All electron calculations of open-shell polyatomic molecules. III. Perturbation treatment of the spin polarization in vinyl and methyl radicals

A first order perturbation treatment starting with SCF-MO 'S in canonical or equivalent quasi-localized form is presented for the hyperfine coupling constants of vinyl and methyl radicals. The spin-polarisation contribution to hyperfine splittings is found to be large, negative for the proton of the radical center in both radicals and positive for the β protons of vinyl.     

A comment on “ESR linewidth studies on naphthalene ion in low bulk dielectric constant media”

It is noted, if one uses the lineshape analysis for unresolved hyperfine splitting proposed by Jones et al. that one must be careful to avoid lineshape distortion from the magnetic field modulation amplitudes and frequencies used. At 100 kHz field modulation the lineshape distortion is significant for linewidths less than ≈ 350 mG and unresolved hyperfine splittings less than ≈ 70 mG.     

High precision measurements of hyperfine structures near 790 nm of I 2

High precision measurements of hyperfine splittings of rovibrational lines of the (ν′-ν″)=(0–15) band of the B0 _u ⁺ — X0 _g ⁺ transition of I ₂ were performed in the near infrared around 790 nm using spectrally narrowed diode lasers. Rotational states with J″ between 0 and 99 were investigated and hyperfine parameters could be derived for the two electronic states separately. For the first time the rotational variation of the quadrupole and the spin-rotational hyperfine coupling parameters could be determined for I ₂. A relation is given, by which the hyperfine parameters for a rotational line of the (0–15) band can be predicted, and by which hyperfine splittings of this band can be calculated with an uncertainty of less than 100 kHz for 16 ≤ J″ ≤ 99.     

Observation of the 3(3)Sigma(+)-X1Sigma+ transition of KRb by resonance enhanced two-photon ionization in a pulsed molecular beam: Hyperfine structures of 39K85Rb and 39K87Rb isotopomers

The 3(3)Sigma(+)-X1Sigma+ transition of KRb is observed by resonance enhanced two-photon ionization in a pulsed molecular beam. Hyperfine splittings of 39K85Rb and 39K87Rb isotopomers are observed. From the magnitude of hyperfine splittings, we found that the main hyperfine structure was dominated by the Fermi contact interaction between the Rb nuclear spin and the unpaired electron spin. The Fermi contact interaction constants were determined to be 291 MHz for 39K85Rb and 665 MHz for 39K87Rb. In the KRb 3(3)Sigma+ state the electron spin couples more strongly with the Rb nuclear spin than with other angular momenta, and the energy level structure is well described by the hyperfine angular momentum coupling scheme of the b(betaS) case. The molecular constants and the Rydberg-Klein-Rees potential energy curve of the 3(3)Sigma+ state were determined.     

Ab initio MO LCAO UHF calculations of the stability in dimeric ethylene radical ions

The stability of ethylene dimer ions has been computed by ab initio methods. The positively charged dimer is stable (0.6–0.7 eV) while the neutral and the negatively charged dimers are unstable with respect to decomposition into monomers. The magnetic hyperfine coupling constants have also been evaluated, hyperfine splittings are half those in the monomer in agreement with experimental data.     

Test of advanced hyperfine structure theory by precision radio-frequency and laser spectroscopy in molybdenum

The hyperfine structure splittings of 32 even parity states and of 26 odd partity states of molybdenum have been measured by atomic beam magnetic resonance and by laser induced fluorescence. The analysis of the hyperfine structure data of the even parity configurations (4d+5s)⁶ yields experimental evidence for second order hyperfine interactions. In addition, theg _J factors of 19 fine structure levels have been determined in order to test the quality of intermediate coupling wave functions for the (4d+5s)⁶ configurations.     

Spectroscopic properties of the methyl radical calculated from UHF SCEP wavefunctions

The potential energy surface of symmetric stretching and out-of-plane bending motions for the methyl radical has been calculated from UHF SCEP wavefunctions. Anharmonic vibrational frequencies are computed by a variational method and transition dipole moments and Einstein coefficients of spontaneous emission are reported. Isotropic hyperfine coupling constants are obtained in agreement with experiment to within 4% when calculated by differentiation of the perturbed CEPA-1 energy and taking vibrational averaging into account. Also, the temperature dependence of the proton hyperfine coupling constant compares well with experimental results. The vibrational fine structure of the first band of the photoelectron spectra of CH₃ and CD₃ is calculated in good agreement with experiment.     

Determining the geometry and magnetic parameters of fluorinated radicals by simulation of powder ESR spectra and DFT calculations: the case of the radical RCF2CF2* in nafion perfluorinated ionomers

The ESR spectrum of the chain-end radical RCF2CF2* detected in Nafion perfluorinated membranes exposed to the photo-Fenton reagent was accurately simulated by an automatic fitting procedure, using as input the hyperfine coupling tensors of the two F alpha and two F beta nuclei as well as the corresponding directions of the principal values from density functional theory (DFT) calculations. An accurate fit was obtained only for different orientations of the hyperfine coupling tensors for the two F alpha nuclei, indicating a nonplanar structure about the C alpha radical center. The fitted isotropic hyperfine splittings for the two F beta nuclei in the Nafion radical, 24.9 and 27.5 G, are significantly larger than those for the chain-end radical in Teflon (15 G), implying different radical conformations in the two systems. The excellent fit indicated that the geometry and electronic structure of free radicals can be obtained not only from single-crystal ESR spectroscopy, but also, in certain cases, from powder spectra, by combination with data from DFT calculations. The optimized structures obtained by DFT calculations for the CF3CF2CF2CF2* or CF3OCF2CF2* radicals as models provided additional support for the pyramidal structure determined from the spectral fit. Comparison and analysis of calculated and fitted values for the hyperfine splittings of the two F beta nuclei suggested that the radical detected by ESR in Nafion is ROCF2CF2*, which originates from attack of oxygen radicals on the Nafion side chain. The combination of spectrum fitting and DFT is considered important in terms of understanding the hyperfine splittings from 19F nuclei and the different conformations of fluorinated chain-end-type radicals RCF2CF2* in different systems, and also for elucidating the mechanism of Nafion fragmentation when exposed to oxygen radicals in fuel cell conditions.     

High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2

Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.     

Towards the truly nonempirical computation of hyperfine interactions: A contribution to the debate on the t-butyl radical

Carefully calibrated large-scale nonempirical CI computations have been performed for the isotropic hyperfine splittings of the t-butyl radical. The results have been used to interpret the effects of out-of-plane vibration of the radical center, with and without coupling to methyl rotations, on the observed splitting at the radical center. In particular, the value computed under rotation-inversion is 39 G, in good agreement with the ESR result of 45 G.     

Sub-Doppler spectra of infrared hyperfine transitions of nitric oxide using a pulse modulated quantum cascade laser: rapid passage, free induction decay, and the ac Stark effect

Using a low power, rapid (nsec) pulse-modulated quantum cascade (QC) laser, collective coherent effects in the 5 μm spectrum of nitric oxide have been demonstrated by the observation of sub-Doppler hyperfine splitting and also Autler-Townes splitting of Doppler broadened lines. For nitrous oxide, experiments and model calculations have demonstrated that two main effects occur with pulse-modulated (chirped) quantum cascade lasers: free induction decay signals, and signals induced by rapid passage during the laser chirp. In the open shell molecule, NO, in which both Λ-doubling splitting and hyperfine structure occur, laser field-induced coupling between the hyperfine levels of the two Λ-doublet components can induce a large ac Stark effect. This may be observed as sub-Doppler structure, field-induced splittings, or Autler-Townes splitting of a Doppler broadened line. These represent an extension of the types of behaviour observed in the closed shell molecule nitrous oxide, using the same apparatus, when probed with an 8 μm QC laser.     

Rotational dynamics of methyl groups in m-xylene

Methyl group dynamics of m-xylene was investigated by using incoherent inelastic and quasi-elastic neutron scattering. Inelastic measurements were carried out at the high flux backscattering spectrometer HFBS at the National Institute of Standards, quasi-elastic measurements at the time-of-flight spectrometer NEAT at the Hahn-Meitner-Institute. Rotational potentials are derived which describe the tunnel splittings, first librational, and activation energies of the two inequivalent CH(3) groups. Indications for coupling of the methyl rotation to low-energy phonons have been found. The finite width of one tunneling transition at He temperature is described by direct methyl-methyl coupling. The combined results of the experiments and the calculations allow a unique assignment of rotor excitations to crystallographic sites.     

Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations

Rotational spectra of ortho-nitrotoluene (2-NT) and para-nitrotoluene (4-NT) have been recorded at low and room temperatures using a supersonic jet Fourier Transform microwave (MW) spectrometer and a millimeter-wave frequency multiplier chain, respectively. Supported by quantum chemistry calculations, the spectral analysis of pure rotation lines in the vibrational ground state has allowed to characterise the rotational energy, the hyperfine structure due to the ¹⁴N nucleus and the internal rotation splittings arising from the methyl group. For 2-NT, an anisotropic internal rotation of coupled −CH₃ and −NO₂ torsional motions was identified by quantum chemistry calculations and discussed from the results of the MW analysis. The study of the internal rotation splittings in the spectra of three NT isomers allowed to characterise the internal rotation potentials of the methyl group and to compare them with other mono-substituted toluene derivatives in order to study the isomeric influence on the internal rotation barrier.     

Nuclear hyperfine splitting in the BX electronic band system of 127I2

The spacings between seven hyperfine components in the R(127) line of the 11-6 band of the B-X electronic transition of ¹²⁷I₂ are fitted, with a standard deviation of 17.3 kHz, by varying the nuclear quadrupole coupling constants eqQ′ and egQ′', the magnetic spin—rotation constant C_I and the tensor and scalar nuclear spin—spin coupling constants d′ and a′ in the hyperfine hamiltonian. The P(13) line of the 430 band is also analysed using an identical hamiltonian and a standard deviation of 6.25 kHz is obtained. No evidence for a magnetic octupole coupling is found to the precision of the data although this effect was invoked by Hackel et al. for the P(13) line.     

Spectroscopic characterization of a molecule with a weak bond: the BrOO radical

Pure rotational spectra of the BrOO radical for the 79Br and 81Br isotopomers have been observed using a Fourier transform microwave spectrometer. The radical was produced in a supersonic jet by discharging a mixture gas containing bromine and oxygen diluted in argon. A-type rotational transitions are observed for N" = 1-5, K(a) = 0 with spin doublings and hyperfine splittings due to the nuclear spin of the bromine atom. High-level ab initio calculations by RCCSD(T) and MRCI have also been performed, and results are compared with the experimental data. Molecular structure of BrOO has been discussed based on the present experimental data, supplemented by the tendency among the halogen peroxide series and the results of the ab initio calculations; the Br-O bond is found to be anomalously long and weak. Systematic comparisons with other halogen peroxides have revealed anomalous nature of the X-O (X = halogen atom) bonds for this series of radicals.     

ΔF = ±2 transitions in the hyperfine spectrum of Er I

The occurrence of 15ΔF=±2 transitions in the hyperfine spectrum of five lines of Er I was observed by means of high-resolution laser-atomic-beam spectroscopy. These normally forbidden transitions are caused by an external magnetic field which mixes closely lying hyperfine levels that have neighbouringF quantum numbers. If the Zeeman splittings under the applied magnetic field are small compared to the hyperfine splittings, the intensities of theΔF=±2 components are proportional to the square of the magnetic field strength. Under the variation of the laser intensity theΔF=±2 transitions show the same behaviour as homogeneously broadenedΔF=0, ±1 transitions. The relative intensities between theΔF=±2 components as well as the intensity ratios of theΔF=±2 to neighbouringΔF=±1 components are studied and interpreted in terms of first order perturbation theory.     

EPR and DFT study on the stabilization of radiation-generated methyl radicals in dehydrated Na-A zeolite

Electron paramagnetic resonance (EPR) spectroscopy was applied to study paramagnetic species stabilized in Na-A zeolite exposed to gaseous methane and gamma-irradiated at 77 K. Two types of EPR spectra were recorded during thermal annealing of zeolite up to room temperature. Owing to the results for the zeolite exposed to (13)CH(4) the multiplet observed at 110 K was assigned to a (.-)CH(3)...Na(+) complex. After decay of the multiplet, the isotropic quartet of methyl radical was recorded in the temperature range of 170-280 K. On the basis of the EPR parameters it is postulated that (.-)CH(3) radicals in this temperature region are able to freely rotate inside the zeolite cage. The structures of the (.-)CH(3)...Na(+) adsorption complex and respective hyperfine coupling constants were calculated by applying DFT quantum chemical methods. Two different models were applied to represent the zeolite framework: the 6T structure of one six-membered ring and the 3T cluster. The hyperfine coupling constants calculated for the (.-)CH(3)...Na(+) adsorption complex for both applied models show very good agreement with those obtained experimentally.     

Fourier transform millimeter-wave spectroscopy of the ethyl radical in the electronic ground state

The pure rotational spectrum of the ethyl radical (C2H5) has been detected for the first time with the Fourier transform millimeter-wave spectrometer. The ethyl radical is produced by discharging the C2H5I gas diluted in Ar. The 1(01)-0(00) rotational transition of the ethyl radical is observed in the frequency range from 43,680 to 43,780 MHz. The observed spectrum shows a very complicated pattern of the fine and hyperfine structures of a doublet radical with the nuclear spins of five protons. The fine and hyperfine components are assigned with the aid of measurements of the Zeeman splittings. As a result, the 22 lines are ascribed to the transitions in the ground vibronic state (A2"). The rotational constant, the spin-rotation interaction constant, and hyperfine interaction constants are determined by the least-squares fit. The Fermi contact term of the alpha-proton is determined to be -64.1654 MHz in the gas phase, indicating that the structure of the -CH2 is essentially planar. The present rotational spectroscopic study further supports that the methyl group of the ethyl radical can be regarded as a nearly free internal rotor with a low energy barrier. A few unassigned lines still remain, which may be vibrational satellites of the internal rotation mode.     

A test of the accuracy of atomic-beam laser spectroscopy

To determine the accuracy to which hyperfine splittings can be measured using a cw dye laser with rf sideband tuning, a series of atomic beam experiments with⁵⁹Co was performed. One hyperfine splitting of the first excited metastable atomic state was measured and compared with the results for the same splitting from magnetic rf resonance experiments. The uncertainty with the methods applied was found to be about 0.05 to 1% of the experimental linewidth in general; it is ±20 kHz or ±0.05% of the linewidth in the present Co experiment. The hyperfine splitting constants of the 3d ⁸ 4p ² F _7/2 state were found to beA=419.3(9) MHz,B=?77(17) MHz.     

Positional and angular dependence of hyperfine interactions in cyclic and bicyclic iminoxy radicals with CO or CH2 group – DFT and EPR studies

UB1LYP method was used to study the geometries together with hyperfine coupling constants (hfccs) and natural atomic occupancies (NAO) for the cyclic (cyclohexanone-type) and bicyclic (camphor-type) iminoxy radicals. The positional and angular dependence of the hyperfine interactions, affected by radical substituents and conformations, was analyzed in terms of different mechanisms of spin density transmission. The calculations predicted a significant distortion of regular conformations and change of hyperfine couplings upon introduction of CO into cyclohexane iminoxyl and the CNO spin label into a boat cyclohexane. Hyperfine splittings of the EPR spectra were compared with the computed hfccs to verify their assignment.