Maude Ferrari

New perspectives in the PAW/GIPAW approach: JP‐O‐Si coupling constants, antisymmetric parts of shift tensors and NQR predictions

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first‐principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid‐state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of 14N and 35Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear 2JPOSi coupling constants in the case of silicophosphates and calcium phosphates [Si5O(PO4)6, SiP2O7 polymorphs and α‐Ca(PO3)2]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C3X4 (X = H, Cl, F) and (iii) 14N and 35Cl NQR predictions in the case of RDX (C3H6N6O6), β‐HMX (C4H8N8O8), α‐NTO (C2H2N4O3) and AlOPCl6. RDX, β‐HMX and α‐NTO are explosive compounds. Copyright

14N Pulsed nuclear quadrupole resonance. 2. Effect of a single radio-frequency pulse in the general case

A novel theory, based on density operator calculations, is provided for assessing the nuclear quadrupole resonance behaviour of a spin 1 (14N) subjected to a single radio-frequency pulse. It is for a powder sample in zero magnetic field for an electric field gradient tensor without symmetry. A complete set of equations is obtained for the quantities of interest. It is derived from the general Liouville–von Neumann equation and from a proper basis on which the density operator is expanded. Theoretical results, in terms of signal evolution as a function of the pulse length (nutation experiments), show that the same nutation curve is expected for the three different transitions which exist when the electric field gradient tensor is without symmetry. This latter nutation curve is, however, different from that which prevails in the case of an axially symmetric tensor, this apparent discrepancy being easily resolved on theoretical grounds. Experimental data (for NaNO2, electric field gradient tensor without symmetry) are checked against values of the radio-frequency field amplitude provided by NMR measurements performed with the same equipment. Good agreement between theory and experiment is obtained.

Quantum Chemical Study of the Thermochemical Properties of Organophosphorous Compounds.

Organophosphorous compounds are involved in many toxic compounds such as fungicides, pesticides, or chemical warfare nerve agents. The understanding of the decomposition chemistry of these compounds in the environment is largely limited by the scarcity of thermochemical data. Because of the high toxicity of many of these molecules, experimental determination of their thermochemical properties is very difficult. In this work, standard gas-phase thermodynamic data, i.e., enthalpies of formation (ΔfH298°), standard entropies (S298°), and heat capacities (Cp°(T)), were determined using quantum chemical calculations and more specifically the CBS-QB3 composite method, which was found to be the best compromise between precision and calculation time among high accuracy composite methods. A large number of molecules was theoretically investigated, involving trivalent and pentavalent phosphorus atoms, and C, H, O, N, S, and F atoms. These data were used to propose 83 original groups, used in the semiempirical group contribution method proposed by Benson. Thanks to these latter group values, thermochemical properties of several nerve agents, common pesticides and herbicides have been evaluated. Bond dissociations energies (BDE), useful for the analysis the thermal stability of the compounds, were also determined in several molecules of interest.

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (14N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T 1 (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T 2 (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.

14N pulsed nuclear quadrupole resonance. 3. Effect of a pulse train. Optimal conditions for data averaging

The calculations developed in this paper aim at determining the optimal conditions of a NQR experiment when a transition is monitored by means of a pulse train with pulses of identical duration and signal acquisition after each pulse; coherences are assumed to vanish by effective transverse relaxation prior to every new pulse. These calculations demonstrate that, as in NMR, a steady state is effectively reached for any value of the recycle time. However, by contrast with NMR, it is shown that, for optimal data averaging under steady state conditions, the recycle time T can be kept as low as possible (the only limitation is the acquisition time). Nutation curves (signal amplitude versus pulse length) calculated in the steady state case are shown to depend strongly on the ratio T/T 1 (T 1: longitudinal relaxation time). The signal growth as a function of T/T 1under averaging of the first transients has been evaluated as well as the number of pulses necessary for reaching a steady state.

Fundamentals of Pulsed Nitrogen-14 Quadrupole Resonance

The essential features of nitrogen-14 Nuclear Quadrupole Reson- ance, a new tool based on density matrix calculations is proposed. After a brief review of the density matrix theory, it is demonstrated that, for each of the three NQR transitions, the (3,3) density matrix can be reduced to a (2,2) matrix, evidently easier to handle. (2,2) rotation matrices are defined for predicting, in a straightforward manner, the system evolution under a rf pulse. The first example treated by this methodology concerns nutation experiments (evolution of the signal amplitude as a function of the pulse length) and it is shown that the NMR (Nuclear Magnetic Resonance) flip angle, in the case of powder samples, should be substituted by a pseudo flip angle which is no longer proportional to the pulse length. Still for powder samples, it is demonstrated that, in NQR, data averaging continuously improves when shortening the repetition time. Finally it has been possible to define proper phase cycles in view of measuring relaxation times (T1 and T2) by a two-pulse sequence. In all cases, experimental verifications were performed in order to assess this methodology.

Study of Dispersion in Porous Media by Pulsed Field Gradient NMR: Influence of the Fluid Rheology

Pulsed field gradient nuclear magnetic resonance (PFG-NMR) is used to measure the molecular displacements for the flow of a fluid through a capillary tube and a packed bed made of monodisperse PMMA beads. The molecules average displacement is studied using both the formalism of propagators and the cumulant method. In the Poiseuille case, the dispersion coefficients determined by the cumulant method compare satisfactorily with the theoretical values obtained. The technique is then extended to study the flow through a porous medium. We thus analyze Newtonian (water) and non-Newtonian (Xanthan) flows and put a particular emphasis on comparing the dispersion mechanisms between Newtonian and non-Newtonian fluids.

Measurement of short transverse relaxation times by pseudo-echo nutation experiments

Very short NMR transverse relaxation times may be difficult to measure by conventional methods. Nutation experiments constitute an alternative approach. Nutation is, in the rotating frame, the equivalent of precession in the laboratory frame. It consists in monitoring the rotation of magnetization around the radio-frequency (rf) field when on-resonance conditions are fulfilled. Depending on the amplitude of the rf field, nutation may be sensitive to the two relaxation rates R1 and R2. A full theoretical development has been worked out for demonstrating how these two relaxation rates could be deduced from a simple nutation experiment, noticing however that inhomogeneity of the rf field may lead to erroneous results. This has led us to devise new experiments which are the equivalent of echo techniques in the rotating frame (pseudo spin-echo nutation experiment and pseudo gradient-echo experiment). Full equations of motion have been derived. Although complicated, they indicate that the sum of the two relaxation rates can be obtained very accurately and not altered by rf field inhomogeneity. This implies however an appropriate data processing accounting for the oscillations which are superposed to the echo decays and, anyway, theoretically predicted. A series of experiments has been carried out for different values of the rf field amplitude on samples of water doped with a paramagnetic compound at different concentrations. Pragmatically, as R1 can be easily measured by conventional methods, its value is entered in the data processing algorithm which then returns exclusively the value of the transverse relaxation time. Very consistent results are obtained that way.