Discrete Variational Xα Method Research Articles

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.

Investigation of Ion Dependence of Electronic Structure for 3d3 Ions in Mg2TiO4 Based on First-Principles Calculations

In this work, the local electronic structures around isoelectronic 3d 3 ions such as V2+, Cr3+, and Mn4+ in Mg2TiO4 crystals were investigated based on first-principles configuration-interaction calculations. The factors to determine tendencies of the crystal field splitting and the multiplet energy among them were analyzed in detail based on the explicit many-electron wave functions. The multiplet energy levels of V2+, Cr3+, and Mn4+ doped in Mg2TiO4 were calculated using the discrete variational multi-electron code, which is a configuration-interaction calculation program based on the discrete variational-Xα method. Overall, the results show that only the calculation with consideration of the lattice relaxation effect can provide a reasonable tendency, where the multiplet energies of 4A2 → 4T2 (U-band) and 4A2 → 4T1a (Y-band) increase as the charge of the transition metal ion increases.

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.

An X α-discrete variation method for calculating the electronic structure and parameters of Mössbauer spectra of 57Fe nuclei in iron oxide compounds exhibiting high states of oxidation

An Xα-discrete variation method is ab initio applied to calculate the electronic structure and chemical bonding parameters in [Fem+O4]m − 8 and m = 3+ … 8+ clusters in iron oxide compounds. The tendencies of change in the Mossbauer spectra parameters of iron within these clusters can be accounted for by the formation of two types of Fe3d-AO sub-bands, the occupied hybrid structureless and the vacant basic.

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.

Analysis of the co‐doping effect of manganese and lanthanide elements in SrGa2S4 by the relativistic DV‐Xα calculation

AbstractThe electronic states of manganese and lanthanide elements in SrGa2S4 are calculated by the relativistic discrete variational Xα method using a FORTRAN program of DVSCATR in order to investigate the mechanism allowing the 3d‐3d transition of Mn in SrGa2S4 by co‐doping a lanthanide element. We use a spherical cluster model of the D2 symmetry which consists of 45 atoms of Sr9Ga12S24, representing SrGa2S4, in our calculation. Doping a lanthanide to SrGa2S4 is represented by substituting a Sr atom with a lanthanide atom (indicated by ‘Ln’) at the cluster centre as (LnSr8)Ga12S24. Two types of co‐doping models are prepared as (LnMn2Sr6)Ga12S24 for MnSr and (LnSr8)(Mn4Ga8)S24 for MnGa with keeping the D2 symmetry. As a result of the self‐consistent charge (SCC) calculation, the averaged distance between a lanthanide atom at the cluster centre and surrounding eight sulphur atoms has to be set as 70 to 80% of that between the original Sr‐S combinations. Calculated electronic states show that the Ln(5d) and Mn(4s,4p) atomic orbitals are highly mixed, and in the lower energy range, the Mn(4s,4p) and Mn(3d) are also highly mixed. This hybridization cascade can explain the co‐doping effect as that the electrons optically excited to the unoccupied states relating to the Ln(5d) would finaly relax to the 3d‐3d transition of Mn. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Soft X-ray absorption spectra in the C K region of carbon black and spectral analysis using the discrete variational Xα method

Soft X-ray absorption spectra in the C K region of carbon black and spectral analysis using the discrete variational Xα method

Soft X-ray absorption spectra in the CK region of carbon black and spectral analysis using the discrete variational Xα method

To investigate the local structure of carbon black (CB) crystallites, soft X-ray absorption spectra (XAS) in the CK region of CB were measured using synchrotron radiation, and the π* peak profile in the CK-XAS was analyzed by the discrete variational (DV) Xα method. Compared to highly oriented pyrolytic graphite (HOPG), CB exhibits a broader π* peak profile where the intensity of the broad portion in CB is proportional to the hydrogen occluded in the CB. However, the broad portion cannot be reduced even in H2-degassed CB by thermal desorption. These findings on the broad π* peak profile can be simulated by the unoccupied C2p density of states (DOS) of the carbon atoms that form the nonbenzenoid rings and hydrogenated edge carbon atoms. Therefore, plausible origins for the broad π* peak in the CK-XAS of CB are the nonbenzenoid structure and/or hydrogenated edge carbon atoms in the graphitic crystallites.

Study on the interaction between hydrogen and metals of LaNi 5 type hydrogen absorbing alloys by means of DV-Xα method

The electronic structures of LaNi 5, LaNi 4.5Co 0.5, La 0.6Ce 0.4Ni 5, LaNi 5H 0.2, LaNi 4.5Co 0.5H 0.2 and La 0.6Ce 0.4Ni 5H 0.2 were studied by means of the discrete variational Xα (DV-Xα) method. The interaction between hydrogen and the hydrogen absorbing alloys was mainly discussed on the basis of the bond orders between hydrogen and its first neighboring metals and the ionicity of the atom by means of the Mülliken population analysis. The bond orders between the hydrogen and the first neighboring metals in LaNi 5H 0.2 were larger than those in LaNi 4.5Co 0.5H 0.2. The weak positive charge of H in LaNi 5H 0.2 interacted attractively with the weak negative charge of first neighboring Ni(1), however the charge of H interacted repulsively with the weak positive charge of the substituted first neighboring Co(1) in LaNi 4.5Co 0.5H 0.2. Therefore, the hydrogen in LaNi 5H 0.2 interacted somewhat strongly with the first neighboring metals compared with that in LaNi 4.5Co 0.5H 0.2. The bond orders between the hydrogen and the first neighboring atoms in LaNi 5H 0.2 were similar to those in La 0.6Ce 0.4Ni 5H 0.2, but the electrostatic interaction between H and Ni(1) of La 0.6Ce 0.4Ni 5H 0.2 was weakened compared with that of LaNi 5H 0.2. So, the hydrogen in LaNi 5H 0.2 interacted more strongly with the neighboring Ni(1) than that in LaNi 4.5Co 0.5H 0.2. These findings were consistent with the thermodynamic experimental results.

Lifetime‐broadening‐suppressed XANES spectra of copper complexes

AbstractLifetime‐broadening‐suppressed (LBS) Cu K‐XANES spectra of several Cu (II) complexes have been measured by partially fluorescent yield technique. The obtained spectra were compared with oscillator strength distributions calculated by discrete variational Xα method. It was demonstrated that LBS‐XANES spectra are sensitive to ligands, and hence are applicable as a helpful probe in coordination chemistry. Copyright © 2008 John Wiley & Sons, Ltd.

The DFT–DVM theoretical study of the differences of quadrupole splitting and the iron electronic structure for the rough heme models for α- and β-subunits in deoxyhemoglobin and for deoxymyoglobin

Quantum chemical calculations of the iron electron structure and 57Pe quadrupole splitting were made by density functional theory and Xα discrete variation method for the rough heme models for α- and β-subunits in deoxyhemoglobin and for deoxymyoglobin accounting stereochemical differences of the active sites in native proteins. The calculations revealed differences of quadrupole splitting temperature dependences for three models indicating sensitivity of quadrupole splitting and Fe(II) electronic structure to small variations of iron stereochemistry.

X α discrete variational analysis and 1H nuclear magnetic resonance study of the dissociation of water molecules on the surface of TiO and TiO2 oxides

The disordered state of hydrogen in titanium oxyhydrate has been investigated by 1H nuclear magnetic resonance. The protonation of TiO and TiO2 oxides has been simulated by the Xα discrete variational method. It is established that an increase in the number of protons decreases the stability of coordination polyhedra of titanium atoms, while an increase in the O-H bond length enhances the ability of water molecules to dissociate.