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

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

Luis Seijo

Departamento de QuímicaUniversidad Autónoma de Madrid

http://www.uam.es/quimica/aimp

http://www.uam.es/

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Simulations and Dynamics for Nanoscale and Biological Systems, Tokyo 09. In honor of Prof. K. Hirao

• Context and motivationContext and motivation• Methodological detailsMethodological details• ResultsResults• ConclusionsConclusions• AcknowledgmentsAcknowledgments

2 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

4f4fN-1N-15d5d11 manifold manifold of heavy divalent lanthanides. of heavy divalent lanthanides.

YbYb2+2+:CsCaBr:CsCaBr33

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Context and motivationContext and motivation

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Excited states of f-elements in solidsExcited states of f-elements in solids

Lanthanides: SSL Lanthanides: SSL (Solid-State Lighting)

Actinides: ANES Actinides: ANES (Advanced Nuclear Energy Systems)

Design of phosphorsDesign of phosphors

Fundamental studiesFundamental studies

Fundamental studiesFundamental studies

CeCe3+3+:Y:Y33AlAl55OO1212

UU4+4+,Pu,Pu4+4+:UO:UO22,PuO,PuO22

Divalent lanthanidesDivalent lanthanides

4

e.g.

e.g.

e.g.

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Divalent lanthanide ions in crystalsDivalent lanthanide ions in crystals

• Difficult to stabilize and to handleDifficult to stabilize and to handle– pioneering work in 60’s (McClure)pioneering work in 60’s (McClure)– most work on Smmost work on Sm2+2+, Eu, Eu2+2+, and Yb, and Yb2+2+ in cubic hosts in cubic hosts

• Upsurge in interest since 2001 (phosphor search)Upsurge in interest since 2001 (phosphor search)• 4f4f5d excitations start at much lower energy than 5d excitations start at much lower energy than

in Lnin Ln3+3+

– near-IR, visible, near-UV; 4fnear-IR, visible, near-UV; 4fN-1N-15d5d11 states accessible states accessible• Several meta-stable 4fSeveral meta-stable 4fN-1N-15d5d11 states seem to be states seem to be

possiblepossible– several gapsseveral gaps– low vibration frequencies, low multi-phonon decayslow vibration frequencies, low multi-phonon decays– multiple spontaneous emissionmultiple spontaneous emission

• TmTm2+2+:CsCaBr:CsCaBr33 (Güdel, 2006) (Güdel, 2006)


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4f4fN-1N-15d5d11 in heavy lanthanides in heavy lanthanides

• 4f4fNN 4f 4fN-1N-15d5d11 excitations of Ln excitations of Ln3+3+

– Low-intensity band on the low energy side Low-intensity band on the low energy side for N>7for N>7

• 4f4fN-1N-15d5d11 4f 4fNN emissions of Ln emissions of Ln3+3+

– Lowest energy: Slow, weekLowest energy: Slow, week– Next: Fast, strong Next: Fast, strong

• Interpretation via Hund’s rule + spinInterpretation via Hund’s rule + spin


lowest energy, spin-forbiddenspin-forbiddenhighest energy, spin-allowedspin-allowed

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HS & LS interpretation challengedHS & LS interpretation challenged

• New Crystal-Field Theory calculations on old YbNew Crystal-Field Theory calculations on old Yb2+2+:SrCl:SrCl22 experimentsexperiments– McClure 1967: 4fMcClure 1967: 4f5d spectrum; 12 out of 18 absorptions5d spectrum; 12 out of 18 absorptions– Loh 1973: CFT based interpretation; anomalies Loh 1973: CFT based interpretation; anomalies – Tanner 2008: New CFT interpretation (parameter cooking; Tanner 2008: New CFT interpretation (parameter cooking;

reassignments)reassignments)• All the lowest 4fAll the lowest 4fN-1N-15d5d1 1 states are HSstates are HS• Their different Their different orbital character orbital character is responsible for is responsible for

the high/low intensitiesthe high/low intensities• Energy separation between HS and LS states cannot Energy separation between HS and LS states cannot

be made by inspection of spectral data. It requires be made by inspection of spectral data. It requires calculations.calculations.


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A quantum chemical point of view...A quantum chemical point of view...

• Ab initio embedded cluster wave function based Ab initio embedded cluster wave function based calculations calculations

• YbYb2+2+:CsCaBr:CsCaBr33 – 4f4f1414 and 4f and 4f13135d5d11: the simplest heavy divalent lanthanide : the simplest heavy divalent lanthanide

• Two-step relativistic approachTwo-step relativistic approach– First step: scalar relativistic; accurate correlation; First step: scalar relativistic; accurate correlation; spinspin– Second step: spin-orbit coupling CI; Second step: spin-orbit coupling CI; superpositionsuperposition of spin of spin

multiplicities multiplicities • Collaborate with experimentsCollaborate with experiments

– Claudia Wickleder, Siegen (Germany)Claudia Wickleder, Siegen (Germany)


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... and its goals... and its goals

• What is the nature of the lowest states of the 4fWhat is the nature of the lowest states of the 4f13135d5d11 configuration of Ybconfiguration of Yb2+2+:CsCaBr:CsCaBr33??– spin characterspin character– orbital characterorbital character

• Is the spin character or the orbital character of the Is the spin character or the orbital character of the lowest 4flowest 4f13135d5d1 1 states what molds their specific spectral states what molds their specific spectral features?features?– How?How?

• What are the details of the whole 4fWhat are the details of the whole 4f13135d5d11 manifold? manifold?• Are several spontaneous emissions possible in this Are several spontaneous emissions possible in this

material?material?


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Methodological detailsMethodological details

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

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Methodological detailsMethodological details

• YbBrYbBr664-4- cluster embedded in CsCaBr cluster embedded in CsCaBr33

• Wood-Boring based relativistic HamiltonianWood-Boring based relativistic Hamiltonian• Two-step wave function based procedureTwo-step wave function based procedure

– scalar: SA-CASSCF + MS-CASPT2scalar: SA-CASSCF + MS-CASPT2– spin-orbit: sfss-SOCI(S) spin-orbit: sfss-SOCI(S)


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An embedded-cluster model of YbAn embedded-cluster model of Yb2+2+:CsCaBr:CsCaBr33

12

4 4

6 63:YbBr CsCaBr YbBrH H

221

( ) ( ) ( )Nelec Lattice Lattice Lattice

AIMP AIMP AIMPCs Ca Br

i Cs Ca Br

i i iV V V


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Embedding AIMP’sEmbedding AIMP’s

13

( 1)

ir

( )AIMPBr

iV

2rk ikk

i

C er

,i i j ji jA

occ.orb. ( 2 )c c cc

point-charge Coulomb (Madelung)

finite-size Coulomb

exchange

linear-independence (Pauli)

Out of self-Out of self-consistent HF embeddedonsistent HF embedded--ions calculations on the undoped ions calculations on the undoped solidsolid MOLCASMOLCAS MakeAIMPMakeAIMP SCEISCEI


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YbBrYbBr664-4- cores + basis sets cores + basis sets

• Wood-Boring based relativistic core AIMP’sWood-Boring based relativistic core AIMP’s– Yb:Yb: [Kr][Kr] 4d,5s,5p,4f,5d,6s4d,5s,5p,4f,5d,6s– Br:Br: [Ar,3d][Ar,3d] 4s,4p4s,4p

• Gaussian valence basis setsGaussian valence basis sets– Yb:Yb: (14s10p10d8f3g)/[6s5p6d4f1g](14s10p10d8f3g)/[6s5p6d4f1g]– Br:Br: (9s9p4d)/[3s5p2d](9s9p4d)/[3s5p2d]– Ca sites:Ca sites: (10s7p)/[1s1p](10s7p)/[1s1p]

14

Out of relativistic Cowan-Griffin-WoodOut of relativistic Cowan-Griffin-Wood-Boring-HF all-electron atomic -Boring-HF all-electron atomic calculationscalculationsMCHF72MCHF72 MakeAIMPMakeAIMP AtBaSetsAtBaSets


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YbBrYbBr664-4- calculations: step 1 (scalar) calculations: step 1 (scalar)

• SA-CASSCFSA-CASSCF– CAS:CAS: [4f,5d,6s][4f,5d,6s]1414 14 e14 e-- in 13 MO in 13 MO

4f: a4f: a2u2u, t, t1u1u, t, t2u2u ; 5d: t; 5d: t2g2g, e, egg; 6s: a; 6s: a1g1g

– SA:SA: 4f4f1414--11AA1g1g; ; <4f<4f1313(5d,6s)(5d,6s)11--11uu> > <4f<4f1313(5d,6s)(5d,6s)11--33uu>> 101055 conf. conf.

• MS-CASPT2MS-CASPT2– PT2:PT2: Yb 4d,5s,5p,4f,5d/6s + Br 4s,4pYb 4d,5s,5p,4f,5d/6s + Br 4s,4p 80 e80 e--

– MS:MS: as in SAas in SA


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YbBrYbBr664-4- calculations: step 2 (spin-orbit) calculations: step 2 (spin-orbit)

• sfss-SOCIsfss-SOCI– Wood-Boring spin-orbit operator scaled by 0.9Wood-Boring spin-orbit operator scaled by 0.9– Basis of double-group adapted CSFsBasis of double-group adapted CSFs– MRCI(S)MRCI(S)

• MR is RAS 4fMR is RAS 4f1313(5d,6s)(5d,6s)11

• Single excitations from open-shell MOsSingle excitations from open-shell MOs– Spin-free state shiftingSpin-free state shifting

• MRCI(S) energies without spin-orbit are MS-CASPT2 energiesMRCI(S) energies without spin-orbit are MS-CASPT2 energies

16

Out of embedded-clusterOut of embedded-cluster calculations with the spin-orbit free calculations with the spin-orbit free HamiltonianHamiltonianMCHF72MCHF72 COLUMBUSCOLUMBUS EPCISOEPCISO


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ProgramsPrograms

• Step 1: Step 1: – MOLCAS (B.O.Roos, R. Lindh, et al., Lund)MOLCAS (B.O.Roos, R. Lindh, et al., Lund)

• Step 2: Step 2: – COLUMBUS (R. M. Pitzer et al., Ohio)COLUMBUS (R. M. Pitzer et al., Ohio)– EPCISO (V. Vallet and J.-P. Flament, Lille)EPCISO (V. Vallet and J.-P. Flament, Lille)


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ResultsResults


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Dynamic correlation effectsDynamic correlation effects

19

SA-CASSCF MS-CASPT2


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Nature of the lowest 4fNature of the lowest 4f13135d5d11 states states


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Spin-orbit coupling effectsSpin-orbit coupling effects


MS-CASPT2 sfss-SOCI

1T1u

ED allowedT1u

ED forbidden Low-spin?High-spin?

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States’ character. 4States’ character. 4ff1313[7/2][7/2]5d(t5d(t2g2g))11 manifold manifold

22

State 1A1g f102 Term analysis (%)3T1u

3T2u3Eu

3A1u1T1u

1T2u1Eu

1 2 3 1 2 1 2 1 1 2 3 1 11T2u 23890 90

1Eu 23900 90 6

1T1u 26560 0.273 9 38 12 34

2T1u 26600 1.260 32 12 6 14 7 15 10

2T2u 26720 22 10 32 34...

3T1u 27200 0.030 24 12 9 4 1 45...

4T1u 28360 0.000 32 47 9...

5T1u 29070 0.084 6 16 12 21 8 28...

6T1u 29880 0.489 5 43 5 39 4 2 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

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Nature of the lowest 4fNature of the lowest 4f13135d5d11 states of states of YbYb2+2+:CsCaBr:CsCaBr33

• The first of them (1TThe first of them (1T2u2u,1E,1Euu) are ) are isolatedisolated and almost and almost pure high-spin pure high-spin statesstates (S=1) (S=1)– in agreement with Hund’s rulein agreement with Hund’s rule– transitions from and to GS (transitions from and to GS (11AA1g1g) can be labeled ) can be labeled spin-forbiddenspin-forbidden

• Then, there is a gap Then, there is a gap – of around 2500 cmof around 2500 cm-1-1

• The next are a bunch of The next are a bunch of mixed-spin statesmixed-spin states (65% of high-spin (65% of high-spin terms)terms)– spin-orbit coupling breaks HS/LS partitionspin-orbit coupling breaks HS/LS partition– strong mixture results from quasidegeneracies due to f-d spin-pairing strong mixture results from quasidegeneracies due to f-d spin-pairing

and f-f redistribution energies being similarand f-f redistribution energies being similar• Some, with a contribution of spin-enabling character (35% Some, with a contribution of spin-enabling character (35% 11TT1u1u))

– which provides intensity to their absorption/emission transitions, which provides intensity to their absorption/emission transitions, which could be labeled which could be labeled spin-enabledspin-enabled


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4f4fN-1N-15d5d11 HS and LS of heavy Ln HS and LS of heavy Ln2+2+ in solids in solids

24

4f4fN-1N-15d5d11

4f4fNN

Low-spin statesLow-spin states

Low-spin ground stateLow-spin ground state

gapgap

spin-forbiddenspin-forbiddenspin-allowedspin-allowed

High-spin statesHigh-spin states

Bunch of mixed-spin statesBunch of mixed-spin states


gapgap

spin-forbiddenspin-forbiddenspin-enabledspin-enabled

Isolated Isolated pure high-spin statespure high-spin states


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4f4fN-1N-15d5d11 HS and LS of heavy Ln HS and LS of heavy Ln2+2+ in solids in solids

25

4f4fN-1N-15d5d11

4f4fNN

Low-spin statesLow-spin states


gapgap

spin-forbiddenspin-forbiddenspin-allowedspin-allowed

High-spin statesHigh-spin states

Bunch of mixed-spin statesBunch of mixed-spin states


gapgap

spin-forbiddenspin-forbiddenspin-enabledspin-enabled

Isolated Isolated pure high-spin statespure high-spin states


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4f4f13135d(t5d(t2g2g))11 manifold of Yb manifold of Yb2+2+:CsCaBr:CsCaBr33

26

LS

HS

MS

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4f4f5d(t5d(t2g2g) ED-allowed absorption spectrum) ED-allowed absorption spectrum


spin-forbidden spin-forbidden transitions to

high-spin stateshigh-spin statesInte

nsity

(arb

itrar

y un

its)

spin-enabled spin-enabled transitions to

mixed-spin statesmixed-spin states

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Lowest 5d(tLowest 5d(t2g2g))4f ED-allowed emission of 4f ED-allowed emission of YbYb2+2+:CsCaBr:CsCaBr33

• ExperimentExperiment– C. Wickleder, U. SiegenC. Wickleder, U. Siegen– 77 K77 K

• CalculationCalculation– assignmentsassignments– 2000 cm2000 cm-1-1 too high (8%) too high (8%)– 200 cm200 cm-1-1 too narrow (20%) too narrow (20%)– HS/MS gap 900 cmHS/MS gap 900 cm-1-1 too wide too wide

(50%)(50%)

28

25000240002300022000

27000260002500024000Energy (cm-1)

2

13 1

141

(7 / 2) ( )4 5

4 1g

g

tf d

f A

21 ,1u uT E

11,2 uT

HS

MS

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Details of the whole 4fDetails of the whole 4f13135d5d11 manifold. manifold.Several emissions?Several emissions?


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4f4f13135d5d11 and 4f and 4f13136s6s11 manifolds of Yb manifolds of Yb2+2+:CsCaBr:CsCaBr33


MS-CASPT2 sfss-SOCIwithout spin-orbit with spin-orbit

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Full 4fFull 4f5d ED-allowed absorption spectrum5d ED-allowed absorption spectrum


27 / 2, gt 25 / 2, gt

7 / 2, ge

5 / 2, 7 / 2,ge s

5 / 2, ge

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Potentially emitting levelsPotentially emitting levels


27 / 2, gt 25 / 2, gt

7 / 2, ge

5 / 2, 7 / 2,ge s

5 / 2, ge

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Potentially emitting levelsPotentially emitting levels

33

configuration levelspin

charactergap calculation experimenttransition

27 / 2, gt 21 ,1u uT E HS23900 128 spin-forbidden 23900 23000max

gap

27 / 2, gt 11,2 uT MS2600 13 spin-enabled 26500 24500

25 / 2, gt 13 uA HS4600 24 spin-forbidden 346007 / 2, ge 8 uE HS4000 22 spin-forbidden 439005 / 2, ge 16 uA HS5200 30 spin-forbidden 53900 in CB

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ConclusionsConclusions


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ConclusionsConclusions

• The lowest state of the 4fThe lowest state of the 4fN-1N-15d5d11 configuration of Yb configuration of Yb2+2+:CsCaBr:CsCaBr33 is a is a high-spinhigh-spin state state– Emission to the low-spin ground state is Emission to the low-spin ground state is spin-forbiddenspin-forbidden (as well as the (as well as the

corresponding absorption)corresponding absorption)• After a gap, a bunch of After a gap, a bunch of mixed-spinmixed-spin states exist states exist

– Emissions from some of them to the ground state are Emissions from some of them to the ground state are spin-enabledspin-enabled (as well as the corresponding absorptions) (as well as the corresponding absorptions)

• These conclusions are expected to be transferred to all heavy These conclusions are expected to be transferred to all heavy divalent lanthanidesdivalent lanthanides

• The whole 4fThe whole 4fN-1N-15d5d11 manifold has been calculated manifold has been calculated– The lowest emissions compare reasonably well with experimentThe lowest emissions compare reasonably well with experiment– Two additional potentially emitting levels Two additional potentially emitting levels are predicted are predicted – A third meta-stable level (of significant 6s character) is predicted to be A third meta-stable level (of significant 6s character) is predicted to be

immerse in the conduction band of the host immerse in the conduction band of the host


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AcknowledgementsAcknowledgements

• Ministry of Science and Innovation, Spain, MAT2008-05379Ministry of Science and Innovation, Spain, MAT2008-05379• Universidad Autónoma de MadridUniversidad Autónoma de Madrid

36

Goar Sánchez

Goar Sánchez

José Luis Pascual

José Luis Pascual

Ana Belén Muñoz

Ana Belén Muñoz

Noèmi Barros

Noèmi Barros

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DedicatoryDedicatory

This paper is dedicated by Zoila Barandiarán and myself to This paper is dedicated by Zoila Barandiarán and myself to our friend, our friend, Professor Kimihiko HiraoProfessor Kimihiko Hirao, on the occasion of his , on the occasion of his retirement. retirement. In this way, we express our special admiration of him as a In this way, we express our special admiration of him as a scientist and as a person. scientist and as a person.

37

Technology

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