The inert pair effect on the heavy noble gases: New insights from radon tetroxide.

doi:10.21203/rs.3.rs-2398926/v1

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The inert pair effect on the heavy noble gases: New insights from radon tetroxide.

https://doi.org/10.21203/rs.3.rs-2398926/v1

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A quantum chemical survey of radon and xenon tetroxides (NgO₄, Ng = Xe,Rn) is reported herein. The intermediate species that will form in their explosive decomposition back to their elemental states (Ng and O₂) were also studied and their energetics compared. While T_d symmetric RnO₄ is a minimum energy structure, its standard enthalpy of formation is 88.6 kJ mol^− 1 higher than for XeO₄. The reason for this higher instability lies in what is known as the inert pair effect. This work adds to what is established wisdom in inorganic chemistry textbooks, a feature of the heavy elements of groups 13–15, extending it to include group 18.

Physical sciences/Chemistry/Inorganic chemistry/Chemical bonding

Physical sciences/Chemistry/Theoretical chemistry/Structure prediction

The chemistry of noble gases has been a subject of intermittent interest in the scientific literature. Indeed since the discovery by Bartlett¹ of xenon hexafluoroplatinate there has been a moderate progress in the development of noble gas compounds. Xenon^{2, 3} in particular presents a rich and varied chemistry and being the least ‘noble’ of the periodic group.

It has been assumed⁴ that, due to its lower ionisation energy, the chemistry of radon should be richer than that of xenon but this proposition has so far not been extensively tested in experimental conditions. The most stable isotope of radon is ²²²Rn having a half-life of 3.8 days. This, along with its radioactivity poses a significant operational challenge in isolating and identifying new compounds. The most widely known compound of radon is its difluoride⁵ (RnF₂) identified in 1962, around the same time as the first xenon complex. A few cations such as RnO⁺, RnH⁺ and RnOH⁺ and RnOH₂⁺ have also been identified in a plasma ion source.⁶ But the vast majority of recent works on radon compounds has been in silico.^{7, 8, 9, 10, 11}

The highest formal oxidation state in the noble gas group is VIII, as exemplified by xenon tetroxide, an explosive gas identified by Selig et al¹² and structurally characterised by electron diffraction some years later by Gundersen et al.¹³. Its explosive character accounts for its high endothermicity¹⁴ (${\text{∆}}_{\text{f}}{\text{H}}_{\text{298K}}^{\text{⊖}}$=+642 kJ mol^− 1). Slepkov et al¹⁵ performed a detailed DFT study of the potential energy surface of XeO₄ and predicted the existence of a short lived isomer Xe(η²-O₂)₂ that would act as an intermediate in the decomposition reaction. Whilst the redox state of the dihaptic dioxo ligand was not clearly stated from their account, the determined (OPBE) HOMO-LUMO gap in Xe(η²-O₂)₂ was just 0.38 eV hinting at a possible multiconfigurational character in the wavefunction. Vent-Schmidt and co-workers¹⁶ identified for the first time the new Xe^VIII species XeO₃(η²-O₂) synthesised by UV photo-irradiation of XeO₄. This was the most recent incursion into Xe^VIII chemistry.

Herein we address the nature of the chemical bond in three molecules RnO₄, RnO₂(η²-O₂) and Rn(η²-O₂)₂ none of which have ever been identified. We investigate their stability toward decomposition, and establish points of commonality and differences in the chemistry of xenon and radon, given that the oxides of the former are better studied. High level coupled-cluster techniques namely CCSD(T) and Mk-CCSD(T) were used in the process as quantitative tools to obtain formation enthalpies.

The experimental Xe-O bond length in XeO₄ determined by electron diffraction is 1.736 Å and the O-O distance is 2.832 Å.¹³ The geometries of NgO₄ (Ng = Xe,Rn) were optimised at the CCSD(T)/DKH-TZVPP level and the bond distances are displayed on Fig. 1. The calculated values are in good agreement with the experimental ones for XeO₄ (1.756 Å and 2.867 Å, respectively) differing at the most by 0.035Å.

RnO₄ exhibits as expected T_d point group symmetry, and is a confirmed minimum on the potential energy surface i.e. possessing all real vibrational modes. The calculated bond lengths of this compound are, as expected, slightly larger than those of the xenon congener.

The bond strengths in RnO₄ however are palpably inferior to those of XeO₄, as is apparent from comparison of the calculated vibrational frequencies (Table 1 and Fig. S1). The Ng-O stretches with t₂ symmetry in particular are both IR active and appear at a lower frequency for RnO₄ than for XeO₄.

Table 1

– Calculated vibrational modes of NgO₄ at the CCSD(T)/DKH-TZVPP level compared to the experimental spectra of XeO₄ measured by Selig et al.¹²
Mode	RnO₄ (cm^− 1)	XeO₄ (cm^− 1)	XeO₄ Exp.¹² (cm^− 1)
e	205	264
t₂	225	306	306
a₁	706	777
t₂	799	873	877

To understand why the Ng-O bonds in RnO₄ are weaker than in XeO_4, a more detailed electronic structure analysis of the CCSD orbitals was carried via Natural Bond Orbital analysis. The Natural Population Analysis (NPA) in particular affords some insight into the distribution of the electrons within the levels of the formally Ng^VIII tetroxides (Table 2) .

Table 2

– NBO analysis of the CCSD/DKH-TZVPP natural orbitals: electron occupation and composition of orbitals.
Natural Population	XeO₄	RnO₄
NAO Ng 5s/6s	1.416	1.534
NAO Ng 5p/6p	2.889	2.691
	NLMO composition
σ(Ng-O)	47.1% Xe + 52.9% O	47.0% Rn + 53.0% O
π₁(Ng-O)	6.2% Xe + 93.8% O	5.4% Rn + 94.6% O
π₂(Ng-O)	6.5% Xe + 93.5% O	5.8% Rn + 94.2% O

It is found that in the XeO₄ case the electrons assigned to Xe are 2.889e⁻ in the 5p orbital set while the 5s orbital holds 1.416e⁻. By comparison the Rn atom in RnO₄ holds more electrons in the 6s orbitals (1.534 e⁻) and fewer electrons in the 6p orbitals (2.691e⁻). The Natural Localised Molecular Orbitals (NLMO) indicate a strong covalent Ng-O σ bond in both tetroxides and a very faint O→Ng π donor-acceptor interaction.

Thus far, the difference in the formation of Ng-O bonds appears to be down to the different radial structure of the valence orbitals in Rn with respect to Xe.

To probe into the origin of the weaker Rn-O bonds, a computational experiment was performed: the formation enthalpies were calculated with and without the DKH2 relativistic Hamiltonian. The experimental¹⁴ standard enthalpy of formation of XeO₄ is + 642.2 kJ mol^− 1 which is extremely well matched by the CCSD(T)/CBS//CCSD(T)/DKH-TZVPP approach that yields + 642.6 kJ mol^− 1 (Fig. 2). Radon tetroxide is less stable by 88.6 kJ mol^− 1 (21.2 kcal mol^− 1).

Since there is no reason to assume that the kinetics of the decomposition process of RnO₄ is substantially different to XeO₄, the former can safely be predicted to exist on account of these results with a degree of confidence.

The non-relativistically optimised structures have very different thermodynamic features from the relativistic models. Without relativity XeO₄ would be more explosive by almost two-fold (521.3 kJ mol^− 1) and RnO₄ would be less endothermic by nearly 200 kJ mol^− 1. This provides evidence that relativistic effects have a drastic influence on the valence orbitals in both Xe and Rn compounds and consequently play a major role in their high valent chemistry.

But this effect can best be exemplified by the mean radial expectation values < r > that provide a measure of the changes that relativity imposes on the valence shells at the Hartree-Fock level (Table S1).

The 5s orbital in Xe already suffers a considerable radial contraction (0.111 a.u.) with respect to its non-relativistic counterpart but Rn by far exhibits the biggest changes with considerable contraction on both the 6s and 6p orbitals, -0.368 and − 0.191 a.u. respectively. This major contraction of the 6s orbital in Rn accounts for the augmented NPA of RnO₄ with relation to the XeO₄ NPA.

The relativistic radial contraction¹⁷ of the s and p shells on heavy elements has been known for some time. In particular, the inert pair effect initially formulated by Sidgwick¹⁸ in the 1930s and later found¹⁹ to be a consequence of relativity has been a mainstay in the chemical behaviour of the heavy elements of groups 13–15. Generally, the electron pair in the 6s² shell of the heavy elements becomes progressively less chemically accessible to engage in chemical bonds that would result in Tl^III, Pb^IV and Bi^V compounds. Such compounds exhibit a more unfavourable standard enthalpy of formation than each of the lighter congeners In^III, Sn^IV and Sb^V. This feature is best exemplified when comparing the values of the standard reduction potentials E(Sn^II/Sn^IV)=-0.088 V vs E(Pb^II/Pb^IV) = + 1.69 V for heavy elements of group 14.

The inert pair effect is generally not considered for elements in groups 16–18 since the chemistry of polonium, astatine and radon is so poorly known. These results clearly show that the chemistry of Rn^VIII is also affected by the inert pair effect.

The paper by Slepkov et al¹⁵ provided a detailed account into the possible decomposition pathway of XeO₄ predicting the existence of a di-haptic isomer Xe(η²-O₂)₂ as intermediate. It is therefore natural to address the next leading question which is how the energetics of this process compares in the case of RnO₄.

While the authors discuss the frontier orbitals of Xe(η²-O₂)₂ they do not provide an in-depth discussion into the oxidation state of the di-haptic oxides. Furthermore, the calculated HOMO-LUMO gap is notoriously small (0.38 eV) making it a species with high chemical potential (reactive) and possible multi-configurational character. Our examination of the CCSD or even MP2 natural orbitals does indeed confirm that there are two competing configurations in the Xe(η²-O₂)₂ molecule. For a more orthodox and accurate treatment of the electronic structure in this molecule, a CASPT2(22,15) geometry optimisation was conducted for the ground states of both Xe(η²-O₂)₂ and Rn(η²-O₂)₂. Both the quintet and triplet states were explored but lead to dissociation of either both or one of the O₂^•• ligands, respectively, so only the singlet state potential energy surface presents a bound minimum.

The outcome of the calculation is that the structure can be described as a superoxide with spin coupling mediated by the Ng fragment (cf. Section 3 of the SI). This indicates that there is significant O₂⁻…O₂⁻ through bond interaction despite the fragments being over 4 Å apart. Formally this amounts to oxidation state II, Rn^II(η²-O₂)₂ and Xe^II(η²-O₂)₂, in both species.

One possibility not covered in the Slepkov paper¹⁵ is the existence of a stepwise decomposition intermediate NgO₂(η²-O₂). Thus, the structure of these dioxides was optimised and their electronic structure analysed herein. Both structures are minima and their ground singlet states exhibit a single configurational description. Triplet states were explored with this geometry but this leads to a local minimum with a dissociated oxygen atom.

Either species is quite unique in their geometry as they show a distorted tetrahedral shape with no symmetry consistent with an AX₃E type VSEPR stereochemistry;²⁰ in addition, one bond of the dihaptic O₂ fragment is weaker than the other (cf. Figure 3 and Section 4 of the SI). The dihaptic η²-O₂ ligand may best be described as a peroxide ligand (O₂²⁻). As such the formal oxidation state of the Ng atom in NgO₂(η²-O₂) may appropriately be considered + VI.

The decomposition processes of the tetroxides will therefore involve a successive descent of oxidation number in the order VIII→VI→II→0.

In a general overview of the xenon and radon species studied so far (Fig. 4), it may be seen that the energetics of the Ng(η²-O₂)₂ and NgO₂(η²-O₂) species is surprisingly similar between the two elements. The biggest contrast remains still the disparate enthalpies of formation of the two noble gas tetroxides. The joining together of two oxygen atoms to form XeO₂(η²-O₂) is endergonic (+ 69.3 kJ mol^− 1) which may be a hint as to why XeO₄ is still isolable given a low temperature or solvent.

The value reached by Slepkov et al for the enthalpy of formation of Xe(η²-O₂)₂ was + 633 kJ mol^− 1; this value is fairly close to the one reached in this work by a proper multi-reference method, + 600.3 kJ mol^− 1. This is indicative that approximate density functionals of the GGA type exhibit some degree of tolerance for multi-reference character if the single determinant represents around 60% of the wavefunction.

In finalising it is important to stress that when performing an in silico prediction of the existence of any species the term ‘stability’ is not very helpful,²¹ particularly if the systems in question are endothermic with respect to decomposition. But it may be concluded that RnO₄ is a more difficult system to synthesise and isolate. XeO₄ is typically obtained from the acid dehydration of a metal perxenonate (XeO₆⁴⁻).¹⁶ Presumably, a perradonate RnO₆⁴⁻ with high enough lattice energy might be isolated and likewise transformed using very low temperature matrices. The e symmetry vibrational modes, corresponding to a scissor like motion of the oxygen atoms in RnO₄ display a lower energy (205 cm^− 1) than in XeO₄ (265 cm^− 1) which is indication that thermal decomposition may occur more easily for RnO₄.

The noble gas tetroxides NgO₄ (Ng = Xe,Rn) were examined computationally, and a systematic comparison of the bonding features, vibrational properties and energetics was carried out.

The most interesting finding is that the inert pair effect is present in group 18 species. This is reflected in the higher standard enthalpy of formation of RnO₄ relative to XeO₄. The cause of this effect was demonstrated to be relativity, in line with what is known for the heavy elements of groups 13–15. Chemical bonding evaluated through NBO analysis is shown to be residually more ionic in the case of RnO₄, largely by less π(O→Ng) donation. Considering the respective Mulliken electronegativities²² of the two elements, Xe: 5.85 eV, Rn: 5.1 eV, this is to be expected.

The fleeting intermediate species in the decomposition process of the tetroxides were also analysed, namely Ng(η²-O₂)₂ and NgO₂(η²-O₂). While the former can be formally classified as a superoxide, it displays unique spin coupling between both the superoxide ligands mediated by the noble gas atom. This multiconfigurational singlet state sets the stage for dioxygen dissociation. NgO₂(η²-O₂) is a unique peroxide structure whereby the dihaptic group is asymmetrically coordinated to the noble gas atom.

The ORCA 5.0.3 package²³ was used in all the single reference systems. The Douglas-Kroll-Hess^{24, 25} relativistic Hamiltonian to second order (DKH2) was employed in all the calculations. Coupled Cluster^{26, 27} Singles Doubles and iterated Triples [CCSD(T)] optimisations and frequencies were obtained using the relativistically recontracted DKH-def2-TZVPP basis sets²⁸ for oxygen and the SARC-DKH-TZVPP basis sets^{29, 30} for Xe and Rn. The Resolution of Identity ^{31, 32} was employed in all the ORCA runs with an automatically³³ generated density fitting basis set (AutoAux). A finite nucleus model was taken into account via the gaussian nucleus model.³⁴ No symmetry constraints were imposed in the optimisations.

A two point extrapolation³⁵ to the complete basis set (CBS) was used employing the Martin³⁶ formula:

$$\text{E=}{\text{E}}_{\text{CBS}}\text{+}\frac{\text{A}}{{\text{(n+1/2)}}^{\text{4}}}$$

where A is a system dependent constant and n is the cardinal number of the basis set in use. To solve this system of equations two single point runs with the x2c-TZVPP (n = 3) and x2c-QZVPP (n = 4) relativistic basis sets were performed and the resulting energies used in the extrapolation.^{35, 37} The notation “method/basis set 1//method 2/basis set 2” is adopted throughout and signifies that geometry optimisation and numerical frequencies were carried out with method 2/basis set 2 while the final energy of the stationary point is obtained with method/basis set 1.

Geometry optimisations of the multi-reference systems Ng(η²-O₂)₂ were all performed using OpenMolcas³⁸ version 19.11 employing the DKH2 relativistic Hamiltonian, the x2c-TZVPP basis set on all the elements with resolution of identity³⁹ charge decomposition (RICD) of multi-centre two electron integrals via the atomic compact (aCCD) auxiliary basis set.⁴⁰ The explicit correlation space was made up of 22 electrons in 15 orbitals [CASSCF(22,15)] corresponding to all the valence p orbitals in Ng and O. The resulting multi-configurational self-consistent field wavefunction was correlated to second order under the CASPT2 formalism. The geometries were optimised using the latest analytic gradient implementations⁴¹ in OpenMolcas whereby state specific (1 root) CASPT2(22,15) nuclear gradients were minimised. A diagonal Fock approximation was used in the CASPT2 optimisations (non-iterative CASPT2). An imaginary level shift of 0.2i au was used in the perturbative step to avoid intruder states and consequent discontinuities in the energy landscape.

The CASPT2(22,15) optimised structures of the Ng(η²-O₂)₂ systems obtained with OpenMolcas underwent a single point energy evaluation in ORCA with Mukherjee’s⁴² multi-reference coupled cluster variant Mk-CCSD(T) with the x2c-TZVPP and x2c-QZVPP basis sets in like manner as above to obtain the CBS extrapolated energies.

Standard enthalpies of formation of NgO₄ and NgO₂(η²-O₂) were computed as the sum of the electronic energies obtained from the CBS extrapolation and the thermal corrections (H_corr) for the enthalpy at standard temperature and pressure at the level of theory of the optimisation [CCSD(T)/DKH-TZVPP]:

$${\text{H}}_{\text{298K}}^{\text{⊖}}\text{=E}\left[\text{CCSD}\left(\text{T}\right)\text{/CBS//CCSD}\left(\text{T}\right)\text{/DKH-TZVPP}\right]\text{+}{\text{H}}_{\text{corr}}\text{[CCSD(T)/DKH-TZVPP]}$$

The enthalpies of the multireference systems Ng(η²-O₂)₂ were calculated with the formula:

$${\text{H}}_{\text{298K}}^{\text{⊖}}\text{=E}\left[\text{Mk-CCSD}\left(\text{T}\right)\text{/CBS//CASPT2(22,15)/x2c-TZVPP}\right]\text{+}{\text{H}}_{\text{corr}}\text{[CASPT2(22,}\text{1}\text{5)/x2c-TZVPP]}$$

where the thermal corrections H_corr were calculated with the optimisation method in OpenMolcas.

Natural Bond Orbital⁴³ (NBO) analyses were performed using the CCSD natural orbitals obtained from the optimisation procedure.

Acknowledgements

Funding from Fundação para a Ciência e a Tecnologia is acknowledged for this work through the RadonChem grant ref. PTDC/QUI-QFI/31896/2017. Institutional grants UIDB/04046/2020 and UIDP/04046/2020 (BioISI), UIDB/00100/2020 (CQE), and LA/P/0056/2020 (IMS) are also acknowledged. The authors thank Prof. Maria José Calhorda for helpful discussions and critical analysis of the manuscript.

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The inert pair effect on the heavy noble gases: New insights from radon tetroxide.

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