Heteronuclear Systems Research Articles

Calculation of spin-forbidden radiative transitions using correlated wavefunctions: Lifetimes of b 1Σ +, a 1Δ states in O 2, S 2 and SO

The radiative lifetimes of the b 1Σ + and a 1Δ states of O 2, S 2 and SO have been evaluated by perturbation expansions including 3Σ g −, 1Δ g, 1Σ g +, 1Π g, 3Π g states for the homonuclear systems and 3Σ − (2), 1Δ, 1Σ + (2), 1Π (2), 3Π (2), 3Σ + states for SO; all wavefunctions are MRD CI expansions up to 5000 terms. The mixing coefficients are obtained from the spin-orbit operator in the Breit-Pauli form evaluating all one- and two-particle terms explicitly. In O 2 and S 2 the radiative lifetime of the b 1Σ g + state is found to be largely determined by the spin-contributions to the magnetic moment in the magnetic dipole operator. The calculated value of 11.65 s for O 2 is in excellent agreement with the measured value of 12 s; the calculations predict a lifetime of 3.4 s for b 1Σ g + in S 2. The calculated lifetime corresponding to the b 1Σ g + −a 1Δ g transition is 720 s in good accord with the experimental intensity determination (400 s within a factor of two). The intensity for the a 1Δ g −X 3Σ g − transition is dominated by the orbital angular momentum term in the magnetic-dipole operator and arises from 1Δ g − 1Π g and X 3Σ g − − 3Π g transitions present in the perturbed X 3Σ − and a 1Δ g wavefunctions. Calculated values are τ(O 2) = 5400 s relative to a measured value of 3900 s, and τ = 350 s for S 2 as a prediction. The absence of the inversion favors electric (rather than magnetic) dipole processes in SO. The b 1Σ + −X 3Σ − transition borrows its intensity predominantly from terms connecting b 1Σ + −2 1Σ + and X 3Σ − −2 3Σ − which occur as perturbers in the pure spin wavefunctions. The calculated b 1Σ + lifetime is 13.6 ms in fair accord with the recently measured 7 ± 2 ms. For τ (a 1Δ) the calculations predict intensity borrowing from A 3Π−X 3Σ − and C 3Π−X 3Σ − as well as 1Δ− 1Π and 1Δ−2 1Π dipole transitions resulting in a value of 450 ms. The decrease in lifetime from the first- to the second-row molecules is quantitatively demonstrated to arise from increased spin-orbit interaction, while a different mechanism is responsible for the change in b 1Σ + lifetimes from homonuclear to heteronuclear systems. Finally, all calculations demonstrate that spin-forbidden radiative transition probabilities can be obtained quite effectively by modern-day quantum chemical calculations.

Heteronuclear zero-field NMR

The NMR spectra of polycrystalline solids are often best resolved in the absence of applied magnetic fields. Additionally, heteronuclear spin systems in zero field display features not observed in homonuclear systems. In this letter, spectra are presented and analyzed for the cases of heteronuclear spin pairs in 13C-enriched β-calcium formate (solid) and in diethyl phosphite (liquid).

Force and torque correlations in diatomic fluids

A simple relationship is derived between the mean squared force and mean squared torque in homonuclear diatomic fluids which successfully accounts for published simulation data spanning a wide range of bond lengths and densities in the liquid range for molecules without quadrupole moments. Modifications required in heteronuclear systems are discussed and found to be consistent with the scant information available in this area. The expression for homonuclear systems can be extended to explain the relation between the force and torque time correlation functions in these and triatomic fluids. Finally, the results are used to link the parameter κ, introduced by Kivelson et al., to the slip limit friction coefficient for molecular reorientation.

The role of accuracy of pulses in polarization transfer in a weakly interacting heteronuclear spin system

Role de l'ajustement de la longueur des impulsions de la sequence, analyse par la theorie de la matrice densite. Verification experimentale sur le systeme CHCl 3 (spins 13 C et 1 H)

HARTREE-FOCK-ROOTHAAN WAVEFUNCTIONS FOR DIATOMIC MOLECULES IN A SAME BASIS SET (Ⅰ)——FIRST-AND SECOND-ROW HYDRIDES AH, AH~±,AND AH~*

Ab initio calculations of wavefunctions for first- and secondrow diatomic hydrides, and for first-row homonuclear and heteronuclear systems have been performed employing the same Gaussian basis set. This is the first one of a series of papers. In this paper the electronic wavefunctions, orbital energies and total energies of the diatomic hydrides are obtained at the experimental and (or) theoretical internuclear separations. These wavefunctions are solutions to the Restricted Hartree-Fock equations in the form of expansion with Double Zeta Contracted Gaussian functions. The repertory of states includes the ground states AH, a few low-lying excited states AH*, and positive and negative ions AH± , where A denotes the elements Li through F and Na through Cl. The calculations are restricted to states involving either closed-shell electron configurations or open-shell configurations with one incompletely filled open shell. Tables of electronic wavefunctions of three ground states AH, as examples, are presented.

Total spin coherence transfer echo spectroscopy

The sensitivity of multiple quantum NMR transitions to magnetic field inhomogeneity and the relative phases and amplitudes of multiple quantum lines are discussed. The technique of total spin coherence transfer echo spectroscopy (TSCTES) is described and experimentally demonstrated. The TSCTES method allows multiple quantum spectra to be obtained which are free of inhomogeneous magnet broadening, yet remain sensitive to spin–spin couplings and chemical shift differences. The method takes advantage of the properties of the total spin coherence, the unique transition between the extreme eigenstates of a coupled spin system. Experimental results are reported for partially oriented acetaldehyde and are analyzed in terms of irreducible tensor operators. Limitations on the method and extensions to heteronuclear spin systems are also discussed.

The influence of a novel irradiating field modulation scheme in nuclear magnetic multiple-resonance spectroscopy

Broadband decoupling of heteronuclear spin systems using double and triple irradiation with a multiply modulated irradiating field is explored experimentally. A novel electronic circuit which modulates a complex signal comprising selected quadrature elements (SEQUEL) derived from digital dividers creates a unique spectral distribution of the irradiating field. The broadband effects of SEQUEL modulation can be a valuable tool to reduce the time required to locate resonances of spin-coupled nuclei, such as rhodium-103, which have a large chemical shift range. Protondecoupled carbon-13 and phosphorus-31 NMR spectra illustrate the uniform characteristics of an irradiating field with SEQUEL Modulation.

Hydrogen-bond energies of FHF–and HOHF–. Ab initio studies of strong hydrogen bonds involving fluoride, using improved fluoride energies

Using a large flexible Gaussian basis set the calculated hydrogen-bond energy of FHF– is 169 kJ mol–1, which agrees well with a recent gas-phase ion cyclotron resonance determination of 163 kJ mol–1. Reoptimization of the 4-31G and double-zeta basis-set scale factors for F results in substantially lower energies for the fluoride ion and also leads to much improved hydrogen-bond energies for FHF–. A similar improvement is found for HOHF–. The hydrogen-bond energy of the CH3OHF– complex is computed for the first time and shows good agreement with experiment. Other heteronuclear systems involving hydrogen bonding to F– have been recalculated using this approach.

Nuclear magnetic resonance studies on the anions [M(SnCl3)5Cl]4− (M = Ru, Os) and [Ru(SnCl3)5(MeCN)]3−: the X-ray crystal structure of [N(C2H5)4]4[Ru(SnCl3)5Cl

The octahedral anions [M(SnCl3)5Cl]4− (M = Ru, Os) have been fully characterized by 119Sn FT nmr spectroscopy. For M = Ru, 117Sn and 115Sn nmr spectra were also recorded, and an X-ray crystallographic study was carried out on the tetraethylammonium salt, isolated as a disolvate from acetonitrile. The Ru—Sn bond lengths indicate some degree of dπ–dπ interactions. The slight distortions from octahedral geometry are discussed in connection with the packing of the chlorine atoms. The Sn nmr spectra reveal the first observed coupling to a 99Ru nucleus (I = 5/2, 12.7% natural abundance), very large 2J(119Sn—117Sn) coupling constants, and the first observed second-order effects on a heteronuclear system. The octahedral anion [Ru(SnCl3)5(MeCN)]3− was also synthesized as the tetraethylammonium salt and characterized spectroscopically.

Relayed coherence transfer spectroscopy of heteronuclear systems: detection of remote nuclei in NMR

Heteronuclear two-dimensional NMR experiments are presented which allow the correlation of nuclei that are not directly coupled but belong to a common coupling network. The techniques involve two or more consecutive coherence transfer steps. The applications discussed include the indirect observation of remote proton signals through phosphorus-31 and carbon-13 detection.

Nuclear magnetic double resonance with a doubly modulated radiofrequency field

Efficient broadband decoupling of heteronuclear spin systems is accomplished by a modulation method which successively phase-modulates the irradiating radiofrequency field with two square-wave frequencies that have a frequency ratio of four to one. Experimental observations show this efficient utilization of decoupler power can increase the signal heights by reducing residual splittings which broaden spectral lines. Compared to random-noise decoupling, line narrowing and signal-to-noise improvements of a factor of 3 are observed for proton-decoupled carbon-13 and phosphorus-31 NMR spectra. Efficient spin decoupling with only 1.5 W of decoupling power is demonstrated using this new modulation method.

Coulomb holes and correlation coefficients in position space for HeH+

Electron correlation in position space is examined in HeH+, the simplest of heteronuclear systems, as a function of the internuclear separation R. Coulomb holes and various partial Coulomb holes are evaluated and compared for He, HeH+ and Li+. Several correlation coefficients tau are also determined. The results are discussed in the light of a recent correlation analysis of HeH+ in momentum space. At the theoretical bond length RTh, the Coulomb hole for HeH+ in position space is found to be very similar to that obtained for the ground state of He. As in momentum space, each tau which assesses angular correlation shows an increase in magnitude on molecular formation. Of particular interest in position space is the dramatic increase in the importance of 'left-right' correlation along the bond axis when R approaches RTh.

Thomas-Fermi approach to diatomic quasimolecules: Correlation diagrams for neutral, heteronuclear systems

Correlation diagrams for the heteronuclear systems C-Ar, O-Ar, C-Ne, Al-F, and I-Cl are calculated with an effective Hartree-Fock-Slater potential constructed from Thomas-Fermi-Dirac-Weizsacker densities.

The measurement of coupling constants from two-dimensional NMR spectra

The errors in coupling constants measured from peak positions in two-dimensional J spectra of homonuclear and heteronuclear systems are discussed for absolute-value and phase-sensitive spectra. The phase-sensitive cross section is shown to give the most accurate results and the equivalence of the phase correction of such cross sections and of conventional Fourier transform spectra is demonstrated.

Nonstationary nutations in heteronuclear double resonance

It is shown that in any coupled heteronuclear system, nonstationary perturbation of some nuclei leads, under certain conditions, to nutation oscillations of the components of the magnetizations of the other nuclei. The nature of these nutations is determined by the relaxation parameters of both subsystems and the conditions under which they are excited.

On the relative importance of spin–spin and spin–rotation relaxation in gas phase NMR

The ratio R of the gas phase spin–spin and spin–rotation relaxation times TSS1 and TSR1 is examined in detail using the factorization of infinite order sudden (IOS) approximation generalized cross sections given recently by Goldflam, Green, and Kouri. General results are obtained in the extreme narrowing limit for both homonuclear and heteronuclear systems. The results are quite simple and, in the low temperature limit, depend primarily upon the characteristics of the relaxing nucleus rather than the intermolecular interaction. Calculations illustrating the theory are presented for He+o-H2.

Selective excitation transfer and separated relaxation measurements of degenerate transitions in NMR spectroscopy

A method is described by which phase coherence induced by selective excitation of a single line in a spin–spin multiplet is transferred to one or more nonirradiated transitions. Under the appropriate conditions, excitation may be transferred to individual members of groups of degenerate lines or to forbidden transitions. Detailed calculations and experimental results are given for heteronuclear AX, AX2, and AX3 systems. Selective excitation of individual transitions in degenerate groups of lines allows their transverse relaxation to be studied. Differing linewidths of various degenerate resonances in 13C-methanol doped with chromium acetylacetonate were measured by the excitation-transfer procedure.

Nuclear-magnetic-resonance methods for identifying and studying diffusion of different spin species in heteronuclear systems

We introduce a new dipolar relaxation time ${{T}_{1D}}^{\ensuremath{'}}$ which characterizes the spin-lattice relaxation of secular dipolar interactions in the presence of a large rf field. Measurements of ${{T}_{1D}}^{\ensuremath{'}}$ are particularly useful for studying slow atomic motions in multispin systems, since such measurements enable us to vary the contribution of a particular spin species's motion relative to the contribution of the other spin species's, thus enabling us to identify the diffusing species. We also show that the anisotropy of the conventional dipolar relaxation time ${T}_{1D}$ can differ enormously for diffusion of different spin species in a multispin system and, accordingly, can be used to identify the dominant diffusing species. Finally, we show that the high-rf-field rotating-frame relaxation time ${T}_{1\ensuremath{\rho}}$, measured as a function of rf frequency, also enables us to identify the diffusing species. We demonstrated experimentally the validity of these techniques by measurements of potassium vacancy diffusion in a KF: ${\mathrm{Ca}}^{++}$ single crystal and measurements of fluorine diffusion in AgF powder.

Heteronuclear cluster systems. Part 12. Synthesis of µ-phenylphosphinediyl-bis(tetracarbonylcobalt) and 1,1,1,2,2,2,3,3,3-nonacarbonyl-µ3-phenylphosphinediyl-triangulo-dicobaltiron

The reaction of Na[Co(CO)4] with PPhCl2 at –78 °C gives [{Co(CO)4}2PPh](1) in good yield. A solution of (1) evolves CO gas at 60 °C giving [Co2(CO)7(PPh)]. Complex (1) reacts with [Fe2(CO)9,] to form a new mixedmetal cluster complex [Co2Fe(CO)9(PPh)].

Proton-coupled carbon-13 J spectra in the presence of strong coupling. II

Proton-coupled carbon-13 NMR spectra have been studied by a technique which involves Fourier transformation of spin echo modulation. When the protons are strongly coupled, the “proton flip” version of this experiment generates a new form of carbon-13 spectrum which is quite distinct from the multiplet structure of the conventional NMR spectrum. The transition frequencies and intensities are exactly symmetrical about the center frequency and some lines have negative intensities. Experimental spectra from the C2 site in pyridine are presented and analyzed by means of an iterative program derived from LAOCOON 111. The resulting proton-carbon coupling constants are in excellent agreement with those obtained by analysis of the conventional spectrum. The new program may also be used to calculate the echo modulation in strongly coupled homonuclear spin systems, and the echo modulation induced in heteronuclear systems by strongly coupled nonresonant spins.