Multiplet Structure Research Articles

Enantiodifferentiation through Frequency‐Selective Pure‐Shift 1H Nuclear Magnetic Resonance Spectroscopy

A frequency-selective 1D (1) H nuclear magnetic resonance (NMR) experiment for the fast and sensitive determination of chemical-shift differences between overlapped resonances is proposed. The resulting fully homodecoupled (1) H NMR resonances appear as resolved 1D singlets without their typical J(HH) coupling constant multiplet structures. The high signal dispersion that is achieved is then exploited in enantiodiscrimination studies by using chiral solvating agents.

Electronic excitations in the edge-shared relativistic Mott insulator:Na2IrO3

We have investigated the excitation spectra of ${j}_{\mathrm{eff}}=\frac{1}{2}$ Mott insulator ${\mathrm{Na}}_{2}$${\mathrm{IrO}}_{3}$. Taking into account a relativistic multiplet structure of Ir ions, we have calculated the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and resonant inelastic x-ray scattering (RIXS) spectra, which manifest different features from those of a canonical ${j}_{\mathrm{eff}}=\frac{1}{2}$ system ${\mathrm{Sr}}_{2}$${\mathrm{IrO}}_{4}$. Distinctly from the two-peak structure in ${\mathrm{Sr}}_{2}$${\mathrm{IrO}}_{4}$, $\ensuremath{\sigma}(\ensuremath{\omega})$ in ${\mathrm{Na}}_{2}$${\mathrm{IrO}}_{3}$ has a broad single peak dominated by interband transitions from ${j}_{\mathrm{eff}}=\frac{3}{2}$ to $\frac{1}{2}$. RIXS spectra exhibit the spin-orbit (SO) exciton that has a two-peak structure arising from the crystal-field effect, and the magnon peak at energies much lower than in ${\mathrm{Sr}}_{2}$${\mathrm{IrO}}_{4}$. In addition, a small peak near the optical-absorption edge is found in RIXS spectra, originating from the coupling between the electron-hole ($e$-$h$) excitation and the SO exciton. Our findings corroborate the validity of the relativistic electronic structure and importance of both itinerant and local features in ${\mathrm{Na}}_{2}$${\mathrm{IrO}}_{3}$.

Probing the metal-insulator transition in nickelates using soft x-ray absorption spectroscopy

We have investigated the spectral changes occurring at the Ni-L3,2 edge X-ray absorption spectrum of SmNiO3 epitaxial thin films as the temperature is varied across the metal-insulator transition. We show that in the low temperature insulating state, a clear multiplet structure gives rise to two peaks at the L3 edge. As the temperature is increased the energy splitting between these peaks remains constant, being reduced only upon crossing the metal-insulator transition. We analyze films with varying strain-engineered metal-insulator transition temperatures and elucidate the separate effects of strain and temperature in the absorption spectra.

On the ground-state splitting, fine structure of multiplets and EPR spectrum of Ni2+ doped in MgF2 crystal with orthorhombic site symmetry

The 45×45 complete energy matrix for 3d8 ion at D2h site symmetry is used to calculate and assign the ground-state splitting and the fine structure of the multiplets of Ni2+(3d8) doped in MgF2 crystal with rutile type structure by the complete diagonalizaton method (CDM) in the frame of semi-empirical molecular orbital (MO) scheme in the strong crystal field (CF) approximation. In the calculation, all the configuration interactions though the cubic CF part, low-symmetry component (tetragonal and orthorhombic parts), Coulomb interaction and the spin–orbit coupling (SOC) interaction (both of the central ion and the liangds) are taken into account completely. The calculated results are in good agreement with the experimental data. In addition, the ground-state splitting is also calculated by the high-order perturbation method (PTM), together with the electron paramagnetic resonance (EPR) parameters D, E and g-factors (gx, gy and gz). The results of the spin–orbit splitting of the ground state calculated by CDM and PTM are not only close to each other, but also in good agreement with the observed data. The relationship between crystalline parameters and the fine structure of multiplets and EPR spectrum is established and the local defect structure is determined.

Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials

AbstractBy applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br −1 + cr 2 and V(r) = ar 2+br −2+cr −4+dr −6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.

ANALYSIS OF CRYSTAL-FIELD MULTIPLETS OF V3+ ION IN PEROVSKITE OXIDES FOR RESONANT INELASTIC X-RAY SCATTERING SPECTROSCOPY

Spectral properties related to the low-energy d–d excitations in nearly cubic vanadium perovskites are examined for the expected L-edge resonant inelastic X-ray scattering (RIXS) measurements. Multiplet structure of V 3+ ion in the basic [Formula: see text] electron configuration is calculated with the help of ab initio quantum-chemical method applied to VO 6 cluster embedded in a crystalline environment. In the intermediate states of the RIXS process the induced 2p-core hole is taken into account by including strong 2p–3d electron interactions. A symmetry-group approach is applied to generate the basis set of many-electron wavefunctions of the intermediate core-hole states accessible in RIXS processes. Although a comprehensive description of the core-hole multiplets still remains a formidable task and requires using specially designed numerical codes, for particular resonant states the analysis is simplified and the calculation of RIXS amplitude can be carried out analytically to the end.

SYNTHESIS AND NMR SPECTRA OF TETRAHYDROFURAN-2- 13 C

An original method was developed for the synthesis of THF labeled selectively with the 13 C isotope at the α-carbon atom. The effective reduction of symmetry brought about by the insertion of the isotopic label removes the excess degeneracy of the spin systems describing the multiplet structure of the 1 H and 13 C NMR spectra, making it possible to undertake a detailed analysis. Exact values for the 1 H– 1 H spin-spin coupling constants through four bonds and also the 13 C– 1 H and 13 C– 13 C spin-spin coupling constants involving the α-carbon atom were determined for the first time. The isotopic chemical shifts of the protons and 13 C nuclei caused by replacement of the 12 C nucleus by 13 C were determined. These data can be used to construct a quantitative model of the conformational behavior of THF as a molecular system in which pseudorotation in terms of vibrations with large amplitude is realized. Authors: A. V. Chertkov, A. K. Shestakova, and V. A. Chertkov. English Translation in Chemistry of Heterocyclic Compounds , 2012, 48 (3), pp 412-421 http://link.springer.com/article/10.1007/s10593-012-1008-0

Strong correlation effects in theA-site ordered perovskite CaCu3Ti4O12revealed by angle-resolved photoemission spectroscopy

We report angle-resolved photoemission spectroscopy (ARPES) results of A-site ordered perovskite CaCu$_3$Ti$_4$O$_{12}$. We have observed the clear band dispersions, which are shifted to the higher energy by 1.7 eV and show the band narrowing around 2 eV in comparison with the local density approximation calculations. In addition, the high energy multiplet structures of Cu 3$d^8$ final-states have been found around 8 - 13 eV. These results reveal that CaCu$_3$Ti$_4$O$_{12}$ is a Mott-type insulator caused by the strong correlation effects of the Cu 3$d$ electrons well hybridized with O 2$p$ states. Unexpectedly, there exist a very small spectral weight at the Fermi level in the insulator phase, indicating the existence of isolated metallic states.

Theoretical Study of Nascent Solvation in Ni+(Benzene)m, m = 3 and 4, Clusters

The ligand versus solvent behavior of Ni(+)(C6H6)3,4 complexes was studied using density functional theory all-electron calculations. Dispersion corrections were included with the BPW91-D2 method using the 6-311++G(2d,2p) basis set. The ground state (GS) for Ni(+)(C6H6)3 has three benzene rings 3d-π bonded to the metal. A two-layer isomer with two moieties coordinated η(3)-η(2) with Ni(+), and the other one adsorbed by van der Waals interactions to the Ni(+)(C6H6)2 subcluster, i.e., a 2 + 1 structure, is within about 8.4 kJ/mol of the GS. Structures with 3 + 1 and 2 + 2 ligand coordination were found for Ni(+)(C6H6)4. The binding energies (D0) of 28.9 and 26.0 kJ/mol for the external moieties of Ni(+)(C6H6)3,4 are much smaller than that for Ni(+)(C6H6)2, 193.0 kJ/mol, obtained also with BPW91-D2. This last D0 overestimates somehow the experimental value, of 146.7 ± 11.6 kJ/mol, for Ni(+)(C6H6)2. The abrupt fall for D0(Ni(+)(C6H6)3,4) shows that such molecules are bound externally as solvent species. These results agree with the D0(Ni(+)(C6H6)3) < 37.1 kJ/mol limit found experimentally for this kind of two-layer clusters. The ionization energies also decrease for m = 2, 3, and 4 (580.8, 573.1, and 558.6 kJ/mol). For Ni(+)(C6H6)3,4, each solvent moiety bridges the benzenes of Ni(+)(C6H6)2; their position and that of one internal ring mimics the tilted T-shape geometry of the benzene dimer (Bz2). The distances from the center of the external to the center of the internal rings for m = 3 (4.686 Å) and m = 4 (4.523 Å) are shorter than that for Bz2 (4.850 Å). This and charge transfer effects promote the (C(δ-)-H(δ+))(int) dipole-π(ext) interactions in Ni(+)(C6H6)3,4; π-π interactions also occur. The predicted IR spectra, having multiplet structure in the C-H region, provide insight into the experimental spectra of these ions.

Implementing homo- and heterodecoupling in region-selective HSQMBC experiments

An NMR method to enhance the sensitivity and resolution in band-selective long-range heteronuclear correlation spectra is proposed. The excellent in-phase nature of the selHSQMBC experiment allows that homonuclear and/or heteronuclear decoupling can be achieved in the detected dimension of a 2D multiple-bond correlation map, obtaining simplified cross-peaks without their characteristic fine J multiplet structure. The experimental result is a resolution improvement while the highest sensitivity is also achieved. Specifically, it is shown that the 1H-homodecoupled band-selective (HOBS) HSQMBC experiment represents a new way to measure heteronuclear coupling constants from the simplified in-phase doublets generated along the detected dimension.

A toolbox of HSQC experiments for small molecules at high 13C‐enrichment. Artifact‐free, fully 13C‐homodecoupled and JCC‐encoding pulse sequences

A set of modified HSQC experiments designed for the study of (13)C-enriched small molecules is introduced. It includes an improved sensitivity-enhanced HSQC experiment eliminating signal artifacts because of high-order (13)C magnetization terms generated at high (13)C enrichment. A broadband homonuclear (13)C decoupling sequence based on Zangger and Sterk's method simplifies the complex (13)C-(13)C multiplet structure in the F1 dimension of HSQC. When recording spectra at high resolution, the combination with a multiple-site modulation of the selective pulse outperforms the constant-time HSQC in terms of sensitivity and reliability. Finally, two pulse sequences reintroducing selected J(CC) couplings with selective pulses facilitate their assignments and measurements either in the splitting of the resulting doublets or by modulation of the signal amplitude. A sample of uniformly 92% (13)C-enriched cholesterol is used as an example.

Vibrational fine structure of C5 via anion slow photoelectron velocity-map imaging

High-resolution anion photoelectron spectra of cryogenically cooled C5(-) clusters are reported using slow photoelectron velocity-map imaging spectroscopy. We resolve vibronic transitions to the ν2 stretching mode and multiply excited ν5, ν6, and ν7 bending modes of neutral C5 with significantly higher accuracy than previous experiments. Weak transitions to Franck-Condon (FC) forbidden singly excited bending modes are made possible by Herzberg-Teller coupling between electronic states of the neutral cluster. In addition, we resolve vibrational fine structure corresponding to different angular momentum states of multiply excited bending modes. The observation of this multiplet structure, some of which is FC forbidden, is attributed to Renner-Teller coupling between vibrational levels in the C5(-) ground electronic state.

Monitoring antiferromagnetism via angle-resolved Auger photoelectron coincidence spectroscopy: The case of NiO/Ag(001)

Spin selectivity in angle-resolved Auger photoelectron coincidence spectroscopy (AR-APECS) is used to probe electronic structure in antiferromagnetic thin films. In particular, exploiting the AR-APECS capability to discriminate Auger electron emission events characterized by a different spin of the ion in its final state, a sharp multiplet structure in the Ni $\mathit{MVV}$ Auger line shape of NiO/Ag(001) thin films is measured below the critical N\'eel temperature. The assignment of multiplet terms follows from a close comparison of the experimental AR-APECS line shapes with the predictions based on semiempirical calculations on a cluster model and an open-band extension of the Cini-Sawatzky approach. In analogy to CoO, also in NiO, above the N\'eel temperature a more featureless Auger spectrum appears and AR-APECS does not disentangle anymore high-spin and low-spin contributions to the total Auger intensity. Such a behavior, which seems to be a general result for metal oxide antiferromagnetic systems, is discussed.

Description of Stark Structure of the Elpasolites Cs&lt;sub&gt;2&lt;/sub&gt;NaPrCl&lt;sub&gt;6&lt;/sub&gt;, Cs&lt;sub&gt;2&lt;/sub&gt;NaYCl&lt;sub&gt;6&lt;/sub&gt; and Cs&lt;sub&gt;2&lt;/sub&gt;NaYBr&lt;sub&gt;6&lt;/sub&gt;

The analysis of the Stark structure of multiplets of the ion Pr 3+ in the Cs2NaPrCl6, Cs2NaYCl6, Cs2NaYBr6 crystal systems is performed in the approximation of the weak and anomalous strong configuration interaction. The calculations in the approximation of the anomalous strong configuration interaction let considerably improve the description of the Stark structure of multiplets and thus provide an opportunity to estimate covalence parameters on the basis of experimental data on the Stark structure. Covalence parameters (the parameters of distribution of electronic density) obtained this way are well conformed to the parameters calculated by means of microscopic models.

Nature of multiplet structure of luminescence spectra of doped naphthalene and benzophenone crystals

Luminescence spectra of naphthalene and benzophenone doped with their monosubstituted derivatives at 4.2 K were studied. The multiplet structure of these spectra was analyzed using the symmetry properties of the free molecules and crystal structures. It was shown that fl uorescence and phosphorescence spectra of the studied objects had a doublet character.

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.

Chemical effects of high‐resolution YbLγ4 emission spectra: a possible probe for chemical analysis

An ‘eccentric’ X‐ray emission, YbLγ4, was measured for Yb metal, Yb2O3, YbF3, β‐YbAlB4, YbNi3Al9, and YbNi3Ga9 with a resolution of ~0.9 eV. Peak splitting of the YbLγ4 line was observed in all the recorded spectra and was attributed to the two components originating from the LS coupling of the Yb5p hole, the Yb5p1/2 (LIOII: Lγ4′) and Yb5p3/2 components (LIOIII: Lγ4). The spectra were substantially different depending on the chemical environment of Yb. The position of the Lγ4 + Lγ4′ band shifts depending on the valence of Yb (v): ~4.4 eV from divalent to trivalent. The Lγ4 + Lγ4′ spectra of the mixed valence intermetallics, i.e. YbNi3Ga9 (v = 2.59) and β‐YbAlB4 (v = 2.75), were fairly well reproduced by averaging the spectra of divalent Yb and trivalent YbNi3Al9, which suggests the possibility of using the YbLγ4 emission for determining the valence of Yb intermetallics. In trivalent Yb compounds, the relative intensity of Lγ4 compared with that of Lγ4′, as well as the appearance of a high‐energy satellite, was found to be influenced by the ligands around the Yb ions. With the aid of preliminary atomic multiplet and band structure calculations, the differences in the valence band structure and resultant screening effects on the OII,III−1 states were determined to be the possible causes for the observed ligand dependence. © 2013 The Authors. X‐ray spectrometry published by John Wiley &amp; Sons, Ltd.

Hybridization, Crystal Anisotropy and Magnetism in Ce Compounds and Core X-Ray Absorption

We demonstrate a usefulness of the Ce 3d· and 4d·core X-ray absorption spectra (XAS) in probing electronic states of Ce compounds on the basis of an Anderson impurity model. The model includes multiplet effects arising from electrostatic interactions between electrons, a crystalline anisotropy and a molecular field acting on the 4/ spin. We first show that our model well elucidates the effect of the hybridization on the multiplet structure in the 4d XAS for rCe, CeRha and CeO.. A difference in the 3d or 4d XAS between the two incident beams with polarizations parallel and perpendicular to the hexagonal c-axis of CeRhaB2 is then shown to be a promising characteristic to study the 4! occupancy among azimuthal quantum numbers under the hexagonal crystalline field. Finally a difference in the spectrum between the right and left circularly polarized beams in the ferromagnetic CeRhaB2 is shown to be very remarkable even for an observed Ce 4! moment of 0.3~0.5 f.La and is furthermore powerful in measuring the spin and orbital contributions to the 4/ moment.

Dd Excitations in CPO-27-Ni Metal–Organic Framework: Comparison between Resonant Inelastic X-ray Scattering and UV–vis Spectroscopy

We identify the dd excitations in the metal-organic framework CPO-27-Ni by coupling resonant inelastic X-ray scattering (RIXS) and UV-vis spectroscopy, and we show that the element selectivity of RIXS is crucial to observing the full dd multiplet structure, which is not visible in UV-vis. The combination of calculations using crystal-field multiplet theory and density functional theory can reproduce the RIXS spectral features, crucially improving interpretation of the experimental data. We obtain the crystal-field splitting and magnitude of the electron-electron interactions and correct previously reported values. RIXS instruments at synchrotron radiation sources are accessible to all researchers, and the technique can be applied to a broad range of systems.

Influence of Axial and Peripheral Ligands on the Electronic Structure of Titanium Phthalocyanines

To discover how molecular changes affect the electronic structure of dye molecules for solar cells, we have investigated four titanium phthalocyanines customized by axial and peripheral ligands (monodentate oxo versus bidentate catechol and tert-butyl versus tert-butylphenoxy, respectively). X-ray absorption spectroscopy and photoelectron spectroscopy were combined with density functional theory (DFT) and crystal-field multiplet calculations to characterize the Ti 3d and N 2p valence electrons that form the frontier orbitals. When a monodentate oxo axial ligand was replaced by a bidentate catechol ligand, the multiplet structure of the Ti 2p-to-3d transitions was found to change systematically. The most noticeable change was an additional transition into the low-lying 3dxy level, which is attributed to a reduction in local symmetry from 4-fold to 2-fold at the Ti center. An increase of the Ti 2p core-level binding energy was observed in the bidentate complex and compared to a calculated core-level stabilization. DFT predicts a change of the LUMO from the inner phthalocyanine ring to the Ti dxy orbital and a reversal of the high-lying dx 2 −y 2 and dz 2 orbitals. The N 1s edge was calculated using time-dependent density functional theory (TDDFT) and compared to experiment.