Supporting Information

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1 Supporting Information Improved Segmented All-Electron Relativistically Contracted Basis Sets for the Lanthanides Daniel Aravena, Frank Neese, Dimitrios A. Pantazis CONTENTS Table S1. SAHF total energies of neutral atoms for QZV and UGBS+8 (ZORA) S-2 Table S2. SAHF orbital eigenvalues for QZV (ZORA) S-3 Table S3. Radial expectation values of innermost orbitals for QZV and SARC-TZV (DKH2) S-4 Table S4. Radial expectation values of innermost orbitals for QZV and UGBS+8 (ZORA) S-5 Table S5. Ionization potentials for QZV basis (ZORA) S-6 Table S6. Ionization potentials for the QZV and Cologne basis (DHK2) S-7 Table S7. CASSCF excitation energies for QZV basis (ZORA) S-8 Table S8. SOC parameter for QZV basis (ZORA) S-9 Table S9 Optimized geometries of Ln III X 3 S-10 Table S10. Calculated dipole moments S-12 Table S11. CASSCF excitation energies for QZV and QZVP S-13 Table S12. NEVPT2 excitation energies for QZV and QZVP S-15 Table S13. Excitation energies for Pr III Cl 3 QZVP and decontracted ANO-RCC S-17 Table S14. Effect of RI approximations on CASSCF excitation energies S-19 Table S15. Effect of RI approximations on NEVPT2 excitation energies S-22 Table S16. Effect of RI approximations on DFT bond energies S-24 Table S17 and S18. Basis pattern for the auxiliary basis sets S-26 References S-27 S-1

2 SAHF total energies of neutral atoms for QZV and UGBS+8 (ZORA) Table S1. Spin-average restricted open Hartree-Fock energies (Hartree) for the neutral ground state for different basis sets with the ZORA Hamiltonian. QZV UGBS+8 E Error E La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAD S-2

3 SAHF orbital eigenvalues for QZV (ZORA) Table S2. Mean absolute deviations for orbital energies (me h ) with respect to the large UGBS+8 basis set for the neutral lanthanide atoms at the CASSCF level (ZORA Hamiltonian). QZV 1s s 3.4 2p s 6.9 3p 4.4 4s 9.2 3d 3.5 4p 7.5 5s 1.6 4d 3.1 5p 2.2 6s 1.3 4f 1.6 S-3

4 Radial expectation values of innermost orbitals for QZV and SARC-TZV basis sets (DKH2) Table S3. Radial expectation values (in Bohr) of the innermost orbitals for each angular momentum from spin-average ROHF calculations for the 3+ oxidation state (DKH2 Hamiltonian). QZV SARC-TZV <r s> <r p> <r d> <r f> <r s> <r p> <r d> <r f> La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAE S-4

5 Radial expectation values of innermost orbitals for SARC-QZV and UGBS+8 (ZORA) Table S4. Radial expectation values of the innermost orbitals for each angular momentum from spin-average ROHF calculations for the 3+ oxidation state (in Bohr) (ZORA Hamiltonian) UGBS+8 QZV <r s> <r p> <r d> <r f> <r s> <r p> <r d> <r f> La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAE S-5

6 Ionization potentials for the QZV and UGBS+8 basis (ZORA) Table S5: First (IP1) to fourth (IP4) ionization potentials (in ev) calculated at the CASSCF level with the ZORA Hamiltonian. Mean absolute deviations of the SARC2 basis sets are given with respect to the reference values obtained with the large UGBS+8 basis set. IP1 IP2 QZV UGBS+8 QZV UGBS+8 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAD IP3 IP4 QZV UGBS+8 QZV UGBS+8 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAD S-6

7 Ionization potentials for the QZV and Cologne basis (DHK2) Table S6: First (IP1) to fourth (IP4) ionization potentials (in ev) calculated at the CASSCF level with the DKH2 Hamiltonian. Mean absolute deviations (MAD) of the two basis sets are given with respect to the UGBS+8 reference values of Table S5. Calculations with the Cologne basis set from Ref. 1 were performed here using the same settings as for the QZV calculations. IP1 IP2 QZV Cologne QZV Cologne La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAD IP3 IP4 QZV Cologne QZV Cologne La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MAD S-7

8 CASSCF excitation energies for the TZV and QZV basis (ZORA) Table S7: CASSCF excitation energies (cm -1 ) for the highest multiplicity terms of the lanthanide trivalent free ions (ZORA Hamiltonian). Pr TZV QZV UGBS+8 3 H F P Nd 4 I G F, 4 S D Pm 5 I G F, 5 S D Sm 6 H F P Dy 6 H F P Ho 5 I G F, 5 S D Er 4 I G F, 4 S D Tm 3 H F P MAD S-8

9 SOC parameter for the TZV and QZV basis (ZORA) Table S8: Spin-orbit coupling (SOC) ζ parameter (cm 1 ) for trivalent lanthanide ions (ZORA Hamiltonian). QZV UGBS+8 Ce Pr Nd Pm Sm Eu Tb Dy Ho Er Tm Yb MAD S-9

10 Optimized geometries of Ln III X 3 Table S9: PBE0 optimized bond distances and angles for the Ln III X 3 (X = F, Cl, Br, I) molecules using the QZV and Cologne basis sets. 1 To avoid any differences in numerical settings or basis sets for the halogen atoms, all geometries were optimized for both lanthanide basis sets with the exact same settings ( def2 basis sets for halides, no symmetry constraints). QZV Cologne Bond distance (Å) Bond Angle ( ) Bond distance (Å) Bond Angle ( ) La F Cl Br I Ce F Cl Br I Pr F Cl Br I Nd F Cl Br I Pm F Cl Br I Sm F Cl Br I Eu F Cl Br I Gd F Cl Br I S-10

11 Tb F Cl Br I Dy F Cl Br I Ho F Cl Br I Er F Cl Br I Tm F Cl Br I Yb F Cl Br I Lu F Cl Br I S-11

12 Calculated dipole moments Table S10: Calculated dipole moments (Debye) for several small molecules. Dipole moments were calculated using the BP86 functional 2,3 and the DKH2 Hamiltonian. Molecular geometries and reference basis were taken from Reference 4. Reference QZVP QZV Reference QZVP QZV CeF LuF CeF LuH CeH NdCl CeO NdF DyCl NdH DyF NdO DyF PmF ErCl PmH ErF PmO EuCl PrCl EuF PrF EuH PrH GdF SmCl GdF SmF GdF SmH GdH TbF HoF TmCl HoO TmF Lu 2 N YbCl LuF YbH LuF MAD S-12

13 CASSCF excitation energies for QZV and QZVP Table S11: CASSCF(n,7) excitation energies (cm 1 ) for the highest multiplicity terms of the Ln III Cl 3 models with the SARC-QZV and SARC-QZVP basis (DKH2 Hamiltonian). The maximum deviation was 84 cm 1 for a 1600 cm 1 excitation for Yb III Cl 3, with an average of 18.7 cm 1 (in percentages, the maximum deviation was 6.2% and the average 1.5%). QZV QZVP QZV QZVP QZV QZVP QZV QZVP Ce Eu Tb Yb Pr Sm 0 0 Dy Tm Nd Pm Ho Er S-13

14 S-14

15 NEVPT2 excitation energies for QZV and QZVP Table S12: NEVPT2 excitation energies (cm 1 ) for the highest multiplicity terms of the Ln III Cl 3 models with the SARC-QZV and SARC-QZVP basis (DKH2 Hamiltonian). The maximum deviation was 2412 cm -1 for a cm -1 excitation for Er III Cl 3, with an average of cm -1 (in percentage, the maximum was 43.1% and the average 5.2%). QZV QZVP QZV QZVP QZV QZVP QZV Ce Eu Tb Yb QZVP Pr Sm Dy Tm Nd Pm Ho Er S-15

16 S-16

17 Excitation energies for Pr III Cl 3 QZVP and decontracted ANO-RCC Table S13. Comparison of CASSCF and NEVPT2 excitation energies for QZVP and decontracted ANO-RCC basis set. The CASSCF(2,12) calculation considered both the 4d and 5d shells in the active space to model f-f and d-f excitations (56 roots, only triplets). QZVP+ANO(g,h) corresponds to the addition of all primitives of the g and h parts of the ANO-RCC basis to the full QZVP basis QZVP CASSCF ANO-RCC QZVP+ ANO(g,h) QZVP NEVPT2 ANO-RCC QZVP+ ANO(g,h) S-17

18 S-18

19 Effect of RI approximations on CASSCF excitation energies Table S14: CASSCF(n,7) excitation energies for Ln III Cl 3 models using the QZVP basis set (DKH2) in conjunction with the RI-JK and RIJCOSX approximations. The maximum deviation for RI-JK is 6.1 cm -1, with an average of 0.29 cm -1. The maximum deviation for RIJCOSX is 10.7 cm -1, with an average of 1.75 cm -1. NORI RI-JK RIJCOSX NORI RI-JK RIJCOSX Ce Tb Pr Dy Nd Ho S-19

20 Pm Er S-20

21 Sm Tm Eu Yb S-21

22 Effect of RI approximations on NEVPT2 excitation energies Table S15: NEVPT2 excitation energies for Ln III Cl 3 models using the QZVP basis set (DKH2) in conjunction with the RI-JK and RIJCOSX approximations. The maximum deviation for RI-JK is cm -1, with an average of 29.0 cm -1 (in percentage, the maximum deviation is 0.39% and the average is 0.18%). The maximum deviation for RIJCOSX is cm -1, with an average of 29.7 cm -1. NORI RI-JK RIJCOSX NORI RI-JK RIJCOSX Ce Tb Pr Dy Nd Ho S-22

23 Pm Er S-23

24 Sm Tm Eu Yb S-24

25 Effect of RI approximations on DFT bond energies Table S16: DFT calculated energy per bond for the process Ln III Cl 3 Ln III + 3 Cl -. The PBE0 functional was employed in conjunction with the Def2-TZVP//Def2- TZVP/JK basis for Cl (DHK2 Hamiltonian). QZVP//QZVP/JK QZV//QZV/JK NORI RI-JK NORI RI-JK La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu S-25

26 Basis pattern for the auxiliary basis sets Table S17: Number of primitive functions of each angular momentum for the auxiliary basis sets QZV/JK and QZVP/JK (DKH2) QZV/JK QZVP/JK L = La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Table S18: Number of primitive functions of each angular momentum for the auxiliary basis sets QZV/JK and QZVP/JK (ZORA) QZV/JK QZVP/JK L = La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu S-26

27 References (1) Dolg, M. J. Chem. Theory Comput. 2011, 7, (2) Becke, A. D. J. Chem. Phys. 1993, 98, (3) Perdew, J. P. Phys. Rev. B 1986, 33, (4) Gulde, R.; Pollak, P.; Weigend, F. J. Chem. Theory Comput. 2012, 8, S-27

Magnetism in low dimensions from first principles. Atomic magnetism. Gustav Bihlmayer. Gustav Bihlmayer

IFF 10 p. 1 Magnetism in low dimensions from first principles Atomic magnetism Gustav Bihlmayer Institut für Festkörperforschung, Quantum Theory of Materials Gustav Bihlmayer Institut für Festkörperforschung