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.     

Calculating the electron paramagnetic resonance parameters of exchange coupled transition metal complexes using broken symmetry density functional theory: application to a MnIII/MnIV model compound

The capability of the density functional broken symmetry approach for the calculation of various EPR parameters of exchange coupled metal clusters is demonstrated by studying the experimentally well-investigated [Mn(III)Mn(IV)(mu-O)(2)(mu-OAc)DTNE](2+) complex. Geometry optimizations of the complex in its broken symmetry and high spin states yielded structures with two distinct manganese sites and geometrical parameters in good agreement with the X-ray structure. Exchange coupling constants were calculated from the energy differences between the high spin and broken symmetry states using the Heisenberg spin Hamiltonian. Very good agreement between theory and experiment was achieved with the B3LYP hybrid functional. The g-tensor calculations were performed employing the coupled perturbed Kohn-Sham equations. A strategy for the computation of g-tensor site values is presented and provides single-site g-tensors that are in good agreement with the expectations for Mn(III) and Mn(IV), respectively. Spin projection gave the g-tensor of the coupled manganese complex in very good agreement with the experimental results. Complete (55)Mn hyperfine tensors, including spin-orbit contributions, were calculated and spin-projected. The source of anisotropy in this system could be traced back to the Mn(III) ion in line with the experimental results. The isotropic manganese hyperfine coupling constants were underestimated by factors between 1.4 and 2.5. It is shown that this deficiency is systematic in character and not anchored in the broken symmetry approach. Nuclear quadrupole splitting of the (55)Mn nuclei is shown to be small in this system. In addition, (14)N and (1)H ligand hyperfine data were calculated and compared well with the experimental results. The quality of the extended point-dipole model was demonstrated in application to (1)H anisotropic hyperfine coupling constants.     

Nuclear quadrupole hyperfine structure in HC14N/H14NC and DC15N/D15NC isomerization: a diagnostic tool for characterizing vibrational localization

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.     

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.     

An ab initio study of the hyperfine structure in the X2 Pi electronic state of CCCH

The results of an ab initio study of the magnetic hyperfine structure in the X (2)Pi electronic state of CCCH are reported. The potential surfaces for two components of the X (2)Pi electronic state were computed by means of an extensive configuration interaction approach. The electronically averaged hyperfine coupling constants of H and (13)C for (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, and (12)C (12)C (13)CH are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The model Hamiltonian is expressed in terms of the normal bending coordinates. It is found that, due to the generally strong geometry dependence of the hyperfine coupling constants, it is necessary to carry out the vibronic averaging of the corresponding functions in order to obtain the values which can be compared to the results of the measurements. The results of the present study help to reliably interpret the experimental data previously published. They also predict the yet unobserved hyperfine structure in excited vibronic states.     

Magnetic hyperfine coupling of a methyl group undergoing internal rotation: a case study of methyl formate

The hyperfine structure of methyl formate was recorded in the 2-20 GHz range. A molecular beam coupled to a Fourier transform microwave spectrometer having an instrumental resolution of 0.46 kHz and limited by a Doppler width of a few kHz was used. A-type lines were found split by the magnetic hyperfine coupling while no splittings were observed for E-type lines. Symmetry considerations were used to account for the internal rotation of the methyl top and to derive effective hyperfine coupling Hamiltonians. Neglecting the spin-rotation magnetic coupling, the vanishing splittings of the E-type lines could be understood and analyses of the hyperfine patterns of the A-type lines were performed. The results are consistent with a hyperfine structure dominated by the magnetic spin-spin coupling due to the three hydrogen atoms of the methyl group.     

An ab initio calculation of the anisotropic hyperfine coupling constants in the low-lying vibronic levels of the X 2Pi electronic state of CCCH

The results of ab initio calculations of the vibronically averaged components of the anisotropic magnetic hyperfine tensor in the low-lying vibronic species of the X (2)Pi electronic state of CCCH and CCCD are reported. The electronically averaged hyperfine coupling constants for hydrogen and (13)C in (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, (12)C (12)C (13)CH, and (12)C (12)C (12)CD are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The results of the present study help to reliably interpret the experimental data previously published and predict the yet unobserved hyperfine structure in excited vibronic states of CCCH and CCCD.     

The interpretation of molecular magnetic hyperfine interactions

Investigations of the hyperfine structure in the excited electronic states of several free radical species have revealed shortcomings in the currently accepted values used for the theoretical interpretation of such interactions. We introduce updated reference atomic values from a combination of experimental observations and ab initio calculations. The latter are at Hartree-Fock and multireference configuration interaction levels of theory and several atomic test cases are discussed. Furthermore, ground and excited electronic state hyperfine coupling constants are calculated using both levels of theory for a range of first- and second-row diatomic hydride and nonhydride radicals. These results, together with a selection of other experimental measurements are then compared with experimental data where available, and the implications of the revised interpretation are discussed.     

Hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2)

The hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2) have been resolved with sub-Doppler continuous wave perturbation facilitated optical-optical double resonance spectroscopy via A (1)Sigma(u) (+) approximately b (3)Pi(u) mixed intermediate levels. The hyperfine patterns of these three states are similar. The hyperfine splittings of the low rotational levels are all very close to the case b(betaS) limit. As the rotational quantum number increases, the hyperfine splittings become more complicated and the coupling cases become intermediate between cases b(betaS) and b(beta J) due to spin-rotation interaction. We present a detailed analysis of the hyperfine structures of these three (3)Sigma(g) (+) states, employing both case b(betaS) and b(beta J) coupling basis sets. The results show that the hyperfine splittings of the (3)Sigma(g) (+) states are mainly due to the Fermi-contact interaction. The Fermi contact constants for the two d sigma Rydberg states, the 2 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+), are 245+/-5 MHz and 225+/-5 MHz, respectively, while the Fermi contact constant of the s sigma 3 (3)Sigma(g) (+) Rydberg state is 210+/-5 MHz. The diagonal spin-spin and spin-rotation constants, and nuclear spin-electronic spin dipolar interaction parameters of the 3 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+) states are also obtained.     

Parameterization of the hyperfine structure of metastable states in103Rh

The experimental data on the hyperfine structure of metastable even parity states in¹⁰³Rh have been analysed by means of an effective-operator formalism. The effective radial parameters of the magnetic dipole interaction are determined, using wave functions in intermediate coupling. The comparison with relativistic calculations gives an estimate of the effects due to configuration interaction.     

Investigations of the EPR parameters for Sm3+ ions in KY3F10 and LiYF4 crystals

In this paper, we calculate the EPR parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) of rare earth ion Sm3+ in fluoride crystals KY3F10 and LiYF4 from the perturbation formulas of EPR parameters for a 4f5 ion in tetragonal symmetry. In these formulas, the crystal-field J-mixing of the first and second excited-state multiplets 6H(7/2) and 6H(9/2) into the ground state multiplet 6H(5/2), the mixtures among the states with the same J value via spin-orbit coupling interaction and the interactions between the ground Kramers doublet Gammagamma and the same irreducible representation as Gammagamma in other 11 Kramers doublets Gammax within 6HJ (J=5/2, 7/2, 9/2) states via crystal-field and orbital angular momentum (or hyperfine structure) are considered. The calculated results (which are in agreement with the observed values) are discussed.     

Nuclear hyperfine interaction of rotating hydrogen: a spectroscopic investigation of hydrogen-OCS van der Waals complexes

The rotational spectra of five weakly bonded hydrogen-OCS complexes (paraH(2), orthoH(2), HD, orthoD(2), and paraD(2)) are measured. Hyperfine structure is resolved and analyzed in all except the complex with paraH(2), where I=0. For the two j=1 species, orthoH(2)-OCS and paraD(2)-OCS, nuclear hyperfine coupling constants are found to be d(a)=21.2(2) and 8.4(2) kHz, respectively, indicative of nearly free uniaxial rotation of the hydrogen around the b-inertial axis. Similar analyses for HD-OCS and orthoD(2)-OCS yield the quadrupole coupling constants eqQ(a)=16(2) and 30(2) kHz, respectively, showing that the internal rotational motions of HD and orthoD(2) in the complex are slightly hindered producing a small nonspherical distribution. For orthoD(2)-OCS, the observed hyperfine structure indicates that the nuclear spin states I=0 and 2 are strongly coupled in the rotation of the complex.     

Simplification of complex EPR spectra by cepstral analysis

As the Fourier transform of time-series data is known as the spectrum, the Fourier transform of the logarithm of the time-series data is called the cepstrum of the data. When cepstral analysis is applied to free induction decay signals of free radicals showing first-order EPR spectra, the identification of nuclear hyperfine coupling constants becomes simple. In a systematic manner, we have examined how the technique of cepstral analysis is affected by the presence of aliasing, noise, uncertainty in the time origin of the free induction decay, the presence of second-order hyperfine couplings, and the applications of various apodization methods. This technique was then applied to analyze the EPR spectrum of anthraquinone anion radical, and anion radicals of porphycene and tetrapropyl-porphycene, and the hyperfine coupling constants thus obtained were compared with published data. A good agreement was always found. We make a case for the usefulness of cepstral analysis in determining the hyperfine coupling constants of complex EPR spectra of organic free radicals.     

Hyperfine structure of SrCl X2∑+ by microwave—optical polarization spectroscopy

The hyperfine structure of the X²∑⁺, υ = 0 state of ⁸⁸Sr³⁵Cl has been investigated using microwave—optical polarization spectroscopy. Resolution of the hyperfine structure in transitions between low-lying rotational states has allowed the first determination of magnetic dipole and electric quadrupole coupling constants. The results are: b = 18.663(89) MHz, c = 7.72(30)MHz, and eqQ = 3.96(84) MHz.     

The NaK 1 1,3delta states: theoretical and experimental studies of fine and hyperfine structure of rovibrational levels near the dissociation limit

Earlier high-resolution spectroscopic studies of the fine and hyperfine structure of rovibrational levels of the 1 3delta state of NaK have been extended to include high lying rovibrational levels with v < or = 59, of which the highest levels lie within approximately 4 cm(-1) of the dissociation limit. A potential curve is determined using the inverted perturbation approximation method that reproduces these levels to an accuracy of approximately 0.026 cm(-1). For the largest values of v, the outer turning points occur near R approximately 12.7 angstroms, which is sufficiently large to permit the estimation of the C6 coefficient for this state. The fine and hyperfine structure of the 1 3delta rovibrational levels has been fit using the matrix diagonalization method that has been applied to other states of NaK, leading to values of the spin-orbit coupling constant A(v) and the Fermi contact constant b(F). New values determined for v < or = 33 are consistent with values determined by a simpler method and reported earlier. The measured fine and hyperfine structure for v in the range 44 < or = v < or = 49 exhibits anomalous behavior whose origin is believed to be the mixing between the 1 3delta and 1 1delta states. The matrix diagonalization method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. The analysis leads to accurate values for A(v) and b(F) for all values of v < or = 49. For higher v (50 < or = v < or = 59), several rovibrational levels have been assigned, but the pattern of fine and hyperfine structure is difficult to interpret. Some of the observed features may arise from effects not included in the current model.     

Computation of hyperfine tensors for dinuclear Mn(III) Mn(IV) complexes by broken-symmetry approaches: anisotropy transfer induced by local zero-field splitting

Based on broken-symmetry density functional calculations, the (55)Mn hyperfine tensors of a series of exchange-coupled, mixed-valence, dinuclear Mn(III) Mn(IV) complexes have been computed. We go beyond previous quantum chemical work by fully including the effects of local zero-field splitting (ZFS) interactions in the spin projection, following the first-order perturbation formalism of Sage et al. [J. Am. Chem. Soc. 1989, 111, 7239]. This allows the ZFS-induced transfer of hyperfine anisotropy from the Mn(III) site to the Mn(IV) site to be described with full consideration of the orientations of local hyperfine and ZFS tensors. After scaling to correct for systematic deficiencies in the quantum chemically computed local ZFS tensors, good agreement with experimental (55)Mn anisotropies at the Mn(IV) site is obtained. The hyperfine coupling anisotropies on the Mn(III) site depend sensitively on structural distortions for a d(4) ion. The latter are neither fully reproduced by using a DFT-optimized coordination environment nor by using experimental structures. For very small exchange-coupling constants, the perturbation treatment breaks down and a dramatic sensitivity to the scaling of the local ZFS tensors is observed. These results are discussed with respect to ongoing work to elucidate the structure of the oxygen-evolving complex of photosystem II by analysis of the EPR spectra.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

Probing the Electronic Structure of Bacteriochlorophyll Radical Ions—A Theoretical Study of the Effect of Substituents on Hyperfine Parameters

In reaction centers (RCs) of photosynthesis, a light‐induced charge separation takes place creating radical cations and anions of the participating cofactors. In photosynthetic bacteria, different bacteriochlorophylls (BChl) are involved in this process. Information about the electronic structure of the BChl radical cations and anions can be obtained by measuring the electron spin density distribution via the electron–nuclear hyperfine interaction using EPR and ENDOR techniques. In this communication, we report isotropic hyperfine coupling constants (hfcs) of the BChl b and g radical cations and anions, calculated by density functional theory, and compare them with the more common radical ions of BChl a and with available experimental data. The observed differences in the computed hyperfine data are discussed in view of a possible distinction between these species by EPR/ENDOR methods. In addition, ¹⁴N nuclear quadrupole coupling constants (nqcs) computed for BChl a, b, g, and also for Chl a in their charge neutral, radical cation and radical anion states are presented. These nqcs are compared with experimental values obtained by ESEEM spectroscopy on several different radical ions.     

The Na2 2 3pi(g) state: new observations and hyperfine structure

Many more Na2 2 3pi(g) v = 0-43, omega = 0, 1, 2 levels have been observed by sub-Doppler continuous wave perturbation facilitated optical-optical double resonance fluorescence excitation spectroscopy and the hyperfine structure of the omega = 0 and 2 levels has been resolved. New molecular constants for the less perturbed v = 0-43 levels have been obtained with these new and the previously reported data. The hyperfine coupling scheme of the observed 2 3pi(g) levels is close to Hund's case a(beta) with a Fermi contact constant b(F) = 160+/-5 MHz, which is smaller than the Fermi contact constants of other Na2 triplet Rydberg states, b(F) = 200-245 MHz.     

Laser spectroscopy of NiBr: new electronic states and hyperfine structure

Laser induced fluorescence spectrum of NiBr in the visible region between 604 and 666 nm has been recorded and analyzed. Fourteen bands belonging to three electronic transition systems, namely, [15.1] (2)Delta(52)-X (2)Pi(32), [15.1] (2)Pi(32)-X (2)Pi(32), and [14.0] (2)Delta(52)-X (2)Pi(32) have been observed. Spectra of isotopic molecules were also observed and analyzed. Detailed analysis of the recorded spectra indicated that the two electronic states [15.1] (2)Pi(32) and [15.1] (2)Delta(52) lie about 1 cm(-1) apart from each other and J-dependent perturbation due to spin-uncoupling interaction has been observed. Least squares fitting procedures involving deperturbation matrix elements were used to fit the observed line positions, which yielded accurate molecular constants for the [15.1] (2)Pi(32) and [15.1] (2)Delta(52) states. In addition, the (1,0) band of the [15.1] (2)Delta(52)-X (2)Pi(32) transition shows partially resolved hyperfine structure that was caused by the interaction of unpaired electron with the magnetic moment of the Br nucleus (nuclear spin of I=32) in the excited state. The rapid decrease in hyperfine width as J increases suggests that the hyperfine coupling in the excited state conforms to Hund's case (a(beta)) coupling scheme.