Xα Method Research Articles

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.

Prediction of 4f-5d Transition Energy of Ce3+ in Oxides By First-Principles Calculations and Machine Learning

A Ce3+ ion has only one electron in the 4f orbitals and its 4f-5d transition energy is strongly influenced by the width of the crystal field splitting of the 5d orbitals. In other words, the absorption and emission wavelengths of Ce3+ in crystals can be widely controlled by changing the ligand field environment. As an example of Ce3+-doped phosphor, Ce:YAG (Y3Al5O12) is widely used as an yellow phosphor for standard white LEDs. Therefore, novel phosphors with desired emission colors can be developed by adding Ce3+ to appropriate host crystals.In this work, we aimed to construct an efficient prediction model for the transition energy of Ce3+ in oxide crystals. Small clusters consisting of the substituted Ce3+ ion and the first-neighbor anions were constructed and molecular orbital calculations were performed using the relativistic discrete-variational Xα (DV-Xα) method. Then machine learning based on structural and electronic state parameters was performed to create a predictive model for the 4f-5d transition energy of Ce3+ in crystals. By creating the correlation diagrams, the influence of each parameter on the transition energy was analyzed in detail.

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).

First-Principles Calculation on the Emission Energy Level of Ruby Based on DV-Xα Molecular Orbital Method and Ligand Field Theory

The transition metal 3d3 ions activated in various host crystals have been studied in a great number of experiments and calculations. Their energy levels in strong crystal field namely 4A2, 2E, 2T1, 2T2, 4T2, and 4T1a play important roles in the luminescence process. Especially, the transition energy from 2E state to 4A2 state or R-line has been utilized for the emission process. Since the development of ligand field theory (LFT), the first-principles calculations have been helpful to understand the behavior of R-line. In 1982, Ohnishi and Sugano [1] carried out the semi-empirical first-principles calculation based on the discrete variational Xα (DV-Xα) method [2] to estimate the emission energy of ruby (Al2O3 doped with Cr3+) at various bond lengths under Oh symmetry. In their estimation, the barycenter of t 2g 3 configuration was an important parameter to estimate the R-line energy. Although the results are reasonable, the barycenter was defined as the average of only 3 multiplet states i.e. 2E, 2T1, and 2T2 states. However, according to LFT, the t 2g 3 configuration consists of 4 multiplet states not only 2E, 2T1, and 2T2 states but also the ground state, 4A2. Therefore, here we proposed a new calculation formula to improve the accuracy of R-line energy by considering 4 multiplet states such as 4A2, 2E, 2T1, and 2T2 states. Two types of model clusters, non-optimized and optimized model clusters consisting of 63 atoms were used for the calculations. The impurity Cr3+ ion was located at the center of the model clusters. The non-optimized model cluster was constructed based on the experimental crystal structures of α-Al2O3 under pressures with hexagonal A2X3 structure. On the other hand, since the local structure in the actual materials is different from the original ones, the optimized model cluster was constructed to consider the effect of lattice relaxation. It was estimated by performing geometry optimization using the CAmbridge Serial Total Energy package (CASTEP) code [3]. Firstly, the structural optimizations of pure α-Al2O3 crystal under various pressures were carried out and then followed by the geometry optimization of α-Al2O3 crystal doped with Cr3+ ion. The molecular orbitals energies were then estimated by performing one-electron calculations using DV-Xα method for both model clusters. During the calculations, the local C 3 symmetry was maintained to minimize the computational error. Next, the R-line energies were then estimated by two different approaches i.e., (1) based on the approach proposed by Ohnishi’s group and (2) based on LFT. Figure 1 shows the theoretical R-line energies of ruby under pressures calculated using the optimized model clusters. E R1 and E R2 indicate the estimated R-line energies based on the approach proposed by Ohnishi’s group and those based on LFT, respectively. For comparison, the R-line energies of ruby at various Cr-O bond length calculated under Oh symmetry [1] and the experimental R-line energies of ruby under pressures observed within C3 symmetry [4] are shown together in Fig. 1. Our results show that by both approaches, the R-line energies decrease as the applied pressure increases. Accordingly, simple estimation based on one-electron calculations has successfully reproduced the tendency of ruby’s emission energies. Compare to the experimental values, the R-line energies estimated based on Ohnishi’s approach were significantly underestimated. On the other hand, the calculated R-line energies based on LFT improved the accuracy towards the experiment excellently.

Optical properties and electronic structure of Lu2SiO5 crystals doped with cerium ions: Thermally-activated energy transfer from host to activator

This paper reports on the optical properties of cerium-doped lutetium oxyorthosilicate (LSO:Ce) crystals. The reflection and X-ray photoelectron spectra are measured, and compared to the electronic structure calculated by a discrete variational Xα method. A sharp exciton band originating from O 2p→Lu 5d transition is observed at 7.27eV at 6K, with the band-gap energy of 7.52eV. Luminescence measurements have also been performed in a wide temperature range of 6–300K. The intensity of Ce luminescence arising from the 5d→4f transition is temperature-independent under the direct excitation of Ce3+ ions, but it is enhanced at around 50K under the excitation of host LSO crystals. This enhancement is found to anti-correlate with a thermal quenching of the intrinsic luminescence due to self-trapped excitons. The present results provide a piece of evidence that thermally-activated energy transfer from host to activator takes place efficiently in LSO:Ce.

Theoretical Enhancement of Thermoelectric Properties of Sr1–xLaxTiO3

The electronic structure and density of state (DOS) of Sr1–xLaxTiO3 (x = 0, 0.06, 0.125, and 0.25) have been investigated on the first principle molecular orbital calculation. The La was substituted Sr site in SrTiO3 and caused an increase of electrical conductivity. The electronic structure, DOS and band structure of Sr1–xLaxTiO3 (x = 0, 0.06, 0.13, and 0.25) were calculated by discrete variational (DV)-Xα method and Material studio to estimated the thermoelectric properties. The Seebeck coefficient and electrical conductivity of Sr1–xLaxTiO3 were estimated form DOS by Boltzmann theory: Mott and Jones equation. It was found that, the substitution of La made high electrical conductivity, made high power factor and enhancement thermoelectric properties. The Sr0.87La0.13TiO3 cluster shows maximum power factor about 2.55×10−3 W/m·K2 at 1200 K. For maximum enhancement thermoelectric properties of SrTiO3 x = 0.13 should be used in the synthesis of Sr1-xLaxTiO3.

Local structure analysis of heavily boron-doped diamond by soft x-ray spectroscopy

To clarify the electronic structure of metallic heavily boron (B)-doped diamonds, the discrete variational (DV)-Xα method was used to analyze the continuous X-ray absorption near edge structure (XANES) in the BK and CK regions of a 71,000-ppm B-doped diamond. The continuous XANES profiles are well reproduced by the unoccupied B2p- and C2p-DOS of the caged B-cluster models, in which an octahedron B6 cluster, a cuboctahedron B12 cluster, or an icosahedron B12 cluster is inserted into the defect space of the diamond lattice. The delocalized conduction band structure can be understood from the hybridization of the B atoms in B-clusters with the surrounding C atoms in the diamond lattice. The results indicate that the B atoms in heavily B-doped diamonds form caged B-clusters in the defect space of the diamond lattice.

Syntheses, crystal structures, and magnetic properties of cyano-bridged Mn(II)–Nb(IV) bimetal assemblies

In this paper, we report the syntheses, crystal structures, and magnetic properties of two manganese(II)–octacyanoniobate(IV)-based magnets: MnII2[NbIV(CN)8](3-pyridinemethanol)8·2H2O (1) and MnII2[NbIV(CN)8](3-aminopyridine)8·2H2O (2). 1 and 2 possess 3D network structures where a [Nb(CN)8]4− ion is connected to four Mn ions, and a Mn ion is connected to two [Nb(CN)8]4− ions via bridged cyanides. The coordination geometry of [Nb(CN)8] in 1 is square antiprism, while that in 2 is dodecahedron. Magnetic measurements show that 1 and 2 are ferrimagnets with Curie temperatures (TC) of 24 and 43K, respectively, although the coordination numbers of the bridged CN groups around Nb and Mn ions are the same. The difference in TC can be understood by considering the difference in the coordination geometries of [Nb(CN)8]. Molecular orbital calculations of [NbIV(CN)8] using the discrete variational (DV)-Xα method indicate that the population of the 2p orbital on the bridged N with a dodecahedron geometry is larger than that with a square antiprism geometry. The calculation results suggest that the charge population of the 2p orbital on the cyano-nitrogen affects the superexchange interaction for the magnetic orbital of NbCNMn, which determines the TC value.

Analysis of autocorrelation functions calculated from Compton profiles of a N2 molecule using the DV-Xα method

Compton profiles and autocorrelation functions for a N2 molecule are calculated using the discrete variational Xα (DV-Xα) method and compared with recent and accurate measurements of the Compton profile of N2 gas and Compton profiles calculated using the Hartree–Fock and the configuration interaction methods. The autocorrelation function shows a position dependence on the electron correlation. The molecular orbital dependence of the autocorrelation function reveals that the π molecular orbitals are the most sensitive to α values in the DV-Xα method.

Experimental and theoretical analysis on the charge transfer band of Y 2O 3:Eu nanocrystals

Nanocrystalline cubic Y 2O 3:Eu were prepared by combustion reaction. The crystal structure and morphology were analyzed by means of X-ray diffraction (XRD) and transmission electron microscopy (TEM). The luminescent properties of the powder were investigated. The charge transfer band position showed redshift from 241 to 251 nm, which was related to the change of the local surroundings of Eu 3+ ions in nanocrystalline Y 2O 3:Eu. The ground-state electronic structure and charge transfer transition of both the bulk and nanocrystalline cubic Y 2O 3:Eu crystals were calculated by the ab initio self-consistent relativistic DV-Xα (discrete variational Xα) method. A complete 35-ion cluster was selected to simulate the local coordination surroundings of Eu doped in Y 2O 3 bulk crystals while five additional incomplete clusters were also selected to simulate the local surroundings of Eu ions in nanocrystals. It could be found that the charge transfer energies of the nanocrystalline Y 2O 3:Eu were less than that of the bulk counterpart, which was consistent with the redshift phenomenon of the CT band in the excitation spectrum of the nanocrystalline Y 2O 3:Eu.

Evaluation of the Hydraulic Reactivity of Calcium Aluminate Glass Containing Silicate Ion with Discrete Variational Xα Method

ABSTRACT This study investigated changes in the chemical properties of calcium aluminate glass with the impurity of silicate ions through computable calculation with discrete variation Xα (DV-Xα). The previous study showed that the hydraulic reactivity of calcium aluminate glass decreased with the increase on the added amount of silicate ion to the component of calcium aluminate glass. From the calculation results of DV-Xα, it was known that the bulk bond strength of calcium aluminate glass increased with the substitution of Si for Al in the cluster crystal structure. The bond strength would be closely related with the hydraulic reactivity. Therefore, the increase of bonding strength lowered the hydraulic activity of calcium aluminate glass. These results clarified the decrease of hydraulic reactivity of calcium aluminate glass containing silicate ions.

Evaluation of the Hydraulic Reactivity of Calcium Aluminate Glass Containing Silicate Ion with Discrete Variational Xα Method

ABSTRACT This study investigated changes in the chemical properties of calcium aluminate glass with the impurity of silicate ions through computable calculation with discrete variation Xα (DV-Xα). The previous study showed that the hydraulic reactivity of calcium aluminate glass decreased with the increase on the added amount of silicate ion to the component of calcium aluminate glass. From the calculation results of DV-Xα, it was known that the bulk bond strength of calcium aluminate glass increased with the substitution of Si for Al in the cluster crystal structure. The bond strength would be closely related with the hydraulic reactivity. Therefore, the increase of bonding strength lowered the hydraulic activity of calcium aluminate glass. These results clarified the decrease of hydraulic reactivity of calcium aluminate glass containing silicate ions.

Selective adsorption of atomic hydrogen on a h-BN thin film

The adsorption of atomic hydrogen on hexagonal boron nitride (h-BN) is studied using two element-specific spectroscopies, i.e., near-edge x-ray absorption fine structure (NEXAFS) spectroscopy and x-ray photoelectron spectroscopy (XPS). B K-edge NEXAFS spectra show a clear change in the energy region of the π* band before and after reaction with atomic deuterium. On the other hand, N K-edge NEXAFS spectra show only a little change. B 1s XPS spectra show a distinct component at the low binding energy side of a main component, while N 1s XPS spectra show peak broadening at the high binding energy side. These experimental results are analyzed by the discrete variational Xα method with a core-hole effect and are explained by a model in which hydrogen atoms are preferentially adsorbed on the B sites of h-BN. Based on the experimental and theoretical results, we propose a site-selective property of BN material on adsorption of atomic hydrogen.

Spectroscopic study of Ni-rich Al–Co–Ni quasicrystal

The valence-band electronic structure of a decagonal Ni-rich Al–Co–Ni quasicrystal, Al72Co8Ni20, was investigated using soft X-ray photoelectron spectroscopy. In particular, the energy distributions of the transition metal 3d bands were determined from the Co and Ni 2p–3d resonance photoemission and compared with those calculated by the discrete variational Xα method for a model cluster based on a proposed Ni-rich Al–Co–Ni approximant, as well as the 3d band observed in the Co-rich Al–Co–Ni quasicrystal, Al72Co16Ni12. In the Ni-rich Al–Co–Ni, the transition metal 3d band exhibits a peak at a binding energy, E B, of 2.3 eV, which is higher than that of the Co-rich Al–Co–Ni. The observed Ni 3d band has a single-peaked distribution around E B ∼ 2.4 eV, in contrast to the calculated bimodal and wide-spread distribution for the proposed Ni-rich Al–Co–Ni model cluster, whereas the Co 3d band is located at E B ∼ 1.7 eV, consistent with the model calculation.

Excitation processes of trivalent cerium ions in calcium thiogallate crystals by hot photocarriers

Excitation spectra for the 5d → 4f emission of Ce3+ ions in CaGa2S4 crystals have been measured at 300 K by using vacuum ultraviolet (VUV) photons, together with reflectivity and absorption-edge spectra. X-ray photoelectron spectroscopy (XPS) experiment has also been performed in order to clarify the contribution of shallow core states to the excitation and reflectivity spectra. Furthermore, cluster calculation by a relativistic discrete variational Xα (DV-Xα) method has been carried out to elucidate the optical transitions resulting in the creation of multiple e-h pairs in CaGa2S4. The excitation processes of Ce3+ ions in CaGa2S4 by hot photocarriers are discussed on the basis of the electronic structure determined from the experiments and calculation.

Electronic structural difference between Li7VN4 and Li7MnN4 due to the replacement of V with Mn: A simulation by a discrete variational Xα method

The difference in electronic structure of Li 7 M N 4 (M=V and Mn) due to the replacement of V with Mn is studied by the discrete variational (DV) X α method. Li 7 VN 4 and Li 7 MnN 4 crystallize in the same zinc-blende-like structure (space group: P-43n) with similar lattice constants of 9.6090 and 9.5548 Å, respectively. The DV-X α calculations show that Li 7 VN 4 is a semiconductor with energy gap between the empty V-3d related band and the completely occupied N-2p band, while Li 7 MnN 4 has a metallic electron configuration because of the partially occupied Mn-3d related band located above the completely filled N-2p band, exhibiting the shift of the Fermi level caused by an increase in electron due to the replacement of V with Mn, where Mn (electron configuration: 3d 5 4s 2 ) owns two more 3d electrons than V (3d 3 4s 2 ) does. Electron paramagnetic resonance and magnetic susceptibility measurements reveal that Li 7 MnN 4 is paramagnetic, resulting from the electrons partially occupying the Mn-3d related band, while Li 7 VN 4 is diamagnetic, arising from the un-occupation of the V-3d related band. These experiments support the computational results.

Exciton transition and electronic structure of PbMoO4 crystals studied by polarized light

Polarized reflectivity spectra of PbMo0 4 crystals have been measured using synchrotron radiation up to 20 eV. The optical constants for the crystallographic axes are derived by using a Kramers-Kronig analysis. It is found that the exciton band at 3.6 eV shows a doublet structure with distinct dichroism. X-ray photoemission spectroscopy (XPS) and the calculation of the electronic structure by a discrete variational Xα method are also carried out. The calculation shows that the valence band and the conduction band are mainly composed of the O 2p and Mo 4d states, respectively, and the Pb state contributes appreciably to the top of the valence band and the bottom of the conduction band. The valence-band XPS spectrum of PbMoO 4 is compared with that of PbW0 4 , which reveals a remarkable difference between them. This difference reflects different magnitudes of hybridization of Mo 4d or W 5d state to the valence band. The exciton transition is explained in terms of the cationic Pb 6s → 6p excitation model taking into account the crystal-field splitting and the spin-orbit interaction of Pb 6p state. From a comparison of the doublet structure of the exciton band of PbMo0 4 and PbW0 4 , it is suggested that the electron-hole exchange interaction plays an important role for the exciton transitions in both materials.

Study of the structural stability of LnNb x O y systems (Ln = La, Ce, Pr, Nd, Pm, Sm, Eu) by the X α method of discrete variation

The electronic structure and Ln-O (Ln = La, Ce, Pr, Nd, Pm, Sm, Eu) bonding parameters have been calculated by the Xα method of discrete variation taking into account the real structure of LaNb7O12 oxoniobate. It is shown that the experimentally observed tendencies in the change in the oxoniobate stability correlate with the decrease in the average electron-proton binding energy of LnO8 clusters and enhanced repulsion between Ln and O orbitals to the end of the lanthanide series.

Electronic structure of vacancy and chemisorptive bond on Si(111) surface by the DV-Xα cluster calculation

The electronic structure of the Si(111) surface is investigated by the first-principle Dv (discrete-variational)-Xα method with the use of several model clusters such as Si13,12, H15, Si16H21, and Si19H21. Chemisorptions of H, Cl, and Ag on the Si(111) surface are also studied. Those characteristics in the electronic structure which are closely related with surface atomic arrangements and chemisorption geometries are clarified in detail. The present calculation shows that surface vacancy is essential in order to give an electronic structure which corresponds well with the observed UPS on the Si(111) 7 × 7 surface. Furthermore, for the Si(111)/Ag system it is elucidated that the Ag atom is chemisorbed on top of the Si atom at the low temperature phase.

Comparison of TFD and Xα methods for molecules and solids

The Thomas–Fermi–Dirac (TFD) and multiple-scattering Xα (MS-Xα) methods are compared, for single atoms and for molecules and solids. Both methods are derived from Hamiltonians by variation of the charge density or spin orbitals, respectively, and the Hamiltonians for the two methods differ only in the kinetic energy term. It is pointed out that the main errors in the TFD method arise from the statistical version of the kinetic energy term. The Xα method, which uses the exact kinetic energy term, can be regarded as a modification of the TFD method which removes all the major errors in that method. The Coulomb energy and the exchange-correlation term are identical in both methods. By the example of the TFD method for the carbon atom we illustrate the various features of both methods, and it is pointed out that many features of the calculation of total energy by the Xα method, as described by the overlapping-sphere approach, can be understood better by studying the same problem from the TFD point of view.