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),