Ab initio studies on the luminescence  of f-elements in solids Luis Seijo Departamento de Química Universidad Autónoma de ...
<ul><li>Context and motivation </li></ul><ul><li>Methodological details </li></ul><ul><li>Results </li></ul><ul><li>Conclu...
Context and motivation
Excited states of f-elements in solids Lanthanides: SSL  (Solid-State Lighting) Actinides: ANES  (Advanced Nuclear Energy ...
Divalent lanthanide ions in crystals <ul><li>Difficult to stabilize and to handle </li></ul><ul><ul><li>pioneering work in...
4f N-1 5d 1  in heavy lanthanides <ul><li>4f N   4f N-1 5d 1  excitations of Ln 3+ </li></ul><ul><ul><li>Low-intensity ba...
HS & LS interpretation challenged <ul><li>New Crystal-Field Theory calculations on old Yb 2+ :SrCl 2  experiments </li></u...
A quantum chemical point of view... <ul><li>Ab initio embedded cluster wave function based calculations  </li></ul><ul><li...
... and its goals <ul><li>What is the nature of the lowest states of the 4f 13 5d 1  configuration of Yb 2+ :CsCaBr 3 ? </...
Methodological details Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Methodological details <ul><li>YbBr 6 4-  cluster embedded in CsCaBr 3 </li></ul><ul><li>Wood-Boring based relativistic Ha...
An embedded-cluster model of Yb 2+ :CsCaBr 3   Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Embedding AIMP’s point-charge Coulomb (Madelung) finite-size Coulomb exchange linear-independence (Pauli) Ce  Pr  Nd  Pm  ...
YbBr 6 4-  cores + basis sets <ul><li>Wood-Boring based relativistic core AIMP’s </li></ul><ul><ul><li>Yb: [Kr]   4d,5s,5p...
YbBr 6 4-  calculations: step 1 (scalar) <ul><li>SA-CASSCF </li></ul><ul><ul><li>CAS: [4f,5d,6s] 14 14 e -  in 13 MO </li>...
YbBr 6 4-  calculations: step 2 (spin-orbit) <ul><li>sfss-SOCI </li></ul><ul><ul><li>Wood-Boring spin-orbit operator scale...
Programs <ul><li>Step 1:  </li></ul><ul><ul><li>MOLCAS (B.O.Roos, R. Lindh, et al., Lund) </li></ul></ul><ul><li>Step 2:  ...
Results Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Dynamic correlation effects SA-CASSCF MS-CASPT2 Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Nature of the lowest 4f 13 5d 1  states Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Spin-orbit coupling effects Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu  MS-CASPT2 sfss-SOCI 1 T 1u ED allowed...
States’ character. 4 f 13 [7/2]  5d(t 2g ) 1  manifold Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu  State 1A ...
Nature of the lowest 4f 13 5d 1  states of Yb 2+ :CsCaBr 3   <ul><li>The first of them (1T 2u ,1E u ) are  isolated  and a...
4f N-1 5d 1  HS and LS of heavy Ln 2+  in solids 4f N-1 5d 1 4f N Low-spin states Low-spin ground state gap spin-forbidden...
4f N-1 5d 1  HS and LS of heavy Ln 2+  in solids 4f N-1 5d 1 4f N Low-spin states Low-spin ground state gap spin-forbidden...
4f 13 5d(t 2g ) 1  manifold of Yb 2+ :CsCaBr 3   LS HS MS
4f  5d(t 2g ) ED-allowed absorption spectrum Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu  spin-forbidden  tra...
Lowest 5d(t 2g )  4f ED-allowed emission of Yb 2+ :CsCaBr 3   <ul><li>Experiment </li></ul><ul><ul><li>C. Wickleder, U. S...
Details of the whole 4f 13 5d 1  manifold. Several emissions? Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
4f 13 5d 1  and 4f 13 6s 1  manifolds of Yb 2+ :CsCaBr 3   Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu  MS-CAS...
Full 4f  5d ED-allowed absorption spectrum Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Potentially emitting levels Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Potentially emitting levels configuration level spin character gap calculation experiment transition HS 23900 128 spin-for...
Conclusions Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb   Lu
Conclusions <ul><li>The lowest state of the 4f N-1 5d 1  configuration of Yb 2+ :CsCaBr 3  is a  high-spin  state </li></u...
Acknowledgements <ul><li>Ministry of Science and Innovation, Spain, MAT2008-05379 </li></ul><ul><li>Universidad Autónoma d...
Dedicatory <ul><li>This paper is dedicated by Zoila Barandiarán and myself to our friend,  Professor Kimihiko Hirao , on t...
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Ab initio studies on the luminescence of f-elements in solids

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Lecture given at the conference: Simulations and Dynamics for Nanoscale and Byological Systems, held in Tokyo 2009, in honor of Professor Kimihiko Hirao

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Ab initio studies on the luminescence of f-elements in solids

  1. 1. Ab initio studies on the luminescence of f-elements in solids Luis Seijo Departamento de Química Universidad Autónoma de Madrid http://www.uam.es/quimica/aimp
  2. 2. <ul><li>Context and motivation </li></ul><ul><li>Methodological details </li></ul><ul><li>Results </li></ul><ul><li>Conclusions </li></ul><ul><li>Acknowledgments </li></ul>4f N-1 5d 1 manifold of heavy divalent lanthanides. Yb 2+ :CsCaBr 3 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  3. 3. Context and motivation
  4. 4. Excited states of f-elements in solids Lanthanides: SSL (Solid-State Lighting) Actinides: ANES (Advanced Nuclear Energy Systems) Design of phosphors Fundamental studies Fundamental studies Ce 3+ :Y 3 Al 5 O 12 U 4+ ,Pu 4+ :UO 2 ,PuO 2 Divalent lanthanides e.g. e.g. e.g.
  5. 5. Divalent lanthanide ions in crystals <ul><li>Difficult to stabilize and to handle </li></ul><ul><ul><li>pioneering work in 60’s (McClure) </li></ul></ul><ul><ul><li>most work on Sm 2+ , Eu 2+ , and Yb 2+ in cubic hosts </li></ul></ul><ul><li>Upsurge in interest since 2001 (phosphor search) </li></ul><ul><li>4f  5d excitations start at much lower energy than in Ln 3+ </li></ul><ul><ul><li>near-IR, visible, near-UV; 4f N-1 5d 1 states accessible </li></ul></ul><ul><li>Several meta-stable 4f N-1 5d 1 states seem to be possible </li></ul><ul><ul><li>several gaps </li></ul></ul><ul><ul><li>low vibration frequencies, low multi-phonon decays </li></ul></ul><ul><ul><li>multiple spontaneous emission </li></ul></ul><ul><ul><ul><li>Tm 2+ :CsCaBr 3 (Güdel, 2006) </li></ul></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  6. 6. 4f N-1 5d 1 in heavy lanthanides <ul><li>4f N  4f N-1 5d 1 excitations of Ln 3+ </li></ul><ul><ul><li>Low-intensity band on the low energy side for N>7 </li></ul></ul><ul><li>4f N-1 5d 1  4f N emissions of Ln 3+ </li></ul><ul><ul><li>Lowest energy: Slow, week </li></ul></ul><ul><ul><li>Next: Fast, strong </li></ul></ul><ul><li>Interpretation via Hund’s rule + spin </li></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu lowest energy, spin-forbidden highest energy, spin-allowed
  7. 7. HS & LS interpretation challenged <ul><li>New Crystal-Field Theory calculations on old Yb 2+ :SrCl 2 experiments </li></ul><ul><ul><li>McClure 1967: 4f  5d spectrum; 12 out of 18 absorptions </li></ul></ul><ul><ul><li>Loh 1973: CFT based interpretation; anomalies </li></ul></ul><ul><ul><li>Tanner 2008: New CFT interpretation (parameter cooking; reassignments) </li></ul></ul><ul><li>All the lowest 4f N-1 5d 1 states are HS </li></ul><ul><li>Their different orbital character is responsible for the high/low intensities </li></ul><ul><li>Energy separation between HS and LS states cannot be made by inspection of spectral data. It requires calculations. </li></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  8. 8. A quantum chemical point of view... <ul><li>Ab initio embedded cluster wave function based calculations </li></ul><ul><li>Yb 2+ :CsCaBr 3 </li></ul><ul><ul><li>4f 14 and 4f 13 5d 1 : the simplest heavy divalent lanthanide </li></ul></ul><ul><li>Two-step relativistic approach </li></ul><ul><ul><li>First step: scalar relativistic; accurate correlation; spin </li></ul></ul><ul><ul><li>Second step: spin-orbit coupling CI; superposition of spin multiplicities </li></ul></ul><ul><li>Collaborate with experiments </li></ul><ul><ul><li>Claudia Wickleder, Siegen (Germany) </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  9. 9. ... and its goals <ul><li>What is the nature of the lowest states of the 4f 13 5d 1 configuration of Yb 2+ :CsCaBr 3 ? </li></ul><ul><ul><li>spin character </li></ul></ul><ul><ul><li>orbital character </li></ul></ul><ul><li>Is the spin character or the orbital character of the lowest 4f 13 5d 1 states what molds their specific spectral features? </li></ul><ul><ul><li>How? </li></ul></ul><ul><li>What are the details of the whole 4f 13 5d 1 manifold? </li></ul><ul><li>Are several spontaneous emissions possible in this material? </li></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  10. 10. Methodological details Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  11. 11. Methodological details <ul><li>YbBr 6 4- cluster embedded in CsCaBr 3 </li></ul><ul><li>Wood-Boring based relativistic Hamiltonian </li></ul><ul><li>Two-step wave function based procedure </li></ul><ul><ul><li>scalar: SA-CASSCF + MS-CASPT2 </li></ul></ul><ul><ul><li>spin-orbit: sfss-SOCI(S) </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  12. 12. An embedded-cluster model of Yb 2+ :CsCaBr 3 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  13. 13. Embedding AIMP’s point-charge Coulomb (Madelung) finite-size Coulomb exchange linear-independence (Pauli) Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Out of self- c onsistent HF embedded-ions calculations on the undoped solid MOLCAS MakeAIMP SCEI
  14. 14. YbBr 6 4- cores + basis sets <ul><li>Wood-Boring based relativistic core AIMP’s </li></ul><ul><ul><li>Yb: [Kr] 4d,5s,5p,4f,5d,6s </li></ul></ul><ul><ul><li>Br: [Ar,3d] 4s,4p </li></ul></ul><ul><li>Gaussian valence basis sets </li></ul><ul><ul><li>Yb: (14s10p10d8f3g)/[6s5p6d4f1g] </li></ul></ul><ul><ul><li>Br: (9s9p4d)/[3s5p2d] </li></ul></ul><ul><ul><li>Ca sites: (10s7p)/[1s1p] </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Out of relativistic Cowan-Griffin-Wood-Boring-HF all-electron atomic calculations MCHF72 MakeAIMP AtBaSets
  15. 15. YbBr 6 4- calculations: step 1 (scalar) <ul><li>SA-CASSCF </li></ul><ul><ul><li>CAS: [4f,5d,6s] 14 14 e - in 13 MO </li></ul></ul><ul><ul><ul><li>4f: a 2u , t 1u , t 2u ; 5d: t 2g , e g ; 6s: a 1g </li></ul></ul></ul><ul><ul><li>SA: 4f 14 - 1 A 1g ; <4f 13 (5d,6s) 1 - 1  u > <4f 13 (5d,6s) 1 - 3  u > </li></ul></ul><ul><ul><li> 10 5 conf. </li></ul></ul><ul><li>MS-CASPT2 </li></ul><ul><ul><li>PT2: Yb 4d,5s,5p,4f,5d/6s + Br 4s,4p 80 e - </li></ul></ul><ul><ul><li>MS: as in SA </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  16. 16. YbBr 6 4- calculations: step 2 (spin-orbit) <ul><li>sfss-SOCI </li></ul><ul><ul><li>Wood-Boring spin-orbit operator scaled by 0.9 </li></ul></ul><ul><ul><li>Basis of double-group adapted CSFs </li></ul></ul><ul><ul><li>MRCI(S) </li></ul></ul><ul><ul><ul><li>MR is RAS 4f 13 (5d,6s) 1 </li></ul></ul></ul><ul><ul><ul><li>Single excitations from open-shell MOs </li></ul></ul></ul><ul><ul><li>Spin-free state shifting </li></ul></ul><ul><ul><ul><li>MRCI(S) energies without spin-orbit are MS-CASPT2 energies </li></ul></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Out of embedded-cluster calculations with the spin-orbit free Hamiltonian MCHF72 COLUMBUS EPCISO
  17. 17. Programs <ul><li>Step 1: </li></ul><ul><ul><li>MOLCAS (B.O.Roos, R. Lindh, et al., Lund) </li></ul></ul><ul><li>Step 2: </li></ul><ul><ul><li>COLUMBUS (R. M. Pitzer et al., Ohio) </li></ul></ul><ul><ul><li>EPCISO (V. Vallet and J.-P. Flament, Lille) </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  18. 18. Results Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  19. 19. Dynamic correlation effects SA-CASSCF MS-CASPT2 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  20. 20. Nature of the lowest 4f 13 5d 1 states Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  21. 21. Spin-orbit coupling effects Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MS-CASPT2 sfss-SOCI 1 T 1u ED allowed T 1u ED forbidden Low-spin? High-spin?
  22. 22. States’ character. 4 f 13 [7/2]  5d(t 2g ) 1 manifold Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu State 1A 1g  f  10 2 Term analysis (%) 3 T 1u 3 T 2u 3 E u 3 A 1u 1 T 1u 1 T 2u 1 E u 1 2 3 1 2 1 2 1 1 2 3 1 1 1T 2u 23890 90 1E u 23900 90 6 1T 1u 26560 0.273 9 38 12 34 2T 1u 26600 1.260 32 12 6 14 7 15 10 2T 2u 26720 22 10 32 34 ... 3T 1u 27200 0.030 24 12 9 4 1 45 ... 4T 1u 28360 0.000 32 47 9 ... 5T 1u 29070 0.084 6 16 12 21 8 28 ... 6T 1u 29880 0.489 5 43 5 39 4 2
  23. 23. Nature of the lowest 4f 13 5d 1 states of Yb 2+ :CsCaBr 3 <ul><li>The first of them (1T 2u ,1E u ) are isolated and almost pure high-spin states (S=1) </li></ul><ul><ul><li>in agreement with Hund’s rule </li></ul></ul><ul><ul><li>transitions from and to GS ( 1 A 1g ) can be labeled spin-forbidden </li></ul></ul><ul><li>Then, there is a gap </li></ul><ul><ul><li>of around 2500 cm -1 </li></ul></ul><ul><li>The next are a bunch of mixed-spin states (65% of high-spin terms) </li></ul><ul><ul><li>spin-orbit coupling breaks HS/LS partition </li></ul></ul><ul><ul><li>strong mixture results from quasidegeneracies due to f-d spin-pairing and f-f redistribution energies being similar </li></ul></ul><ul><li>Some, with a contribution of spin-enabling character (35% 1 T 1u ) </li></ul><ul><ul><li>which provides intensity to their absorption/emission transitions, which could be labeled spin-enabled </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  24. 24. 4f N-1 5d 1 HS and LS of heavy Ln 2+ in solids 4f N-1 5d 1 4f N Low-spin states Low-spin ground state gap spin-forbidden spin-allowed High-spin states Bunch of mixed-spin states Low-spin ground state gap spin-forbidden spin-enabled Isolated  pure high-spin states Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  25. 25. 4f N-1 5d 1 HS and LS of heavy Ln 2+ in solids 4f N-1 5d 1 4f N Low-spin states Low-spin ground state gap spin-forbidden spin-allowed High-spin states Bunch of mixed-spin states Low-spin ground state gap spin-forbidden spin-enabled Isolated  pure high-spin states Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  26. 26. 4f 13 5d(t 2g ) 1 manifold of Yb 2+ :CsCaBr 3 LS HS MS
  27. 27. 4f  5d(t 2g ) ED-allowed absorption spectrum Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu spin-forbidden transitions to high-spin states Intensity (arbitrary units) spin-enabled transitions to mixed-spin states
  28. 28. Lowest 5d(t 2g )  4f ED-allowed emission of Yb 2+ :CsCaBr 3 <ul><li>Experiment </li></ul><ul><ul><li>C. Wickleder, U. Siegen </li></ul></ul><ul><ul><li>77 K </li></ul></ul><ul><li>Calculation </li></ul><ul><ul><li>assignments </li></ul></ul><ul><ul><li>2000 cm -1 too high (8%) </li></ul></ul><ul><ul><li>200 cm -1 too narrow (20%) </li></ul></ul><ul><ul><li>HS/MS gap 900 cm -1 too wide (50%) </li></ul></ul>25000 24000 23000 22000 27000 26000 25000 24000 Energy (cm -1 ) HS MS
  29. 29. Details of the whole 4f 13 5d 1 manifold. Several emissions? Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  30. 30. 4f 13 5d 1 and 4f 13 6s 1 manifolds of Yb 2+ :CsCaBr 3 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu MS-CASPT2 sfss-SOCI without spin-orbit with spin-orbit
  31. 31. Full 4f  5d ED-allowed absorption spectrum Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  32. 32. Potentially emitting levels Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  33. 33. Potentially emitting levels configuration level spin character gap calculation experiment transition HS 23900 128 spin-forbidden 23900 23000 MS 2600 13 spin-enabled 26500 24500 HS 4600 24 spin-forbidden 34600 HS 4000 22 spin-forbidden 43900 HS 5200 30 spin-forbidden 53900 in CB
  34. 34. Conclusions Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  35. 35. Conclusions <ul><li>The lowest state of the 4f N-1 5d 1 configuration of Yb 2+ :CsCaBr 3 is a high-spin state </li></ul><ul><ul><li>Emission to the low-spin ground state is spin-forbidden (as well as the corresponding absorption) </li></ul></ul><ul><li>After a gap, a bunch of mixed-spin states exist </li></ul><ul><ul><li>Emissions from some of them to the ground state are spin-enabled (as well as the corresponding absorptions) </li></ul></ul><ul><li>These conclusions are expected to be transferred to all heavy divalent lanthanides </li></ul><ul><li>The whole 4f N-1 5d 1 manifold has been calculated </li></ul><ul><ul><li>The lowest emissions compare reasonably well with experiment </li></ul></ul><ul><ul><li>Two additional potentially emitting levels are predicted </li></ul></ul><ul><ul><li>A third meta-stable level (of significant 6s character) is predicted to be immerse in the conduction band of the host </li></ul></ul>Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
  36. 36. Acknowledgements <ul><li>Ministry of Science and Innovation, Spain, MAT2008-05379 </li></ul><ul><li>Universidad Autónoma de Madrid </li></ul>Goar Sánchez José Luis Pascual Ana Belén Muñoz Noèmi Barros
  37. 37. Dedicatory <ul><li>This paper is dedicated by Zoila Barandiarán and myself to our friend, Professor Kimihiko Hirao , on the occasion of his retirement. </li></ul><ul><li>In this way, we express our special admiration of him as a scientist and as a person. </li></ul>

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