses.

a

FXeGeF into F + Xe + GeF, FXeSiF is less stable by nearly 9 kcal mol−1 with respect to dissociation into F + Xe + SiF (24.2 kcal mol−1 at the CCSD(T)/MP2 level of theory).40 F. Comparison between FKrGeF3 and FXeGeF3. The structure, stability, and harmonic vibrational frequencies of FKrGeF3 were so far investigated by various ab initio and DFT methods, including the MP2 and the B3LYP, used in conjunction with the correlation consistent basis sets cc-pVnZ and aug-cc-pVnZ basis sets (n = D, T, Q).42 The Kr−Ge bond distance of FKrGeF3, computed, in particular, as 2.430 Å at the MP2/aug-cc-pVTZ and 2.486 Å at the B3LYP/aug-cc-pVTZ level of theory, are shorter than the Xe−Ge distance of FXeGeF3, obtained at the same computational levels as 2.584 and 2.653 Å, respectively (see Table 1). These differences roughly reflect the difference of the single-bond covalent radii60 of Kr (1.17 Å) and Xe (1.31 Å). As a matter of fact, it was noted42 that the Kr−Ge bond of FKrGeF3 is only ca. 0.1 Å longer than the sum of the covalent radii of Kr and Ge, and this was taken as a suggestion that FKrGeF3 contains a krypton− germanium chemical bond. Based on our results for FXeGeF3, the bonding situations of FKrGeF3 and FXeGeF3 appear therefore qualitatively similar. This is also confirmed by the comparison of the NBO atomic charges, computed in particular at the B3LYP/aug-cc-pVTZ level of theory as −0.670 e for F(Kr), 0.484 e for Kr, 2.039 e for Ge, and −0.618 e for F(Ge).42 The corresponding values of FXeGeF3 are −0.694 e for F(Ge), 0.675 e for Xe, 1.910 e for Ge, and −0.631 e for F(Ge) (see Table S2). We note, however, that the atomic charge of Xe is higher than that of Kr, and this suggests that the degree of covalency of the Kr−Ge bond of FKrGeF3 is lower than the Xe−Ge bond of FXeGeF3. A quantitative appraisal of this difference would require the comparative analysis of the wave functions of the two species. In any case, an indirect suggestion of the lower compactness of FKrGeF3 comes from the examination of its thermochemical stability. Thus, compared with the 3B dissociation of FXeGeF3, the dissociation of FKrGeF3 into F + Kr + GeF3 is significantly less endothermic, and predicted, in particular, as 12.1 kcal mol−1 at the CCSD(T)/aug-cc-pVTZ level of theory.42 The dissociation into Kr + GeF4 resulted exothermic by 115.9 kcal mol−1, but the involved TS was not investigated. Thus, it is not presently possible to compare the overall kinetic stability of FKrGeF3 and FXeGeF3. We close this section by commenting on recent theoretical results on the decomposition of FXeCF3 into Xe + CF4.29 Thus, consistent with a previous study,30 it was found that this dissociation passes through a “bent” TS structurally analogous to that involved in the 2B decomposition of FXeGeF3 (see Figure 1). However, at variance with the previous assignment,30 the IRC analysis revealed29 that this TS connects the staggered and the eclipsed conformations of a FXeCF3 isomer of Cs

symmetry (F−Xe−C angle: ca. 77°), which is less stable than the C 3v global minimum by ca. 29 kcal mol−1. The conformational barrier resulted as ca. 6 kcal mol−1, but the eventual decomposition of FXeCF3 into Xe + CF4 remained unexplored. Based on these findings, we searched for conceivable FXeGeF3 isomers of Cs symmetry, but we did not locate any structure with such connectivity. Work is in progress to further investigate these somewhat unexpected differences in the topologies of the FXeCF3 and FXeGeF3 potential energy surfaces.

4. CONCLUSIONS FXeGeF and FXeGeF3 are predicted examples of neutral compounds with Xe−Ge bonds. These species are kinetically stable with respect to the 2B decomposition into Xe and GeF2 or GeF4, and could be probably observed at low temperatures. In this regard, it is of interest to note that the XeGeF3+ cation, which is a constituting moiety of FXeGeF3, was already detected in the gas phase.41 Likewise the previously investigated FXeSiF40 and FKrGeF3,42 which feature shared-electron Xe−Si and Kr−Ge bonds, the Xe−Ge bonds of FXeGeF and FXeGeF3 feature a significant degree of covalency. This suggests the general capability of xenon to combine with silicon and germanium, and encourages the further theoretical and experimental exploration of this chemistry.

■

ASSOCIATED CONTENT

* Supporting Information S

Geometric parameters, atomic charges, Wiber bond indices, NBO analysis, AIM data, and harmonic vibrational frequencies of the FXeGeF and FXeGeF3 energy minima and TS computed at the MP2 and B3LYP levels of theory with the def2-TZVPP and the aug-cc-pVnZ-PP (n = D, T) basis sets. A discussion of the geometric parameters is also included. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +39-0761-357126. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the Università della Tuscia and the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) for financial support.

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REFERENCES

(1) Pauling, L. The Formulas of Antimonic Acid and the Antimonates. J. Am. Chem. Soc. 1933, 55, 1895−1900.

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Article

(2) Yost, D. M.; Kaye, A. L. An Attempt to Prepare a Chloride or Fluoride of Xenon. J. Am. Chem. Soc. 1933, 55, 3890−3892. (3) Bartlett, N. Xenon Exafluoroplatinate(V), Xe+(PtF6)−. Proc. Chem. Soc. 1962, 218. (4) Graham, L.; Graudejus, O.; Jha, N. K.; Bartlett, N. Concerning the Nature of XePtF6. Coord. Chem. Rev. 2000, 197, 321−334. (5) Hoppe, R.; Dähne, W.; Mattauch, H.; Rödder, K. M. Fluorination of Xenon. Angew. Chem., Int. Ed. Engl. 1962, 1, 599. (6) Claassen, H. H.; Selig, H.; Malm, J. G. Xenon Tetrafluoride. J. Am. Chem. Soc. 1962, 84, 3593. (7) For a historical account of the discovery of xenon compounds, see: Laszlo, P.; Schröbilgen, G. One Pioneer or Many Pioneers? The Discovery of the Noble Gas Compounds. Angew. Chem., Int. Ed. Engl. 1988, 27, 495−506. (8) Malm, J. G.; Selig, H.; Jortner, J.; Rice, S. A. The Chemistry of Xenon. Chem. Rev. 1965, 65, 199−236. (9) Lehmann, J. F.; Mercier, H. P. A.; Schrobilgen, G. J. The Chemistry of Krypton. Coord. Chem. Rev. 2002, 233−234, 1−39. (10) Grochala, W. Atypical Compounds of Gases, Which Have Been Called “Noble”. Chem. Soc. Rev. 2007, 36, 1632−1655. (11) Turbini, L. J.; Aikman, R. E.; Lagow, R. J. Evidence for Synthesis of a “Stable” σ-Bonded Xenon-Carbon Compound: Bis(trifluoromethyl)xenon. J. Am. Chem. Soc. 1979, 101, 5833−5834. (12) Naumann, D.; Tyrra, W. The First Compound with a Stable Xenon-Carbon Bond: 19F- and 129Xe-n.m.r. Spectroscopic Evidence for Pentafluorophenylxenon(II) Fluoroborates. J. Chem. Soc., Chem. Commun. 1989, 47−50. (13) Frohn, H. J.; Jakobs, S. The Pentafluorophenylxenon(II) Cation: [C6F5Xe]+; The First Stable System with a Xenon-Carbon Bond. J. Chem. Soc., Chem. Commun. 1989, 625−627. (14) Frohn, H. J.; Jacobs, S.; Henkel, G. The Acetonitrile(pentafluorophenyl)xenon(II) Cation, (MeCN-Xe-C6F5)+: the First Structural Characterization of a Xenon-Carbon Bond. Angew. Chem., Int. Ed. Engl. 1989, 28, 1506−1507. (15) Frohn, H. J.; Bardin, V. V. Preparation and Reactivity of Compounds Containing a Carbon-Xenon Bond. Organometallics 2001, 20, 4750−4762. (16) Brel, V. K.; Pirkuliev, N. Sh.; Zefirov, N. S. Chemistry of Xenon Derivatives. Synthesis and Chemical Properties. Russ. Chem. Rev. 2001, 70, 231−264. (17) Tyrra, W.; Naumann, D. Organoxenon Compounds. In Inorganic Chemistry Highlights; Mayer, G., Naumann, D., Wesemann, L., Eds.; Wiley-VCH: Weinheim, Germany, 2002; pp 297−316. (18) Frohn, H.-J.; Bilir, V.; Westphal, U. Two New Types of XenonCarbon Species: the Zwitterion, 1-(Xe+)C6F4-4-(BF3−), and the Dication, [1,4-(Xe)2C6F4]2+. Inorg. Chem. 2012, 51, 11251−11258. (19) Goedecke, C.; Sitt, R.; Frenking, G. Spacer Separated Donor− Acceptor Complexes [D→C6F4→BF3] (D = Xe, CO, N2) and the Dication [Xe→C6F4←Xe]2+. A Theoretical Study. Inorg. Chem. 2012, 51, 11259−11265. (20) Bilir, V.; Frohn, H.-J. C6F5XeY Molecules (Y = F and Cl): New Synthetic Approaches. First Structural Proof of the Organoxenon Halide Molecule C6F5XeF. Acta Chim. Slov. 2013, 60, 505−512. (21) Pettersson, M.; Lundell, J.; Khriachtchev, L.; Räsänen, M. Neutral Rare-Gas Containing Charge-Transfer Molecules in Solid Matrices. III. HXeCN, HXeNC, and HKrCN in Kr and Xe. J. Chem. Phys. 1998, 109, 618−625. (22) Arppe, T.; Khriachtchev, L.; Lignell, A.; Domanskaya, A. V.; Räsänen, M. Halogenated Xenon Cyanides ClXeCN, ClXeNC, and BrXeCN. Inorg. Chem. 2012, 51, 4398−4402. (23) Khriachtchev, L.; Tanskanen, H.; Lundell, J.; Pettersson, M.; Kiljunen, H.; Räsänen, M. Fluorine-Free Organoxenon Chemistry: HXeCCH, HXeCC, and HXeCCXeH. J. Am. Chem. Soc. 2003, 125, 4696−4697. (24) Feldman, V. I.; Sukhov, F. F.; Orlov, A. Y.; Tyulpina, I. V. Experimental Evidence for the Formation of HXeCCH: The First Hydrocarbon with an Inserted Rare-Gas Atom. J. Am. Chem. Soc. 2003, 125, 4698−4699.

(25) Khriachtchev, L.; Domanskaya, A.; Lundell, J.; Akimov, A.; Räsänen, M.; Misochko, E. Matrix-Isolation and Ab Initio Study of HNgCCF and HCCNgF Molecules (Ng = Ar, Kr, and Xe). J. Phys. Chem. A 2010, 114, 4181−4187. (26) Khriachtchev, L.; Lignell, A.; Tanskanen, H.; Lundell, J.; Kiljunen, H.; Räsänen, M. Insertion of Noble Gas Atoms into Cyanoacetylene: An Ab Initio and Matrix Isolation Study. J. Phys. Chem. A 2006, 110, 11876−11885. (27) Tanskanen, H.; Khriachtchev, L.; Lundell, J.; Kiljunen, H.; Räsänen, M. Chemical Compounds Formed from Diacetylene and Rare-Gas Atoms: HKrC4H and HXeC4H. J. Am. Chem. Soc. 2003, 125, 16361−16366. (28) Lovallo, C. C.; Klobukowsi, M. Improved Model Core Potentials: Application to the Thermochemistry of Organoxenon Complexes. Int. J. Quantum Chem. 2002, 90, 1099−1107. (29) Fitzsimmons, A.; Klobukowski, M. Structure and Stability of Organic Molecules Containing Heavy Rare Gas Atoms. Theor. Chem. Acc. 2013, 132, 1314. (30) Semenov, S. G.; Sigolaev, Y. F. Quantum-Chemical Study of Organoxenon Molecules Xe(CF3)2 and FXeCF3. Russ. J. Org. Chem. 2004, 40, 1757−1759. (31) McDowell, S. A. C. Are Insertion Compounds of CH2CHF and the Rare Gases Stable? A Computational Study. J. Chem. Phys. 2004, 120, 9077−9079. (32) Baker, J.; Fowler, P. W.; Soncini, A.; Lillington, M. Rare-Gas Insertion Compounds of Perfluorobenzene: Aromaticity of Some Unstable Species. J. Chem. Phys. 2005, 123, 174309. (33) Liu, G.; Yang, Y.; Zhang, W. Theoretical Study on the CH3NgF Species. Struct. Chem. 2010, 21, 197−202. (34) Zhang, M.; Sheng, L. Ab Initio Study of the Organic Xenon Insertion Compound into Ethylene and Ethane. J. Chem. Phys. 2013, 138, 114301. (35) Sheng, L.; Gerber, R. B. High Coordination Chemically Bound Compounds of Noble Gases with Hydrocarbons: Ng(CCH)4 and Ng(CCH)6 (Ng = Xe or Kr). J. Chem. Phys. 2006, 124, 231103. (36) Lundell, J.; Cohen, A.; Gerber, R. B. Quantum Chemical Calculations on Novel Molecules from Xenon Insertion into Hydrocarbons. J. Phys. Chem. A 2002, 106, 11950−11955. (37) Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry; Wiley: New York, 1999; p 595. (38) Cipollini, R.; Grandinetti, F. The Gaseous Trifluorosilylxenon Cation, F3SiXe+: A Stable Species with a Silicon-Xenon Bond. J. Chem. Soc., Chem. Commun. 1995, 7, 773−774. (39) Cunje, A.; Baranov, V. I.; Ling, Y.; Hopkinson, A. C.; Bohme, D. K. Bonding of Rare-Gas Atoms to Si in Reactions of Rare Gases with SiF3+. J. Phys. Chem. A 2001, 105, 11073−11079. (40) Lundell, J.; Panek, J.; Latajka, Z. Quantum Chemical Calculations on FXeSiF. Chem. Phys. Lett. 2001, 348, 147−154. (41) Antoniotti, P.; Bottizzo, E.; Operti, L.; Rabezzana, R.; Borocci, S.; Grandinetti, F. F3Ge-Xe+: A Xenon-Germanium Molecular Species. J. Phys. Chem. Lett. 2010, 1, 2006−2010. (42) Yockel, S.; Garg, A.; Wilson, A. K. The Existence of FKrCF3, FKrSiF3, and FKrGeF3: A Theoretical Study. Chem. Phys. Lett. 2005, 411, 91−97. (43) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C. et al. Gaussian 03, revision D.02; Gaussian, Inc.: Wallington, CT, 2004. (44) Møller, C.; Plesset, M. S. Note on the Approximation Treatment for Many-Electrons Systems. Phys. Rev. 1934, 46, 618−622. (45) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (46) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behaviour. Phys. Rev. A 1988, 38, 3098−3100. (47) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. 3333

dx.doi.org/10.1021/jp500518b | J. Phys. Chem. A 2014, 118, 3326−3334

The Journal of Physical Chemistry A

Article

(71) Grochala, W. On Chemical Bonding between Helium and Oxygen. Pol. J. Chem. 2009, 83, 87−122.

(48) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle− Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (49) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-d Group 16−18 Elements. J. Chem. Phys. 2003, 119, 11113−11123. (50) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (51) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (52) Wilson, A. K.; Woon, D. E.; Peterson, K. A.; Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. IX. The Atoms Gallium Through Krypton. J. Chem. Phys. 1999, 110, 7667−7676. (53) Gonzalez, C.; Schlegel, H. B. Reaction Path Following in MassWeighted Internal Coordinates. J. Phys. Chem. 1990, 94, 5523−5527. (54) Weinhold, F. Natural Bond Orbital Analysis: A Critical Overview of Relationships to Alternative Bonding Perspectives. J. Comput. Chem. 2012, 33, 2363−2379 and references therein.. (55) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001. (56) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, 1990. (57) Keith, T. A. AIMAll, version 12.11.09; TK Gristmill Software: Overland Park KS, USA, 2012. http://aim.tkgristmill.com. (58) Keith, T. A.; Frisch, M. J. Subshell Fitting of Relativistic Atomic Core Electron Densities for Use in QTAIM Analyses of ECP-based Wave Functions. J. Phys. Chem. A 2011, 115, 12879−12894. (59) Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem. 1989, 36 (Suppl. S23), 199−207. (60) Pyykkö, P.; Atsumi, M. Molecular Single-Bond Covalent Radii for Elements 1−118. Chem.Eur. J. 2009, 15, 186−197. (61) Zou, W.; Nori-Shargh, D.; Boggs, J. On the Covalent Character of Rare Gas Bonding Interactions: A New Kind of Weak Interaction. J. Phys. Chem. A 2013, 117, 207−212. (62) Lignell, A.; Khriachtchev, L.; Lundell, J.; Tanskanen, H.; Räsänen, M. On Theoretical Predictions of Noble-Gas Hydrides. J. Chem. Phys. 2006, 125, 184514. (63) Li, T.-H.; Liu, Y.-L.; Lin, R.-J.; Yeh, T.-Y.; Hu, W.-P. On the Stability of Noble Gas Molecules. Chem. Phys. Lett. 2007, 434, 38−41. (64) Hastie, J. W.; Hauge, R.; Margrave, J. L. Infrared Vibrational Properties of Germanium Difluoride. J. Phys. Chem. 1968, 72, 4492− 4496. (65) Grochala, W. A Metastable He-O Bond Inside a Ferroelectric Molecular Cavity: (HeO)(LiF)2. Phys. Chem. Chem. Phys. 2012, 14, 14860−14868. (66) Li, T.-H.; Mou, C.-H.; Chen, H.-R.; Hu, W.-P. Theoretical Prediction of Noble Gas Containing Anions FNgO− (Ng = He, Ar, and Kr). J. Am. Chem. Soc. 2005, 127, 9241−9245. (67) Liu, Y.-L.; Chang, Y.-H.; Li, T.-H.; Chen, H.-R.; Hu, W.-P. Theoretical Study on the Noble-Gas Anions F−(NgO)n (Ng = He, Ar, and Kr). Chem. Phys. Lett. 2007, 439, 14−17. (68) Borocci, S.; Bronzolino, N.; Grandinetti, F. Noble Gas-Sulfur Anions: A Theoretical Investigation of FNgS− (Ng = He, Ar, Kr, Xe). Chem. Phys. Lett. 2008, 458, 48−53. (69) Bronzolino, N.; Borocci, S.; Grandinetti, F. Noble Gas-Selenium Molecular Species: A Theoretical Investigation of FNgSe− (Ng = He− Xe). Chem. Phys. Lett. 2009, 470, 49−53. (70) Antoniotti, P.; Bronzolino, N.; Borocci, S.; Cecchi, P.; Grandinetti, F. Noble Gas Anions: Theoretical Investigation of FNgBN− (Ng = He−Xe). J. Phys. Chem. A 2007, 111, 10144−10151. 3334

dx.doi.org/10.1021/jp500518b | J. Phys. Chem. A 2014, 118, 3326−3334