Discrete Variational Multi-electron Method Research Articles

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.

Color coordination of emerald on CIE color space based on first-principles calculations

Be3Al2(SiO3)6 including Cr3+ known as emerald have been widely studied and utilized for solid-state laser materials. Numerous theoretical investigations on these systems have also been published in the literature since the electronic energy levels, optical properties, and structures of Cr3+ impurities in emerald systems have been thoroughly investigated using a variety of experimental approaches. In general, semi-empirical computations have been used to accomplish the majority of theoretical interpretations of experimental data. Although in the case of non-empirical calculations, the agreement between theoretical and experimental optical properties was improved by taking into account the energy corrections, quantitative evaluation of the color of emitted light was not feasible until recently. Here, the color coordinates of emerald under the standard illuminant has been calculated to perform a quantitative evaluation based on the optical spectra. The “theoretical” color was calculated and presented visually on the Commission Internationale d’Eclairage (CIE) color space based on the theoretical spectra obtained non-empirically using the so-called first-principles discrete variational multi-electron method, known as DVME. The absorption spectra of emerald were calculated using CrO69− model cluster with D3 symmetry. Several key effects in reproducing optical spectra were investigated in detail, such as lattice relaxation, energy correction, and orbital effects. The accuracy of this approach in predicting absorption spectra was analyzed thoroughly under various computational conditions. The results show that accounting for all of the above effects is important to producing the absorption spectra. Specifically, enlarging the considered orbital in the calculation improved the agreement between the computed and experimentally-observed colors. This study is crucial for validating the non-empirical calculations made using the DVME approach to assess the color of emitted light quantitatively.

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.

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).

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.

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.

Study of multiplet structures of Mn4+ activated in fluoride crystals

We investigated the optical properties of Mn4+ in some fluoride crystals such as Cs2MnF6, Cs2GeF6, Rb2GeF6, Cs2SiF6, K2SiF6, Rb2MnF6, Rb2SiF6, K2GeF6, K2TiF6, Li2MnF6, Na2GeF6, Na2SiF6, and Na2TiF6 based on the first-principle calculation using the discrete-variational multi-electron method. In order to estimate the lattice relaxation, we performed EXAFS measurement of Mn4+ doped in K2SiF6, K2TiF6, and K2GeF6. The relaxation rates of A2BF6:Mn4+ were fixed to be the above estimated values, 102.24%, 107.37% or 96.80% for crystal having Si, Ge, or Ti at the B cation site, respectively. In this work, we also considered some corrections such as configuration dependent correction and correlation correction to improve the theoretical energies. It has been shown that to reproduce multiplet energy levels quantitatively, the lattice relaxation is very important. On the other hand, for a qualitative prediction of the tendencies of the multiplet energies, the combination of lattice relaxation effect, configuration dependent correction, and correlation correction is effective.

Study on Multiplet Energies of V2+, Cr3+, and Mn4+ in MgO Host Crystal Based on First-Principles Calculations with Consideration of Lattice Relaxation

A comparative study of the multiplet energies of the isoelectronic 3d3 ions in MgO host crystal using the first-principles calculation has been performed by discrete-variational multi-electron method. In this investigation, the effect of lattice relaxation was considered based on geometry optimization using first-principles band-structure calculation. The spin-polarization effect and the effect of Hubbard U were also investigated. The estimated multiplet energies were reasonably well reproduced when we used the optimized cluster with spin-polarization effect and some corrections such as configuration dependent correction and correlation correction. The results also show that the lattice relaxation is important to reproduce the tendency of the transitions from 4A2 state to 4T2 and 4T1a states, while the tendency of the transition from 2E state to 4A2 state is mainly determined by the effect of electron correlation.

Electronic states of Nd 3+ ions in phosphate glasses calculated by the discrete-variational multi-electron method

The electronic states of Nd 3+ ions in phosphate glasses were calculated by the relativistic discrete-variational multi-electron (DVME) method. This method is a configuration-interaction (CI) calculation program using the molecular orbitals obtained by the relativistic DV-Xα method. This method could be applicable to obtaining the electronic state of any kinds of rare-earth ions in crystals. Although the DVME method has been used previously for rare-earth ions in crystals, in the present work we applied it to the glassy materials and calculated the electronic state and the absorption spectra of the Nd 3+ ions in phosphate glasses. A cluster model H 18MNdP 7O 28 (M = Li, Na, K) was used to discuss the influence of the glass matrices to the electronic state of the Nd 3+ ion. We obtained theoretical ultraviolet–visible (UVV) absorption spectra and compared them with the experimental ones. The results suggested that this method was useful for the analyses of multiplet structures of the Nd 3+ ion in phosphate glasses.

Spectroscopic study of the Pr-doped BiBO glass and Ca 4GdO(BO 3) 3 single crystals

Detailed spectroscopic studies of Pr 3+ ions in BiBO glass and Ca 4GdO(BO 3) 3 crystal were performed. Experimental absorption spectra were measured at room temperature and assigned. The first principles discrete variational multielectron method was used to model the polarized absorption spectra of the Ca 4GdO(BO 3) 3:Pr 3+; without any fitting parameters, the overall appearance of the spectra was reproduced satisfactorily. The energy intervals between different molecular orbitals in the [PrO 6] cluster were estimated. The conventional Judd-Ofelt theory was used to calculate the oscillator strengths of the 4f-4f transitions in the BiBO:Pr 3+ system; the set of the phenomenological intensity parameters was determined.

Fluorescence spectra of Pr3+ ions in phosphate materials calculated by the DVME method

AbstractRecently, fluorescence spectra of rare‐earth ions in oxide materials are very attractive for the applications of the optical amplification in optical fiber communications, white LED, etc. However, it has been difficult to calculate the fluorescence spectra of rare‐earth ions by the first principle method. In this study, we used the relativistic discrete‐variational multielectron (DVME) method, which is a configuration‐interaction (CI) calculation program using the molecular orbitals obtained by the relativistic DV‐Xα method. We applied this method for the calculation of the fluorescence spectrum of the Pr3+ ions in phosphate materials. The transition probability of the fluorescence was calculated in the same manner of the absorption. The obtained theoretical fluorescence spectrum was in good agreement with the experimental one, though the intensity of each peak was deeply dependent on the configuration of the surrounding structural units. The results suggested that the DVME method was useful for the calculation of not only absorption but also fluorescence spectra of rare‐earth ions in oxide materials. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Theoretical Analysis of Phosphors Based on First-Principles Cluster Calculations Using the Relativistic DVME Method

We have performed the theoretical calculations on the electronic structures of host crystals used for phosphors and those of rare-earth-doped phosphors using the computational programs of the relativistic discrete-variational Xα potential (DV-Xα) method and one of its extension programs known as the discrete-variational multi-electron (DVME) method. Both of them are powerful tools for the study of the optical properties of conventional and novel phosphors.

Fully relativistic analysis of the absorption spectra of Ca3Sc2Ge3O12:Ni2+

AbstractSystematic analysis of the energy level schemes, ground state absorption (GSA) and covalency effects for the Ni2+ ion in Ca3Sc2Ge3O12 was performed. The recently developed first‐principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi‐electron method (DV‐ME) [K. Ogasawara et al., Phys. Rev. B 64, 115413 (2001)] was used in the calculations. As a result, complete energy level schemes of Ni2+ and its absorption spectra at both possible crystallographic positions (distorted octahedral Sc3+ and tetrahedral Ge4+ positions) were calculated, assigned and compared with experimental data. Energies of the charge transfer (CT) transitions for both positions are estimated. Numerical contributions of all possible electron configurations into the calculated energy states were determined. By performing analysis of the molecular orbitals (MO) population, it was shown that the covalency of the chemical bonds between the Ni2+ and O2− ions increases in passing from the hexa‐ to the tetra‐coordinated complex. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

First-principles calculations of the V3+ absorption spectra in LiAlO2 and LiGaO2

The systematic first-principles analysis of the energy level schemes and ground state absorption (GSA) of the V3+ ion in two oxide crystals LiAlO2 and LiGaO2 was performed. The recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi-electron method (DV-ME) [K. Ogasawara, T. Iwata, Y. Koyama, T. Ishii, I. Tanaka, H. Adachi, Phys. Rev. B 64 (2001) 115413] was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, complete energy level schemes of V3+ ion and its absorption spectra in both crystals were calculated, assigned and compared with experimental data.

Comparative first-principles study of the Ni 2+ absorption spectra and covalence effects in isostructural crystals NiCl 2, NiBr 2 and NiI 2

Systematic ab initio calculations of the ground-state absorption spectra and covalence effects in three isostructural anisotropic crystals with layered structure (NiCl 2, NiBr 2 and NiI 2) are presented. The recently developed first-principles approach to the analysis of the absorption spectra based on the discrete variational multi-electron method (K. Ogasawara et al., Phys. Rev. B 64 (2001) 115413) was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, energies of the Ni 2+-ion multiplets and absorption spectra of all above-mentioned crystals were calculated, assigned and compared with experimental spectra. By performing analysis of the molecular orbital population, it was shown that the degree of covalence of the chemical bond between Ni 2+ ion and ligands is in the following order: NiI 2>NiBr 2>NiCl 2.

Fully relativistic analysis of the covalence effects for the isoelectronic 3d3 ions (Cr3+, Mn4+, Fe5+) in SrTiO3

Fully relativistic calculations of the energy levels, absorption spectra, molecular orbitals (MO) compositions, covalence effects and energies of the charge transfer (CT) transitions for three isoelectronic ions Cr3+, Mn4+, Fe5+ in the SrTiO3 (STO) crystal have been performed. The recently developed first-principles approach to the analysis of the absorption spectra based on the first principles discrete variational multi-electron method (DV-ME) (K. Ogasawara et al., Phys. Rev. B 64 (2001) 115413) was used in the calculations. As a result, energy levels of the above ions, their absorption spectra and energies of the lowest CT transitions were all calculated. By performing analysis of the MO population, it was shown that the degree of covalence of the chemical bonds between 3d ions and oxygen ions in SrTiO3 increases in the following order: Cr3+→Mn4+→Fe5+, whereas the CT energies monotonically decrease in the same order.

Calculations of the Transitions Intensities in the Optical Spectra of Dy3+:LiYF4

AbstractFor Abstract see ChemInform Abstract in Full Text.

Calculations of the transitions intensities in the optical spectra of Dy 3+:LiYF 4

Optical spectra of Dy 3+:LiYF 4 (Dy 3+:YLF) single crystal were analyzed using Judd–Ofelt theory and discrete variational multielectron method (DVME). Oscillator strengths (OS) of transitions up to 39 000 cm −1 in the absorption spectrum, branching ratios and nonradiative transition rates were calculated; assignment of the absorption transitions was given. A good agreement between calculated and experimental values of branching ratios for transitions from quartet 4 F (3) 9/2 to the low-lying sextet levels is demonstrated. Ab initio calculations of OS were performed.