Multiplet Energies Research Articles

Prediction of 1Eg energies in Ni2+ in Crystals Based on Racah Parameters B and C By First-Principles Calculations and Machine Learning

Recently, demand of infrared phosphors is increasing because they can be used not only for lighting applications such as night vision camera and plant growth but also in various fields such as biomarkers that emit light by binding to abnormal sites in living organisms. Since the Ni2+-doped phosphors are drawing attentions as potential infrared phosphors, analysis of multiplet energies and emission mechanism of Ni2+ in crystals is very important for the development of novel infrared phosphors. For Mn4+, Cr3+ and Ni2+ in crystals, Brik et al. analyzed a large amount of experimental data in literature and indicated the importance of the Racah parameter C in addition to B and proposed a new Nephelauxetic parameter. Considering their results, we have recently created prediction models of 2Eg levels of Mn4+ and Cr3+ in oxides and fluorides based on the Racah parameters B and C using machine learning.For theoretical design of infrared phosphors, a similar prediction model for 1Eg level of Ni2+ would be useful. According to the Tanabe-Sugano diagram for the d8 configuration, the energy of 1Eg is almost independent of Δ/B which is a measure of the strength of the ligand field normalized by the Racah parameter B. Therefore, the energy of 1Eg seems to be determined by the Racah parameter B. However, as pointed out by Brik et al., in actual experimental values in literature, there are Ni2+-doped crystals which have different 1Eg energies despite having almost the same B values, indicating the necessity of consideration of the Racah parameter C as well. In this work, we created systematic model clusters for Ni2+ ions in crystals and performed first-principles calculations of the multiplet energies using the DV-Xα and DVME methods. Using these systematic data as the training data, predictive models of 1Eg based on the Racah parameters B and C were created by machine learning and the influence of these parameters on the multiplet energies was investigated in detail.

Exploring the Luminescent Properties of Transition Metal Ions in Solids through Theoretical Insights and the Prospects of Machine Learning

This work delineates over a decade of rigorous first-principles computational investigations into compounds doped with transition metal (TM) ions, such as Sc3+, Ti3+, V2+, V3+, Cr3+, Mn3+, Mn4+, Fe3+, Co3+, Ni3+, and Cu3+, within host matrices including α-Al2O3, MgTiO3, and various fluorides, devoid of empirical parameters. Our methodological framework employs discrete variational Xα (DV-Xα) and discrete variational multielectron (DVME) techniques, enhanced by configuration-dependent and correlation corrections to refine accuracy. Notably, our analysis integrates lattice-relaxation estimations through the use of Shannon crystal radii and the Cambridge Serial Total Energy Package (CASTEP), facilitating the examination of pressure-induced effects on lattice structures.Our comprehensive studies, particularly on α-Al2O3 doped with TM 3d3 ions, have not only successfully replicated known optical characteristics but have also provided new insights into the variation of transition energies across different TM ion charges, alongside pressure-dependent behavior of multiplet energies in alignment with experimental findings. These endeavors highlight the complex interplay of dopant characteristics, including charge states and ionic radii, on the optical properties of host crystals, with precise attention to colorimetry within the International Commission on Illumination (abbreviated CIE) color space framework to evaluate the quality and perception of emitted light.Furthermore, this work will introduce a discussion on the emerging potential of machine learning (ML) in advancing our understanding and predictive capabilities concerning the luminescence of materials. ML approaches promise to revolutionize the identification of optimal dopant-host combinations, predict novel luminescent materials, and enhance the accuracy of theoretical predictions through data-driven insights. By bridging traditional computational methods with ML, we aim to pave new pathways in the exploration of luminescent materials, potentially leading to innovative applications in lighting, display technologies, and beyond.

Prediction of Emission Energy of d3 Ions in Oxides Based on Local Structures Using First-Principles Calculations and Machine Learning

Red phosphors activated with Mn4+ are attracting attention as potential phosphor materials that can improve the color rendering properties of white LEDs. However, since Mn4+: KSF which is currently in practical use is unstable and toxic, a special surface treatment is required in actual usage. Therefore, in order to theoretically design stable and inexpensive red phosphors, we focused on oxide phosphors activated with Mn4+ and other d3 ions. Since emission energies of Mn4+ in oxides are always lower than the desired value, it is important to explore local structures which realize higher emission energies. For this purpose, we have recently created emission energy maps based on local structures using systematic first-principles calculations for CrO6 and MnO6 clusters with D4h and C4v symmetries. In this work, in order to investigate the influence of the ionic species, we created the emission energy maps of the other d3 ions such as V2+ and Fe5+. We constructed VO6 clusters and FeO6 clusters with gradually changed local structures and performed systematic first-principles calculations using the DV-Xα method and the DVME method. The emission energy maps of VO6 and FeO6 based on local structures were created and compared to those of CrO6 and MnO6. By using the obtained multiplet energies as the training data, we also created predictive models of emission energies of d3 ions in oxides by machine learning.

Pressure-dependent multiplet-excitation energies of α-Al2O3:Cr3+ by the first-principles method

We apply a method [Phys. Rev. B 108, 035141 (2023)], which can treat the multiplet excitations in the first-principles method, to a typical pressure indicator α-Al2O3:Cr3+. After optimizing the crystal structure under hydrostatic pressure from 0.0 to 35.0 GPa in the usual first-prinicple calculations, we obtain the multiplet energies in the method. That is, we conduct the exact diagonalization of the crystal-field model Hamiltonian which is directly determined based on the result of the quasiparticle self-consistent GW method. Our method has no parameters by hand. The calculated pressure dependences of the excitation energies agree well with those of experiments.

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+.

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.

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.

Reproduction of absorption spectra and analysis of multiplet energies for [formula omitted] phosphors using first-principles calculations

In recent years, M2VO4ClM=Ca,Sr and M3VO42M=Mg,Zn have been synthesized as rare-earth-free, self-activated phosphors. It is generally accepted that charge transfer transitions between V5+ and O2− are responsible for their absorption and emission of light. In this study, we attempted to reproduce the experimental absorption spectra and analyze the multiplet energy structure of the symmetric TdVO43− cluster using a first-principles calculation method, DV-Xα. This is a type of density functional theory based on the linear combination of atomic orbitals approximation and discrete variational multi-electron method that can account for multiplet effects by including configuration interaction (CI) in the calculation. Herein, we show that although the experimental absorption spectra could not be reproduced by considering only the VO43− clusters, they were successfully reproduced by considering M8VO413+(M=Ca,Sr) clusters and M9VO415+(M=Mg,Zn) clusters. However, we discovered that Zn9VO415+ differs from the other three crystals because its molecular orbitals in the valence band are formed from Zn 3d orbitals and O 2p orbitals. This makes it extremely difficult to calculate the appropriate multi-electron wavefunctions using molecular orbitals using single-electron calculations. Accordingly, we obtained an approximately suitable multi-electron wavefunction using a CI calculation. We grouped the molecular orbitals according to the O 2p orbital population. It was found that the absorption spectra calculated using molecular orbitals with a high O 2p population reproduced the experimental absorption spectra. In addition, calculated multiplet energies and spectra of the Td symmetry VO43− cluster suggest that in this case the excitation model may differ from the conventional one.

Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states.

Due to the sheer size of chemical and materials space, high-throughput computational screening thereof will require the development of new computational methods that are accurate, efficient, and transferable. These methods need to be applicable to electron configurations beyond ground states. To this end, we have systematically studied the applicability of quantum alchemy predictions using a Taylor series expansion on quantum mechanics (QM) calculations for single atoms with different electronic structures arising from different net charges and electron spin multiplicities. We first compare QM method accuracy to experimental quantities, including first and second ionization energies, electron affinities, and spin multiplet energy gaps, for a baseline understanding of QM reference data. Next, we investigate the intrinsic accuracy of "manual" quantum alchemy. This method uses QM calculations involving nuclear charge perturbations of one atom's basis set to model another. We then discuss the reliability of quantum alchemy based on Taylor series approximations at different orders of truncation. Overall, we find that the errors from finite basis set treatments in quantum alchemy are significantly reduced when thermodynamic cycles are employed, which highlights a route to improve quantum alchemy in explorations of chemical space. This work establishes important technical aspects that impact the accuracy of quantum alchemy predictions using a Taylor series and provides a foundation for further quantum alchemy studies.

First-Principles calculations of the interconfigurational transition energies of 4f - 4f-15d of Ln3+ ions in LiYF4 and CaF2

In studying the design of novel phosphors and solid-state laser materials, luminescence with a characteristically long lifetime originates from f - f emissions (infrared, visible and ultraviolet). However, due to high demand for novel luminescence materials which excite in the ultraviolet (UV) and vacuum ultraviolet (VUV) ranges, the interconfigurational f - d transition has been of great interest. In this work, we investigated the 4 f n - 4 f n -1 5 d transition energy of trivalent lanthanide ions in LiYF 4 and CaF 2 host crystals (LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ ) without referring to any empirical parameters. These crystals are considered to be promising fluoride hosts for solid-state laser crystals. LnF 8 5− atomic clusters were built based on the crystal structures of LiYF 4 and CaF 2 . The relativistic MO calculations were done using the relativistic Discrete Variational Xα (DV-Xα) algorithm. The relativistic version of discrete variational multi-electron method (DVME) algorithm was used to calculate the multiplet energies. We considered the effect of lattice relaxation by a simple estimation using Shannon's crystal radii. Given that the theoretical transition energies are typically underestimated due to the underestimation of the corresponding effects, the absolute transitional energies have received corrections based on one-electron calculations utilizing the Slater's transition-state technique. The in-depth study indicates that the lattice-relaxation effect does not substantially impact LiYF 4 : Ln 3+ , but greatly affects the transitional energy of heavy lanthanides doped in CaF 2 from 4 f n - 4 f n -1 5 d . The energy corrections based on Slater's transition-state method are necessary to improve the accuracy of our calculations. By a combination of these two methods, the transition energies of 4 f n - 4 f n -1 5 d of LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ agree very well with the experimental data. This research is important to providing guidance in the search for new lanthanide-based phosphors in UV or VUV regions. • The 4 f n - 4 f n -1 5 d transition energies of LiYF 4 :Ln 3+ and CaF 2 :Ln 3+ have been studied. • Effect of lattice relaxation was simply estimated based on Shannon's crystal radii. • Energy corrections utilizing Slater's transition-state method were considered. • The lattice relaxation greatly affects the transitional energy of heavy CaF 2 :Ln 3+ . • The energy corrections are necessary to improve the accuracy.

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.

Ab initio based ligand field approach to determine electronic multiplet properties

A method is developed to calculate the ligand field (LF) parameters and the multiplet spectra of local magnetic centers with open $d$ and $f$ shells in solids in a parameter-free way. This method proceeds from density functional theory and employs Wannier projections of nonmagnetic band structures onto local $d$ or $f$ orbitals. Energies of multiplets and optical, as well as x-ray spectra are determined by exact numerical diagonalization of a local Hamiltonian describing Coulomb, LF, and spin-orbit interactions. The method is tested for several $3d$ and $5f$ compounds for which the LF parameters and multiplet spectra are experimentally well known. In this way, we obtain good agreement with the experiments for ${\mathrm{La}}_{2}{\mathrm{NiO}}_{4}, {\mathrm{CaCuO}}_{2}, {\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$, ZnO:Co, and ${\mathrm{UO}}_{2}$.

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+.

Rotational dynamics of O2 in the electronic ground XΣg−3 state induced by an intense femtosecond laser field

We theoretically and numerically investigate rotational dynamics of ${\mathrm{O}}_{2}$ in the electronic $X^{3}\mathrm{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}$ ground state induced by an intense femtosecond laser field. The rotational dynamics are calculated by two different models. One of the models includes triplet splittings explicitly in rotational energy levels originated from an electronic spin (a spin-dependent model), and the other omits the triplet splittings (a spin-independent model). We find that the final rotational population after the interaction with the laser field does not depend on the models. On the other hand, we find that the rotational dynamics evaluated by alignment degrees and angular distributions of molecular axes depend on the models. Although the rotational dynamics calculated by the spin-independent model is similar to that calculated by the spin-dependent model within 5 ps, the triplet splittings in the rotational energy levels affect the rotational dynamics after 5 ps. This is explained by the inverse of the energy difference between triplet splittings in the rotational levels. We show that the multiplet energy splittings in rotational energies should be included when the rotational dynamics in the multiplet electronic state are considered. We also investigate excitation processes on the basis of time evolutions of state populations and find that there are excitation pathways with double as well as single bifurcations depending on the initial state.

Combined multiplet theory and experiment for the Fe 2p and 3p XPS of FeO and Fe2O3.

The Al K alpha, 1486.6 eV, based x-ray photoelectron spectroscopy (XPS) of Fe 2p and Fe 3p for Fe(III) in Fe2O3 and Fe(II) in FeO is compared with theoretical predictions based on ab initio wavefunctions that accurately treat the final, core-hole, multiplets. The principal objectives of this comparison are to understand the multiplet structure and to evaluate the use of both the 2p and 3p spectra in determining oxidation states. In order to properly interpret the features of these spectra and to use the XPS to provide atomistic insights as well as atomic composition, it is necessary to understand the origin of the multiplet energies and intensities. The theoretical treatment takes into account the ligand field and spin-orbit splittings, the covalent mixing of ligand and Fe 3d orbitals, and the angular momentum coupling of the open shell electrons. These effects lead to the distribution of XPS intensity into a large number of final, ionic, states that are only partly resolved with energies spread over a wide range of binding energies. For this reason, it is necessary to record the Fe 2p and 3p XPS spectra over a wide energy range, which includes all the multiplets in the theoretical treatment as well as additional shake satellites. We also evaluate the effects of differing assumptions concerning the extrinsic background subtraction, to make sure our experimental spectrum may be fairly compared to the theory. We conclude that the Fe 3p XPS provides an additional means for distinguishing Fe(III) and Fe(II) oxidation states beyond just using the Fe 2p spectrum. In particular, with the use of the Fe 3p XPS, the depth of the material probed is about 1.5 times greater than for the Fe 2p XPS. In addition, a new type of atomic many-body effect that involves excitations into orbitals that have Fe f,ℓ = 3, symmetry has been shown to be important for the Fe 3p XPS.

(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).

Enhance electron-correlation effect on the ruby multiplet energy dependence on pressure

Development of white light-emitting diode (LED) device is especially important due to the lack of red emissions. As candidates for white LED's novel red phosphors, Mn 4+ -doped crystals have received growing attention. Hence, the factors that decide the multiplet energies of d 3 ions such as Mn 4+ and Cr 3+ in crystals are very important to understand. Especially Cr 3+ activated in α-Al 2 O 3 or the well-known ruby has been widely studied for solid-state laser source. Here we calculated the multiplet energies of ruby under different pressures non-empirically. We also investigated the variables that define the correlation between the local structure and the multiplet energy levels. The results show that the first-principles calculations well reproduced the pressure dependence of 2 E transition energy. We found that the behavior of effective Coulomb integral which mainly determines 2 E transition energy is consistent from the point of view of delocalization of the 3d orbitals and decrease of the parameters of the Coulomb repulsion. • Multiplet energies of α-Al2O3: Cr3+ (ruby) under pressure were calculated. • Effect of lattice relaxation and CDC-CC were investigated thoroughly. • The doublet states were red-shifted, while the quartet states were blue-shifted. • The trend of doublet states mainly due to the effective Coulomb integral ( J eff ).

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+.

Optimization of first-principles calculation conditions for multiplet energies of Fe3 + and Co3 + in α-Al2O3

Corundum can contain various transition metals as impurities, for example, ruby. Ruby is used as solid state laser. The prediction of the electronic state of these transition metals is very important for the development of novel optical materials. The CI calculation used finite Slater determinants, the calculated mutiplet energies is overestimated generally. In this study, we optimized the calculation multiplet energy of transition metals in α-Al2O3 by considering some corrections.

Lattice Relaxation Effects on the Multiplet Energies of Ruby Under Pressure using One-Electron Calculations

Up to recently, it has been difficult to calculate the multiplet energies of compounds using one-electron approach. Since it only considers one electron and one nuclei, the interaction among the electrons are neglected. Previously we have successfully estimated the 2E→ 4A2 (R-line) levels of ruby at 0 pressure using one-electron approach based on one-electron calculation using the first-principles Discrete Variational-Xα (DV-Xα) method. Here we want to perform similar investigation, not only for 0 pressure but up to 110 GPa. We estimated the lattice relaxation effect due to the Cr3+ substitution and due to the applied pressure by using two different methods i.e., Shannon’s crystal radii and geometry optimizations. Two different types of model cluster consisting of 7 and 63 atoms will be used. The 2E level is estimated by the barycenter of t2g 3 configuration which consists of 4 multiplets.