Figure 1. Born–Haber cycle for the preparation of via preparative route
(1).
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(V1/3=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), ∆HL=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),
∆Hs(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
∆Hf298(2SbF5+F−→Sb2F11−).
The F ionization enthalpy of
Sb2F11−1,
∆Hf298(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,
∆Hf298(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.
The above success in predicting the
existence and stability of allows us to adopt a similar methodology for
effectively predicting the
existence and stability of in the next step.
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 D4h symmetry with the
ion at the center connected to the 4Ng atoms and manifests the2B1g 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.
Existence and stability prediction of based on
Born–Haber cycles
Here, we use the synthetic route of reaction 2 similar to that
used in
the previous study of
to prepare
. Figure 2 shows the corresponding
Born–Haber cycles.