First-principles study of electronic structure of Ce3+ centers in alkaline-

earth fluorides including spin-orbit and scalar relativistic effects.

N.V. Popov, A.S.Mysovsky, E.A.Radzhabov

National Research Irkutsk State Technical

University (NR ISTU), Irkutsk, 83 Lermontov street

A.P. Vinogradov Institute of Geochemistry SB RAS,

Irkutsk, 1a Favorsky St.

Introduction

Due to the fast 5d → 4f emission of Ce3+ in the blue and UV spectralregions cerium-doped compounds(Ce3+ in CaF2,SrF2) have considerableinterest in application of scintillators and solid state lasers.

Picture of 4f-5d transitions state depend strongly on the local crystallineenvironment of the dopant Ce3+, due to the large crystal-field interactionexperienced by the 5d electron.

ProblemOur purpose is to study electronic structure and optical transitions incrystal-defect systems (CaF2, SrF2) using embedding quantum clusterformalism, including scalar and spin-orbit effects.

Calculation details

● We developed a set of utilities for embedded quantum cluster calculation, including:

– embedding.exe — calculating classical gradient and energies– optimus_lbfgs.exe — “glue” for our classical code and third-

party quantum chemistry package, it performs geometry optimization in a combined QM/MM fashion

– Pre- and postrpocessing tools, scripts

● As a “calculator” we use Molcas 7.8

[1] http://www.chokkan.org/software/liblbfgs/

● We used 2-th order Douglas-Kroll-Hess method to includescalar relativistic effects

● Basis set - ANO Relativistic core correction full electron basis(B.O. Roos, V. Veryazov and P.-O. Widmark)

● Non-quantum cluster atoms were described by Ab initio modelpotential (AIMPs)

● For large-scale nonlinear optimization problem we use LimitedMemory Broyden-Flebsche-Gordano (aka L-BFGS)[1]

● Restricted Active Space State Interaction (RASSI) for accountingfor spin-orbit effects

Quantum cluster

Point charges, pair potentials & AIMPs; geometry opt. available

Fixed point charges

Ce3+ cubic centre

“Cubic” Ce3+ centre

Due to asymmetric charge localizationgeometry optimization brings structure tothe lower symmetry.Symmetry breaks from Oh to D4h!

F-

Ce3+

CeF8 clusterCaF2

X, Å Y, Å Z, Å

1.38 1.38 1.38

ΔX, Å ΔY, Å ΔZ, Å

-0.043 -0.043 0.024

SrF2

X, Å Y, Å Z, Å

1.47 1.47 1.47

ΔX, Å ΔY, Å ΔZ, Å

-0.095 -0.095 -0.026

Ce3+ 4f orbitals (“cubic” centre)

Eu

ε=-0.5351 a.u.Eu

ε=-0.5351 a.u.A2u

ε=-0.5351 a.u.Eu

ε=-0.5334 a.u

Eu

ε=-0.5334 a.uB1u

ε=-0.5334 a.uB1u

ε=-0.5259 a.u.

Eg

ε=-0.5064 a.u.Eg

ε=-0.5064 a.u.B2g

ε=-0.5064 a.u.

B1g

ε=-0.3901 a.uA1g

ε=-0.3901 a.u

Ce3+ 5d orbitals (“cubic” centre)

CAS states of CaF2:Ce3+

Without spin-orbit coupling With spin-orbit coupling

SF State

Symm. State energy(eV)

State energy (cm-1)

1 Eu 0.00 0.02 Eu 0.00 2.33 ? 0.02 147.54 ? 0.03 258.95 Eu 0.04 284.16 Eu 0.04 285.97 B1u 0.30 2411.38 ? 3.91 31526.39 ? 4.09 33027.9

10 ? 6.73 54293.511 Eg 7.07 57015.512 Eg 7.07 57017.3

SF State

State energy (eV)

State energy (cm-1)

1 0.00 0.02 0.02 199.83 0.08 617.94 0.28 2223.05 0.30 2451.66 0.31 2476.07 0.51 4081.78 4.05 32698.79 4.24 34199.0

10 6.87 55406.511 7.16 57751.412 7.32 59010.2

Note: 4f orbitals, 5d orbitals, each SOC state is doubly degenerate

SrF2:CeF8 relaxed «Oh» ciEnergy Levels

Without spin-orbit coupling With spin-orbit coupling

SF State

State Energy(a.u)

Rel lowest level(eV)

D:o,cm^(-1)

1 -803.94530534 0.000000 0.0002 -803.94529314 0.000332 2.6763 -803.94464855 0.017872 144.1484 -803.94427790 0.027958 225.4975 -803.94415992 0.031168 251.3896 -803.94415282 0.031361 252.9477 -803.93629335 0.245229 1977.9028 -803.79439250 4.106547 33121.5389 -803.78825812 4.273472 34467.880

10 -803.70622350 6.505748 52472.39811 -803.69535003 6.801630 54858.84912 -803.69534627 6.801732 54859.675

SF State

State Energy(a.u)

Rel lowest level(eV)

D:o,cm^(-1)

1 -803.95103338 0.000000 0.000

2 -803.95019927 0.022697 183.067

3 -803.94842548 0.070965 572.3694 -803.94080888 0.278223 2244.018

5 -803.93985982 0.304048 2452.314

6 -803.93976930 0.306511 2472.1797 -803.93403490 0.462552 3730.736

8 -803.79473876 4.252993 34302.7039 -803.78861021 4.419760 35647.767

10 -803.70680007 6.645927 53603.017

11 -803.69754226 6.897845 55634.87112 -803.69188017 7.051918 56877.555

Jahn-Teller induced lines

CaF2:Ce3+ absorption without SOC

SOC induced lines

CaF2:Ce3+ absorption without Jahn-Teller relaxation

CaF2:Ce3+ absorption with Jahn-Teller relaxation

Ce3+ OA lines in CaF2:

Calc. energy,

cm-1

Oscillator strength

Expt. energycm-1 [1]

Calc. energycm-1[2]

32698,7 2.2E-02 32300 3363334199,0 3,9E-0455406,5 2,4E-02 51600 4807157751,4 2,6E-03 5300059010,2 1,3E-03 55200

References:

[1] L. van Pieterson, FM Reid, RT Wegh, S Soverna, A Meijerink, PRB 65, 045113 (2002)[2]A. Myasnikova, A. Mysovsky, E. Radzhabov, Opt. i Specktr. 114, 445 (2013)

SrF2:CeF8 «Oh» absorption spectrum

Spectral lines

Transition energy, cm^-1[calculated]

Oscillator Strength

Line frequencycm^ -1[1]

34302.703 1,92E-02 33955.943

34302.703 3,54E-03

35647.767 3,36E-05

35647.767 4,31E-04

53603.017 1,67E-03 46538.192

53603.017 2,10E-02

55634.871 2,24E-03

55634.871 1,74E-04

56877.555 5,99E-04

56877.555 6,06E-04

References:

[1]First Principle Calculation of 4fn-4f(n-1) 5d Absorption Spectra of Ce3+ and Pr3+ Ions in Alkaline Earth FluoridesAlexandra Myasnikova, Andrey Mysovsky, and Evgeny Radzhabov

Insufficient correlation accounting come from small active space: only one 4f electron for Ce3+

Absorption spectrum

Ce3+ with interstitial fluorine ion

Atom X, Å Y, Å Z, Å ΔX, Å ΔY, Å ΔZ, ÅCE 1.38 0 0 -0.16 0 0

CA0-CA3 -1.38 0 2.76 -0.03 0 -0.15

CA4 -4.14 0 0 0.16 0 0FI -1.38 0 0 0.04 0 0

Ce

CA4

Interstitial Fluorine

CA0-CA3

Ce3+Fi- in CaF2

Atom X, Å Y, Å Z, Å ΔX, Å ΔY, Å ΔZ, ÅCE0 1.47 0 0 -0.09 0 0

SR0-SR3 -1.47 0 2.94 0 0 -0.23SR4 -4.41 0 0 0.23 0 0FI -1.47 0 0 0.12 0 0

Ce3+Fi- in SrF2

Ce

SR4

Interstitial Fluorine

SR0-SR3

CaF2:Ca5CeF13 C4V 4f HF orbitals

Symmetry:c1Energy:-0.5064 a.u.

Symmetry:c1Energy:-0.5064 a.u.

Symmetry:c1Energy:-0.5064 a.u.

Symmetry:t2uEnergy:-0.3901 a.u

Symmetry:t2uEnergy:-0.3901 a.u.

Symmetry:t2uEnergy:-0.3901 a.u.

Symmetry:t2uEnergy:-0.3901 a.u.

CaF2:Ca5CeF13 C4V 5d HF orbitals

Symmetry:c1Energy:-0.5064 a.u.Cubic Notation: dx2-y2

Symmetry:c1Energy:-0.5064 a.u.Cubic Notation:dz2

Symmetry:c1Energy:-0.5064 a.u.Cubic Notation:dxy

Symmetry:t2uEnergy:-0.3901 a.uCubic Notation:dxz

Symmetry:t2uEnergy:-0.3901 a.u.Cubic Notation: dyz

CaF2:Ce3+Fi- absorption

W/o SOC

With SOC

W/o SOC

With SOC

SrF2:Ce3+Fi- absorption

CaF2:Ca5CeF13 C4v absorption spectrumSpectral lines

Energy, cm-

1

[calculated]Oscillator strength

Linefrequencycm^ -1[1]

32986,13 0,00981 3290732986,13 0,01206841680,98 0,002818 4145741680,98 0,0028853236,06 0,001499 4637753236,06 0,00152753536,85 0,009555 4750653536,85 0,00974155020,82 0,00174755020,82 0,002242

[1] Calculations by Alexandra Myasnikova, Andrey Mysovsky, andEvgeny Radzhabov

Absorption spectrum

SrF2:Ce3+Fi- absorption spectrum

Spectral lines

Transition energy, cm^-1

[calculated]Oscillator strength

Line frequencycm^ -1[1]

35269,89 0,013039 34117

35269,89 0,009742

39762,28 0,000746 40247

39762,28 0,000695

51888 0,002082 46861

51888 0,002113

52522,33 0,005922 47829

52522,33 0,006764

54419,72 0,003892

54419,72 0,004181

References:

[1]First Principle Calculation of 4fn-4f(n-1) 5d Absorption Spectra of Ce3+ and Pr3+ Ions in Alkaline Earth FluoridesAlexandra Myasnikova, Andrey Mysovsky, and Evgeny Radzhabov

Absorption spectrum

SrF2:Ce3+ absorption spectrum

Experimental Reference:Cubic and tetragonal Ce3+ ions in strontium fluoride (E. Radzhabov, T. Kurobori)

Experimental: Calculated:

Conclusion

1. We have developed an approach for embedded cluster QM/MM calculations with MOLCAS quantum chemistry package used for electronic structure calculations. The approach itself is similar to GUESS method (AL Shluger, PV Sushko).

2. This allows to use the strong side of MOLCAS - sophisticated post-SCF and multiconfigurational techniques – for calculations of defects in solids.

3. 4f-5d Ce3+ electronic transitions in CaF2 and SrF2(Oh and C4v centers) were studied using CASPT2 and scalar-relativistic Douglas-Kroll-Hess approach. Spin-orbit coupling was treated with the restrictive active space state interaction (RASSI).

4. It is shown that cubic Ce3+ centers in CaF2 and SrF2 undergoes asymmetric relaxation due to Jahn-Teller effect. Optical absorption spectrum calculated with this asymmetric relaxation demonstrates good agreement with experiment, moreover, allows to explain and identify the absorption lines.

5. Calculated optical absorption for Ce3+ with interstitial fluorine ion shows good agreement with experiment as well.