二、 Methodology
The theoretical investigations reported here were carried out for a
series of salt compounds by using
the GAUSSIAN 03 suite of programs(41). Geometries were
fully optimized at the B3LYP and MP2 levels, and relativistic and
quasirelativistic effective core potentials of the Stuttgart/Koeln group
(the Stuttgart/Cologne Group) were used for Cu, Ag, Au, and Xe with the
corresponding basis sets. Our research system involving the weak bond
between Au and noble gases is likely to be particularly sensitive to the
basis set quality and the level at which electron correlation is
accounted for; thus, the selected basis set with at least one f-symmetry
function is needed to produce reliable correlation
energy(42). Xe employed the large-core pseudopotential
ECP46MWB scheme with the contraction basis set
(6s6p3d1f)/4s4p3d1f(43,44). The Gaussian basis set for
Cu, Ag, and Au is (12s12p9d3f2g), which is contracted to
[6s6p4d3f2g](45). The aug-cc-pVTZ basis set is
used for He, Ne, and Ar(46-48). Vibrational
frequencies and zero-point energies (ZPEs) are determined at the B3LYP
and MP2 levels. The structures studied here are local minima on the
corresponding potential energy surfaces, as indicated by their having
only positive eigenvalues of the diagonalized force–constant matrix.
The improved relative energy is obtained by using a large aug-cc-pVQZ
basis set(49) for the salt compounds on the MP2
optimized geometry. In the AuXe42+case, the improved relative energy is obtained from MP2 calculations
with a small-core relativistic pseudopotential ECP28MDF basis
set(50). The standard counterpoise
method(51,52) was adopted to account for the basis set
superposition error (BSSE) for the theoretically predicted dissociation
energy at all levels of theory.
Eq. (1),(53)
(1)
was used to estimate the lattice energy, UPOT, of the
salts. Here, Zk represents the respective charges on the
cations and anions, nk is the number of ions of charge
Zk in the formula unit, α(kJ mol−1 nm)
and β ( kJ mol−1) are coefficients of the best fit, α
and β take the values 133.5 kJ mol−1 nm and
60.9 kJ mol−1,
respectively, for 1:2 salts, and V (nm3) is the
molecular (formula unit) volume of the salt. The individual ion volumes
can be estimated from an ion volume database, inferred in some cases
from established crystal structural
data or calculated when the crystal structural data are missing. The
electron densities are calculated at the MP2 level, and the volume is
taken to be that inside the 0.001 au contour of the electron density.
The UPOT of a salt
(MpXq) is related to its lattice
enthalpy, ∆HL, via Eq. (2)(54):
where nM and nX are equal to 3 for
monatomic ions, 5 for linear polyatomic ions, and 6 for polyatomic
nonlinear ions.
三、Results a nd Discussion
The calculated energy at various levels of theory for 1–10 and the
corresponding dissociation products are listed in Table 1. Table 2 shows
the optimized interatomic distances determined by using different
methods, along with previous data from the literature. The experimental
bond lengths are also listed in Table 2. The calculated dissociation
energies, Do, for 1–10 are shown in Table 3.
Table 1. Calculated Total Energies, E, (hartrees), Zero-Point
Vibrational Energies, ZPE (kcal/mol), and Basis Set Superposition
Errors, BSSE (kcal/mol),