Hfs Parameters Research Articles

Second spectrum of Manganese (Mn II), Part II: Revised fine and hyperfine structure analysis of odd-parity levels

In the first part of this global work, we have achieved the fine and hyperfine structure (fs and hfs) parametric study of even-parity levels, which confirmed in the whole the well-founded basis of previous analyses. Unfortunately, in the present work devoted to odd-parity levels, some divergences appear. For instance, the three levels w5P3, w5P2, w5P1 located respectively at 86898, 86937 and 86961 cm−1 should not belong to the 3d4(5D)4s4p configuration, as indicated earlier, but rather to 3d5(4P)5p. In the other hand, the levels whose energies are: 88840, 89079 and 89429 cm−1 should belong this time to 3d4(5D)4s4p instead of 3d55p, as mentioned previously. Our analysis is strengthened when using experimental hfs data as finger prints, even if the comparison between these experimental hfs data, given in the literature, and our calculated results also shows in numerous cases some notable discrepancies, concerning particularly the sign of the electric quadrupole factor. The main monoelectronic hfs parameter values, extracted from our least square fitting procedure, are: a3d01(3d54p)= 17.58 mK, b3d02(3d54p)= 10.27 mK, a3d01 (3d44s4p)= 18.74 mK and a4s10(3d44s4p)= 274.9 mK. These parameter values, displayed for the first time, were analyzed and compared with ab-initio calculations. As in the first part, we conclude this work by giving the predicted hfs A and B constants of low-lying levels of these two configurations, whose splitting are not yet measured.

Second spectrum of Manganese (Mn II), Part I: Fine and hyperfine structure analysis of even-parity levels

We have taken advantage of the existence of some experimental Mn II hyperfine magnetic dipole constant (A) values given in literature with low uncertainties to achieve for a first time an accurate hyperfine structure (hfs) parametric study. The monoelectronic hfs parameter values were extracted in their entirety for the alone stable 55Mn II. For example for 3d44s configuration we obtain: a4s10=198.08 mk and a3d01=17.14 mk. These semi-empirically extracted single-electron parameters were analyzed and compared with ab-initio calculations. In this first part of a global work, devoted particularly to even-parity levels we have at beginning studied a fine structure of two hundred levels, giving their leading eigenvector percentages and their calculated Landé-factor gJ. We present also predicted singlet, triplet and quintet positions of missing experimental levels up to 120000 cm−1, not far from Mn II ionization energy of 126000 cm−1. We close this work by giving predicted values of magnetic dipole hfs constants of all known levels of the most relevant Mn II even-parity configuration: 3d44s, whose splitting is not yet measured.

Activation of the subthalamic nucleus suppressed by high frequency stimulation: A c-Fos immunohistochemical study

Deep brain stimulation applied at high frequency (HFS) to the subthalamic nucleus (STN) is used to ameliorate the symptoms of Parkinson’s disease. The mechanism by which this is achieved remains controversial. In particular, it is uncertain whether HFS has a suppressive or excitatory action locally within the STN. Brief exposure of rats to ether anesthesia evokes pathological burst firing and associated expression of the immediate early gene c-Fos in STN neurons. We used this ether model of STN activation to test the effect of a range of HFS parameters on c-Fos expression evoked by the anesthetic. The elevated baseline of c-Fos expression afforded the possibility of detecting further excitatory, or suppressive effects of STN HFS. Four HFS protocols were examined; 130, 200 and 260 Hz with 60 µs, and 130 Hz with 90 µs pulse width (HFS intensity:150-300 µA). All HFS protocols were applied for 20 min while the animals were exposed to ether. Ether-evoked expression of c-Fos immunoreactivity was suppressed by HFS at 200 and 260 Hz with a pulse width of 60 µs, and by 130 Hz when the pulse width was increased to 90 µs. HFS at 130 Hz with the 60 µs pulse width had no significant effect and HFS alone caused negligible c-Fos expression in the STN. These findings suggest that HFS of the STN causes significant suppression of evoked neuronal activity. It remains to be determined whether this locally suppressive property of HFS is associated with the efficacy of STN deep brain stimulation to relieve the symptoms of Parkinson’s disease.

Parametric study of hyperfine structure of Zr II even-parity levels

Until now experimental hyperfine structure (hfs) data of 12 even-parity Zr II levels were given in the literature. Recently new hyperfine splitting measurements of 11 other Zr II levels, of the same parity are achieved, applying fast-ion-beam laser-fluorescence spectroscopy. The hfs of these 23 gathered levels has been analysed by simultaneous parametrisation of the one- and two-body interactions, first in model space (4d + 5s)3 and secondly in extended space. For the three lowest configurations, radial parameters of the magnetic dipole A and quadrupole electric B factors are deduced in their entirety for 91Zr II, compared and discussed with calculated values, available in the literature, and also with ours, computed by means of the ab initio method. For instance we give the main experimental values of the extracted single-electron hfs parameters of 4d25s: [Formula: see text] = –2701 MHz, [Formula: see text] = –122.4 MHz, and [Formula: see text] = –113.5 MHz.

Extended analysis of the system of even configurations of Ta II

We performed a parametric study of the fine (fs) and hyperfine structure (hfs) for the even parity configurations of ionized tantalum (Ta II) using improved experimental fs and hfs data for 88 levels. A multi-configuration fitting procedure was performed for 47 configurations taking into account second-order perturbation theory including the effects of closed to open shell excitations. The fs and hfs parameters were calculated. Predicted values of level energies up to 86000cm−1 are given, as well as gJ-Landé factors, magnetic dipole and electric quadrupole hyperfine structure constants A and B, when no experimental values are available.

Fine, hyperfine and Zeeman structures of levels of 123Sb I

The hyperfine and Zeeman structures of 14 lines of isotope 123Sb covering the UV-NIR spectral range have been measured. The experimental data have been used in order to reanalyse and revise Sb I energy levels. We named majority of them for the first time since they were previously labelled only by their energy values, without any term designations. In both cases of odd- and even-parity levels we took into consideration up to 7 interacting configurations; the set of fine structure parameters and the leading eigenvector percentages of levels as well as their calculated Lande-factors are given. Semi-empirical hfs parameter values extracted from experimental data were compared with ab initio results computed by the use of Cowan code.

Electronic states and spectra of BiH

Emission spectra of bismuth monohydride (BiH) radicals excited by energy transfer from O2(a1Δg) or NF(a1Δ) or by a DC discharge in a mixture of bismuth vapor and hydrogen in a fast-flow system were studied in the wavenumber range from 4000 to 25000cm−1 with a Fourier-transform spectrometer. The X21→X10+ transition between the spin components of the X3Σ− ground state was remeasured at high spectral resolution and signal/noise. Six bands of the Δv=0 and +1 sequences near 4950 and 6600cm−1 have been observed. The low-J lines of these bands are split into up to 10hfs components due to magnetic hyperfine structure splitting of the X21 levels. In addition to the previously observed electric dipole lines, weak magnetic dipole lines show up in the Δv=0 but not in the Δv=+1 bands. The intensities of the Δv=+1 bands are about a factor of 10 higher than expected from Franck–Condon factors indicating that the electric dipole transition moment μX2–X1 shows a strong dependence on internuclear distance. Near 5450cm−1, the 0-0 and 1-1 bands of the transition a2→X21 from the hitherto unknown first excited state a1Δ(a2) to the upper component of the ground state have been observed. The lines in these bands show the magnetic hfs splitting of both the a2 and X21 states. In the visible range near 21300 and 16300cm−1, the 0-0 and 1-1 bands of the b0+→X10+ system and the 0-0 band of the b0+→X21 transition likewise have been measured at high resolution. The lines of the latter band also show the hfs splitting of the X21 state. Least-squares fits have yielded rotational and vibrational constants of the X10+, X21, a2, and b0+ states as well as hfs parameters of the X21 and a2 states and the electronic energy of the hitherto unknown a1Δ(a2) level.

Fine Structure Analysis of the Configuration System of V II. Part I: Even-Parity Levels

Using a linked-parameter technique of level-fitting calculations in a multi configuration basis, a parametric analysis of fine structure (fs) for even-parity levels of V II, involving six configurations, has been performed. This led us to exchange the assignments of two triplets, 3d3(2F)4s c 3F and 3d4 d 3F, reported in earlier analyses as being located at 30,300 cm-1 and 30,600 cm-1, respectively. This is confirmed by experimental hyperfine structure (hfs) A constants, used as fingerprints. Moreover, the current singlet 3d24s2 1D2 position is likely too high. The fs parameters, magnetic Lande g-factors, and the percentage of leading eigenvectors of levels are calculated. We present also predicted singlet, triplet and quintet positions for missing experimental levels up to 100,000 cm-1. The single-electron hfs parameters are determined in their entirety for 51V II for the model space (3d + 4s)4 with good accuracy. For the model space (3d + 4s)4 of 51V II the single-electron hfs parameters are computed; furthermore, our achieved theoretical evaluations of the single-electron hfs parameters, thanks to the use of ab initio calculations, reinforce the validity of these hfs parameter values, deduced from experimental data.

Reasons for the line broadening in the epr spectra of copper ions in Li2-2x Zn2+x (MoO4)3 lithium-zinc molybdate crystals

An EPR study of Li2−2xZn2+x(MoO4)3 crystals activated by copper ions shows that they occupy the M2 site, one of the three possible sites of both lithium and zinc. In the EPR spectra of Cu2+ copper a broadening of HFS lines and a nonequidistant splitting between them, which are unusual for the orientation H‖gzz, Azz, are observed. In this work possible reasons for such a broadening of HFS lines from copper ions are analyzed: a distortion of the oxygen octahedron due to the introduction of copper ions, second order perturbation theory corrections, superposition of HFS from 63Cu and 65Cu isotopes, and the effect of the charge redistribution in the oxygen octahedron because the cation vacancy providing charge compensation can be located at different distances from the copper ion. It is shown that the first three reasons do not explain the features observed in the EPR spectra. In the case of cation vacancies located in the M3 site and remote at different distances from the copper ion, the charge redistribution in the oxygen octahedron of copper should occur along with the dispersion of HFS parameters and the g-factor. The studies performed in X and Q bands confirm this assumption. The width of HFS lines from copper ions in the EPR spectra measured in the Q band is three times more compared to that measured in the X band.

Full hyperfine structure study of singly ionized tantalum

The configuration system of Ta II, both for odd- and even-parities has been considered on the basis of the experimental data available in the literature. The interpretation has been carried out based on a model space for even-parity and refined multiconfigurational fine structure (fs) calculation including the main Rydberg series configurations mutually interacting for odd parity. The sets of fs parameters, the assignments of term designations, as well as the leading eigenvector percentages of levels relevant for this paper are given very often for the first time. The hyperfine structure (hfs) study that follows reveals erroneous experimental data given previously in the literature and some new data are proposed in their place. The single-electron hfs parameters are determined in their entirely for 181Ta II for the lowest configurations with a good accuracy and compared with ab-initio calculations. Finally, a complete list of the predicted hfs constants A and B of all levels of the model space (5d + 6s)4 was generated.

Analytic Calculation of Isotropic Hyperfine Structure Constants Using the Normalized Elimination of the Small Component Formalism

Based on the normalized elimination of the small component relativistic formalism, a new approach to the calculation of hyperfine structure parameters of paramagnetic molecules is developed and implemented. The new method is tested in the calculation of the isotropic hyperfine structure constant for a series of open-shell molecules containing mercury. The results of calculations carried out in connection with ab initio methods of increasing complexity demonstrate the high accuracy of the formalism developed. In view of its computational simplicity, the new approach provides the basis for an efficient and accurate calculation of the HFS parameters of large molecules.

The A 2Π u state of [formula omitted]: Electric properties, fine and hyperfine coupling constants, and magnetic moments ( g-factors). A theoretical study

Several properties are calculated for A 2Π u of N 2 + —the majority for the first time—including electric and magnetic moments, and fine/hyperfine structure (fs/hfs) parameters. The new results are compared with our previous ones for X 2 Σ g + and B 2 Σ u + of N 2 + [P.J. Bruna, F. Grein, J. Mol. Spectrosc. 227 (2004) 67–80]. The electric quadrupole Θ and hexadecapole Φ moments, polarizability α, and hfs constants a, b, c, d, eQq 0, eQq 2 are evaluated at the density functional theory (DFT) level [B3LYP/aug-cc-pVQZ]. The fs constants (spin–orbit coupling A Π, Λ-doubling p, q, spin-rotation γ Π), and magnetic moments ( g-factors) are obtained via 2nd-order sum-over-states expansions, using wavefunctions and matrix elements obtained with a multireference configuration interaction (MRDCI) method, and the Breit–Pauli Hamiltonian. At equilibrium, 2nd-order properties of A 2Π u are dominated by its coupling with B 2 Σ u + . For the A state, two independent components are reported for traceless tensor properties (multipoles Θ and Φ; hfs parameters c/d and q 0/ q 2) and three for traced properties (polarizability α and g-factors), i.e., one more component than for axially symmetric Σ states. The currently available experimental data on A 2 Π u ( N 2 + ) — limited to A Π, p, and q—are well reproduced by our theoretical results.

Finite-temperature properties of the muonium substituted ethyl radical CH2MuCH2: nuclear degrees of freedom and hyperfine splitting constants*

The finite-temperature (T) properties of the muonium substituted ethyl radical CH2MuCH2 have been theoretically studied by Feynman path integral quantum Monte Carlo (PIMC) simulations. To derive the ensemble averaged expectation values we have combined the PIMC formalism with an efficient tight-binding (TB) Hamiltonian and a density functional operator of the B3LYP type in the EPRIII basis. The TB operator has been used to calculate the potential energy surface (PES) of the ethyl radical in the doublet ground state, the harmonic and anharmonic vibrational wave numbers as well as several probability density functions of the nuclei. The harmonic linear response approximation, which makes use of the Feynman centroid density, has been adopted to evaluate the anharmonic wave numbers. The large anharmonicities in the nuclear potential lead to bond lengths in thermal equilibrium which exceed the vibrationless parameters at the PES minimum. This enhancement is particularly strong for the C–Mu bond. It is responsible for the suppression of the intramolecular rotation for temperatures below room temperature. In C2 H5 the rotation is allowed down to 10 K. The dissimilar rotational dynamics for H2MuCH2 and C2 H5 has been studied with the help of TB-based probability density functions. The nuclear configurations of CH2MuCH2 and C2 H5, which are populated in thermal equilibrium, have been used to evaluate the isotropic and anisotropic hyperfine splitting (hfs) constants under explicit consideration of the nuclear vibrations and the internal rotation. The hfs constants have been determined with the help of the B3LYP-EPRIII Hamiltonian. The hindered low-temperature rotation in the Mu isomer is responsible for roto-vibrational corrections to the isotropic hfs constants which are smaller than the corrections in C2 H5. The shortcomings of single-configuration approaches for the evaluation of isotropic hfs constants have been demonstrated for both radicals. The ensemble corrections to the isotropic hfs parameters are correlated with fluctuations in the atomic spin densities. Differences in the absolute values of the isotropic hfs parameters in CH2MuCH2 and C2 H5 can be traced back to differences in the nuclear degrees of freedom. The ensemble shift for each isotropic hfs parameter can be explained by characteristic nuclear motions. For this discussion we make use of the distribution functions of the isotropic hfs constants. Roto-vibrational corrections to the anisotropic hfs constants are rather small. PIMC simulations have been performed between 25 and 1000 K, i.e. in a T interval that is large enough to consider nuclear effects beyond zero-point motions. The TB and B3LYP-EPRIII based physical quantities of CH2MuCH2 and C2 H5 have been compared with experimental findings whenever possible.

Feynman path integral – ab initio study of the isotropic hyperfine coupling constants of the muonium substituted ethyl radical CH 2MuCH 2

The isotropic hyperfine coupling (hfs) constants of the muonium substituted ethyl radical CH 2MuCH 2 have been studied at T = 25 K by a Feynman path integral Monte Carlo (PIMC)–density functional (DFT) formalism. The DFT Hamiltonian employed is of the B3LYP–EPRIII type. The hfs constants of the rotationally hindered CH 2MuCH 2 isomer have been compared with the hfs constants of C 2H 5 which exhibits free internal rotation. The dissimilar rotational dynamics in both radicals leads to significant differences between some of the isotropic hfs parameters. The PIMC results show the strong coupling between nuclear fluctuations and calculated hfs constants.

Nuclear degrees of freedom in calculated isotropic hyperfine coupling constants of the ethyl radical: a Feynman path integral – ab initio study

The Feynman path integral quantum Monte Carlo formalism has been combined with an electronic Hamiltonian of the B3LYP-EPRIII type to study the isotropic hyperfine coupling (hfs) constants of the ethyl radical in thermal equilibrium ( T=25 K). The nuclear vibrations and the intramolecular rotation around the C–C bond have a sizeable influence on the hfs parameters. The thermally averaged numbers differ from single-nuclear configuration values calculated at the minimum of the potential energy surface. The analysis of the distribution functions for the isotropic hfs constants of C 2H 5 offers insight into the strong coupling between calculated hfs parameters and the nuclear configuration adopted.

Parameter extraction of accurate and scaleable substrate resistance components in RF MOSFETs

Parameter extraction of the substrate resistance, which becomes important in radio frequency (RF) and mixed signal integrated circuit (IC) design, is discussed based on a simple substrate network of lumped components. By using the measured HF s-parameter data from a set of devices with different geometries, the scaleable parameters for substrate resistances components can be obtained. The simple substrate model with extracted scaleable parameters is accurate for devices with different widths and fingers in a frequency range up to 10 GHz.

Doppler limited laser spectroscopy on hafnium lines. Part II: Hyperfine structure of odd-parity levels

The hyperfine structure of selected odd-parity levels of the configurations 5d6s26p and 5d26s6p of \(\) I was studied in 10 lines lying in the red spectral region. Hyperfine spectra were obtained by the method of laser induced fluorescence in the plasma of a liquid nitrogen cooled hollow cathode discharge. The observed hyperfine structure constants A and B, together with results from earlier studies were analyzed by means of a parametric method. The interpretation has been carried out based on a refined multiconfigurational fine structure calculation including the main Rydberg series configurations mutually interacting. The set of fine structure parameters as well as the leading eigenvector percentages of levels relevant for this paper are given. The following single electron hfs parameters were deduced for \(\): \(\), \(\),\(\), \(\) for the lowest configuration.

Experimental and theoretical study of the hyperfine structure in the (5d+6s)96p configurations of Pt I

The hyperfine structure of the odd configurations 5d96p and 5d86s6p was studied with laser optogalvanic spectroscopy and high resolution interferometry in a platinum hollow cathode. A parametric hyperfine structure analysis for the configurations (5d+6s)96p with 10 excited odd-parity levels was performed for195Pt. We obtained one-electron hfs parameters,a 5d 01 =1160(320) MHz,a 6s 10 =35600(5300) MHz anda 6p 01 =1300(780) MHz for the configuration 5d86s6p. The corresponding\(\left\langle {r^{ - 3} } \right\rangle _{nl}^{k_s k_l } \) values are compared with those known for other 5d-elements.

E.p.r. HFS spectral characteristics of Mn 2+ impurity ions in Argonne and Alberta coals

A new, more comprehensive study of the 9 and 33 GHz CW e.p.r. Mn 2+ impurity ion spectral characteristics of the eight Argonne premium coals and two Alberta h.v. bituminous coals is reported. These characteristics include the HFS a 1 relative amplitude, linewidth and lineshape as well as a more accurate and reliable determination of the g-value, the HFS parameter A and the c 0 2 and c 0 4 ZFS parameters for powdered coal samples from the ΔM = ±1, Δm = 0 central and weak non-central transitions using the spin Hamiltonian diagonalization spectral simulation method of analysis. The six Mn 2+ Δm = 0 HFS central transitions observed in coal samples do not have two component resonances, unlike those for Mn 2+ in polycrystalline calcite, which is attributed to lineshape broadening. However, the a 1 amplitude and linewidth variation for the six Mn 2+ HFS central transitions observed in each of the coal samples studied is consistent with that observed in polycrystalline calcite. The consistency of the a 1 amplitude and linewidth analysis as well as of the improved values of the e.p.r. spectral parameters for Mn 2+ impurity ions in calcite and coal provides more conclusive confirmation that the e.p.r. spectrum of Mn 2+ originates from the calcite mineral component of coal.

Laser-rf double-resonance spectroscopy of 177,179Hf.

The atomic-beam laser-rf double-resonance technique has been used to make precision measurements of the hyperfine structure (hfs) splittings in the 5${\mathit{d}}^{2}$6${\mathit{s}}^{2}$ $^{3}$${\mathit{F}}_{\mathit{J}}$ (J=2--4) states in $^{177,179}\mathrm{Hf}$ i. By making corrections to the second-order hfs effects, magnetic dipole (A), electric quadrupole (B), and magnetic octupole (C) hfs constants are obtained for the $^{3}$${\mathit{F}}_{\mathit{J}}$ states in $^{177,179}\mathrm{Hf}$: The constant C has a strong J dependence as well as does A and B; the isotopic ratio of the constant A between $^{177}\mathrm{Hf}$ and $^{179}\mathrm{Hf}$ has a significant J dependence, indicating J-dependent hyperfine anomalies, while that of the constant C is independent of J within experimental uncertainties, which is taken to be the ratio of the nuclear-ground-state magnetic octupole moments \ensuremath{\Omega}, i.e., \ensuremath{\Omega}${(}^{177}$Hf)/\ensuremath{\Omega}${(}^{179}$Hf)=-0.41(9). It is also pointed out that there is a clear indication of nuclear-spin dependence of the isotopic ratios of C. The single-electron hfs parameters of the 5d electron for the 5${\mathit{d}}^{2}$6${\mathit{s}}^{2}$ configuration in Hf i are obtained, and the Sternheimer shielding factor ${\mathit{R}}_{5\mathit{d}}$=-0.397(8) is derived.