This letter reports an ab initio study
This letter reports an ab initio study on the X peaks of PES by including the SO effect. The multiplet split energies are calculated with the SO-MCQDPT2 method , and the so-called pole strengths are evaluated to simulate the relative intensities. The results are compared with the experimental PES and the MCQDPT2 calculations.
Results and discussion Fig. 1 shows the calculated PES for the entire Ln series. Although Eu(COT)2− and Yb(COT)2− are experimentally considered the complexes of the divalent Ln2+ ions, their PES were also calculated to investigate the systematic Ln dependence of the X peaks by assuming the trivalent electronic structure with D8h symmetry. For ease of comparison with the experimental PES, a Lorentzian linewidth is given to the calculated line spectra (Fig. S1 in the Supplementary material). The full width at half maximum parameter was set to be 0.08eV to fit the broadened peaks, which were measured at the detachment laser wavelength 355nm (see Fig. 1 of Ref. ). Fig. 1 shows that the splitting of the X peaks appears in the entire Ln series except for the Ce and Pr complexes. The splitting represents the clearly difference between two groups of final states: the one stabilized by the 4f-ligand interaction and the other without such stabilization; the latter higher-energy peaks are assigned as X′ in the experimental PES . In Fig. 1, to compare the splitting patterns in detail, the experimental peak position and height are represented by two red bars for Sm, Gd, Tb, Dy, and Ho complexes, for which the X peak splitting was observed. The experimental peak positions are shifted so that the X′ peak coincides to the theoretical one on the higher-energy side. In Table 1, these split energy values, which were calculated using the current SO-MCQDPT2 method, are compared with the MCQDPT2 results  and experimental values . It should be noted that the previous MCQDPT2 calculation used the one-electron orbitals that were individually optimized for each anion and neutral high- and low-spin states, but the current SO-MCQDPT2 calculation always used the optimized orbitals for the anion complex even for neutral states. To observe the effect caused by different sets of one-electron orbitals, in Table 1, we show the MCQDPT2 results (denoted as MCQDPT2 II), which were obtained using the optimized orbitals for the anion complex as in the SO-MCQPDT calculation. In addition, the PES generated by the MCQDPT2 II results are shown in Fig. 2. Fig. 1, Fig. 2 show a notable difference in intensity ratio of the X and X′ peaks; the lower-energy X peaks in SO-MCQDPT2 have enhanced intensity compared to MCQDPT2 II. Although the vibrational contributions to PES are not considered, the SO-MCQDPT2 PES (Fig. 1) is reasonably consistent with the experimental one. In connection with vibrational motions, some peaks on the 0.18–0.20eV higher-energy side from the X peak were previously considered due to vibrationally excited states, most likely of the CC stretching vibrational mode for the COT . The D8h equilibrium structure of the anion complexes corresponds to a conical intersection point of the neutral complexes. Thus, the complexes are subject to a sudden Jahn-Teller distortion after the electron detachment from the HOMO. This distortion can produce the vibrationally excited neutral states, as easily understood from the PES study of the ligand COT anion . Thus, every X peak is accompanied by the vibrational progressions to some extent. Because the magnitude of the X peak splittings due to the electronic origin is in the order of 0.1–0.2eV as shown in Fig. 1, the vibrational peaks that accompany the lower-energy X peaks can overlap the higher-energy X′ peaks if the vibrational structures are included. This vibrational contribution increases the relative intensity ratio I (X′)/I (X). In other words, the intensity ratio without the vibrational contribution should be smaller than the experimental one. This expectation is actually observed in the SO-MCQDPT2 results for Tb-Ho complexes (Fig. 1(h)–(j)). However, contrary to the expectation, the X′ peaks in these MCQDPT2 II spectra (Fig. 2(h)–(j)) have stronger intensities than the X peaks, and if the vibrational contribution is included, the deviation from the experimental peak ratio is exaggerated.