Paramagnetic Term Research Articles

Magnetic, dielectric and thermal study of CoNiFe2O4 nanoparticles

CoxNi1-xFe2O4 (x = 0.2–0.8) (CNFO) nanoparticles have been prepared using a low temperature hydrothermal technique. X-ray diffraction confirmed the cubic spinel structure of the nanoparticles, offering an increasing trend of lattice parameters from 8330 to 0.8345 nm as a function of Co-content. The microstructures were analysed using FESEM and TEM. The average grain size determined using FESEM images for x = 0.2–0.8 was found in the range from 110 to 183.7 nm. The TEM images show asymmetrical sphere-like particles, with the particle size changing from 69.4 to 82.1 nm as a function of ‘x’. The hysteresis curves were recorded for x = 0.2–0.8 to understand the ferrimagnetic behavior. The saturation magnetization (Ms) varies unsystematically between 35.3 and 43.3 emu/g with ‘x’, while a high magnetic moment of 1.819 μB/f.u. is found at a high Co-content. The paramagnetic term (χ x 10−5) goes on increasing from 125 to 148 emu/g.Oe with ‘x’. The zero-field cooled (ZFC) and field cooled (FC) curves provide the decreasing trend of variation blocking temperature (TB) from 270 to 260 for x = 0.2–0.6, whilst for x = 0.8, it is increased to 280 K. The high real part of the permittivity of ∼ 12.42 and low imaginary part of the permittivity of ∼0.638 are recorded at 8 MHz for x = 0.2, indicting energy storage applications. The power law fit was applied to log σac-log ω plots and the dc-electrical conductivity was evaluated. The TG-DTG and DSC curves revealed mass loss and transition temperatures for x = 0.2–0.8 as a function of temperature.

Origin of 17O NMR chemical shifts based on molecular orbital theory: paramagnetic terms of the pre-α, α and β effects from orbital-to-orbital transitions, along with the effects from vinyl, carbonyl and carboxyl groups.

17O NMR chemical shifts (δ(O)) were analysed based on the molecular orbital (MO) theory, using the diamagnetic, paramagnetic and total absolute magnetic shielding tensors (σd(O), σp(O) and σt(O), respectively). O2- was selected as the standard for the analysis. An excellent relationship was observed between σd(O) and the charges on O for O6+, O4+, O2+, O0 and O2-. The data from H2O, HO+, HO- and H3O+ were on the correlation line. However, such relationship was not observed for the oxygen species, other than above. The pre-α, α and β effects were evaluated bases on σt(O), where the pre-α effect arises from the protonation to a lone pair orbital on O2-, for an example. The 30-40 ppm and 20-40 ppm (downfield shifts) were predicted for the pre-α and β effects, respectively, whereas the values for the α effect was very small in magnitude, where the effect from the hydrogen bond formation should be considered. Similarly, the carbonyl effect in H2C[double bond, length as m-dash]O and the carboxyl effects in H(HO)C[double bond, length as m-dash]O were evaluated from MeOH, together with H2C[double bond, length as m-dash]CHOH from CH3CH2OH. Very large downfield shifts of 752, 425 and 207 ppm were predicted for H2C[double bond, length as m-dash]O*, H(HO)C[double bond, length as m-dash]O* and H(HO*)C[double bond, length as m-dash]O, respectively, together with the 81 ppm downfield shift for H2C[double bond, length as m-dash]CHO*H. The origin of the effect were visualized based on the occupied-to-unoccupied orbital transitions. As a result, the origin of the 17O NMR chemical shifts (δ(17O)) can be more easily imaged and understand through the image of the effects. The results would help to understand the role of O in the specific position of a compound in question and the mechanisms to arise the shift values also for the experimental scientists. The aim of this study is to establish the plain rules founded in theory for δ(17O), containing the origin, which has been achieved through the treatments.

Solid-State 19F NMR Chemical Shift in Square-Planar Nickel-Fluoride Complexes Linked by Halogen Bonds.

The halogen bond (XB) is a highly directional class of noncovalent interactions widely explored by experimental and computational studies. However, the NMR signature of the XB has attracted limited attention. The prediction and analysis of the solid-state NMR (SSNMR) chemical shift tensor provide useful strategies to better understand XB interactions. In this work, we employ a computational protocol for modeling and analyzing the 19F SSNMR chemical shifts previously measured in a family of square-planar trans NiII-L2-iodoaryl-fluoride (L = PEt3) complexes capable of forming self-complementary networks held by a NiF···I(C) halogen bond [Thangavadivale, V.; Chem. Sci. 2018, 9, 3767-3781]. To understand how the 19F NMR resonances of the nickel-bonded fluoride are affected by the XB, we investigate the origin of the shielding in trans-[NiF(2,3,5,6-C6F4I)(PEt3)2], trans-[NiF(2,3,4,5-C6F4I)(PEt3)2], and trans-[NiF(C6F5)(PEt3)2] in the solid state, where a XB is present in the two former systems but not in the last. We perform the 19F NMR chemical shift calculations both in periodic and molecular models. The results show that the crystal packing has little influence on the NMR signatures of the XB, and the NMR can be modeled successfully with a pair of molecules interacting via the XB. Thus, the observed difference in chemical shift between solid-state and solution NMR can be essentially attributed to the XB interaction. The very high shielding of the fluoride and its driving contributor, the most shielded component of the chemical shift tensor, are well reproduced at the 2c-ZORA level. Analysis of the factors controlling the shielding shows how the highest occupied Ni/F orbitals shield the fluoride in the directions perpendicular to the Ni-F bond and specifically perpendicular to the coordination plane. This shielding arises from the magnetic coupling of the Ni(3d)/F(2p lone pair) orbitals with the vacant σNi-F* orbital, thereby rationalizing the very highly upfield (shielded) resonance of the component (δ33) along this direction. We show that these features are characteristic of square-planar nickel-fluoride complexes. The deshielding of the fluoride in the halogen-bonded systems is attributed to an increase in the energy gap between the occupied and vacant orbitals that are mostly responsible for the paramagnetic terms, notably along the most shielded direction.

Graphite-like Charge Storage Mechanism in a 2D π-d Conjugated Metal-Organic Framework Revealed by Stepwise Magnetic Monitoring.

Quasi-two-dimensional (2D) fully π-d conjugated metal-organic frameworks (MOFs) have been widely employed as active materials of secondary batteries; however, the origin of their high charge storage capacity is still unknown. Some reports have proposed a mechanism by assuming the formation of multiple radicals on one organic ligand, although there is no firm evidence for such a mechanism, which would run counter to the resonance theory. In this work, we utilized various magnetometric techniques to monitor the formation and concentration of paramagnetic species during the electrochemical process of 2D π-d conjugated Cu-THQ MOF (THQ = tetrahydroxy-1,4-benzoquinone). The spin concentration of the fully reduced (discharged 1.5 V) electrode was estimated to be around only 0.1 spin-1/2 per CuO4 unit, which is much lower than that of the expected "diradical" form. More interestingly, a significant elevation of the temperature-independent paramagnetic term was simultaneously observed, which indicates the presence of delocalized π electrons in this discharged state. Such results were corroborated by first-principles density functional theory calculations and the electrochemically active density of states, which reveal the microscopic mechanism of the charge storage in the Cu-THQ MOF. Hence, a graphite-like charge storage mechanism, where the π-electron band accepts/donates electrons during the charge/discharge process, was suggested to explain the excessive charge storage of Cu-THQ. This graphite-like charge storage mechanism revealed by magnetic studies can be readily generalized to other π-d conjugated MOFs.

Effect of erbium concentration on the Verdet constant dispersion of LiY1.0-xErxF4 single crystal

The dispersion of the Verdet constant of LiY1.0-xErxF4 crystals was evaluated from 190 nm to 500 nm for different doping concentrations of Er ions. A 15% doping concentration yielded a high Verdet constant of 54.5 rad/(T·m) at 193 nm. This value can be explained by the contribution of the diamagnetic term associated with LiYF4 and the paramagnetic term of the Er ions. Although the LiYF4 crystal yielded a lower value of −36.6 rad/(T·m) at 193 nm from Er-doped LiYF4, it can be used in the vacuum–ultraviolet region because of its high transmittance at wavelengths longer than 120 nm.

Covalence and π-electron delocalization influence on hydrogen bonds in proton transfer process of o-hydroxy aryl Schiff bases: A combined NMR and QTAIM analysis.

Within the framework of the density functional theory approach, we studied the relationship between the chemical nature of intramolecular hydrogen bonds (HBs) and nuclear magnetic resonance (NMR) parameters, J-couplings and 1H-chemical shifts [δ(1H)], of the atoms involved in such bonds in o-hydroxyaryl Schiff bases during the proton transfer process. For the first time, the shape of the dependence of the degree of covalence in HBs on 1J(N-H), 1J(O-H), 2hJ(O-N), and δ(1H) during the proton transfer process in o-hydroxyaryl Schiff bases was analyzed. Parameters obtained from Bader's theory of atoms in molecules were used to assess the dependence of covalent character in HBs with both the NMR properties. The influence of π-electronic delocalization on 2hJ(N-O) under the proton transfer process was investigated. 2hJ(O-N) in a Mannich base was also studied in order to compare the results with an unsaturated system. In addition, substituent effects on the phenolic ring were investigated. Our results indicate that the covalent character of HBs on both sides of the transition state undergoes a smooth exponential increase as the δ(1H) moves downfield. The degree of covalence of the N⋯H (O⋯H) bond increases linearly as 1J(N-H) (1J(O-H)) becomes more negative, even after reaching the transition state. Non-vanishing values of spin dipolar (SD) and paramagnetic spin orbital terms of 2hJ(O-N) show that π-electronic delocalization has a non-negligible effect on tautomeric equilibrium and gives evidence of the presence of the resonance assisted HB.Variation of the SD term of 2hJ(O-N) follows a similar pattern as the change in the para-delocalization aromaticity index of the chelate ring.

Corrigendum: Entrapment of a Pseudo-Tetrahedral CoII Center by Thioether Sulfur Bound {Co2 (μ-L)} Fragments: Synthesis, Field-Induced Single-Ion Magnetism and Catechol Oxidase Mimicking Activity.

It has come to the attention of the authors that Figure 6, the values of effective magnetic moments for complexes 1 and 2, giso, E/D values in Abstract section and in the Magnetic properties sections, giso and E/D values in Table 1, and D value for complex 2 in Conclusions section were changed mistakenly in the final stage of manuscript preparation. The data published in Figure 6 reveal the results obtained for older measurement on different batches of the complexes. The correct values, corresponding to the results obtained for the same batches of complexes for which the DC and AC magnetic measurements were done, are presented below. These mistakes do not affect the integrity of the research and overall conclusions of the published paper. The corrected Figure 6 and corresponding text are given below. Magnetic properties. Investigation of the magnetic features of complexes 1 and 2 proceeded using a PPMS device on which the temperature (1.9–300 K) and field (0–9 T) dependent magnetic data were obtained (Figure 6). Figure 6 Temperature dependence of the effective magnetic moment (inset: temperature dependence of the molar magnetic susceptibility) for complexes 1 and 2 (Left). The isothermal magnetizations measured in the range of B=0–9 T and at T=2, 5 and 10 K (Right). The magnetic properties of the complexes are primarily due to the presence of central tetrahedral CoII ion since octahedral LS-CoIII ions are diamagnetic. The value of effective magnetic moment (μeff) of complex 1 at 300 K is 3.5 μB, slightly lower than the spin-only value of 3.9 μB for S=3/2, g=2.0. Thereafter upon cooling the μeff value raises slightly up to ca 75 K and then, it drops sharply to a minimum at 1.9 K, where it adopts the value of 3.2 μB. In the case of complex 2, the μeff value at 300 K is 5.0 μB which is again much higher that the calculated value for isotropic S=3/2 spin. It decreases gradually upon cooling up to ca 50 K and then, it declines sharply to a minimum at 4.4 K reaching the value of 4.2 μB. The high μeff value at 300 K indicates considerable contribution of a spin-orbit coupling to the ground state in the complex 2. Isothermal magnetization experiments (Figure 6) for 1 and 2 in the applied field range of B=0–9 T at different constant temperatures T=2, 5 and 10 K reveal that the magnetization does not show saturation suggesting the presence of magnetic anisotropy. To extract the parameters affected by magnetic anisotropy arising from crystal field effects (g, D), both the susceptibility and magnetization data were fitted simultaneously. The best fit parameters were calculated using the PHI program package[26] for S=3/2 and they are as follows: giso=2.05, D=−23.6 cm−1, E/D=0, zJ/hc=0 cm−1, χTIP=−13.0×10−4 cm3 mol−1 for 1 and giso=2.61, D=−24.3 cm−1, E/D=0.01, zJ/hc=0.05 cm−1, χTIP=2.0×10−4 cm3 mol−1 for 2. The presence of temperature-independent paramagnetism (TIP) term accounts for the four surrounding CoIII ions. The observed D values for 1 and 2 are relatively close compared to those (−31.31 cm−1 and −21.88 cm−1) obtained in our previous investigations with complexes having similar molecular structures.[10] The authors wish to emphasize that with these corrections, the reported ZFS parameters relevant for the discussion of single molecule magnetism (i.e. the D values) did not change at all and the overall conclusions published in the original version of the article are not affected.

Nonperturbative path integral quantization of the electroweak model: The Maxwell integration

The non-perturbative path integral quantization of the electroweak model is confronted with an apparent instability when integrating over the Maxwell potential $A_{\mu}$ due to the fast growth of the box graphs $AAAA$ and $AAAZ$ for large amplitude variations of $A_{\mu}$. $Z_{\mu}$ is from the vector part of the weak neutral current. These graphs are unavoidable because they are conditionally convergent and have to be isolated in the model's exact Euclidean one-loop effective action arising from its fermion determinants. A previous QED calculation of the large amplitude variation of its fermion determinant for a class of random potentials showed that the $AAAA$ box graph cancels in this limit. Using this result it is shown that within the electroweak model large amplitude variations of $A_{\mu}$ for fixed $Z_{\mu}$ in a superposition of these fields cancel the $AAAA$ and $AAAZ$ graphs, thereby removing an apparent obstacle to the model's non-perturbative quantization. A negative paramagnetic term in the remainder opposes the effective action's growth for such variations. Its calculation requires knowledge of the degeneracy of the bound states of a charged fermion in the four-dimensional magnetic fields generated by the functional measure of $A_{\mu}$.

One-bond 1 J(15 N─19 F) spin-spin coupling constants of cationic fluorinating reagents: Insights from DFT calculations.

We have investigated, by means of density functional theory protocols, the one-bond 1 J(15 N─19 F) spin-spin coupling constants in a series of fluorinating reagents, containing the N─F bond, recently studied experimentally. The results of the calculations show a very good linear relationship with the experimental values, even though only the M06-2X(PCM)/pcJ-2//B3LYP/6-311G(d,p) level affords a very low mean absolute error. The calculations allow to analyze the various molecular orbitals contributions to the J coupling and to rationalize the observed positive sign, corresponding to a negative sign of the reduced spin-pin coupling constant K(N─F). Moreover, of the four Ramsey contributions, only the diamagnetic spin orbit is negligible, whereas the paramagnetic spin orbit and spin dipole terms decrease the magnitude of the Fermi contact (FC) term by an amount that goes from a minimum of 35% up to more than 60% of the FC term itself. Several effects have been investigated, namely, the contribution of the long-range solvent reaction field, relativistic corrections, and conformational and vibrational effects.

13C and 207Pb NMR Chemical Shifts of Dirhodio- and Dilithioplumbole Complexes: A Quantum Chemical Assessment.

Density functional theory (DFT) and zeroth-order regular approximation DFT calculations were performed to investigate the electronic structures and 13C and 207Pb nuclear magnetic resonance (NMR) chemical shifts of metal-coordinated plumboles, namely, monorhodioplumbole ([Rh-plumbole]-), dirhodioplumbole (Rh2-plumbole), and dilithioplumbole (Li2-plumbole), which have a five-membered ring containing lead. The molecular orbital correlation diagram and extended transition state-natural orbitals for chemical valence analysis of the [Rh-plumbole]- and Rh2-plumbole complexes showed that the plumbole is primarily a π-donor, with π-donation being dominant in the Rh2-plumbole complex. The present calculations show that the Pb-Cα internuclear distances are longer in the Rh2-plumbole complex than in [Rh-plumbole]- because of the combined effect of strong π-donation and weak π-back-donation in the Rh2-plumbole complex. The calculated 207Pb and 13Cα NMR chemical shifts agree with the experimental trends reasonably well. The influences of the relativistic effect, role of the functional, effect of the solvent, and dependence of the exact exchange admixture on the calculated 207Pb and 13Cα NMR chemical shifts were investigated. The NMR chemical shift trend of the 207Pb atom in the complexes originates from the paramagnetic and spin-orbit contributions. NMR component analysis revealed that the upfield shift of the 13Cα atoms of the [Rh-plumbole]- and Rh2-plumbole complexes compared to that of the Li2-plumbole complex is mainly due to the decrease in the paramagnetic term.

Evidence of magnetism in RF magnetron sputtered deposited carbon films and investigation of its origin

The origin of magnetism in RF magnetron sputtered deposited carbon thin films is reported. Three different carbon thin films were deposited using RF magnetron sputtering of carbon target by Ar ions at RF power of 50 W, 100 W and 150 W, respectively. Microstructural characterization of films using Raman spectroscopy confirms the presence of graphitic crystallites in all three films and the crystallite edges are terminated with the sp3 bonding. However, increasing RF power results in an increase in graphitic crystallite size as well as the sp2/sp3 hybridization ratio, while the average density of the films decreases. The observed magnetization (measured using SQUID-VSM) in all the three-carbon films has a contribution from both superparamagnetic (SPM) particles (due to the interaction between unpaired spins) and the paramagnetic term due to isolated unpaired spins distributed throughout the film. The origin of experimentally observed magnetization in the carbon thin films and their correlation with the change in density and sp2/sp3 hybridization ratio due to variation in RF power is discussed.

Physical and thermophysical properties of a commercial Ni–Ti shape memory alloy strip

Some physical properties like the thermal, thermomechanical, calorimetric, magnetic, and adhesive properties of a commercial shape memory alloy (SMA) with rectangular geometry were studied. Depending on the applied forces, there were identified range of elasticity, the elasticity–viscoelasticity coexistence domain, and the domain in which a maximum force of 18 N is applied, for the SMA strip. The controlled force module, in the tension mode, was used for the determination of the SMA strip elongation at application of the stretching forces from 0 to 13 N, at 30 °C, maintaining each static force value for 3 min. By employing the multi-frequency strain–stress modulus in the tension mode, DMA cyclic heating–cooling measurements were carried out. The measured dynamic mechanical properties for SMA strip were Storage Modulus, Loss Modulus, tanδ, and Stiffness, both at heating and cooling. Thus, the characteristic temperatures of the phase transitions (As, Af, Ms, Mf), of SMA strip were identified. Also, the values of the elasticity modulus (Young’s Modulus) of the SMA strip were calculated at 30 °C. With the DSC Q2000 device, using temperature-modulated differential scanning calorimetry method, a multi-step temperature variation program was applied to the rectangular strip in two stages (heating–cooling). Through the interpretation of heat fluxes (reversible, nonreversible, and total), the phase transitions in the formation of martensite, austenite, and also of the rhombohedral phase (R phase) and moreover enabled for the R phase identification, thermomechanical analysis confirmed the results obtained by classical DSC method. The adherence of some commercial azoic dyes on the rectangular SMA strip, as well as the modification of the surface roughness of the strip after the deposition of the dye, was also studied. By magnetic measurements, it was established that the SMA strip had magnetic properties at room temperature, in which magnetization is the sum of a superparamagnetic contribution and a paramagnetic term, linear in the intensity of the magnetizing magnetic field.

Carbon-13 NMR Chemical Shift: A Descriptor for Electronic Structure and Reactivity of Organometallic Compounds.

Metal-bonded carbon atoms in metal-alkyl, metal-carbene/alkylidene, and metal-carbyne/alkylidyne species often show significantly more deshielded isotropic chemical shifts than their organic counterparts (alkanes, alkenes, and alkynes). While isotropic chemical shift is universally used to characterize a chemical compound in solution, it is an average value of the three principal components of the chemical shift tensor (δ11 > δ22 > δ33). The tensor components, which are accessible by solid-state NMR spectroscopy, can provide detailed information about the electronic structure (frontier molecular orbitals) at the observed nuclei. This information can be accessed in detail by quantum chemical calculations, most notably by an analysis of the paramagnetic contribution to the NMR shielding tensor. The paramagnetic term mainly results from the coupling of occupied and empty molecular orbitals close in energy-the frontier molecular orbitals-under the effect of the external magnetic field (B0). In organometallic compounds, a large deshielding of the isotropic carbon-13 chemical shift of the metal-bonded carbon atom is commonly related to the coupling between the occupied σM-C orbital and low-lying vacant orbitals of πM═C* character. The deshielding at the α-carbon hence probes the extent of σM-C and πM═C* interactions. This molecular orbital view readily explains the strong deshielding and large anisotropy (evidenced by the span Ω = δ11 - δ33) observed in metal alkylidenes and alkylidynes (200 < δiso < 400 ppm). Fischer carbenes are generally more deshielded than Schrock or Grubbs alkylidenes due to their low-lying πM═C* orbital. Chemical shift hence shows their higher electrophilic character, connecting NMR spectroscopy to reactivity patterns. Similarly, the α-carbon of metal-alkyls display deshielded chemical shifts in specific coordination environments. This deshielding, which is often prominently pronounced for cationic species, indicates the presence of partial π-bond character in the metal-carbon bond, making these bonds topologically equivalent to alkylidene π-bonds. The π-character in metal-alkyl bonds favors (i) α-H abstraction processes in metal bis-alkyl compounds yielding metal alkylidenes, (ii) [2 + 2]-retrocyclization of metallacyclobutanes that participate in olefin metathesis, (iii) olefin insertion in cationic metal alkyls thus explaining polymerization activity trends and the importance of α-H agostic interactions, and (iv) C-H bond activation on metal-alkyls via σ-bond metathesis. The presence of π-character in the metal-carbon bonds involved in these processes rationalizes the parallel reactivity patterns of metal-alkyls toward olefin insertion and σ-bond metathesis and the fact that σ-bond metathesis, olefin insertion, and olefin metathesis are commonly observed with metal atoms in the same ligand field. Because of the similarities in the frontier molecular orbitals involved in these processes, these reactions can be viewed as isolobal. This explains why certain fragments, such as bent metallocenes (d0 Cp2M) or T-shaped L3M, are ubiquitous in these reactions.

Sublinear scaling quantum chemical methods for magnetic shieldings in large molecules.

It is shown that quantum chemical calculations of the nuclear magnetic shieldings of a group of vicinal nuclei in a large molecule can be made sublinear scaling [i.e., O(1)] with respect to the molecular size. This is achieved by making both the diamagnetic and paramagnetic terms translation invariant [following the work of Ochsenfeld et al. J. Chem. Phys. 134, 074102 (2011)] and by making use of a local representation that is independent of the molecular size. Although only Hartree-Fock results are reported here, the idea can readily be extended to correlated wave function methods as well as the relativistic domain.

Nuclear spin-lattice relaxation time in TaP and the Knight shift of Weyl semimetals

We first analyze the recent experimental data on the nuclear spin-lattice relaxation rate of the Weyl semimetal TaP. We argue that its non-monotonic temperature dependence is explained by the temperature dependent chemical potential of Weyl fermions. We also develop the theory of the Knight shift in Weyl semimetals, which contains two counteracting terms. The diamagnetic term follows $-\ln[W/\max(|\mu|,k_BT)]$ with $W$, $\mu$ and $T$ being the high energy cutoff, chemical potential and temperature, respectively, and is always negative. The paramagnetic term scales with $\mu$ and changes sign depending on the doping level. Altogether, the Knight shift is predicted to vanish or even change sign upon changing the doping or the temperature, making it a sensitive tool to identify Weyl points. We also calculate the Korringa relation for Weyl semimetals which shows an unusual energy dependence rather than being constant as expected for a non-interacting Fermi system.

Scaling laws of Rydberg excitons

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as the magnetic field for level crossing. While bearing striking similarities to Rydberg atoms, fundamentally new insights may be obtained for Rydberg excitons, as the crystal environment gives easy optical access to many states within an exciton multiplet. Here we study experimentally and theoretically the scaling of several characteristic parameters of Rydberg excitons with $n$. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a $B_r \propto n^{-4}$ dependence of the resonance field strength, $B_r$, due to the dominant paramagnetic term unlike in the atomic case where the diamagnetic contribution is decisive. By contrast, in electric field we find scaling laws just like for Rydberg atoms. The resonance electric field strength scales as $E_r \propto n^{-5}$. We observe anticrossings of the states belonging to multiplets with different principal quantum numbers. The energy splittings at the avoided crossings scale as $n^{-4}$ which we relate to the crystal specific deviation of the exciton Hamiltonian from the hydrogen model. We observe the exciton polarizability in the electric field to scale as $n^7$. In magnetic field the crossover field strength from a hydrogen-like exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as $n^{-3}$. The ionization voltages demonstrate a $n^{-4}$ scaling as for atoms. The width of the absorption lines remains constant before dissociation for high enough $n$, while for small $n \lesssim 12$ an exponential increase with the field is found. These results are in excellent agreement with theoretical calculations.

Orbital Analysis of Carbon‐13 Chemical Shift Tensors Reveals Patterns to Distinguish Fischer and Schrock Carbenes

AbstractFischer and Schrock carbenes display highly deshielded carbon chemical shifts (&gt;250 ppm), in particular Fischer carbenes (&gt;300 ppm). Orbital analysis of the principal components of the chemical shift tensors determined by solid‐state NMR spectroscopy and calculated by a 2‐component DFT method shows specific patterns that act as fingerprints for each type of complex. The calculations highlight the role of the paramagnetic term in the shielding tensor especially in the two most deshielded components (σ11 and σ22). The paramagnetic term of σ11 is dominated by coupling σ(M=C) with π*(M=C) through the angular momentum operator perpendicular to the σ and π M=C bonds. The highly deshielded carbon of Fischer carbenes results from the particularly low‐lying π*(M=C) associated with the CO ligand. A contribution of the coupling of π(M=C) with σ*(M=C) is found for Schrock and Ru‐based carbenes, indicating similarities between them, despite their different electronic configurations (d0 vs. d6).

Orbital Analysis of Carbon-13 Chemical Shift Tensors Reveals Patterns to Distinguish Fischer and Schrock Carbenes.

Fischer and Schrock carbenes display highly deshielded carbon chemical shifts (>250 ppm), in particular Fischer carbenes (>300 ppm). Orbital analysis of the principal components of the chemical shift tensors determined by solid-state NMR spectroscopy and calculated by a 2-component DFT method shows specific patterns that act as fingerprints for each type of complex. The calculations highlight the role of the paramagnetic term in the shielding tensor especially in the two most deshielded components (σ11 and σ22 ). The paramagnetic term of σ11 is dominated by coupling σ(M=C) with π*(M=C) through the angular momentum operator perpendicular to the σ and π M=C bonds. The highly deshielded carbon of Fischer carbenes results from the particularly low-lying π*(M=C) associated with the CO ligand. A contribution of the coupling of π(M=C) with σ*(M=C) is found for Schrock and Ru-based carbenes, indicating similarities between them, despite their different electronic configurations (d0 vs. d6 ).

Computation provides chemical insight into the diverse hydride NMR chemical shifts of [Ru(NHC)4(L)H]0/+ species (NHC = N-heterocyclic carbene; L = vacant, H2, N2, CO, MeCN, O2, P4, SO2, H-, F- and Cl-) and their [Ru(R2PCH2CH2PR2)2(L)H]+ congeners.

Relativistic density functional theory calculations, both with and without the effects of spin-orbit coupling, have been employed to model hydride NMR chemical shifts for a series of [Ru(NHC)4(L)H]0/+ species (NHC = N-heterocyclic carbene; L = vacant, H2, N2, CO, MeCN, O2, P4, SO2, H-, F- and Cl-), as well as selected phosphine analogues [Ru(R2PCH2CH2PR2)2(L)H]+ (R = iPr, Cy; L = vacant, O2). Inclusion of spin-orbit coupling provides good agreement with the experimental data. For the NHC systems large variations in hydride chemical shift are shown to arise from the paramagnetic term, with high net shielding (L = vacant, Cl-, F-) being reinforced by the contribution from spin-orbit coupling. Natural chemical shift analysis highlights the major orbital contributions to the paramagnetic term and rationalizes trends via changes in the energies of the occupied Ru dπ orbitals and the unoccupied σ*Ru-H orbital. In [Ru(NHC)4(η2-O2)H]+ a δ-interaction with the O2 ligand results in a low-lying LUMO of dπ character. As a result this orbital can no longer contribute to the paramagnetic shielding, but instead provides additional deshielding via overlap with the remaining (occupied) dπ orbital under the Lz angular momentum operator. These two effects account for the unusual hydride chemical shift of +4.8 ppm observed experimentally for this species. Calculations reproduce hydride chemical shift data observed for [Ru(iPr2PCH2CH2PiPr2)2(η2-O2)H]+ (δ = -6.2 ppm) and [Ru(R2PCH2CH2PR2)2H]+ (ca. -32 ppm, R = iPr, Cy). For the latter, the presence of a weak agostic interaction trans to the hydride ligand is significant, as in its absence (R = Me) calculations predict a chemical shift of -41 ppm, similar to the [Ru(NHC)4H]+ analogues. Depending on the strength of the agostic interaction a variation of up to 18 ppm in hydride chemical shift is possible and this factor (that is not necessarily readily detected experimentally) can aid in the interpretation of hydride chemical shift data for nominally unsaturated hydride-containing species. The synthesis and crystallographic characterization of the BArF4- salts of [Ru(IMe4)4(L)H]+ (IMe4 = 1,3,4,5-tetramethylimidazol-2-ylidene; L = P4, SO2; ArF = 3,5-(CF3)2C6H3) and [Ru(IMe4)4(Cl)H] are also reported.

A Localized Molecular Orbital Study of the Halogen Substitution Effect on (103)Rh NMR Shielding in [Cp*RhX2]2, Where X = Cl, Br, or I.

(103)Rh NMR parameters and the bonding structure of three complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have been studied with the help of natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have similar bonding structures, with the major difference being in the degree of covalency of the Rh-X bonds. The decomposition of (103)Rh NMR shielding into diamagnetic, paramagnetic, and spin-orbit terms shows that normal halogen dependence (NHD) of the (103)Rh NMR shift is defined mostly by the paramagnetic term, with the spin-orbit term being significantly smaller. The decomposition of (103)Rh shielding into spin-free NBO and NLMO contributions shows that (103)Rh shielding is dominated by Rh d-orbital deshielding contributions. We explain the NHD of the (103)Rh NMR shift with the increase in the energies of the virtual antibonding Rh-X orbitals along the X = Cl, Br, and I series.