1. 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.
2. Introduction
Due to the fast 5d → 4f emission of Ce3+ in the blue and UV spectral
regions cerium-doped compounds(Ce3+ in CaF2,SrF2) have considerable
interest in application of scintillators and solid state lasers.
Picture of 4f-5d transitions state depend strongly on the local crystalline
environment of the dopant Ce3+, due to the large crystal-field interaction
experienced by the 5d electron.
Problem
Our purpose is to study electronic structure and optical transitions in
crystal-defect systems (CaF2, SrF2) using embedding quantum cluster
formalism, including scalar and spin-orbit effects.
4. ● 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
5. [1] http://www.chokkan.org/software/liblbfgs/
● We used 2-th order Douglas-Kroll-Hess method to include
scalar 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 model
potential (AIMPs)
● For large-scale nonlinear optimization problem we use Limited
Memory Broyden-Flebsche-Gordano (aka L-BFGS)[1]
● Restricted Active Space State Interaction (RASSI) for accounting
for spin-orbit effects
8. “Cubic” Ce3+ centre
Due to asymmetric charge localization
geometry optimization brings structure to
the 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
9. 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.u
B1u
ε=-0.5334 a.u
B1u
ε=-0.5259 a.u.
16. Ce3+ OA lines in CaF2:
Calc.
energy,
cm-1
Oscillator
strength
Expt.
energy
cm-1 [1]
Calc.
energy
cm-1[2]
32698,7 2.2E-02 32300 33633
34199,0 3,9E-04
55406,5 2,4E-02 51600 48071
57751,4 2,6E-03 53000
59010,2 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)
17. SrF2:CeF8 «Oh» absorption spectrum
Spectral lines
Transition energy,
cm^-1[calculated]
Oscillator
Strength
Line frequency
cm^ -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 Fluorides
Alexandra Myasnikova, Andrey Mysovsky, and Evgeny Radzhabov
Insufficient correlation accounting come from small active space:
only one 4f electron for Ce3+
Absorption spectrum
19. Atom X, Å Y, Å Z, Å ΔX, Å ΔY, Å ΔZ, Å
CE 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 0
FI -1.38 0 0 0.04 0 0
Ce
CA4
Interstitial
Fluorine
CA0-CA3
Ce3+Fi
- in CaF2
20. Atom X, Å Y, Å Z, Å ΔX, Å ΔY, Å ΔZ, Å
CE0 1.47 0 0 -0.09 0 0
SR0-SR3 -1.47 0 2.94 0 0 -0.23
SR4 -4.41 0 0 0.23 0 0
FI -1.47 0 0 0.12 0 0
Ce3+Fi
- in SrF2
Ce
SR4
Interstitial
Fluorine
SR0-SR3
28. 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.
