Multiplet States Research Articles

Alkylation Effects in Lanthanide Complexes Involving Tetrathiafulvalene Chromophores: Experimental and Theoretical Correlation between Magnetism and Near‐Infrared Emission

AbstractMononuclear complexes with the formula [Ln(hfac)3(L1)] and [Ln(hfac)3(L2)] with hfac– = 1,1,1,5,5,5‐hexafluoroacetylacetonate, L1 = 2‐{4,5‐[4,5‐bis(propylthio)tetrathiafulvalenyl]‐1H‐benzimidazol‐2‐yl}pyridine and L2 = 2‐{1‐methylpyridyl‐4,5‐[4,5‐bis(propylthio)tetrathiafulvalenyl]‐1H‐benzimidazol‐2‐yl}pyridine are reported for Ln = YIII, ErIII and YbIII. The X‐ray structures reveal that the Ln(hfac)3 moieties are coordinated to the bidentate 1‐(2‐pyridylmethyl)benzimidazole acceptor. The coordination polyhedron is described as a more or less distorted triangular dodecahedron prism (D2d symmetry), depending on the degree of alkylation of the ligand. The influence of this distortion on the magnetic and photophysical properties is determined by the fit of the static magnetic measurements and luminescence spectra. Irradiation of the lowest‐energy intraligand charge transfer (ILCTs) bands (21740 cm–1) induces the metal‐centred 4I13/2 → 4I15/2 and 2F5/2 → 2F7/2 luminescence for the ErIII and YbIII complexes, respectively. The alkylation enhances both the intensity and lifetime of the YbIII luminescence. The ErIII luminescence can be sensitised by the antenna effect, whereas the YbIII luminescence could involve a photoinduced electron transfer (PET). Finally, the evolution of the YbIII luminescence spectra shape due to the alkylation is directly correlated to the energy splitting of the MJ states that stem from the 2F7/2 multiplet ground state. Ab initio calculations give evidence of the nature of the MJ ground state as well as the orientation of the associated magnetic anisotropy axis (i.e., the one that lies along the less electronegative direction). The key role of the imidazole proton of L2 is highlighted. The calculated energy splitting of the 2F5/2 multiplet state perfectly matches the emission lines.

Magnetism and multiplets in Fe-phthalocyanine molecules

Magnetism and multiplets for Fe-phthalocyanine molecules were investigated based on the constraint density functional theory (DFT) by imposing a density matrix constraint on the d-orbital occupation numbers. We demonstrate that for a single FePc molecule, there are three stationary states of multiplets, 3Eg, 3A2g, and 3B2g, and that the magnetic anisotropy (MA) strongly depends on the multiplet structures. The ground state of the 3A2g obtained from the constraint DFT total energy calculations has planar MA, with the spin moments pointing along the molecule’s planar direction. The columnar stacking structure for α-FePc, with the ground state of the 3Eg, shows planar MA.

Sequential and click-type postfunctionalization of regioregular poly(3-hexylthiophene) for realization of n-doped multiplet state

Regioregular poly(3-hexylthiophene) was postfunctionalized by a three-step high-yielding reaction producing an electron-accepting 1,1,4,4-tetracyanobuta-1,3-diene unit at the regioregular position of the thiophene rings. Electrochemical measurements of the postfunctionalized polythiophene derivative showed two one-electron reduction waves with the first reduction potential of −0.66 V (vs. Fc/Fc+). The electrochemically generated poly(anionic radical)s were confirmed by their electron spin resonance (ESR) signals. The magnetic measurements of the poly(anionic radical)s, produced by chemical reduction with cobaltocene or decamethylcobaltocene, suggested the multiplet state (S ∼ 2/2) at low temperatures.

“Short” spinning strings and structure of quantumAdS5×S5spectrum

Using information from the marginality conditions of vertex operators for the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension $\ensuremath{\sim}\sqrt{\ensuremath{\lambda}}$. We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in ${\mathrm{AdS}}_{5}$ or ${S}^{5}$ and an orbital momentum in ${S}^{5}$, with Konishi multiplet states being particular cases. We argue that the coefficients in the energy may be found by using a semiclassical expansion. By analyzing the examples of folded spinning strings in ${\mathrm{AdS}}_{5}$ and ${S}^{5}$, as well as three cases of circular two-spin strings, we demonstrate the universality of transcendental (zeta-function) parts of few leading coefficients. We also show the consistency with target space supersymmetry with different states belonging to the same multiplet having the same nontrivial part of the energy. We suggest, in particular, that a rational coefficient (found by Basso for the folded string using Bethe Ansatz considerations and which, in general, is yet to be determined by a direct two-loop string calculation) should, in fact, be universal.

Linking nuclear masses with nucleon-removal thresholds and the mass of the proton-emitter 17Na

We have surveyed known threshold excitations of mirror systems seeking systematic trends to predict masses of nuclear systems that are unmeasured. For the same purpose, we review mass equations for the ground states of isobaric multiplets. We use both methods to estimate the mass of the unmeasured 17Na ground state, as well as its energy gap to the p + 16Ne threshold. The results are discussed and compared to calculations performed recently in model-dependent studies.

Theoretical and numerical assessments of spin-flip time-dependent density functional theory

Spin-flip time-dependent density functional theory (SF-TD-DFT) with the full noncollinear hybrid exchange-correlation kernel and its approximate variants are critically assessed, both formally and numerically. As demonstrated by the ethylene torsion and the C(2v) ring-opening of oxirane, SF-TD-DFT is very useful for describing nearly degenerate situations. However, it may occasionally yield unphysical results. This stems from the noncollinear form of the generalized gradient approximation, which becomes numerically instable in the presence of spin-flip excitations from the closed- to vacant-shell orbitals of an open-shell reference. To cure this defect, a simple modification, dubbed as ALDA0, is proposed in the spirit of adiabatic local density approximation (ALDA). It is applicable to all kinds of density functionals and yields stable results without too much loss of accuracy. In particular, the combination of ALDA0 with the Tamm-Dancoff approximation is a promising tool for studying global potential energy surfaces. In addition to the kernel problem, SF-TD-DFT is also rather sensitive to the choice of reference states, as demonstrated by the spin multiplet states of closed-shell molecules of H(2)O, CH(2)O, and C(2)H(4). Surprisingly, SF-TD-DFT with pure density functionals may also fail for valance excitations with large orbital overlaps, at variance with the spin-conserving counterpart (SC-TD-DFT). In this case, the inclusion of a large amount of Hartree-Fock exchange is mandatory for quantitative results. Nonetheless, for spatially degenerate cases such as CF, CH, and NH(+), SF-TD-DFT is more advantageous than SC-TD-DFT, unless the latter is also space adapted. These findings are very instructive for future development and applications of TD-DFT.

A Charge‐Transfer Challenge: Combining Fullerenes and Metalloporphyrins in Aqueous Environments

A series of truly water-soluble C(60)/porphyrin electron donor-acceptor conjugates has been synthesized to serve as powerful mimics of photosynthetic reaction centers. To this end, the overall water-solubility of the conjugates was achieved by adding hydrophilic dendrimers of different generations to the porphyrin moiety. An important variable is the metal center of the porphyrin; we examined zinc(II), copper(II), cobalt(II), nickel(II), iron(III), and manganese(III). The first insights into electronic communication between the electron donors and the electron acceptors came from electrochemical assays, which clearly indicate that the redox processes centered either on C(60) or the porphyrins are mutually affected. Absorption measurements, however, revealed that the electronic communication in terms of, for example, charge-transfer features, remains spectroscopically invisible. The polar environment that water provides is likely to be a cause of the lack of detection. Despite this, transient absorption measurements confirm that intramolecular charge separation processes in the excited state lead to rapid deactivation of the excited states and, in turn, afford the formation of radical ion pair states in all of the investigated cases. Most importantly, the lifetimes of the radical ion pairs were found to depend strongly on several aspects. The nature of the coordinated metal center and the type of dendrimer have a profound impact on the lifetime. It has been revealed that the nature/electronic configuration of the metal centers is decisive in powering a charge recombination that either reinstates the ground state or any given multiplet excited state. Conversely, the equilibrium of two opposing forces in the dendrimers, that is, the interactions between their hydrophilic regions and the solvent and the electronic communication between their hydrophobic regions and the porphyrin and/or fullerene, is the key to tuning the lifetimes.

Erratum: Electron-correlation-induced interchange of lifetime broadenings of5s−1multiplet states in atomic Cs [Phys. Rev. A80, 042518 (2009)

Received 12 October 2011DOI:https://doi.org/10.1103/PhysRevA.84.049903©2011 American Physical Society

Quantum folded string in S 5 and the Konishi multiplet at strong coupling

The Konishi superconformal multiplet is an important theoretical laboratory where one can test AdS/CFT methods to compute strong coupling corrections to the spectrum of superstrings in AdS_5 x S^5. In particular, one can exploit integrability for finite charge states/operators. The multiplet ground state is a singlet operator with two simple descendants in the rank-1 sectors sl(2) and su(2) of N=4 super Yang-Mills theory. Recently, the next-to-leading quantum correction to the sl(2) state has been computed. Here, we use the algebraic curve approach to determine the correction to the other state recovering universality of the correction inside the multiplet.

A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice

We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.

Excited Multiplets of Eu in GaN

ABSTRACTA method to calculate the multiplet states of lanthanide impurities in solids is presented. This approach is based on a semi-empirical density functional method which includes corrections to account for the correlation and spin-orbit coupling of the 4f electrons. Specific multiplet states of the rare earth are produced by constraining the system. This approach is then used to investigate some of the properties of substitutional europium impurities in gallium nitride, reproducing the relative energy of two multiplets, and discussing a potential excitation mechanism for these centers.

Effect of Impurities with Internal Structure on Multiband Superconductors –Possible Enhancement of Transition Temperature–

We study inelastic (dynamical) impurity scattering effects in two-band superconductors with the same ($s_{++}$ wave) or different ($s_\pm$ wave) sign order parameters. We focus on the enhancement of the superconducting transition temperature $T_{\rm c}$ by magnetic interband scattering with the interchange of crystal-field singlet ground and multiplet excited states. Either the $s_{++}$-wave or $s_\pm$-wave state is favored by the impurity-mediated pairing, which depends on the magnetic and nonmagnetic scattering strengths derived from the hybridization of the impurity states with the conduction bands. The details are examined for the singlet-triplet configuration that is suggestive of Pr impurities in the skutterudite superconductor LaOs$_4$Sb$_{12}$.

ISOBARIC ANALOGUE STATES STUDIED IN MIRRORED FRAGMENTATION AND KNOCKOUT REACTIONS

A Gamma-ray spectroscopic study of excited states of isobaric multiplets has been performed in recent years, with a view to gaining a quantitative understanding of energy differences between excited states in terms of a range of Coulomb and other isospin breaking phenomena. Recently, the experimental programme has been augmented by a study of isobaric analogue states of mirror nuclei populated in mirrored fragmentation reactions. In this presentation, recent results on the [Formula: see text] analogue states in the [Formula: see text] mirror pair 53 Ni /53 Mn will be summarised. In this work, further strong evidence is found for the need to include an anomalous isospin-breaking two-body matrix element for angular-momentum couplings of J = 2, in addition the expected Coulomb contribution, in order to account for the experimental data.

Synthesis, crystal structure and magnetism of a new mixed germanium–polyoxovanadate cluster

A new germanium–polyoxovanadate, (H 3aep) 4[V 14Ge 8O 50]·2(aep)·13H 2O ( 1), has been synthesized under solvothermal conditions applying GeO 2, NH 4VO 3, Cu(NO 3) 2·3H 2O and an aqueous solution of 1-(2-aminoethyl)-piperazine (aep, C 6H 18N 3) in the temperature range from 110 to 150 °C. The compound crystallizes in the non-centrosymmetric tetragonal space group P-42 1 c with a = 17.193(1) Å, c = 16.501(1) Å, V = 4877.9(5) Å 3 and Z = 2. The structure consists of isolated spherical [V IV 14Ge IV 8O 50] 12− cluster anions and protonated amine molecules as counterions. The cluster anion can be viewed as a derivative of the [V 18O 42] archetype by replacing four VO 5 pyramids by four Ge 2O 7 units. The latter are formed by corner-sharing of two [GeO 4] 4− tetrahedra. At temperatures above 150 °C the compound (H 2pip) 4(Hpip) 4[V IV 14Ge IV 8O 50(H 2O)] ( 2) (pip = piperazine, C 4N 2H 10) is formed and during the reaction Cu 2+ is reduced to elemental copper. This redox reaction is essential for the formation of 2. The crystal water molecules in the structure of 1 are emitted at low temperatures. The magnetic properties are dominated by strong intra-cluster antiferromagnetic coupling and the strongest exchange between edge- and corner-sharing VO 5 square pyramids results in an eight-membered spin ring to which two three-membered spin bridges are joined. The magnetic susceptibility data suggest that even at the low temperature of 2 K several multiplet states are still significantly populated.

ChemInform Abstract: The Excited Multiplet States of Metalloporphyrins and Metallophthalocyanines Coordinated or Linked to Nitroxide Radicals

Abstract We have reviewed several time-resolved electron paramagnetic resonance (TREPR) studies focusing on influences of nitroxide radicals on the photophysical properties of metalloporphyrins and metallophthalocyanines, which are coordinated or linked to nitroxide radicals. This paper summarizes TREPR studies on the excited multiplet states of metalloporphyrins and metallophthalocyanines coordinated by several kinds of nitroxide radicals, where the excited doublet and quartet states generated by the interaction between the excited triplet chromophore and doublet radical have been analyzed in detail. Selective population from the excited multiplet states to the triplet ground state is also discussed for phthalocyaninatosilicon covalently linked to two TEMPO radicals in terms of a new concept for controlling magnetic properties by photoexcitation.

Internal electronic structure and fine structure of multiexcitons in semiconductor quantum dots

We perform a detailed theoretical study of the characteristic internal electronic structure of various multiexcitons $({N}_{h},{N}_{e})$, where ${N}_{h}$ is number of holes and ${N}_{e}$ is the number of electrons in the self-assembled semiconductor quantum dots (QDs). For each of the leading $({N}_{h},{N}_{e})$ excitonic complexes we start from the single-particle configuration (e.g., a specific occupation pattern of $S$ and $P$ electron and hole levels by a few carriers) and then show the many-particle multiplet levels for the initial state of emission $({N}_{h},{N}_{e})$ and the final state of emission $({N}_{h}\ensuremath{-}1,\text{ }{N}_{e}\ensuremath{-}1)$. We denote which states are dark and which are bright; the order and multiplicity, the leading single-particle character of each multiplet state, and the fine-structure splittings. These are of general utility. We also show explicit numerical values for distances between various transitions for four specific QDs. Here the presented information is important and potentially useful for a few reasons: (i) the information serves as a guide for spectroscopic interpretation; (ii) the information reveals non-Aufbau cases, where the dot does not have Aufbau occupation of carriers' levels; (iii) the information shows which transitions are sensitive to random-alloy fluctuations (if the dot is alloyed) and importance of this effect. We show that because of such alloy information, distances between peaks cannot be used to gauge structural information.

Electron-correlation-induced interchange of lifetime broadenings of5s−1multiplet states in atomic Cs

The lifetime broadenings of the most intense $5s$ photolines of Cs were studied. The aim of this study was to understand the origin of the remarkable differences in the lifetime widths of different $5{s}^{\ensuremath{-}1}$ multiplet states. The $5s$ photoelectron spectra of the $6s\ensuremath{\rightarrow}6{p}_{1/2,3/2}$ laser-excited states are presented in the binding energy region of 30--34 eV showing the main $5s$ photolines of the ground state and laser-excited states as well as the $5s5{p}^{6}6p$ shakeup satellites. The lifetime widths of the states were determined. The Hartree-Fock calculations were carried out to predict the $5s$ photoelectron spectrum. The lifetime broadenings of the $5s$ photolines were found to be due to the transition rates of the subsequent Coster-Kronig transitions to the $5{s}^{2}5{p}^{5}$ states. It was found that a straightforward single-configuration explanation cannot be given for the lifetime differences. Instead, electron correlation plays an essential role and the lifetime broadenings were found to be predicted well only when configuration interaction between the $5{s}^{\ensuremath{-}1}$ and $5{p}^{\ensuremath{-}2}5d$ configurations is taking into account.

Plasmonic Enhancement or Energy Transfer? On the Luminescence of Gold‐, Silver‐, and Lanthanide‐Doped Silicate Glasses and Its Potential for Light‐Emitting Devices

AbstractWith the technique of synchrotron X‐ray activation, molecule‐like, non‐plasmonic gold and silver particles in soda‐lime silicate glasses can be generated. The luminescence energy transfer between these species and lanthanide(III) ions is studied. As a result, a significant lanthanide luminescence enhancement by a factor of up to 250 under non‐resonant UV excitation is observed. The absence of a distinct gold and silver plasmon resonance absorption, respectively, the missing nanoparticle signals in previous SAXS and TEM experiments, the unaltered luminescence lifetime of the lanthanide ions compared to the non‐enhanced case, and an excitation maximum at 300–350 nm (equivalent to the absorption range of small noble metal particles) indicate unambiguously that the observed enhancement is due to a classical energy transfer between small noble metal particles and lanthanide ions, and not to a plasmonic field enhancement effect. It is proposed that very small, molecule‐like noble metal particles (such as dimers, trimers, and tetramers) first absorb the excitation light, undergo a singlet‐triplet intersystem crossing, and finally transfer the energy to an excited multiplet state of adjacent lanthanide(III) ions. X‐ray lithographic microstructuring and excitation with a commercial UV LED show the potential of the activated glass samples as bright light‐emitting devices with tunable emission colors.

Photoionization in molecular oxygen

Theoretical studies are reported of partial-channel photoionization cross sections in molecular oxygen employing the static exchange approximation and Stieltjes-Tchebycheff moment theory techniques. It is found to be particularly important in this prototypical open-shell case to specify the correct ionic parentages of the various multiplet photoionization states that arise in order to account for all the experimental features in the relatively complex photoelectron spectra, and to obtain corresponding partial-channel photoionization cross sections in good accord with measured values. Resonancelike structures in certain of the cross sections are attributed to contributions from diabatic valencelike states that appear in the appropriate photoionization continua, rather than in the corresponding discrete spectral intervals. These and other aspects of the photoionization spectrum in molecular oxygen are contrasted and compared with the results of previously reported studies in molecular nitrogen and carbon monoxide.

Classes of admissible exchange‐correlation density functionals for pure spin and angular momentum states

AbstractWe analyze various approaches to construct exchange‐correlation functionals which are able to describe states of definite spin multiplicity in the density functional theory (DFT) realm and outline the characteristics of possible functionals consistent with the Kohn–Sham theory. To achieve this goal the unitary group technique is applied to label many‐electron states of definite total spin and to calculate the corresponding analogs of the Roothaan coupling coefficients. The possibility of using range separated Coulomb potential of electron–electron interaction for constructing functionals discriminating multiplet states in the d‐shells is explored and a tentative system of state‐specific functionals, covering nontrivial correlations in d‐shells of transition metal ions, is proposed for the Fe2+ ions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010