An estimation of the enthalpy change for reaction 1, ∆H(1), can be acquired via a thermochemical cycle, such as that in Figure 1. The cycle requires estimation of the lattice potential energy of , . We obtain V=0.6217 nm³(V^1/3=0.853 nm), which provides a value of =312.06 kcal/mol, via Eq. (1). This goal is achieved according to the well-established crystal structural data of with cell dimensions of a=794.0±1 pm, b =917.7±1 pm, c =1739.1(3) pm, α=99.539±5°, β=92.640±4°, and γ=94.646±5°, unit cell volume V=1243.4×10⁶pm³, and number of molecular units in the unit cell Z=2⁽²⁴⁾. The RT terms are corrected by means of Eq. (2), ∆H_L=313.84 kcal/mol.

As we’ll see later,we need to calculate the volume of ions at the MP2 level because of the absence of the crystal structural data of salts. This task is necessary to estimate the lattice potential energy of . Here, we also calculate the volume of the ion at the MP2 level to verify the accuracy and validity of the calculation of the ion volume. The obtained ion volume of 0.198 nm³ is in good agreement and within the allowable error range of the volume estimated 0.168±0.040 nm³ by subtracting 2V=2×0.227±0.020 nm³ ( Table 6, Ref. 53) from the reported crystal structural volume V=0.6217 nm³ ;.

The necessary ancillary thermochemical data are as follows: the energy of the F–F bond, BE (F₂,g)⁽⁵⁶⁾=37 kcal/mol, sublimation enthalpy of the solid phase Au(s)⁽⁵⁶⁾, ∆H_s(Au(s)→Au(g))=85.7 kcal/mol, ionization potential of gaseous Au⁽⁵⁶⁾, IE (Au,g)=I₁+I₂=684.47 kcal/mol, dissociation energy of , D₀()=208 kcal/mol (taking the average of the last two columns in Table 3), electron affinity of gaseous F⁽⁵⁶⁾, 2EA(F,g)=−2×81.1=−162.2 kcal/mol, and ∆H_f²⁹⁸(2SbF₅+F⁻→Sb₂F₁₁⁻). The F ionization enthalpy of Sb₂F₁₁⁻¹, ∆H_f²⁹⁸(Sb₂F₁₁⁻→2SbF₅+F⁻) has not been measured. However, SbF₆⁻is as stable with respect to F⁻ loss as AsF₆⁻, for which the enthalpy change has been estimated⁽⁵⁷⁾ to be 111 kcal/mol. Anion Sb₂F₁₁⁻¹ is more stable⁽²⁵⁾ than anion sbF₆⁻. Thus, ∆H_f²⁹⁸(2SbF₅+F⁻→Sb₂F₁₁⁻) must be <−111 kcal/mol. The corresponding enthalpy change ∆H(1) is estimated to be <−98.87 kcal/mol.

The compound stability depends on free energy changes ∆G and not on enthalpy ones. Hence, the entropy contributions from the T∆S term to the free energy must be included. The entropy change of reaction 1 will be negative (i.e., the products are more ordered than the reactants) and equal to S°–S°(Au,s)–4S°(Xe,g)–S°(F₂,g)–4S°(SbF₅,g). The entropies of SbF₅(g) and are unknown. Nevertheless, we can use the entropies of PF₅(g)⁽⁵⁶⁾and Ca₅(IO₆)₂(s)⁽⁵⁶⁾, which are 72.66 and 108.4 kcal/mol, respectively, to estimate the value for SbF₅(g) and . The well-established entropies of Au(s), Xe(g), and F₂(g)⁽⁵⁶⁾ are 11.33, 40.529, and 48.51 kcal/mol, respectively. Based on these values, we obtain an estimate for the entropy of reaction 1, ∆S=−404.196 kcal/mol.

The free energy change of the chemical reaction must be negative for it to be thermodynamically favorable. The use of the above-mentioned estimation of the entropy change ∆S and enthalpy change ∆H(1) leads us to predict that the free energy change ∆G=∆H−T∆S is negative when the temperature T is <244.61 K=−28.39 °C. Specifically, the solid salt compound may exist at a temperature lower than −28.39 °C. This prediction is consistent with the observation that the salt compound can be prepared at −40 °C.

3.2 Specific studies: The optimized bond lengths for determined using different methods are reported in Table 2. As already observed in the AuXe₄²⁺ benchmark work, the optimized exhibits a square planar D_4h symmetry with the ion at the center connected to the 4Ng atoms and manifests the²B_1g electronic ground state. The data in Table 2 also show that our theoretically determined equilibrium distances for at the MP2 level are shorter than the corresponding B3lyp values. In comparison with the available previous theoretical data, our predicted equilibrium distances for at the MP2 level are in excellent agreement with the values predicted by Li⁽⁴⁰⁾ at the high theoretical level ccsd(T). Some previous studies by Walker⁽⁵⁸⁾ using pseudopotentials and smaller basis sets predicted bond distances (Ng=Ar, M=Au,Ag,Cu) longer than our MP2 results. This finding reconfirms that electron correlations at high levels and large basis sets are required to describe these weak interaction systems.

We now discuss the dissociation energy of . As observed in the AuXe₄²⁺work, Table 3 shows that, at all levels of theory employed in our study, is predicted to be stable toward dissociating into ions and 4Ng atoms in the ground state. The data in Table 3 also show that the dissociation energy of at the MP2 level of theory is basically consistent with the corresponding value at the ccsd(T) level. Our calculations provide trends essentially similar to those of Walker⁽⁵⁸⁾. The calculated dissociation energy of at all levels of theory employed are consistently lower than those of either or while that of increase along the series Ag, Au, and Cu.