High‐lying core‐excited quartet states in Li‐like N4+ and F6+ ions

The variational method with mutilconfiguration interaction wave function is used to obtain the energies, fine structures, and hyperfine structures of high‐lying core‐excited quartet states 1s2lnl' ⁴P^o(m) (m = 1–5) and 1s2pnp ⁴P(m) (m = 1–5) in Li‐like N⁴⁺ and F⁶⁺ ions, including the mass polarization and relativistic corrections. Restricted variational method is carried out to extrapolate a better energy. The oscillator strengths, lifetime, wavelengths, fine structure, and hyperfine structure for this system are also investigated to compare with other theoretical and experimental data in the literature. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Accurate solutions for the spiked oscillators

The one‐dimensional harmonic oscillator potential plus a term of the form λ / x^α is known as the spiked oscillator potential; it constitutes a very interesting system because of its difficulties to accept perturbative and variational solutions for certain regimes of the α parameter. By the use of a numerical method, we obtain accurate energy eigenvalues and eigenfunctions for a wide range of λ values and a few α values. The accuracy of the present results is by much higher than previously published results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

SWKB formalism for confined quantum systems

A formalism is developed to study spatially confined one‐dimensional quantum mechanical systems in the framework of the supersymmetric Wentzel–Kramers–Brillouin (SWKB) method. The approximation technique is applied to estimate the energy eigenvalues of two confined potentials—the harmonic oscillator V(x)=x² and the screened Coulomb potential V(x)=−V₀sech²x. The results thus obtained are found to be in better agreement with the exact numerical values than are those from the ordinary WKB approach. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 267–273, 2000     

Degeneracy of confined D‐dimensional harmonic oscillator

Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D‐dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius R_c. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Ladder operators for the Kratzer oscillator and the Morse potential

Taking a close look at the Infeld–Hull ladder operators for the Kratzer oscillator system, V(x) = [x² + β(β ? 1)x^?2]/2, we deduce and explicitly construct energy‐raising and ‐lowering operators for the generalized Morse potential system V(z) = (Ae^?4αz ? Be^?2αz)/2, through a canonical transformation that exists between the two systems. For the Morse potential system, we obtain a system of raising and lowering operators P_±(n) (n = 0, 1, 2, 3, … , n_max) with the specific property that P_±(n)Φ_n = c_±(n)Φ_n±1, where Φ_n denotes the nth energy eigenfunction. While P_?(0) annihilates the ground‐state Φ₀, the operator P₊(n_max), instead of annihilating the highest bound‐state Φ, actually knocks it out of the L₂ space spanned by the discrete bound states and becomes inadmissible. Yet, raising and lowering operators _± with proper end‐of‐spectrum behavior (i.e., _?|0〉 = 0 and ₊|n_max〉 = 0) can be constructed in a straightforward way in the energy representation. We show that the operators ₊, _?, and ₀ (where ₀ ≡ (1/2)[ ₊, _?]) form a su(2) algebra only if we restrict them to the (N ? 1)‐dimensional subspace spanned by the lowest (N ? 1) basis vectors, but not in the full (N + 1)‐dimensional space spanned by the discrete bound states [N ≡ n_max ≡ integral part of (1/2)(B/(2α ) ? 1)]. Realization of this su(2) algebra in the position representation (when restricted to the (N ? 1)‐dimensional subspace) is also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A Genuine Jahn–Teller System with Compressed Geometry and Quantum Effects Originating from Zero‐Point Motion

First‐principle calculations together with analysis of the experimental data found for 3d⁹ and 3d⁷ ions in cubic oxides proved that the center found in irradiated CaO:Ni²⁺ corresponds to Ni⁺ under a static Jahn–Teller effect displaying a compressed equilibrium geometry. It was also shown that the anomalous positive g_∥ shift (g_∥?g₀=0.065) measured at T=20 K obeys the superposition of the |3 z²?r²? and |x²?y²? states driven by quantum effects associated with the zero‐point motion, a mechanism first put forward by O'Brien for static Jahn–Teller systems and later extended by Ham to the dynamic Jahn–Teller case. To our knowledge, this is the first genuine Jahn–Teller system (i.e. in which exact degeneracy exists at the high‐symmetry configuration) exhibiting a compressed equilibrium geometry for which large quantum effects allow experimental observation of the effect predicted by O'Brien. Analysis of the calculated energy barriers for different Jahn–Teller systems allowed us to explain the origin of the compressed geometry observed for CaO:Ni⁺.     

Controlled Uptake and Release of Metal Cations by Vanadium Oxide Nanotubes

Vanadium oxide nanotubes (C_n‐VO_x‐NTs) contain α‐monoamines (C_nH_2n+1NH₂ with 4≤n≤22) as templates intercalated between crystalline VO_x layers comprising multilayer tube walls. The present study reveals that a large proportion of the amines can easily be exchanged by metal cations. The tubular morphology is not affected by this reaction, but the distance between the VO_x layers, i.e., 2.8 nm in C₁₂‐VO_xNTs, decreases in the reaction product to 0.9 – 1.2 nm, depending on the metal salt actually applied. Alkali (Na⁺, K⁺), alkaline‐earth (Mg²⁺, Ca²⁺, Sr²⁺), and transition‐metal salts (Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺) have successfully been intercalated. This reaction is partly reversible since intercalated sodium cations can be resubstituted by dodecylamine. This exchange produces again C₁₂‐VO_x‐NTs with the original inter‐layer spacing. However, this release is successful only when sodium is complexed by a crown ether. Under these reaction conditions, even a cyclic uptake and release of Na⁺ and amine, respectively, accompanied by a corresponding shrinkage and widening of the inter‐layer distance, is observed while the tubular structure is widely preserved. Furthermore, a distinct selectivity of the metal‐cation exchange has been observed.     

Effective utilization of off-diagonal hypervirial relations considering diagonal hypervirial relation: Harmonic oscillator case

The effective utilization of hypervirial relations is scrutinized to improve the approximate excited-state functions in the harmonic oscillator system. A new method is presented which simultaneously employs the off-diagonal hypervirial relations with the diagonal hypervirial relation. In order to use these relations effectively, the following points are pointed out: (i) the presented method is useful to get better reasonable results for the excitation energies and the state functions; (ii) the ground state given must satisfy the virial theorem; (iii) in the hypervirial operator used here as x^m, the smaller integers of m's present better results; and (iv) the employment of the comparatively small number of trial basis functions of the type exp (?γ|x|) is sufficient for reproducing the exact excited state. Especially among them, condition (ii) plays an important role. Applying all the proposals to the first and the second excited states, one gets a highly improved excitation energy, state function, and other physical quantities (e.g., transition moment and oscillator strength). The presented method is also found to be more effective than the employment of only the off-diagonal hypervirial relations or the method of the scaling operation.     

Synthesis and UCST‐type phase behaviors of OEGylated random copolypeptides in alcoholic solvents

A series of OEGylated random copolypeptides with similar main‐chain lengths and different oligo(ethylene glycol) (OEG) molar content and chain lengths were prepared from triethylamine initiated ring‐opening polymerization (ROP) of OEGylated γ‐benzyl‐_L‐glutamic acid based N‐carboxyanhydride (OEG_mBLG–NCA, m = 2, 3) and γ‐benzyl‐_L‐glutamic acid based N‐carboxyanhydride (BLG–NCA). ¹H NMR analysis verified copolypeptides structures and determined the OEG molar content (x). FTIR analysis further confirmed the molecular structures, indicated α‐helical conformations of copolypeptides in the solid‐state, and revealed H‐bonding interactions between OEG pendants and alcoholic solvents. The copolypeptides exhibited a reversible upper critical solution temperature (UCST)‐type phase behavior in various alcoholic solvents (i.e., methanol, ethanol, 1‐propanol, 1‐butanol, and 1‐pentanol) depending on the x values and OEG side‐chain lengths (m). Variable‐temperature UV–vis analysis revealed that the UCST‐type transition temperatures (T_pts) of the copolypeptides in alcohols decreased as x or m value increased or as polymer concentration decreased. T_pts of copolypeptides with high x values (x ≥ 0.50) increased as the number of methylene of the alcoholic solvent increased from 3 (i.e., 1‐propanol) to 5 (i.e., 1‐pentanol). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3444–3453     

Structural Variations in the Solid‐Solution Series LnxCa2−xAl[Al1+xSi1−xO7] with 0 ≤ x ≤ 1 and Ln = La,Eu, Er

Gehlenite, Ca₂Al[AlSiO₇], has melilite‐type structure with space group . It contains two topologically distinct positions coordinated tetrahedrally by oxygen. One is completely occupied by Al³⁺, whereas the other one contains Al³⁺ and Si⁴⁺. Normally, the Al³⁺ molar fraction in the second tetrahedrally coordinated position does not exceed x_Al = 0.5, i.e. the so‐called Loewenstein‐rule is obeyed. In this contribution the structural variations in the melilite‐type compounds of the compositions La_xCa_2?xAl[Al_1+xSi_1?xO₇], Eu_xCa_2?xAl[Al_1+xSi_1?xO₇] and Er_xCa_2?xAl[Al_1+xSi_1?xO₇] are discussed. All members of the solid solution except the end‐members violate Loewenstein's rule. Rietveld refinements against X‐ray powder diffraction patterns confirm that the compounds have space group , without changes in the Wyckoff‐positions of the ions compared to gehlenite.     

Clarifying and illustrating the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria allophycocyanin within the framework of Förster theory

Within the framework of the Förster theory, the electronic excitation energy transfer pathways in the cyanobacteria allophycocyanin (APC) trimer and hexamer were studied. The associated physical quantities (i.e., excitation energy, oscillator strength, and transition dipole moments) of the phycocyanobilins (PCBs) located in APC were calculated at time‐dependent density functional theory (TDDFT) level of theory. To estimate the influence of protein environment on the preceding calculated physical quantities, the long‐range interactions were approximately considered with the polarizable continuum model at the TDDFT level of theory, and the short‐range interaction caused by surrounding aspartate residue of PCBs were taken into account as well. The shortest energy transfer time calculated in the framework of the Förster model at TDDFT/B3LYP/6–31+G* level of theory are about 0.10 ps in the APC trimer and about 170 ps in the APC monomer, which are in qualitative agreement with the experimental finding that a very fast lifetime of 0.43–0.44 ps in APC trimers, whereas its monomers lacked any corresponding lifetime. These results suggest that the lifetime of 0.43–0.44 ps in the APC trimers determined by Sharkov et al. was most likely attributed to the energy transfer of α¹‐84 ? β³‐84 (0.23 ps), β¹‐84 ? α²‐84 (0.11 ps) or β²‐84 ? α³‐84 (0.10 ps). So far, no experimental or theoretical energy transfer rates between two APC trimmers were reported, our calculations predict that the predominate energy transfer pathway between APC trimers is likely to occur from α³‐84 in one trimer to α⁵‐84 in an adjacent trimer with a rate of 32.51 ps. © 2014 Wiley Periodicals, Inc.     

A new disordered langbeinite‐type compound,K2Tb1.5Ta0.5P3O12, and Eu3+‐doped multicolour light‐emitting properties

For the first time, a new langbeinite‐type phosphate, namely potassium terbium tantalum tris(phosphate), K₂Tb_1.5Ta_0.5(PO₄)₃, has been prepared successfully using a high‐temperature flux method and has been structurally characterized by single‐crystal X‐ray diffraction. The results show that its structure can be described as a three‐dimensional open framework of [Tb_1.5Ta_0.5(PO₄)₃]_∞ interconnected by K⁺ ions. The Tb^III and Ta^V cations in the structure are disordered and occupy the same crystallographic sites. The IR spectrum, the UV–Vis spectrum, the morphology and the Eu³⁺‐activated photoluminescence spectroscopic properties were studied. A series of Eu³⁺‐doped phosphors, i.e. K₂Tb_1.5–xTa_0.5(PO₄)₃:xEu³⁺ (x = 0.01, 0.03, 0.05, 0.07, 0.10), were prepared via a solid‐state reaction and the photoluminescence properties were studied. The results show that under near‐UV excitation, the luminescence colour can be tuned from green through yellow to red by simply adjusting the Eu³⁺ concentration from 0 to 0.1, because of the efficient Tb³⁺→Eu³⁺ energy‐transfer mechanism.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Light‐Harvesting Photocatalysis for Water Oxidation Using Mesoporous Organosilica

An organic‐based photocatalysis system for water oxidation, with visible‐light harvesting antennae, was constructed using periodic mesoporous organosilica (PMO). PMO containing acridone groups in the framework (Acd‐PMO), a visible‐light harvesting antenna, was supported with [Ru^II(bpy)₃²⁺] complex (bpy=2,2′‐bipyridyl) coupled with iridium oxide (IrO_x) particles in the mesochannels as photosensitizer and catalyst, respectively. Acd‐PMO absorbed visible light and funneled the light energy into the Ru complex in the mesochannels through excitation energy transfer. The excited state of Ru complex is oxidatively quenched by a sacrificial oxidant (Na₂S₂O₈) to form Ru³⁺ species. The Ru³⁺ species extracts an electron from IrO_x to oxidize water for oxygen production. The reaction quantum yield was 0.34 %, which was improved to 0.68 or 1.2 % by the modifications of PMO. A unique sequence of reactions mimicking natural photosystem II, 1) light‐harvesting, 2) charge separation, and 3) oxygen generation, were realized for the first time by using the light‐harvesting PMO.     

High‐Pressure Synthesis and Physical Properties of the Europium‐Substituted Barium Clathrate Ba8−xEuxGe43□3 (x ≤ 0.6)

The new clathrate Ba_8–xEuxGe₄₃□₃ (x = 0.6) was synthesized at a pressure of 1 GPa and temperatures of up to 1220 K by means of a multi‐anvil device (Walker module) and a hydraulic 1000 ton press. X‐ray powder diffraction data indicate that the crystal structure of Ba_8–xEuxGe₄₃□₃ (x = 0.6, space group , a = 21.2588(3) Å) corresponds to that of Ba₈Ge₄₃□₃. Measurements of the magnetic susceptibility of Ba_8–xEuxGe₄₃□₃ reveal Curie‐paramagnetic behaviour and prove that the electronic state of europium corresponds to 4f⁷, i.e., Eu²⁺. Electrical resistivity shows a metal‐like temperature dependence and ρ(300) ≈ 2mΩ cm for x = 0.6. Heat capacity measurements reveal an upturn of c_p/T(T) below 7 K that is attributed to magnetic interaction of the europium ions.     

Novel Derivatives of the CaIn2 Type of Structure: Yb1+xMg1—xGa4 (0 ≤ x ≤ 0.058) and YLiGa4

The compounds Yb_1+xMg_1—xGa₄ (0 ≤ x ≤ 0.058) and YLiGa₄ were synthesized by direct reaction of the elements in sealed niobium crucibles. The atomic arrangement of Yb_1+xMg_1—xGa₄ (x = 0.058) represents a new structure type (space group P6¯m2, a = 4.3979(3)Å and c = 6.9671(7)Å) as evidenced by single crystal structure analysis and can be described as an ordered variant of CaIn₂. YLiGa₄ is isotypic to the ytterbium compound according to X‐ray Guinier powder data (a = 4.3168(1)Å and c = 6.8716(2)Å). Measurements of the magnetic susceptibility of both compounds reveal intrinsic diamagnetic behaviour, i.e., ytterbium in the 4f¹⁴ configuration for Yb_1+xMg_1—xGa₄ (x = 0). From electrical resistivity data both compounds can be classified as metals. The compressibility of Yb_1+xMg_1—xGa₄ (x = 0.058) as measured in diamond anvil cells by angle‐dispersive X‐ray diffraction is compatible with a valence change of the ytterbium atoms at high‐pressures and indicates a slight anisotropy which is in accordance with the structural organisation of the gallium network. X‐ray absorption spectra of the Yb L_III edge of Yb_1+xMg_1—xGa₄ (x = 0.058) at pressures up to 25.0 GPa show a two‐peak structure which reveals the presence of Yb in the 4f¹⁴ and 4f¹³ states. The amount of ytterbium in the 4f¹³ state increases in two steps with progressing compression. The bonding analysis by means of the electron localization function reveals the Zintl‐like character of both compounds and confirms the 4f¹⁴ state for the majority of ytterbium atoms.     

Color Point Tuning in Lu3−x−yMnxAl5−xSixO12:yCe3+ for White LEDs

A series of the solid‐solution phosphors Lu_3?x?yMn_xAl_5?xSi_xO₁₂:yCe³⁺ is synthesized by solid‐state reaction. The obtained phosphors possess the garnet structure and exhibit similar excitation properties as the phosphor Lu₃Al₅O₁₂:Ce³⁺, but with an effectively improved red component in the emission spectrum. This can be attributed to the energy transfer from Ce³⁺ to Mn²⁺. Our investigation reveals that electric dipole–quadrupole interactions dominate the energy‐transfer mechanism and that the critical distance determined by the spectral overlap method is about 9.21 Å. The color‐tunable emissions of the Lu_3?x?yMn_xAl_5?xSi_xO₁₂:yCe³⁺ phosphor as a function of Mn₃Al₂Si₃O₁₂ content are realized by continuously shifting the chromaticity coordinates from (0.354, 0.570) to (0.462, 0.494). They indicate that the obtained material may have potential application as a blue radiation‐converting phosphor for white LEDs with high‐quality white light.     

Energy resonance and inverse population of the product vibrational states for the reaction F + H2(v = 0) → HF(v′) + H,LCAC‐SW theoretical quantum scattering study

LCAC‐SW (linear combination of arrangement channel‐scattering wavefunction) method was used to calculate collinear state‐to‐state reaction probabilities for the reaction F + H₂(v = 0) → HF(v′) + H on the 6SEC potential energy surface. The results show that reaction probabilities P₀₂ and P₀₃ [i. e., v′ = 2,3 for reaction F + H₂ (v = 0) + HF(v′) + H] are primary, the population of product vibrational states is inverse and the reaction probabilities are oscillatory with collision energies, i.e., there is energy resonance in this reaction, which agrees with a new experiment.     

Dissociation mechanisms and implication for the presence of multiple conformations for peptide ions with arginine at the C‐terminus: time‐resolved photodissociation study

Time‐resolved photodissociation (PD) patterns of singly protonated peptides with arginine at the C‐terminus (C‐arg peptide ions) have been used to classify the dissociation channels into two categories, i.e. high‐energy channels generating v, w and x and low‐energy ones generating b, y and z. x + 1 formed by C_α? CO cleavage seems to be the intermediate ion in high‐energy channels just as a + 1 is for N‐arg peptide ions. Difference in time‐resolved pattern indicates that the two sets of channels, high‐ and low‐energy ones, are not in direct competition. Noncompetitive dissociation is also indicated by the observation of anomalous effect of matrix used in matrix‐assisted laser desorption ionization, a cooler matrix generating more high‐energy product ions both in spontaneous dissociation and in PD. Results from detailed investigation suggest that the two sets of channels start from two (or more) different conformations. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis,Persistent Luminescence,and Thermoluminescence Properties of Yellow Sr3SiO5:Eu2+,RE3+ (RE=Ce,Nd, Dy,Ho, Er,Tm, Yb) and Orange‐Red Sr3−xBaxSiO5:Eu2+, Dy3+ Phosphor

Sunlight‐excitable orange or red persistent oxide phosphors with excellent performance are still in great need. Herein, an intense orange‐red Sr_3?xBa_xSiO₅:Eu²⁺,Dy³⁺ persistent luminescence phosphor was successfully developed by a two‐step design strategy. The XRD patterns, photoluminescence excitation and emission spectra, and the thermoluminescence spectra were investigated in detail. By adding non‐equivalent trivalent rare earth co‐dopants to introduce foreign trapping centers, the persistent luminescence performance of Eu²⁺ in Sr₃SiO₅ was significantly modified. The yellow persistent emission intensity of Eu²⁺ was greatly enhanced by a factor of 4.5 in Sr₃SiO₅:Eu²⁺,Nd³⁺ compared with the previously reported Sr₃SiO₅:Eu²⁺, Dy³⁺. Furthermore, Sr ions were replaced with equivalent Ba to give Sr_3?xBa_xSiO₅:Eu²⁺,Dy³⁺ phosphor, which shows yellow‐to‐orange‐red tunable persistent emissions from λ=570 to 591 nm as x is increased from 0 to 0.6. Additionally, the persistent emission intensity of Eu²⁺ is significantly improved by a factor of 2.7 in Sr_3?xBa_xSiO₅:Eu²⁺,Dy³⁺ (x=0.2) compared with Sr₃SiO₅:Eu²⁺,Dy³⁺. A possible mechanism for enhanced and tunable persistent luminescence behavior of Eu²⁺ in Sr_3?xBa_xSiO₅:Eu²⁺,RE³⁺ (RE=rare earth) is also proposed and discussed.