An algorithm for the generation of nuclear spin species and nuclear spin statistical weights

This article develops a set of algorithms for the computer generation of nuclear spin species and nuclear spin statistical weights potentially useful in molecular spectroscopy. These algorithms generate the nuclear spin species from group structures known as generalized character cycle indices (GCCI s). Thus the required input for these algorithms is just the set of all GCCI s for the symmetry group of the molecule which can be computed easily from the character table. The algorithms are executed and illustrated with examples.     

Comment on nuclear spin weights of C60 and C60 buckminsterfullerene

The nuclear spin statistical weights obtained in a Letter by Harter and Reimer differ from the values obtained by the author a year earlier. However, the corrected numbers reported in the Erratum by Harter and Reimer agree with our values.     

Relativistic double group spinor representations of nonrigid molecules

The character theory of relativistic double group spinor representations is developed in order to represent the total rovibronic states of nonrigid molecules. It is shown that the double groups can be represented in terms of wreath products and powerful matrix cycle type generators that are used to construct their character tables. It is shown that these tables are of use when spin-orbit coupling is included in the Hamiltonian even for molecules containing lighter atoms. Applications to nonrigid molecules such as Tl2H4/Tl2H4+ are considered. It is shown that the tunneling splittings and the nuclear spin statistical weights can be obtained for such species using the character tables thus constructed. The spinor double groups of several other molecules such as hexamethyl dilead and heavy weakly bound clusters such as (PoH2)4 are also considered.     

The rotational spectrum,nuclear spin—spin coupling,nuclear quadrupole coupling,and molecular structure of KrHF

Rotational spectra have been assigned for the ⁸²Kr, ⁸³Kr, ⁸⁴Kr, and ⁸⁶Kr isotopic species of the KrHF and KrDF van der Waals molecules by using pulsed microwave Fourier transform spectroscopy in a Fabry—Perot cavity with a pulsed supersonic nozzle molecular source. The rotational, centrifugal distortion, nuclear spin—spin, and nuclear quadrupole coupling constants are used to determine the structure and obtain intramolecular potential binding information. The ⁸³Kr nuclear quadrupole coupling constants are 10.28 ± 0.08 MHz and 13.83 ± 0.13 MHz for KrHF and KrDF respectively. The electric field gradient at the krypton nucleus is calculated from the coupling constant and the known nuclear quadrupole moment and explained by Sternheimer shielding and formation of the van der Waals bond. There is a negligible charge transfer in the KrHF bond.     

Imaging mesoscopic nuclear spin noise with a diamond magnetometer

Magnetic resonance imaging can characterize and discriminate among tissues using their diverse physical and biochemical properties. Unfortunately, submicrometer screening of biological specimens is presently not possible, mainly due to lack of detection sensitivity. Here we analyze the use of a nitrogen-vacancy center in diamond as a magnetic sensor for nanoscale nuclear spin imaging and spectroscopy. We examine the ability of such a sensor to probe the fluctuations of the "classical" dipolar field due to a large number of neighboring nuclear spins in a densely protonated sample. We identify detection protocols that appropriately take into account the quantum character of the sensor and find a signal-to-noise ratio compatible with realistic experimental parameters. Through various example calculations we illustrate different kinds of image contrast. In particular, we show how to exploit the comparatively long nuclear spin correlation times to reconstruct a local, high-resolution sample spectrum.     

Toward separation of nuclear spin isomers with coherent light.

We propose an approach for separating nuclear spin isomers with coherent light and illustrate it by numerical calculations using fulvene as a model system. The scheme employs the equivalence of torsion and interchange of equivalent H-atoms in a class of molecules of which fulvene is a simple example. The exchange symmetry couples with the rotational symmetry to produce a spatial distinction between the two photo-excited nuclear spin isomers, and wavepacket interferometry is applied to separate the species.     

Nonrigid water octamer: Computations with the 8-cube

A 8-cube model of the fully nonrigid water octamer is considered within the 8-dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by employing computational and mathematical techniques. For the two lowest-lying isomers of (H₂O)₈ with D_2d and S₄ symmetries of a rigid (H₂O)₈, correlation tables and nuclear spin statistics are constructed for the tunneling splittings of the rotational levels are computed by a computational matrix polynomial generating function technique combined with Möbius inversion, and the relationship to the 8-cube multinomials are pointed out. Multinomial generating functions combined with the induced representation techniques are employed to compute and construct the nuclear spin species, nuclear spin statistical weights and tunneling splittings of rovibronic levels. We have also computed the spin statistical weights and tunneling splittings of the rotational levels for a semirigid water octamer within the wreath product O_h[S₂] consisting of 12,288 operations.     

Graphical unitary group approach to spin–spin interaction

A detailed exposition of spin–spin operator matrix elements is presented in the context of the graphical unitary group approach (GUGA ) to atomic and molecular physics and quantum chemistry. A compendium of subgraph types and formulae is given. Aspects of computer implementation within the structure of the Columbus CI programs is discussed.     

Dynamic nuclear polarization assisted spin diffusion for the solid effect case

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole-dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core-bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and cross-relaxation rates. The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of (13)C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.     

Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that agrees with the well known Borghini prediction based on thermodynamic arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows us to calculate nuclear polarization and relaxation times, once the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species are specified. Numerical results are shown to account for the manifold dynamic behaviours of typical DNP samples.     

Nuclear spin–spin coupling and nuclear motion

The vibration and rotation of molecules affects nuclear spin–spin coupling constants. This manifests itself as a temperature dependence of the coupling and also as an isotope effect (after allowing, where necessary, for differing magnetogyric ratios of the two nuclei involved in the isotopic substitution). Within the Born–Oppenheimer approximation, a nuclear spin–spin coupling surface can be defined for each pair of coupled nuclei. This surface is sampled by the nuclei as they undergo the excursions about equilibrium geometry that are governed by the force field. An accurate ab initio carbon–proton spin–spin coupling surface for the methane molecule has been calculated. This was obtained by summing the surfaces for each of the four contributions—Fermi contact, spin–dipolar, orbital paramagnetic, and orbital diamagnetic—expressed as power series in terms of symmetry coordinates. Preliminary calculations for ¹³CH₄ and ¹³CD₄ give a difference of only 6% between the calculated and observed nuclear motion contributions. The observed temperature dependence is also accounted for by the calculations. For these isotopomers, bond stretching plays the dominant role. © 1994 John Wiley & Sons, Inc.     

The role of relaxation in the nuclear spin conversion process

The nuclear spin conversion rate depends on the collisions, which break the coherence created by magnetic intramolecular interactions between pairs of quasi degenerate levels belonging to the different spin isomers. The collisions act similarly to break the coherence created by a radiation field between two levels inducing pressure broadening of molecular transitions. Collisional relaxation rates have been extensively studied in this last situation using semi-classical approach and rectilign trajectory for collisional path.Taking advantage of the analogy, the present paper shows that calculations can be efficiently adapted for the collisional relaxation terms present in the ‘quantum relaxation’ model of nuclear spin conversion.For ¹³CH₃F, numerous experimental measurements of spin conversion rates in the presence of an electric field have allowed to derive directly relaxation rates. Our calculation appears to agree satisfactorily with these experimental values. For ¹²CH₃F, calculated relaxations rates are also given for the pairs involved in nuclear spin conversion.     

Effect of rapidly relaxed electron spin anisotropically coupled to nearby nuclear partners

In practice, many situations arise when a perturbed nuclear spin relies upon the aid of a rapidly relaxed spin neighbor in order to realize thermal equilibrium. Conventional treatments view the efficiently relaxed spin as part of the 'lattice', invoke the secular approximation, and consider the associated time correlation of the lattice variables, phenomenologically. Recently, an ab initio perturbative approach has been proposed for investigation of these spin systems. In this work, a similar formalism is applied to the scenario, in which nuclear spin relaxation is effected via an anisotropically coupled, efficiently relaxed, spin. Interesting conflicts with standard theory are revealed. Furthermore, although left mostly unexplored, this approach lends insight into numerous related aspects of magnetic relaxation including separation of timescales, distinction between spin and spatial averaging, paramagnetic relaxation, Curie spin relaxation, and the dynamic frequency shift.     

Semi-empirical MO calculations of nuclear spin coupling constants

The results obtained using different semi-empirical approaches, namely EHMO, IEHMO, CNDO/2 and INDO, in the calculation of spin–spin coupling constants within the framework of the one-electron MO approximation are systematically compared in the case of several classes of organic molecules. While, at a semi-empirical level SCF methods normally provide satisfactory wave function, the use of the simple EHMO seems better able to satisfy the problem connected with the calculation of spin–spin coupling constants, expecially when an appropriate set of AO's is chosen, in order to avoid parametrisation of Dirac monocentric integrals. Charge iteration (IEHMO) seems to improve the results slightly only when heteroatoms are present, but the complexity introduced into the calculations and the greatly increased computer time do not justify the slight improvement achieved, particularly as the method is applied to large molecules and organometallic compounds.     

The effect of nuclear spin on the polarisation ratio of resonance fluorescence

The nuclear quadrupole interaction causes the rotational angular momentum of a molecule with nuclear spin to precess about the total angular momentum whose projection along a space fixed axis is conserved. This effects the degree of orientation in the excited state of molecules optically pumped with circularly polarised light and reduces the polarisation ratio of fluorescence from molecules with large nuclear spin. Calculations are presented for the circular polarisation ratio of the forward scattered fluorescence when the exciting radiation is sufficiently broad-banded that it excites the full manifold of quadrupole split components of a given J″ → J′ transition. Results are also presented for the variation of the polarisation ratio and intensity as a narrow excitation source is tuned across the absorption.     

Resonant transfer of the nuclear spin dipolar order in the rotating frame

A method for transferring the nuclear spin dipolar energy in a solid lattice is presented. It is shown that order may be transferred between the Zeeman and nuclear spin dipolar systems in either direction by rf pulses of suitable amplitude. This method may also be used to measure the dipolar relaxation time. Experimental data on ammonium chloride are shown to be in close agreement with the theory.     

Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. I. Singlet states in low magnetic field

We have recently demonstrated the existence of exceptionally long-lived nuclear spin states in solution-state nuclear magnetic resonance. The lifetime of nuclear spin singlet states in systems containing coupled pairs of spins-12 may exceed the conventional relaxation time constant T1 by more than an order of magnitude. These long lifetimes may be observed if the long-lived singlet states are prevented from mixing with rapidly relaxing triplet states. In this paper we provide the detailed theory of an experiment which uses magnetic field cycling to observe slow singlet relaxation. An approximate expression is given for the magnetic field dependence of the singlet relaxation rate constant, using a model of intramolecular dipole-dipole couplings and fluctuating external random fields.     

Surface nuclear spin relaxation of 199Hg

We report the results of a detailed study of surface relaxation of 199Hg nuclear spins in paraffin coated cells. From measurements of the magnetic field and temperature dependence of the spin relaxation rates we determine the correlation time for magnetic fluctuations and the surface adsorption energy. The data indicate that surface relaxation is caused by dipolar coupling to paramagnetic sites on the surface. We also observe changes in the spin relaxation rate caused by ultraviolet radiation resonant with the 254 nm transition in Hg.     

Characterization of the motion of spin probes and spin labels in amorphous polymers with two-dimensional field-step ELDOR

The motion of nitroxide spin probes and spin labels in amorphous polymers is studied below the glass transition temperature with a two-dimensional pulsed electron double-resonance experiment. Polystyrene and a liquid crystalline side group polymer are studied using both spin probes and spin labels covalently bound to specific sites along the polymer chain. Two methyl acrylic polymers differing only in their side group structure and polyvinylacetate are compared and large differences in the molecular dynamics deduced from both the nuclear and the electron spin relaxation rates are observed as the glass transition is approached. The results demonstrate the complexity of small amplitude motion in simple polymers below the glass transition temperature and show that it is very sensitive to the packing in the polymer. © 1996 John Wiley & Sons, Inc.