Electronic structure and photoluminescence properties of Eu(η9-C9H9)2

(1)

Electronic Structure and Photoluminescence Properties of

Eu(

η

9

-C

9

H

9

)

2 Harry Ramanantoanina,*

,†

_{Lynda Merzoud,}

‡

_{Jules Tshishimbi Muya, Henry Chermette,*}

,‡

_{and Claude}

Daul*

,§

†_{Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland; E-mail: harry.ra@hotmail.com}

‡_{Université de Lyon; Université de Lyon 1, UMR CNRS 5280, Institut Sciences Analytiques, 5 rue de la Doua, 69100}

Villeurbanne, France; E-mail: henry.chermette@univ-lyon1.fr

Department of Chemistry, Faculty of Sciences, Kinshasa, DR Congo; Department of Chemistry, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea

§_{Department of Chemistry, University of Fribourg, CH-1700 Fribourg, Switzerland; E-mail: claude.daul@unifr.ch}

(2)

Table S1. Calculated geometrical parameters for Eu(η9-C9H9)2 in the ground Eu configuration 4f 7 within the D9d point group: bond distances (d in Å) and bond angles (A in deg.).

D

9d

LDA/TZ2P

PBE/TZ2P

PBE/TZ2P-D3(BJ)

B3LYP/TZ2P B3LYP/TZP

Good

Boost-Very-Good

Excellent

Very-Good

d(Eu-C) 2.779 2.887 2.887 2.875 2.956 2.953

d(C-H) 1.095 1.093 1.093 1.096 1.084 1.085

d(Eu-X) 1.888 2.025 2.026 2.009 2.131 2.125

d(C-X) 2.039 2.057 2.057 2.057 2.048 2.050

A(X-C-H) 176.6 177.1 177.1 176.8 177.7 177.5

Table S2. Calculated geometrical parameters for Eu(η9-C9H9)2 in the ground Eu configuration 4f 7 within the D9h point group: bond distances (d in Å) and bond angles (A in deg.).

D

9h

LDA/TZ2P

PBE/TZ2P

PBE/TZ2P-D3(BJ) B3LYP/TZ2P B3LYP/TZP

Good

Boost-Very-Good

Excellent

Boost-excellent Very-Good

Very-Good

d(Eu-C) 2.779 2.888 2.888 2.888 2.888 2.876 2.954 2.950

d(C-H) 1.095 1.093 1.093 1.093 1.093 1.093 1.084 1.085

d(Eu-X) 1.888 2.027 2.026 2.027 2.027 2.011 2.129 2.121

d(C-X) 2.039 2.057 2.057 2.057 2.057 2.057 2.048 2.050

(3)

Figure S1. The displacement vectors of the both lower frequencies 15cm-1 (left) and 50cm-1 (right) corresponding to the

(4)

Table S3. Calculated Slater-Condon integrals ( ) and spin-orbit coupling constant (ζ ) (in eV) for Eu2+_{configuration 4f}7_in

the free ion and Eu(η9_-C₉_H₉₎₂_{obtained from DFT using the LDA, PBE and B3LYP DFT functional.}

LDA PBE B3LYP

Free ion Eu(η9_-C

9H9)2 Free ion Eu(η9-C9H9)2 Free ion Eu(η9-C9H9)2 (4 , 4 ) 12.2962 9.7008 12.2785 10.2458 12.2137 10.4719 (4 , 4 ) 7.6303 6.0239 7.6190 6.3612 7.5774 6.4992 (4 , 4 ) 5.4656 4.3161 5.4575 4.5575 5.4273 4.6557 ζ 0.1610 0.1447 0.1604 0.1479 0.1585 0.1478

Table S4. Calculated ligand-field ( ) matrix elements (in eV) for the 4f electrons of Eu2+_{configuration 4f}7_{in Eu(}_η9_-C₉_H₉₎₂

with D9 symmetry obtained from DFT using the LDAPBE and B3LYP DFT functional. For clarity, non-zero matrix elements

are highlighted. LDA 4 4 4 4 4 4 4 |4 , -0.3683 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.1980 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.1089 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.1231 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.1089 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.1980 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3683 PBE 4 4 4 4 4 4 4 |4 , -0.2771 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.1426 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0898 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0897 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0898 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.1426 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2771 B3LYP 4 4 4 4 4 4 4 |4 , -0.1013 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0317 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0501 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0389 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0501 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0317 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1013

(5)

Table S5. Calculated Slater-Condon integrals ( and ), energy gap parameter (∆!"#) and spin-orbit coupling constant (ζ )

(in eV) for Eu2+_{configuration 4f}6_5d1_{in the free ion and Eu(}_η9_-C₉_H₉₎₂_{obtained from DFT using the LDA, PBE and B3LYP}

DFT functional.

LDA PBE B3LYP

Free ion Eu(η9_-C₉_H₉₎₂ _{Free ion} _Eu(_η9_-C₉_H₉₎₂ _{Free ion} _Eu(_η9_-C₉_H₉₎₂ (4 , 4 ) 13.1953 10.2288 13.1782 10.4472 13.0985 10.0889 (4 , 4 ) 8.2380 6.3689 8.2270 6.5053 8.1751 6.2793 (4 , 4 ) 5.9145 4.5679 5.9065 4.6659 5.8687 4.5030 (4 , 5%) 2.8803 2.2676 2.8538 2.2197 2.6649 2.1353 (4 , 5%) 1.4223 1.0247 1.4098 1.0295 1.3102 0.9960 (4 , 5%) 1.4871 1.1747 1.4770 1.1682 1.3872 1.1381 (4 , 5%) 1.1501 0.8351 1.1408 0.8438 1.0627 0.8208 (4 , 5%) 0.8631 0.6096 0.8559 0.6192 0.7951 0.6019 ∆E"# - 2.9511 - 2.7517 - 3.0898 ζ 0.1741 0.1514 0.1735 0.1524 0.1713 0.1480 ζ' 0.1176 0.0700 0.1149 0.0744 0.1036 0.0722

(6)

Table S6. Calculated ligand-field ( ) matrix elements (in eV) for the 4f electrons of Eu2+ configuration 4f65d1 in Eu(η9-C9H9)2 with D9 symmetry obtained from DFT using the LDA, PBE and

B3LYP DFT functional. For clarity, non-zero matrix elements are highlighted.

LDA 4 4 4 4 4 4 4 5% 5% 5% 5% 5% |4 , -0.1506 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.2797 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 -0.0723 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 -0.1138 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 -0.0723 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.2797 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1506 0.0000 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2184 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.3516 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -2.2665 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.3516 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2184 PBE 4 4 4 4 4 4 4 5% 5% 5% 5% 5% |4 , -0.0962 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.2209 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 -0.0608 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 -0.1279 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 -0.0608 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.2209 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0962 0.0000 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1612 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0892 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.8558 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0892 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1612

(7)

Table S6. (continued.) B3LYP 4 4 4 4 4 4 4 5% 5% 5% 5% 5% |4 , 0.0357 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 -0.0857 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0679 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 -0.0358 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0679 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0857 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 |4 , 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0357 0.0000 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1830 0.0000 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9682 0.0000 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.5706 0.0000 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9682 0.0000 |5%, 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1830

(8)

Figure S2. Graphical representations of the four totally symmetric (a1g) vibrational modes that are involved in the emission

spectrum through vibronic coupling.