Discrete Variational Multi-electron Research Articles

First-Principles Calculations of the Optical Spectra of Uranium Ions in Oxide Crystals

Recently U6+-doped phosphors are attracting attentions as potential green phosphors for the white LED application. However, the origins of the peaks in the optical spectra in some U-doped phosphors have not been clarified yet. For the development of the novel uranium phosphors, detailed analysis of the absorption and emission mechanisms of these materials is indispensable.In this study, we have performed the first-principles electronic structure calculations of U in oxide crystals using the relativistic discrete-variational multi-electron (DVME) code which is a configuration-interaction calculation program based on the four-component fully relativistic wave functions obtained by the relativistic discrete-variational Xα (DV-Xα) molecular orbital method. The optical spectra due to the charge transfer transitions of U6+ in oxides were calculated using the explicitly obtained many-electron wave functions. For comparison, the 5f-6d transitions of U3+ in oxide crystals were also calculated and the influence of the valency was investigated. The theoretical spectra were compared with the experimental spectra and the origins of the peaks were clarified based on the configuration analysis of the corresponding relativistic many-electron wave functions.

Theoretical Analysis of Anomalous Emission of Eu2+ in Crystals By First-Principles Calculation

The 5d-4f transition energies of lanthanides are very versatile, especially the 4f65d1-4f75d0 transition energy of Eu2+ has high luminescence efficiency and is used in various luminescent materials such as phosphors like SrxCa1-xAlSiN3: Eu2+, scintillators, and solid-state lasers, etc. However, there are materials that do not undergo pure 5d-4f transitions, showing the so-called anomalous luminescence instead. The anomalous luminescence is caused by the formation of excitons due to the overlap of the 5d level of Eu2+ with the conduction band and the transition of electrons from the conduction band to the 4f level, resulting in a shift to a lower energy than the general 5d-4f transition energy. A more detailed analysis of this phenomenon is important for the development of novel luminescent materials using Eu2+.In this study, we aimed to theoretically analyze the anomalous luminescence based on first-principles electronic structure calculations. The model clusters of Eu2+-doped crystals consisting of Eu2+ at the substitution site and the surrounding ions were created. Then molecular orbital calculations were performed by the relativistic discrete-variational Xα (DV-Xα) method and subsequently multiplet calculations were performed by the relativistic discrete-variational multi-electron (DVME) method. These first-principles calculations were carried out for Eu2+-doped crystals that show anomalous luminescence and those that do not show anomalous luminescence, and the electronic states of these materials were compared in detail.

Optimization of the First-Principles Calculation Conditions of d3 Ions in SrTiO3

Since transition metal ions are generally more stable in supply than rare earth ions and are inexpensive, researches on alternative materials based on transition metal elements to those based on rare earth elements are actively conducted. As phosphors using transition metal ions, Cr3+ and Mn4+ with d3 configuration are used for red emission while Mn2+ with d5 configuration is used for green emission. For theoretical search of novel phosphor materials, first-principles calculations of the transition energies based on the cluster approach are useful. However, in order to establish an efficient and effective method for prediction, optimization of computational conditions is indispensable.In this study, first-principles calculations of the d-d transition energies of d3 ions such as Cr3+ and Mn4+ in SrTiO3 were performed using the discrete-variational multi-electron (DVME) method. The clusters with Ti4+ at the center were constructed based on the crystal structure data of SrTiO3, and then Ti4+ was replaced with Cr3+ or Mn4+. In order to determine an appropriate cluster size, model clusters consisting of 7, 15, 63, 89, 143, 199, and 391 atoms were constructed. In order to improve the accuracy, the first-principles calculations were carried out considering the configuration-dependent correction (CDC) and the correlation correction (CC), which correct the overestimation of the multiplet energies. The effect of the lattice relaxation was also considered based on the structural optimization using the CASTEP code. Then the cluster size dependence and the effect of the lattice relaxation were clarified based on the detailed comparison of the first-principles calculation results.

Prediction of Emission Level Energy of Mn4+ in Oxides Based on the Local Structure Using First-Principles Calculations and Machine Learning

The white LED is an important next-generation light source. Most of the high color rendering white LEDs that have become popular in recent years consist of blue LEDs combined with green and red phosphors. For example, Eu2+:SrxCa1-xAlSiN3 (SCASN) and Mn4+:K2SiF6 (KSF) are used as red phosphors. However, considering the production cost and the stability against high temperature and high humidity, novel red phosphors obtained by adding Mn4+ to oxide crystals are still desired. To realize a Mn-doped oxide red phosphor for white LEDs, it is indispensable to clarify the relationship between the multiplet energies and the local structures. Semi-empirical methods based on experimental data are generally used to analyze luminescent materials, but these methods cannot be applied to unknown or hypothetical materials. In this work, we analyzed the relationship between the local structure and the energy levels of hypothetical Mn4+-doped oxides by performing first-principles electronic structure calculations using the discrete-variational multi-electron (DVME) method. The local structures around Mn4+ were systematically changed by changing the bond distances and angles and the multiplet energies corresponding to each local structure were calculated non-empirically. Then the relationship between the energy and the local structure was visually represented by creating energy-structure maps. Using these systematic theoretical values as the training data, a machine learning model for the prediction of the first-principles calculation results based only on the structural parameters was also created. The results of this study would provide guidelines for the development of novel phosphors based on oxide crystals doped with Mn4+.

Study on Local-Structure Symmetrization of K2XF6 Crystals Doped with Mn4+ Ions by First-Principles Calculations.

The crystals of Mn4+-activated fluorides, such as those of the hexafluorometallate family, are widely known for their luminescence properties. The most commonly reported red phosphors are A2XF6: Mn4+ and BXF6: Mn4+ fluorides, where A represents alkali metal ions such as Li, Na, K, Rb, Cs; X=Ti, Si, Ge, Zr, Sn, B = Ba and Zn; and X = Si, Ge, Zr, Sn, and Ti. Their performance is heavily influenced by the local structure around dopant ions. Many well-known research organizations have focused their attention on this area in recent years. However, there has been no report on the effect of local structural symmetrization on the luminescence properties of red phosphors. The purpose of this research was to investigate the effect of local structural symmetrization on the polytypes of K2XF6 crystals, namely Oh-K2MnF6, C3v-K2MnF6, Oh-K2SiF6, C3v-K2SiF6, D3d-K2GeF6, and C3v-K2GeF6. These crystal formations yielded seven-atom model clusters. Discrete Variational Xα (DV-Xα) and Discrete Variational Multi Electron (DVME) were the first principles methods used to compute the Molecular orbital energies, multiplet energy levels, and Coulomb integrals of these compounds. The multiplet energies of Mn4+ doped K2XF6 crystals were qualitatively reproduced by taking lattice relaxation, Configuration Dependent Correction (CDC), and Correlation Correction (CC) into account. The 4A2g→4T2g (4F) and 4A2g→4T1g (4F) energies increased when the Mn-F bond length decreased, but the 2Eg → 4A2g energy decreased. Because of the low symmetry, the magnitude of the Coulomb integral became smaller. As a result, the decreasing trend in the R-line energy could be attributed to a decreased electron-electron repulsion.

Chromaticity coordinates of ruby based on first-principles calculation

Understanding the local atomic configuration is crucial for studying phosphor materials. Their performance in many applications is strongly dependent upon their optical properties. Much experimental and theoretical effort has been made to meet the requirements. Specifically, ab-initio studies have extensively reported the absorption spectra and the multiplet energies of phosphors. However, the qualitative analysis on the emitted light has not yet been reported. In this work, we characterized the emitted light of ruby, which is a widely studied phosphor material. The absorption spectra of ruby were calculated utilizing the non-empirical discrete variational Xα (DV-Xα) and discrete variational multi-electron (DVME) software. Then, the investigation on the ( x , y ) chromaticity coordinates of was performed under the standard illuminant D65 utilizing ColorAC software, a chromaticity diagram maker. In this work, we used a ruby model cluster generated from an α-Al 2 O 3 crystal. The model consists of seven atoms, where one chromium atom surrounded by six oxygen atoms. We compared the absorption spectra obtained via simple configuration interaction (CI) and those obtained which include energy corrections called configuration dependent correction (CDC) and correlation correction (CC). We successfully reproduced the color that is observed in experiment. The chromaticity coordinates approach red region for higher concentration. The results show that the calculation with CDC-CC shows better agreement with experiment. This research confirms the non-empirical calculations based on the DV-Xα and DVME methods, in the terms of emitted light. • The emitted light of α-Al2O3: Cr3+ (ruby) was characterized non-empirically. • Effects of CDC-CC correction were investigated thoroughly. • The “theoretical color” reproduced the tendency of the “experimental color”. • The calculation with CDC-CC correction shows better agreement.

Prediction on the multiplet energy diagram of α-Al2O3: Mn4+ under pressure

To review the recommendations for the production of novel red phosphor materials, in this work we established the multiplet energy diagram of Mn4+ in a-Al2O3 under pressure. By the discrete variational multi-electron (DVME), the calculations were conducted based on many-electron approaches. Since the experimental data of Mn4+ in a-Al2O3 at zero pressure was the only data reported so far, the results in this work are our predictions. The effect of increasing pressure is naturally similar with the effect of decreasing bond length. This work indicates that the multiplet energies responsible for the absorption process increase as the pressure increase. Whereas, those responsible for the emission process decrease. These tendencies are the same as our previous calculations on a-Al2O3: Cr3+.

(Luminescence and Display Materials Division Centennial Outstanding Achievement Award Address) Investigation of Luminescent Materials based on First-principles Calculations of Multiplet States

The transitions between multiplet states of rare-earth (RE) and transition-metal (TM) ions in crystals are utilized in variety of luminescent materials. Therefore, for the theoretical design of novel luminescent materials, a deep understanding of multiplet states and a nonempirical prediction of multiplet spectra are indispensable. For these purposes, a configuration interaction calculation program based on the discrete-variational Xa (DV-Xa) molecular orbital method [1] was developed, which is known as the discrete-variational multi-electron (DVME) program [2]. There is also a relativistic version of the DVME program [3] based on the relativistic DV-Xa method [4], which is especially useful for the analysis of RE-doped luminescent materials [5] since both the relativistic effects and the many-electron effects can be considered simultaneously without any empirical parameters. The DVME calculations have been applied to analyze various luminescent materials such as ruby [2], Mn4+-doped fluorides [6] and RE-doped LiYF4 [5]. Various types of multiplet spectra originating from d-d, f-f, f-d, and charge transfer (CT) [7, 8] transitions have been reproduced without any empirical parameters and the origins of the spectral peaks have been elucidated based on the configuration analysis of the explicitly obtained many-electron wave functions. In addition, relationships between the multiplet energy and the local structure of TM ions in crystals have been investigated in detail by creating various energy-structure maps based on systematic DVME calculations. The systematic data obtained by first-principles calculations can be also used as the training data for machine learning to create a simple predictive model. In this lecture, some representative results of the investigation of luminescent materials based on first-principles calculations of multiplet states using the DVME program will be presented.[1] H. Adachi, M. Tsukada, and C. Satoko, J. Phys. Soc. Jpn., 45, 875 (1978).[2] K. Ogasawara T. Ishii, I. Tanaka, and H. Adachi, Phys. Rev. B, 61 143 (2000).[3] K. Ogasawara, T. Iwata, Y. Koyama, and T. Ishii, I. Tanaka, and H. Adachi, Phys. Rev. B, 64, 115413 (2001).[4] A. Rosén, D.E. Ellis, H. Adachi, and F.W. Averill, J. Chem. Phys., 65, 3629 (1976).[5] K. Ogasawara, S. Watanabe, H. Toyoshima, M.G. Brik, Handbook on Physics and Chemistry of Rare Earths, 37, 1 (2007).[6] M. Novita, T. Honma, B. Hong, A. Ohishi, K. Ogasawara, J. Lumin. 169, 596 (2016).[7] S. Takemura, K. Ogasawara, Opt. Mater.: X, 1, 100005 (2019).[8] S. Takemura, K. Ogasawara, J. Lumin. 214, 116542 (2019).

First-Principles Study of the Crystal-Field and Racah Parameters of Cr3+ in Alumina

The development of blue LEDs [1] enabled one to construct white LEDs by combining them with appropriate phosphors. Recently Mn4+-doped fluorides have been put into commercial use as the red phosphors for high color-rendering white LEDs [2]. However, in order to suppress the degradation due to high humidity and high temperature, a special surface treatment is required for these phosphors. Therefore, the search of other red phosphors activated by Mn4+ is still desired. For theoretical design of novel phosphors, non-empirical prediction of optical parameters such as the crystal-field and Racah parameters is quite important. The purpose of this study is to establish a first-principles approach to predict these parameters of transition metal ions in crystals.In this work, the crystal-field and Racah parameters of ruby (Cr3+ doped α-Al2O3) were evaluated based on the first-principles calculations using the relationship between the ligand-field theory and the molecular orbital (MO) theory derived by Sambe and Felton [3]. Two types of first-principles methods were adopted. One is the discrete-variational (DV)-Xα method [4], which is an MO calculation method based on the one-electron approximation. The other is the discrete variational multi-electron (DVME) method [5], which is a configuration-interaction (CI) calculation method based on the explicit many-electron wave functions. The estimation of the crystal-field and Racah parameters were performed in the following three approaches.(1) Estimation based only on the DV-Xα method(2) Estimation based only on the DVME method(3) Estimation based on the combination of the DVME method and the DV-Xα methodThe results show that the values of the crystal-field and Racah parameters obtained by the approach (3) are in the best agreement with the values obtained by fitting to the experimental data [6], indicating that CI calculations using some corrections based on the one-electron MO calculations are effective for the non-empirical estimation of the crystal-field and Racah parameters [7]. These results also provide theoretical basis for the configuration-dependent correction and the correlation correction introduced in our previous CI calculations of ruby [5]. This approach could be applied to prediction of d-d transitions of Mn4+ in crystals to find a suitable host for novel Mn4+-activated red phosphors for white LEDs.[1] I. Akasaki and H. Amano, Jpn. J. Appl. Phys. 45, 9001 (2006).[2] J. E. Murphy, F. Garcia-Santamaria, A. A. Setlur, and S. Sista, SID 2015 DIGEST, 927 (2015).[3] H. Sambe and R. Felton, Int. J. Quant. Chem., 10, 155 (1976).[4] H. Adachi, M. Tsukada, and C. Satoko, J. Phys. Soc. Jpn. 45, 875 (1978).[5] K. Ogasawara T. Ishii, I. Tanaka, and H. Adachi, Phys. Rev. B 61, 143 (2000).[6] W. M. Fairbank, Jr., G. K. Klauminzer, and A. L. Schawlow, Phys. Rev. B 11, 60 (1975).[7] K. Ogasawara, K.C. Mishra, and J. Collins, ECS J. Solid State Sci. Technol. 9, 016011 (2020).

Study on the Optical Luminescence Properties of Li2TiO3: Mn4+ and Cr3+

Abstract We studied the optical luminescence properties of Li2TiO3: Mn4+ based on first-principles calculations. The optical luminescence properties such as Mn-O distance, molecular orbital (MO) energy, crystal field splitting, multiplet energy levels, and Coulomb interaction are discussed in detail. The impact of lattice relaxation was examined through geometry optimizations based on first-principles band-structure calculations using Cambridge Serial Total Energy Package (CASTEP) software. Both Discrete Variational-Xα (DV-Xα) and the Discrete Variational Multi-electron (DVME) software were used to estimate the optical luminescence properties. Here we also predicted the optical luminescence properties of Li2TiO3: Cr3+. The results imply that the multiplet energy levels tend to decline in the order of Mn4+ to Cr3+. The integral Coulomb's decreasing tendency is in excellent agreement with the declining tendency of 2E, 2T1, 2T2 energies of Li2TiO3: Mn4+ and Li2TiO3: Cr3+.

Prediction of 4f7-4f65d1 transition energy of Eu2+ in oxides based on first-principles calculations and machine learning

In order to establish a method to predict the 4f7-4f65d1 transition energy of Eu2+ in oxides, linear regression models were created based on first-principles calculations and machine learning. The model clusters consisting of the central Eu2+ and O2- ions closer than the nearest cation were constructed and the 4f7-4f65d1 absorption energy of Eu2+ in these clusters were calculated by first-principles many-electron calculation using the relativistic discrete variational multi-electron (DVME) method. However, the 4f7-4f65d1 absorption energies of Eu2+ in oxides calculated by relatively simple first-principles calculations tend to be overestimated by ca. 1.6 eV. In order to improve the accuracy of the prediction, we performed machine learning considering the calculated absorption energy as well as the other electronic and structural parameters as the attributes. As a result, the regression formula to predict the 4f7-4f65d1 absorption energy of Eu2+ in oxides has been created by machine learning. The 4f7-4f65d1 absorption energy predicted by this model are in good agreement with the experimental ones. Therefore, accuracy of the prediction was significantly improved compared to the simple first-principles calculations. In a similar way, a predictive model of the 4f65d1-4f7 emission energy of Eu2+ in oxides has been also created

Recent applications of discrete variational multi-electron method

The discrete variational multi-electron (DVME) method is a first-principles many-electron calculation method based on the discrete-variational Xα (DV-Xα) molecular orbital method. There is also the relativistic version of the DVME method, which is based on the relativistic DV-Xα method. Since the explicit many-electron wave functions of the multiplet states of transition-metal (TM) or rare-earth (RE) ions in crystals can be obtained, the DVME method has been applied to the analyses of various luminescent materials such as solid-state lasers and phosphors. In this paper, as examples of the recent applications of the DVME method, the following researches will be briefly presented: (1) Visualization of the energy-structure relationship of Cr3+ in oxides, and (2) Creation of the predictive model of the multiplet energy using machine learning.

Optical properties of Co3+ doped in α-Al2O3 with Considering Lattice Relaxation Effect

Search of new luminescence materials to improve the current white-ight emitting diode (LED) is still ongoing. Several investigations such as the ion dependence, the host crystal dependence has been done previously. Since we want to get a complete picture of ion-host combination dependence, we investigated α-Al2O3: TM3+. In this work we estimated the optical properties of α-Al2O3 doped with Co3+. We constructed model clusters consisting of 7 atoms. The lattice relaxation effects due to the Co3+ substitution were calculated using Shannon’s crystal radii method and geometry optimizations in the Cambridge Serial Total Energy Package (CASTEP) method. The one-electron Discrete Variational-Xα (DV-Xα) method was used to estimate the molecular orbital energies, while the many-electron Discrete Variational Multielectron (DVME) method was used to estimate the d-d absorption spectra. Since Co3+ belongs to 3d 6 configuration, there are two possible spin states i.e., high-spin (HS) and low-spin (LS) states.

Prediction of 4f2−4f15d1 transition energy of Pr3+ in fluorides based on first-principles calculations and machine learning

The 4f2−4f15d1 transition energy of Pr3+ in fluorides are utilized for various optical materials such as solid-state lasers, phosphors, and scintillators. Therefore, it is important to predict such energies of unknown materials for theoretical design of novel optical materials. In this study, we tried to predict the 4f2−4f15d1 transition energies of Pr3+ in fluorides based on first-principles calculations and machine learning. The first-principles calculations were performed based on the relativistic discrete variational multi-electron (DVME) method using the model clusters composed of the central Pr3+ and the anions closer than the nearest cation. Although the calculated 4f2−4f15d1 transition energies of Pr3+ in fluorides showed a relatively good correlation with the experimental ones, the calculated values tend to be overestimated by ca. 2 eV. In order to improve the accuracy of the prediction, we used the calculated transition energies as an attribute for machine learning. As a result, the regression formula to predict the 4f2−4f15d1 transition energy of Pr3+ in fluorides has been derived by machine learning using the calculated 4f2−4f15d1 transition energy as well as some other electronic and structural parameters as the attributes. The accuracy of the prediction was significantly improved compared to the simple first-principles calculations.

First-Principles Calculations of Charge Transfer Transitions of Eu3+ in Y2O3 and Y2O2S

In order to investigate the ligand to metal charge transfer (LMCT) energies of Eu3+ in Y2O3 and Y2O2S, we performed first-principles calculations using and clusters for Y2O3 and and clusters for Y2O2S by the relativistic Discrete Variational Multi-Electron (DVME) method based on the configuration interaction (CI) approach, and constructed theoretical energy diagram. In order to improve the quantitative agreement between theoretical LMCT energies and the experimental ones, we considered the configuration-dependent correction (CDC) and the effect of lattice relaxation based on the Shannon’s crystal radii. The experimental CT energies have been successfully reproduced the experimental LMCT energies of Eu3+ in Y2O3 and Y2O2S by the relativistic DVME method without any empirical parameters. In addition, we clarified the nature of states in CT transition and the assignments of the experimental CT bands of Eu3+ in Y2O3 and Y2O2S by an analysis of the configuration composition.

Effect of trivalent manganese substitution in α-Al2O3 crystal on the absorption spectra based on first-principles calculations

The absorption spectra of α-Al2O3: Mn3+ at low-spin (LS) state have been estimated based on first-principles calculations without referring to any experimental parameter. The effect of lattice relaxation due to the Mn3+ substitution was considered under several computational procedures such as the Shannon’s crystal radii method and the geometry optimization using Cambridge Serial Total Energy Package (CASTEP) code. Two different sizes of model clusters consisting of 7 and 63 atoms were compared. Next, the molecular orbitals (MO) were estimated using the one-electron calculations discrete variational-Xα (DV-Xα) method while the absorption spectra were estimated using the many-electron calculations discrete variational multi-electron (DVME) method. The results show that the lattice-relaxation ratio is about ca. 104.05-106.43% depending on the computational conditions. Due to the Mn-O bond-length elongation, the crystal field splitting (10Dq) decreased ca. 0.24-0.41 eV. Thus, the peak position originating from 3T1 → 3E transition energy shifted toward the lower energy ca. 0.10-0.26 eV. Both of the larger-cluster size and the lattice-relaxation effect decrease the peak energies.

First-Principles Calculation of Laser Crystal Multiplet Levels via Hybridized Density Functional Theory and Configuration Interaction within the OLCAO Method

Computation of highly-localized multiplet energy levels of transition metal dopants is essential to the design of materials such as laser host crystals. A purely first-principles density functional theory-configuration interaction (DFT-CI) hybrid computational method has been developed to accurately compute multiplet energy levels for single atoms of carbon, nitrogen, oxygen, sodium, aluminum, silicon, titanium, and chromium. The multiplet energy levels have been computed with close experimental agreement in terms of magnitude and degeneracy, and the method does not depend on empirical information (i.e. Racah parameters). The computed multiplet energy level results are distributed according to term symbols, which are then compared to experimentally-observed multiplet energy levels. The hybrid method consists of analytic computation of two-electron integrals via the DFT-based orthogonalized linear combination of atomic orbitals (OLCAO) method, which are subsequently used as input for the CI-based discrete variational multi-electron (DVME) method to obtain the multiplet energy values.Keywords: exchange-correlation; elecron repulsion integral; multiplet; DVME; OLCAO; density functional theory; configuration interaction

A First-Principles Investigation of the Crystal-Field and Racah Parameters of Transition Metal Ions: Cr3+ in Alumina

The crystal-field and Racah parameters of ruby were evaluated based on the first-principles calculations using the relationship between the ligand-field theory and the molecular orbital theory derived by Sambe and Felton. It is found that the combination of the discrete variational (DV)-Xα calculations and the discrete variational multi-electron (DVME) calculations is effective for prediction of reasonable values for the crystal-field and Racah parameters for Cr3+ in alumina. These results indicate that the corrections to the DVME calculations based on the DV-Xα method provide a theoretical basis for the configuration-dependent correction and the correlation correction which were introduced in the previous calculation based on an intuition that the average transition energy should be reproduced better by one-electron calculations than many-electron calculations. This method could be used to predict the d-d transitions for Mn4+ to find a suitable host for a red phosphor for LED applications.

Comparative Study on R-line and U-band Energies of Ruby Estimated from One-Electron and Many-Electron First-Principles Approaches

We carried out a comparative study on R-line and U-band energies of α-Al2O3: Cr3+ material, or the so-called ruby, estimated from one-electron and many-electron first-principles calculations. The estimations were performed without relating to any observed parameter. Although there are numerous reports on the ab-initio calculations of absorption spectra and multiplet energies of ruby based on many-electron approach, the investigation based on one-electron approach is basically impossible except for some particular states such as 4T2 and 2E. Here we compared the transition energies from the 4A2 state (ground state) to 4T2 state (U-band) and to 2E (R-line) of ruby estimated by one-electron and many-electron first-principles approaches. The one-electron calculations were carried out utilizing using discrete variational Χα (DV-Χα) method combined with ligand field theory, while the many-electron calculations were carried out utilizing using the discrete variational multi-electron (DVME) method. The results show that generally both of the one-electron and the many-electron first-principles calculations can be utilized to estimate the multiplet energies such as U-band and R-line energies. Nevertheless, the refined formula to estimate the R-line energy based on one-electron approach is necessary to enhance the concurrence with the observed data.

Systematic first-principles calculations of charge transfer transitions of trivalent rare earth ions in CaF2

In order to predict the LMCT energies for various trivalent rare earth (RE) ions in CaF2 nonempirically, we performed first-principles calculations using REF85− cluster using the relativistic Discrete Variational Multi-Electron (DVME) method, which is based on the configuration interaction (CI) approach, and constructed the theoretical energy diagram of the RE 4f levels within the band gap. The theoretical Ligand to Metal Charge Transfer (LMCT) energies were overestimated in the case of simple CI calculations. Therefore in order to overcome this problem we considered the configuration-dependent correction (CDC) and the effect of lattice relaxation based on the Shannon's crystal radii. As a result, the quantitative agreement between the theoretical LMCT energies and the experimental ones was greatly improved and the characteristic dependence of the LMCT energies on atomic species was also successfully reproduced without any experimental parameter.