Supporting Information

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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2018 Supporting Information Beryllium-Beryllium only double-π bonds in the octahedral cluster of Be 2 (μ 2 -X) 4 (X=Li, Cu, BeF) Xingman Liu a, Min Zhang* a, Shuang Yu b, Yun Geng a, Xingxing Zhang a, Yihong Ding* b and Zhongmin Su* a a Institute of Functional Material Chemistry, Faculty of Chemistry & National & Local United Engineering Laboratory for Power Battery, Northeast Normal University, Changchun (P.R. China). b Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun (P.R. China) Corresponding Author mzhang@nenu.edu.cn (M. Zhang) yhdd@jlu.edu.cn (Y. Ding) zmsu@nenu.edu.cn (Z. Su) 1

2 Table of Contents SI1 A description of the other simulated molecular structures and the corresponding orbital information for octahedral Be 2 (BeF) 4 and Be 2 Cu 4 shown in Figure S1 and S2. SI2 The ADNDP, LOL, ELF analysis for octahedral Be 2 (BeF) 4 and Be 2 Cu 4 shown in Figure S3 and S4. SI3 The CDA results for octahedral Be 2 (BeF) 4 and Be 2 Cu 4 shown in Figure S5 and S6. SI4 The Laplacian plot of the electron density for octahedral Be 2 Li 4 and Be 2 Cu 4 presented in Figure S7 and S8. SI5 The AIM analysis for three octahedral Be 2 (BeF) 4, Be 2 Li 4 and Be 2 Cu 4 listed in Figure S9. SI6 The lowest frequency and corresponding Be-Be stretching vibrational modes for Be 2 complexes shown in Figure S10. SI7 The structures data for three octahedral clusters and their other lowest-lying isomers using G3B3 approach, together with their relative energy difference given in Figure S11. SI8 Detailed orbital component analysis results (important Be-Be σ, π, σ*and π*) for Be 2 Li 4, Be 2 Cu 4 and Be 2 (BeF) 4 listed in Table S1-S3. SI9 The data on other optimized structures by this universal strategy including Be 2 (BeCl) 4 and Be 2 Na 4 shown in Figure S12. SI10 Several possible reactions and thermodynamic values for octahedral Be 2 Cu 4, Be 2 Li 4 and Be 2 (BeF) 4 shown as in Scheme S1. SI11 The weight of degenerate double-π bonds configuration under CASSCF(8,8)/6-31G* level for the octahedral Be 2 X 4 (X = Li, Cu, BeF) in Table S4. SI12 The detailed structural coordinates. 2

3 SI1 Figure S1. The global minimum of Be 2 (BeF) 4 with the D 4h symmetry and its important FMOs under CCSD/cc-pVTZ level. It should be noted that the isolated orbitals of F from HOMO-9 to HOMO-2 have been omitted here. Figure S2. The global minimum of Be 2 (Cu) 4 with the D 4h symmetry and its important FMOs under CCSD/cc-pVTZ/LANL2DZ level. The inner orbital of Cu and Be omitted here. 3

4 SI2 Figure S3. a) AdNDP orbitals. b) LOL profile. c) ELF profile for Be 2 (BeF) 4 did under CCSD/cc-pVTZ level. ON stands for the occupation number. Figure S4. a) AdNDP orbitals. b) LOL profile. c) ELF profile for Be 2 Cu 4 under CCSD/cc-pVTZ/LANL2DZ level. ON stands for the occupation number. 4

5 SI3 Figure S5. The dominant FMOs correlation diagram in Be 2 (BeF) 4 under CCSD/cc-pVTZ level between vertex-be 2 and (BeF) 4 fragments. Figure S6. The dominant FMOs correlation diagram under CCSD/cc-pVTZ/LANL2DZ level in Be 2 Cu 4 between Be 2 and Cu 4 fragments. 5

SI4 Figure S7. Laplacian plot of the electron density 2 ρ(r) of Be 2 Li 4 under CCSD/cc-pVTZ level in different perspectives.

b) Front view that contains two vertex-be atoms and two opposing Li atoms bisecting the plane of the Li 4 ring.

charge depletion ( 2 ρ(r)>0). Figure S8. Laplacian plot of the electron density 2 ρ(r) of Be 2 Cu 4 under CCSD/cc-pVTZ/LANL2DZ level in different perspectives.

6 SI4 Figure S7. Laplacian plot of the electron density 2 ρ(r) of Be 2 Li 4 under CCSD/cc-pVTZ level in different perspectives. a) The plane of the Li 4 ring from the vertical view. b) Front view that contains two vertex-be atoms and two opposing Li atoms bisecting the plane of the Li 4 ring. The orange lines including corresponding region indicate the areas of charge concentration ( 2 ρ(r)<0) while blue lines and corresponding region show the areas of charge depletion ( 2 ρ(r)>0). Figure S8. Laplacian plot of the electron density 2 ρ(r) of Be 2 Cu 4 under CCSD/cc-pVTZ/LANL2DZ level in different perspectives. a) The plane of the Cu 4 ring from the vertical view. b) Front view that contains two vertex-be atoms and two opposing Cu atoms bisecting the plane of the Cu 4 ring. The orange lines including corresponding region indicate the areas of charge concentration ( 2 ρ(r)<0) while blue lines and corresponding region show the areas of charge depletion ( 2 ρ(r)>0). 6

7 SI5 Figure S9. AIM results under the same level as their optimization progress for a) Be 2 (BeF) 4, b) Be 2 Li 4 and c) Be 2 Cu 4. It is clear that there no BCP along Be-Be axle meaning there no direct σ bonding interaction between two Be atom. Here the orange dots are bond critical points(bcp), yellow dots are ring critical points(rcp), and the two green dots are the cage critical points(ccp). The purple dots in Be 2 (BeF) 4 and Be 2 Li 4 including two parts. In addition to the nucleus critical points(ncp), the Non-nuclesr-attractor(NNA) is marked pink color.( Please refer to Organometallics 2013, 32, ; Inorg. Chem. 2000, 39, and Angew. Chem. Int. Ed. 1984, ) There exist four NNAs in both in Be 2 (BeF) 4 and Be 2 Li 4 separately. The orange solid lines represent the path connected the BCP and NCP and the green solid lines connected RCP and CCP. Indicators in the graph: Covalent indicates the covalent bond, Dative indicates the dative bond, Metal-Metal means the metallic bond. 7

8 SI6 Figure S10. a) The lowest frequency and the corresponding vibrational modes. b) The normal modes of Be-Be stretching vibrational frequency in Be 2 -containing complexes under the same level as their optimization progress. (unit: cm -1.) 8

SI7 0.0 1a (D 4h, 1 A) 11.9 1b (C s, 1 A) 36.2 1c (C s, 1 A) 20.0 1d (D 4h, 3 A) 0.0 2a (D 4h, 1 A) 4.

9 SI a (D 4h, 1 A) b (C s, 1 A) c (C s, 1 A) d (D 4h, 3 A) 0.0 2a (D 4h, 1 A) 4.9 2b (C 2v, 1 A) 7.8 2c (C s, 1 A) d (C 2h, 1 A) e (C 2h, 1 A ) f (C s, 1 A) g (D 2h, 1 A) h (C s, 3 A ) 9

0.0 3a (D 4h, 1 A) 12.8 3b (C 2v, 1 A) 15.8 3c (C 1, 1 A) 24.0 3d (C 2v, 1 A) 35.4 3e (D 4h, 3 A) Figure S11.

approach (please refer to J. Chem. Phys. 109, 1998, 7764). 1d, 2h and 3e represent the lowest triplet isomers on the PES, respectively.

10 0.0 3a (D 4h, 1 A) b (C 2v, 1 A) c (C 1, 1 A) d (C 2v, 1 A) e (D 4h, 3 A) Figure S11. The lowest-lying isomers of Be 2 Li 4, Be 2 (BeF) 4 and Be 2 Cu 4 shortened as 1, 2 and 3 respectively with energy in kcal/mol using G3B3 approach (please refer to J. Chem. Phys. 109, 1998, 7764). 1d, 2h and 3e represent the lowest triplet isomers on the PES, respectively. It is noteworthy that many of the structures will be transformed to the octahedral conformation after the re-optimization under higher basis set level, so some transformed isomers are omitted here. 10

SI8 Table S1. The orbital composition of Be 2 Li 4 under CCSD/cc-pVTZ level. The molecular orbitals originated from the inner shell AOs are omitted.

Occupied molecular orbital Unoccupied Be 2 Li 4 molecular orbital σ 2 π σ* 2 π* Diagram Energy/eV -11.15-5.19-5.03 2.98 Li Component 4 2s~30.4% Li 4 2s~65.

The orbital composition of Be 2 Cu 4 under CCSD/cc-pVTZ/LANL2DZ level Be 2 Cu 4 Occupied molecular orbital Unoccupied molecular orbital σ 2 π σ* 2 π* Diagram Energy/eV -12.

0% 4 4p z ~46.4% Be Be 2 2s~33.4% Cu 4 3s~7.1% Be 2 2s~53.2% 2 2p x,y ~52.7% Be 2 2p x,y ~10.5% Be 2 2p z ~19.9% Table S3.

11 SI8 Table S1. The orbital composition of Be 2 Li 4 under CCSD/cc-pVTZ level. The molecular orbitals originated from the inner shell AOs are omitted. The coefficient of each orbital is given by the contribution from the Be 2 and Li 4 fragments. The same way for Be 2 Cu 4 Be 2 (BeF) 4. Occupied molecular orbital Unoccupied Be 2 Li 4 molecular orbital σ 2 π σ* 2 π* Diagram Energy/eV Li Component 4 2s~30.4% Li 4 2s~65.3% Li Be Be 2 2s~53.0% Be 2 2p x,y ~18.7% 2 2s~94.4% 4 2p z ~38.4% Be 2 2p x,y ~59.7% Table S2. The orbital composition of Be 2 Cu 4 under CCSD/cc-pVTZ/LANL2DZ level Be 2 Cu 4 Occupied molecular orbital Unoccupied molecular orbital σ 2 π σ* 2 π* Diagram Energy/eV Cu 4 4s~63.5% Cu 4 4p z ~10.7% Component Cu 4 4s~21.8% Cu 4 4p x,y ~9.2% Cu 4 d xy ~5.0% Cu Cu 4 3dz 2 ~35.6% Cu 4 dx 2 -y 2 ~7.8% Cu 4 d yz ~5.0% 4 4p z ~46.4% Be Be 2 2s~33.4% Cu 4 3s~7.1% Be 2 2s~53.2% 2 2p x,y ~52.7% Be 2 2p x,y ~10.5% Be 2 2p z ~19.9% Table S3. The orbital composition of Be 2 (BeF) 4 under CCSD/cc-pVTZ level. Be 2 (BeF) 4 occupied molecular orbital unoccupied molecular orbital σ 2 π σ* 2 π* Diagram Energy/eV Be 4 2s~16.6% Component Be 4 2p x,y ~7.5% Be 4 2s~42.1% Be Be 4 2pz~5.6% Be 4 2p x,y ~19.7% Be 2 2s~92.3% 4 2p z ~8.8% Be F 4 2p x,y ~6.8% Be 2 2p x,y ~24.9% 2 2p x,y ~88.2% Be 2 2s~56.7% 11

12 SI9 Figure S12. The data on other two optimized structures by this universal strategy including Be 2 (BeCl) 4 and Be 2 Na 4 under B3LYP/cc-pVTZ level. The same conclusion can be drawn, since the same trend is for Be 2 (BeF) 4, Be 2 Cu 4, Be 2 Li 4 under the same level. The frequency analysis is achieved also under B3LYP/cc-pVTZ level. They are all the lowest-energy structure under this level. The most-important bond-lengths and WBIs for Be 2 (BeCl) 4 and Be 2 Na 4 are also shown under CCSD/cc-pVTZ level. 12

13 SI10 4 Li 2 Be G= kcal/mol Li 4 (rhombus) 2 Be Be 2 Li 4 G= kcal/mol Be 2 Li 2 (rhombus) Li 2 ( octahedron) G= kcal/mol 2 BeLi 2 G= kcal/mol 4 Cu 2 Be G= kcal/mol Cu 4 (rhombus) 2 Be Be 2 Cu 4 G= kcal/mol Be 2 Cu 2 (rhombus) Cu 2 ( octahedron) G=-71.75kcal/mol 2 BeCu 2 G=-61.15kcal/mol 4 F 6 Be Be 6 (C s ) 2 Be 2 F 2 2 F 2 2 Be Be F Be Be F Be 2 F 2 Be Be 2 (BeF) 4 ( octahedron) G= kcal/mol G= kcal/mol G= kcal/mol G= kcal/mol Scheme S1. Several possible reactions and thermodynamic values for the generation of octahedral Be 2 Li 4, Be 2 Cu 4 and Be 2 (BeF) 4 using CCSD method. The LANL2DZ basis set for Cu, cc-pvtz for Be, Li and F. The Gibbs free energy differences (ΔG) of all reactions are always negative, so in thermodynamics, Be 2 Cu 4, Be 2 Li 4 and Be 2 (BeF) 4 are stable and can most likely be obtained by some reactions. 13

14 SI11 The octahedral Be 2 X 4 (X = Li, Cu, BeF) structures is optimized and calculated at the CASSCF(8,8)/6-31G* level. These active orbitals are including 4 σ and 4 orbitals, in which 6 orbitals (2 σ + 4 ) are shown in SI8. Since the 2 σ orbitals in SI8 are occupied, we introduced LUMO (σ orbital) and the corresponding σ* orbital in the active space. As expected, the CASSCF(8,8) results are consistent with the CCSD results. All the dominant configurations in octahedral Be 2 X 4 (X = Li, Cu, BeF) are the degenerate double-π bonds state, and the corresponding weights are all over 83%. It is suggested that there are no multi-reference configurations in nature. Table S4. The weight of degenerate double-π bonds configuration under CASSCF(8,8)/6-31G* level for the global minimums. Be 2 Li 4 Be 2 Cu 4 Be 2 (BeF) 4 Basis set 6-31G* 6-31G*/LANL2DZ 6-31G* Weight (%) SI12 Coordinates and energies (unit: a.u.) of Be 2 Li 4, Be 2 (BeF) 4, Be 2 Cu 4, Be 2 (BeCl) 4, Be 2 Na 4, Be 2, Be 2 F 2, Be 2 (CO) 4, Be 2 (NHCs) 2. Methods and Basis Sets are shown in brackets. Part-A Be 2 Li 4 (octahedron) (CCSD/cc-pVTZ) E= Li Li Li Li Be Be Be 2 Cu 4 (octahedron) (CCSD/LANL2DZ/cc-pVTZ) E= Cu Cu Cu Cu Be Be Be 2 (BeF) 4 (octahedron) (CCSD/cc-pVTZ) E= Be Be Be Be Be Be F F F F Be 2 Na 4 (octahedron, shown as Figure S12) (B3LYP/cc-pVTZ) 14

15 E= Be Be Na Na Na Na Be 2 (BeCl) 4 (octahedron, shown as Figure S12) (B3LYP/cc-pVTZ) E= Be Be Be Be Be Be Cl Cl Cl Cl Part-B The lowest-lying isomers coordinates of Be 2 Li 4, Be 2 (BeF) 4 and Be 2 Cu 4 respectively using G3B3 approach. Be 2 Li 4 (B3LYP/6-31g*) 1a E= Li Li Li Be Be Li b E= Li Li Be Li Be Li c E= Li Li Be Li Li Be d E= Li Li Be Li Li Be

16 Be 2 (BeF) 4 (B3LYP/6-31g*) 2a E= Be Be Be Be Be Be F F F F b E= Be Be Be Be Be Be F F F F c E= Be Be Be Be Be Be F F F F d E= Be Be Be Be Be Be F F F F e E= Be Be Be Be Be Be F F

17 F F f E= Be Be Be Be Be Be F F F F g E= Be Be Be Be Be Be F F F F h E= Be Be Be Be Be Be F F F F Be 2 Cu 4 (B3LYP/6-31g*) 3a E= Be Cu Cu Cu Be Cu b E= Be Cu Cu Cu Cu Be c E=

18 Be Be Cu Cu Cu Cu d E= Cu Be Cu Be Cu Cu e E= Be Cu Cu Cu Be Cu Part-C (Other related molecular structural coordinates) Be 2 (CCSD(T)/cc-pVTZ) E= Be Be Be 2 F 2 (CCSD/cc-pVTZ) E= Be Be F F Be 2 (CO) 4 (CCSD/cc-pVTZ) E= Be Be C C C C O O O O Be 2 (NHCs) 2 (B3LYP/cc-pVTZ) E= Be Be C N N

19 C C C N N C C C H H H C H H H C H H H C H H H H H H H

List of Figures Page Figure No. Figure Caption No. Figure 1.1.

List of Figures Page Figure No. Figure Caption No. Figure 1.1. List of Figures Figure No. Figure Caption Page No. Figure 1.1. Cation- interactions and their modulations. 4 Figure 1.2. Three conformations of benzene dimer, S is not a minimum on the potential energy