PD Research Report for the 2016 year
Name（Research group） Mega Novita(Ogasawara Lab., Graduate School of Science and Technology）
Research Theme

Creation of Practical Energy Diagram for Transition Metal and Rare EarthIons Using Non-Empirical First Principles Calculations

Research Period
Research Results

4, 2016 ~ 3, 2017
（about 2,500 characters in Japanese, about 65 lines times 90 characters in English）

Transition metal (TM) and rare earth (RE) ions doped compounds have attracted great interest due
to a wide variety of applications such as phosphors used in white light emitting diode (LED). The current
white LED was constructed by combination of a blue InGaN LED chip and yellow Y 3 Al 5 O 12 : Ce3+phosphor. However, with the current two-color white LED it is impossible to obtain white LEDs withhigh color rendering index. The combination of yellow Y 3 Al 5 O 12 : Ce3+ emission and blue LED
radiation produces a pseudo white light due to a deficiency of red emission. The easiest way to improve
the quality of the current white LED can be done by either adding the red phosphor component or
broadening the yellow phosphor emission. Recently, Mn4+ activated in K 2 SiF 6 crystal has received
increasing attention as potential red phosphor. However, they are unstable against high temperature andhigh humidity. Hence, Mn4+ doped in more stable host materials such as oxides are desired. On the otherhand, search of new luminescence materials in the higher energy region which generally correspond tothe high-lying 4fn and 4fn-15d1 configuration of lanthanide ions (Ln) is also important. Since, the trial anderror experiments are rather ineffective, the theoretical prediction of the optical spectra is indispensablefor theoretical design of novel optical materials. In this work, we constructed practical energy diagramsof TM and RE ions in crystals non-empirically using first-principles calculations. Several effects such as
lattice relaxation and the energy corrections are taken into account. The multiplet energy levels of ruby(α-Al 2 O 3 : Cr3+) were estimated using one-electron discrete variational Xα (DV-Xα) method.1 On theother hand, the 4fn-4fn-15d1 transition energies of LiYF 4 : Ln3+ and CaF 2 : Ln3+ were estimated using therelativistic versions of discrete variational multi-electron (DVME) method.2
1. α-Al 2 O 3 : Cr3+
We used two different types of model clusters consisting of 7 atoms and 63 atoms with C 3 symmetry.
The effect of lattice relaxation was taken into account by performing the geometry optimization using
CAmbridge Serial Total Energy Package (CASTEP) code3 with pressure from 0-110 GPa. One Cr3+ ion
was located at the center of the model clusters. The 4A 2 → 4T 2 transition energy or the so called U-band
energy (𝜀(4T 2 )) was calculated from the energy difference between 4A 2 and 4T 2 (ΔE U ). On the otherhand, the 2E → 4A 2 transition energy or the so called R-line energy was calculated using two different
methods. First is based on Ohnishi and Sugano’s work,4 the R-line energy is described as 𝜀1 � 2E� =4⁄5 × ∆𝐸𝑅 . Here, ΔE R is the spin-flip transition energy based on one-electron calculations from t 2g ↑spin to t 2g ↓ spin. However, if we see carefully, Ohnishi-Sugano interpreted ΔE R to the transition fromquartet 4A 2 state to doublets 2E, 2T 1 , and 2T 2 states, which is similar with the transition from S Z =1/2 toS Z =-1/2. Nevertheless, the spin-flip transition is actually occur from S Z =3/2 to S Z =1/2. The initial state isS Z =3/2 consists of only 4A 2 states, while the final state is S Z =1/2 consists of 2T 2 , 2T 1 , 2E, and 4A 2 states.
Since they belong to different spin states, the transition from 4A 2 of S Z =3/2 to 4A 2 of S Z =1/2 should also
be taken into account. Therefore, the R-line energy should be estimated by 𝜀2 � 2E� = 9⁄10 × ∆𝐸𝑅 .

Next, in order to obtain the energies of ΔE R and ΔE U , Slater’s transition state (TS) method5 was utilized.
In this case, the spin polarization calculation is performed. Since the 3d configuration is defined as (t 2g ↑),(e g ↑), (t 2g ↓) and (e g ↓) levels, the energy of ΔE R can be obtained by a transition from (t 2g ↑) to (t 2g ↓)while the energy of ΔE U can be obtained by a transition from (e g ↑) to (t 2g ↑).
Fig.1 shows the practical energy diagram of ruby calculated based on one-electron calculations
using 7-atom (left) and 63-atom (right) model clusters constructed from optimized ruby structures. Theenergies of R-line (𝜀(2E)) and U-band (𝜀(4T 2 )) are indicated by circle (●) and square (■) symbols,respectively. The experimental data6,7 are also shown together. The results show that 𝜀1 (2E) calculated

based on 7-atom model clusters agree the experiment very well. However, when we used the larger
clusters, the R-line energy calculated using the Ohnishi-Sugano’s method was no longer agreed theexperiment. Despite of the underestimation of U-band energy, we suggest the theoretical R-line energy
obtained by 63-atom model clusters is reasonable. According to ligand field theory, the U-band energy isactually higher than 10Dq, the discrepancy of 𝜀(4T 2 ) is therefore inferred. This study has been presented

at ECS conference on Oct 2-7, 2016 in Honolulu, Hawaii, USA (oral presentation) and at 2nd SENS
conference on Oct 15, 2016 in University of PGRI Semarang, Indonesia (keynote speaker).
2. LiYF 4 : Ln3+ and CaF 2 : Ln3+
Nine-atom model clusters (LnF 8 6-) were constructed based on the crystal structures of LiYF 4 andCaF 2 . One Ln3+ ion i.e., Ce3+, Pr3+, Nd3+, Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, or Yb3+
was substituted into Y3+ and Ca2+ sites of the clusters. The effect of lattice relaxation was considered bya simple correction of bond lengths using the Shannon’s crystal radii [8]. As the energy correction, weadopted a combination of CI calculation and TS method [5]. The energy difference corresponding to theinterconfiguration f-d transition obtained from many-electron CI calculations was equated to thoseobtained from one-electron TS calculations.
Fig.2 shows the practical energy diagram of LiYF 4 : Ln3+ and CaF 2 : Ln3+ calculated based on
many-electron calculations. The theoretical 4fn-4fn-15d1 transition energies obtained based on theunrelaxed and the relaxed cluster models were presented by square (■) and circle (○), respectively. The
solid lines connected the theoretical energies calculated with simple CI, without any energy correction.
On the other hand, the dashed lines connected the theoretical energies calculated with energy correction
TS. The experimental energies9-13 are indicated by triangle (▲). The results obtained by simple CI
calculations show that the theoretical 4fn-4fn-15d1 transition energies of light lanthanides areoverestimated, while underestimated for heavy lanthanides. When the correction based on one-electron
TS method was considered, the overestimation of 4fn-4fn-15d1 transition energies in the light lanthanide
and the underestimation of 4fn-4fn-15d1 transition energies in the heavy lanthanide have been successfullyreduced. This study has been presented at DV-Xα conference on Aug 8-9, 2016 in Tokyo Univ. ofTechnology (poster presentation) and to be published in the 29th DV-Xα Bulletin.

Fig. 1. Practical energy diagram of ruby under pressure calculated based on
one-electron calculations using (a) 7-atom and (b) 63-atom model clusters.

Fig. 2. Practical energy diagram of (a) LiYF4: Ln3+ and (b) CaF2: Ln3+calculated based on many-electron calculations.

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ACHIEVEMENT
1. (Poster Presentation) First-Principles Calculation of 4fn - 4fn-15d Transition Energy of Trivalent
Lanthanides Ions in CaF 2
Mega Novita and Kazuyoshi Ogasawara
The 29th DVXα Workshop, 8-9 Aug, 2016, Tokyo Univ. of Technology, Japan.
2. (Oral Presentation) First-Principles Calculation on the Emission Energy Level of Ruby Based on
DV-Xα Molecular Orbital Method and Ligand Field Theory,
Mega Novita, Akane Ito, and Kazuyoshi Ogasawara,
230th ECS Meeting, 2-7 October, 2016, Honolulu, Hawaii, USA.
3. (Keynote Speaker) Investigation on the excitation and emission energies of ruby based on
one-electron and many-electron quantum mechanical calculations.
Mega Novita
2nd SENS Conference, 15 October 2016, Univ. of PGRI Semarang, Indonesia. .
4. (Non-referred paper) First-Principles Calculation of 4fn - 4fn-15d Transition Energy of Trivalent
Lanthanides Ions in CaF 2Mega Novita and Kazuyoshi Ogasawara
Bulletin of the Society for Descrete Variational Xα 29 (2016) In Press.