Introduction:

Structures and relative energies of low-lying isomers The global minimum of La2B8 − was searched using the TGMin program, in combination with manual structural constructions. More than 2000 structures were generated and Fig. S1 presents all the isomers located within 130 kcal/mol above the global minimum of La2B8 − . The D4h structure with a B8 ring sandwiched by the two La atoms was found to be the global minimum. Because of their similar PE spectra, many di-lanthanide octa-boron clusters can form presumably similar Ln2B8 inverse sandwiches, as confirmed for Pr2B8 − .

Source:

W.-L. Li, T.-T. Chen, D.-H. Xing, X. Chen, J. Li, L.-S. Wang, “Observation of Highly Stable and Symmetric Lanthanide Octa-Boron Inverse Sandwich Complexes”, Proc. Natl. Acad. Sci. USA., 2018, 115(30), E6972-E6977, DOI: 10.1073/pnas.1806476115

Fig. S1. Relative energies (in kcal/mol) of the low-lying isomers of La2B8 − within 130 kcal/mol at the levels of PBE, PBE0 and CCSD(T) (in 1st, 2nd and 3rd row, respectively) with triple-ζ basis sets and polarization functions.

Coordinates of the global minima of Ln2B8 − and its neutral species Table S1. Coordinates of the global minimum La2B8 − and La2B8 at the PBE0/TZP level (in Å) .

La2B8− (D4h)                                                           Download the structure

1.B -0.792642 -1.889389 0.000000

2.B 0.792642 -1.889389 0.000000

3.B 1.889389 -0.792642 0.000000

4.B 1.889389 0.792642 0.000000

5.B 0.792642 1.889389 0.000000

6.B -0.792642 1.889389 0.000000

7.B -1.889389 -0.792642 0.000000

8.B -1.889389 0.792642 0.000000

9.La 0.000000 0.000000 1.823152

10.La 0.000000 0.000000 -1.823152

La2B8 (D8h)                                                           Download the structure

1.B 0.000000 2.038317 0.000000

2.B -1.441308 1.441308 0.000000

3.B -2.038317 0.000000 0.000000

4.B -1.441308 -1.441308 0.000000

5.B 0.000000 -2.038317 0.000000

6.B 1.441308 -1.441308 0.000000

7.B 1.441308 1.441308 0.000000

8.B 2.038317 0.000000 0.000000

9.La 0.000000 0.000000 1.859782

10.La 0.000000 0.000000 -1.859782

Table S2. Coordinates of the global minimum Pr2B8 − and Pr2B8 at the PBE0/TZP level (in Å).

Pr2B8− (D4h)                                                           Download the structure

1.B 0.000000 2.043389 0.000000

2.B -1.439931 1.439931 0.000000

3.B -2.043389 0.000000 0.000000

4.B -1.439931 -1.439931 0.000000

5.B 0.000000 -2.043389 0.000000

6.B 1.439931 -1.439931 0.000000

7.B 2.043389 0.000000 0.000000

8.B 1.439931 1.439931 0.000000

9.Pr 0.000000 0.000000 1.766446

10.Pr 0.000000 0.000000 -1.766446

Pr2B8 (D8h)                                                           Download the structure

1.B 0.000000 2.032004 0.000000

2.B -1.436844 1.436844 0.000000

3.B -2.032004 0.000000 0.000000

4.B -1.436844 -1.436844 0.000000

5.B 0.000000 -2.032004 0.000000

6.B 1.436844 -1.436844 0.000000

7.B 2.032004 0.000000 0.000000

8.B 1.436844 1.436844 0.000000

9.Pr 0.000000 0.000000 1.778874

10.Pr 0.000000 0.000000 -1.778874