Fermi Contact Parameter Research Articles

Pure rotational spectrum of CaCH3(X̃ 2A1) using the pump/probe microwave-optical double resonance (PPMODR) technique

The pure rotational spectrum of calcium monomethyl, CaCH3(X 2A1), was recorded using the pump/probe microwave-optical double resonance (PPMODR) technique. The determined Fermi contact and dipolar parameters are: aF=−1.965(11) and Taa=2.180(18) MHz. The spin-rotation parameters are: eaa=6.702(49) and (ebb+ecc)/2=55.5730(27) MHz. The mm-wave data [M. A. Anderson and L. M. Ziurys, Astrophys. J. 460, L77 (1996)] were reanalyzed to produce a set of fine structure parameters that are consistent with the PPMODR values and for which the standard deviation of the mm-wave data set is greatly reduced. A global fit of the two sets of data was performed to give an improved set of fine and hyperfine parameters for the X 2A1 state. The negative value for aF is inconsistent with a simple σ-bond spin polarization model. A comparison among calcium containing molecules is made using hyperfine and spin-rotation parameters.

Properties of the ground state of the hydrogen molecular ion

The ground-state energies of the ions ${\mathrm{H}}_{2}^{+}$ and ${\mathrm{D}}_{2}^{+}$ have been calculated without making use of the Born-Oppenheimer approximation. Instead, the ions are treated as three-body systems whose ground states are spherically symmetric. The wave function of the ground state is taken to be a generalized Hylleraas form, but it is necessary to use high powers of the internuclear coordinate to simulate the localized motion of the nuclei. We obtain good values of the ground-state energies and compare them with those obtained from earlier calculations. Expectation values are calculated for various operators, the Fermi contact parameter, and the permanent quadrupole moment. The cusp condition is also calculated. The results are compared with the results of other calculations, where available.

A spectroscopic study of CaOCH3 using the pump/probe microwave and the molecular beam/optical Stark techniques

The Stark effect on the R22q(0,0.5) (ν=17 682.9251 cm−1) and P11q(0,1.5) (ν=17 682.1966 cm−1) branch features of the (0,0) B 2A1–X 2A1 band system of calcium methoxide, CaOCH3, was measured and analyzed to give the magnitude of the permanent electronic dipole moments, |μ|, of 1.58(8) D and 1.21(5) D for the X 2A1 and B 2A1 states, respectively. The dipole moments are compared with other monovalent calcium compounds and those predicted from a simple electrostatic model. Pure rotational transitions in the X 2A1 state were recorded using the pump/probe microwave-optical double resonance technique. The proton magnetic hyperfine splitting pattern confirms a C3v symmetry of the ground electronic state. The determined Fermi contact and dipolar parameters are: aF=−0.421(27) MHz; Taa=1.070(45) MHz, and |Tbb−Tcc|=0.292(47) MHz. The latter parameter is associated with the lifting of the K-degeneracy of this symmetric top molecule and mixing the I0=1/2 and I0=3/2 levels.

The millimeter wave spectrum of silver monoxide, AgO

The pure rotational spectra of AgO107 and AgO109 were recorded in the 117–380 GHz spectral region using a dc-sputtering absorption cell. The Ag107(I=1/2) and Ag109(I=1/2) magnetic hyperfine parameters are interpreted in terms of plausible electronic configuration contributions to the X 2Πi state. It is shown that the determined unusual sign of the Λ-doubling and Fermi contact parameters implies that the X 2Πi state is dominated by a three open shell configuration. A comparison with isovalent CuO is made.

A Rotational and Hyperfine Analysis of the [14.0]2Σ+–X2Σ+Band System of Cobalt Monocarbide

The cobalt monocarbide molecule has been produced by laser ablation of a cobalt rod in the presence of 1.5% methanol in a helium carrier gas. The mixture was expanded into a vacuum, yielding a free jet withTrot∼ 30 K. Low resolution laser-induced fluorescence studies showed the [14.0]2Σ+–X2Σ+band system as a long vibrational progression between 500 and 720 nm. Several vibrational bands were analyzed at high resolution; least squares fitting of the data led to the determination of rotational and hyperfine constants for both states. TheX2Σ+state is best described by a Hund's case (bβS) coupling scheme, while the [14.0]2Σ+state conforms to case (bβJ). Analysis of the hyperfine parameters indicates that theX2Σ+state arises from a valence (8σ)2(3π)4(1δ)4(9σ)1electronic configuration and that the [14.0]2Σ+state originates from a (8σ)1(3π)4(1δ)4(9σ)2configuration. The vibrational levels of the [14.0]2Σ+state appear to be perturbed by other nearby states; this is reflected in unusual distortions in the spin–rotation parameters from one vibrational level to the next. The effects of the perturbations are also observed in the sign and magnitude of the hyperfine dipolar interaction parameters of the [14.0]2Σ+state, and effects are also observed on the Fermi contact and electric quadrupolar parameters.

Density functional calculations of Fermi contact hyperfine coupling parameters

Fermi contact parameters are calculated with a range of one-particle basis sets and functionals. The parameters are determined at all nuclei in the following eleven radicals: C 2H 3, C 2H 2F, CH, NH +, NH, OH +, OH, FH, FF −, CN, NO 2. Results show that using Becke's new three-parameter exchange functional leads to improved agreement with experiment.

Perturbation facilitated optical–optical double resonance spectroscopy of the 2 3Σ+g, 3 3Σ+g, and 4 3Σ+g Rydberg states of 7Li2

This paper reports the experimental observation of the 2 3Σ+g, 3 3Σ+g, and 4 3Σ+g states of 7Li2 by cw perturbation facilitated optical–optical double resonance spectroscopy. Molecular constants and RKR potential curves have been obtained. Our experimental Te and Re for the 2 3Σ+g state are 27 297.45(16) cm−1 and 3.0797(18) Å, respectively, and for the 3 3Σ+g state are 31 043.93(53) cm−1 and 3.0378(19) Å, respectively. The above values are in very good agreement with theoretical calculations. Hyperfine splitting for both states has been resolved. Both states follow Hund’s case (bβS) hyperfine coupling scheme. The experimental Fermi contact parameter, bF, is approximately 96±2 MHz for the 2 3Σ+g state and 95.6±3 MHz for the 3 3Σ+g state. These values are in good agreement with the previously obtained value 98.6±4 MHz [Li et al., J. Chem. Phys. 96, 3342 (1992)]. One level of the 4 3Σ+g state has been observed and its hyperfine structure has been resolved and characterized with Hund’s coupling case (bβS).

Intracavity laser spectroscopy of VO: Hyperfine parameters and electron configuration of the B4Π state

The low- J structure of the B 4Π- X 4Σ − (1, 0) band of VO has been investigated at sub-Doppler resolution by intracavity laser-induced fluorescence spectroscopy. Values of the principal hyperfine parameters a and ( b + c) for the B 4Π state have been deduced from the lines of the 4 Π 5 2 -X and 4 Π 3 2 -X subbands: a = 0.00964 cm −1 and ( b + c) = −0.01295 cm −1. Estimates of the dipolar parameter c show that it is small compared to b, so that the Fermi contact parameter b is sizeable and negative; this allows the electron configuration of the B 4Π state to be assigned as (3 dδ) 2(3 dπ) 1(4 sσ) 1. The very great sensitivity of intracavity laser spectroscopy in the visible region is emphasized.

Accurate nonrelativistic expectation values for H +2

Two separate approaches (a perturbation theory which extends the Born—Oppenheimer approximation of molecular physics and finite element analysis of the three body Coulomb problem) are used to solve the nonrelativistic Schrödinger equation for the hydrogen molecular ion ground state. For both approaches, expectation values are calculated for the bond length, the rotational constant, the permanent quadrupole moment, the Fermi contact parameter, and other operators. These results are compared with “nonadiabatic” variational results, where available.

Electron-nuclear coupling in the hyperfine structure of the hydrogen molecular ion.

A perturbation theory for determining the electron-nuclear coupling corrections to the adiabatic expectation values of operators of molecular systems is developed and applied to the hyperfine Hamiltonian of the hydrogen molecular ion. The expectation values of the Fermi contact parameter for the rotation-vibration states N=1, v=4--8 are compared with experimental results. Previous adiabatic expectation values differ from the empirical values by about 600 kHz. Inclusion of the first-order corrections reduces the discrepancies to less than 9 kHz.

Hyperfine structure of the MnH X 7Σ+ state: A large gas-to-matrix shift in the Fermi contact interaction

Sub-Doppler spectra of the A 7Π–X 7Σ+ (0,0) band of gas phase MnH near 5680 Å were recorded by intermodulated fluorescence spectroscopy. The spectra reveal hyperfine splittings arising from both the 55Mn and 1H nuclear spins. Internal hyperfine perturbations have been observed between the different spin components of the ground state at low N″. From a preliminary analysis of several rotational lines originating from the isolated and unperturbed F1(J″=3) spin component of the X 7Σ+(N″=0) level, the 55Mn Fermi contact interaction in the ground state has been measured as bF=Aiso =276(1) MHz. This value is 11% smaller than the value obtained by Weltner et al. from an electron-nuclear double resonance (ENDOR) study of MnH in an argon matrix at 4 K. This unprecedented gas-to-matrix shift in the Fermi contact parameter is discussed.

The permanent dipole moment of TiN and the nuclear magnetic hyperfine structure in its X 2Σ+ and A 2Π electronic states

The permanent dipole moment of TiN in its X 2Σ+ and A 2Σ states has been determined from the complete resolution of the first- and second-order Stark splitting of the Q21(1.5)+R2(0.5) line of the (0,0) band of the A 2Π–X 2Σ+ system. Values of 3.56±0.05 D (2σ) and 4.63±0.04 D (2σ) have been derived for the X and A states respectively, from least-squares fits to plots of Stark splitting vs electric field strength. Electric fields up to 12 kV/cm have been employed avoiding voltage breakdown. The zero-field spectrum shows resolution of the nuclear magnetic hyperfine structure of the 47TiN and 49TiN isotopes. This hyperfine structure is that of the ground X 2Σ+ state only and is shown to follow closely the coupling case bβS. The value of the Fermi contact parameter is −570 MHz which implies a 4s occupation of the 9σ molecular orbital (MO) of 72%. The results are compared with calculated and available experimental values for early first-row transition metal oxides and nitrides.

Fine and hyperfine structure in thea 3II state of CH+

Spectroscopic and theoretical studies concerning thea 3II state of CH+ are reviewed, with particular consideration given to the infrared predissociation spectrum of the ion. This spectrum is primarily due to vibration-rotation transitions of thea 3II state involvingv=5 to 12 andJ=20 to 35. Some results of a spectral simulation, making use of a rotationally-adiabatic model, are presented to justify the proposed assignment. The nuclear-hyperfine structure of the observed transitions is studied in detail, with a new calculation of splittings presented. Some semi-quantitative conclusions can be drawn with reference to the variation of the Fermi Contact parameter,b, as a function of internuclear distance.

Nuclear hyperfine structure in sub-Doppler electronic spectra of the Swan (d 3Π g -a 3Π u ) system of 13C2

High-resolution electronic spectra of the 0–1 band of the Swan system (d 3Π g -a 3Π u ) of 13C2 have been recorded using sub-Doppler laser spectroscopy. Carbon-13 nuclear hyperfine structure is resolved in many of the rotational lines. The orbital-nuclear, Fermi contact, spin-dipolar and hyperfine lambda-doubling hyperfine parameters in both electronic states are obtained from an analysis of the spectra and their values are discussed in terms of the electronic wavefunctions for the electronic states.

Rotational and hyperfine analysis of the C4Σ −- X4Σ − (blue) system of niobium oxide, NbO

The C 4Σ −- X 4Σ − (0, 0) band of NbO, whose R heads lie near 4690 Å, has been analyzed from high-resolution grating spectra. Both 4Σ − states have second-order spin-orbit splittings, 4 λ = E( 4 Σ 3 2 )-E( 4 Σ 1 2 ) , of about 60 cm −1, so that they are in good case (a) coupling at low J, although the appearance of the band had been interpreted by previous workers as 4Σ( b)- 4Σ( b). the 93Nb nuclear hyperfine structure ( I= 9 2 ) is very impressive in the R 1, P 1, R 4, and P 4 branches, with the 10 hyperfine components of a rotational line spread over more than 0.9 cm −1 in the F 1 branches. The hyperfine linewidths vary considerably with J, in the manner expected for the rapid spin uncoupling from case (a β) to (b β J ) which occurs in a high-multiplicity state. The very great hyperfine linewidths arise because the sign of the Fermi contact parameter b (the coefficient of I·S in the magnetic hyperfine Hamiltonian) is different in the two 4Σ states, so that the observed patterns are the sums of the splittings in the two electronic states.

Vibrational levels of HD+near dissociation

The transformed Schrodinger equation, in which the g/u symmetry breaking terms appear in the potential energy, is solved in an adiabatic approximation to give vibration-rotation energies and vibrationally averaged Fermi contact parameters near dissociation for the ground and first excited states of HD+. The electronic part of the equation is solved variationally, using basis functions modelled on the Hylleraas expansion. These results are found to be in close agreement with those from a coupled states calculation, for which improved values for other hyperfine parameters are also given. By extending the range of integration in the numerical solution of the vibration-rotation equation, the highest bound levels of HD+ are found to be v=22, J=1 for the ground electronic state and v=1, J=0 for the first excited state.

Spectroscopic observation of the highest vibrational level of the HD+(2Σ+) molecule

Spectroscopic observation of the highest vibrational level of HD+(v=21) in its ground electronic state is reported. Calculations of constants from the resolved hyperfine structure allow unambiguous determination of the Fermi contact parameters for the levels 17,1 and 21,0, showing that in the level 21,0 the electron distribution is asymmetric toward the lower dissociation limit H++D, with an average electron density of 0.094 at the proton and 0.902 at the deuteron.

The microwave spectrum of CuO, X 2Π, measured with optical detection

The microwave pure rotational transitions J=3/2←1/2 and 5/2←3/2 have been measured for gas phase CuO in its X 2Π state, using microwave-optical double resonance. The copper hyperfine structure was observed, and has been analyzed for the first time for the ground state of an orbitally degenerate transition metal-containing molecule in the gas phase. Rotational, lambda-doubling, and magnetic and electric hyperfine parameters have been evaluated; the Fermi contact parameter bF has been found to be very large and negative. The problem of determining the signs of the ‘‘off-diagonal’’ hyperfine parameters in 2Π electronic states is discussed.

Low‐symmetry doped Cu(II) complexes in (gly)2CaCl2 · 4 H2O single crystal: EPR studies

AbstractEPR results for copper(II) ions doped in (gly)2CaCl2 · 4H2O single crystals are reported. The copper(II) complex formed in the chromophore CuN2Cl4 displays rhombic crystal field symmetry with an unusual spin‐Hamiltonian parameter sequence: gx = 2.115, gy = 2.034, gz = 2.308, and Ax = 40.1, Ay = 113.4, Az = −73.0 × 10−4 cm−1. The g‐factors are related to the ground state wave function α |ad−bd〉 with α2 = 0.86, a = 0.9835, and b = 0.181, and the untypical hyperfine splitting parameters result from the very low value of the Fermi contact parameter of χ = 0.087.

EPR study of the Jahn-Teller effect ofCu2+inZnTiF6·6H2O

The 34-GHz EPR spectrum of ${\mathrm{Cu}}^{2+}$ in $\mathrm{ZnTi}{\mathrm{F}}_{6}\ifmmode\cdot\else\textperiodcentered\fi{}6{\mathrm{H}}_{2}\mathrm{O}$ shows a Jahn-Teller effect with a transition from a single-line spectrum at high temperatures to a multiline anisotropic spectrum. The transition temperature on cooling varied with Cu concentration from 172 K for a sample containing 0.2 at.% Cu to roughly 90 K for a 46-at.% Cu sample. For dilute samples, the single-line spectrum was isotropic at 300 K with $g=2.223\ifmmode\pm\else\textpm\fi{}0.005$, but showed axial symmetry about the trigonal axis at 180 K with ${g}_{\ensuremath{\parallel}}^{\ensuremath{'}}=2.226\ifmmode\pm\else\textpm\fi{}0.005$ and ${g}_{\ensuremath{\perp}}^{\ensuremath{'}}=2.223\ifmmode\pm\else\textpm\fi{}0.005$. At 4.2 K, a "static" Jahn-Teller effect was observed with six axially symmetric ${\mathrm{Cu}}^{2+}$ spectra, each with ${g}_{\ensuremath{\parallel}}=2.470\ifmmode\pm\else\textpm\fi{}0.005$, ${g}_{\ensuremath{\perp}}=2.100\ifmmode\pm\else\textpm\fi{}0.005$, $|{A}_{\ensuremath{\parallel}}|\ensuremath{\simeq}106\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and $|{A}_{\ensuremath{\perp}}|\ensuremath{\simeq}30\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The $z$ axis of these spectra was found to lie along the fourfold axes of two cubes with a common [111] axis, rotated by 40\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{} with respect to each other about this axis. Analysis of the 4.2-K data leads to the values $q\ensuremath{\simeq}0.50$ for the Ham reduction factor and $\ensuremath{\kappa}\ensuremath{\simeq}0.26$ for the Fermi contact parameter, with ${A}_{\ensuremath{\parallel}}{A}_{\ensuremath{\perp}}<0$. An activation energy of about 100 ${\mathrm{cm}}^{\ensuremath{-}1}$ was deduced from the gradual increase of the anisotropy of the spectrum on cooling in the low-temperature region.